isl_basic_map_plain_cmp: specifically handle unknown local variables

[isl.git] / isl_input.c

/*
 * Copyright 2008-2009 Katholieke Universiteit Leuven
 * Copyright 2010      INRIA Saclay
 * Copyright 2012-2013 Ecole Normale Superieure
 * Copyright 2019      Cerebras Systems
 *
 * Use of this software is governed by the MIT license
 *
 * Written by Sven Verdoolaege, K.U.Leuven, Departement
 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 
 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
 * and Cerebras Systems, 175 S San Antonio Rd, Los Altos, CA, USA
 */

#include <ctype.h>
#include <stdio.h>
#include <string.h>
#include <isl_ctx_private.h>
#include <isl_map_private.h>
#include <isl_id_private.h>
#include <isl/set.h>
#include <isl_seq.h>
#include <isl_stream_private.h>
#include <isl/obj.h>
#include "isl_polynomial_private.h"
#include <isl/union_set.h>
#include <isl/union_map.h>
#include <isl_mat_private.h>
#include <isl_aff_private.h>
#include <isl_vec_private.h>
#include <isl/list.h>
#include <isl_val_private.h>

struct variable {
        char                    *name;
        int                      pos;
        struct variable         *next;
};

struct vars {
        struct isl_ctx  *ctx;
        int              n;
        struct variable *v;
};

static struct vars *vars_new(struct isl_ctx *ctx)
{
        struct vars *v;
        v = isl_alloc_type(ctx, struct vars);
        if (!v)
                return NULL;
        v->ctx = ctx;
        v->n = 0;
        v->v = NULL;
        return v;
}

static void variable_free(struct variable *var)
{
        while (var) {
                struct variable *next = var->next;
                free(var->name);
                free(var);
                var = next;
        }
}

static void vars_free(struct vars *v)
{
        if (!v)
                return;
        variable_free(v->v);
        free(v);
}

static void vars_drop(struct vars *v, int n)
{
        struct variable *var;

        if (!v || !v->v)
                return;

        v->n -= n;

        var = v->v;
        while (--n >= 0) {
                struct variable *next = var->next;
                free(var->name);
                free(var);
                var = next;
        }
        v->v = var;
}

static struct variable *variable_new(struct vars *v, const char *name, int len,
                                int pos)
{
        struct variable *var;
        var = isl_calloc_type(v->ctx, struct variable);
        if (!var)
                goto error;
        var->name = strdup(name);
        var->name[len] = '\0';
        var->pos = pos;
        var->next = v->v;
        return var;
error:
        variable_free(v->v);
        return NULL;
}

static int vars_pos(struct vars *v, const char *s, int len)
{
        int pos;
        struct variable *q;

        if (len == -1)
                len = strlen(s);
        for (q = v->v; q; q = q->next) {
                if (strncmp(q->name, s, len) == 0 && q->name[len] == '\0')
                        break;
        }
        if (q)
                pos = q->pos;
        else {
                pos = v->n;
                v->v = variable_new(v, s, len, v->n);
                if (!v->v)
                        return -1;
                v->n++;
        }
        return pos;
}

static int vars_add_anon(struct vars *v)
{
        v->v = variable_new(v, "", 0, v->n);

        if (!v->v)
                return -1;
        v->n++;

        return 0;
}

/* Obtain next token, with some preprocessing.
 * In particular, evaluate expressions of the form x^y,
 * with x and y values.
 */
static struct isl_token *next_token(__isl_keep isl_stream *s)
{
        struct isl_token *tok, *tok2;

        tok = isl_stream_next_token(s);
        if (!tok || tok->type != ISL_TOKEN_VALUE)
                return tok;
        if (!isl_stream_eat_if_available(s, '^'))
                return tok;
        tok2 = isl_stream_next_token(s);
        if (!tok2 || tok2->type != ISL_TOKEN_VALUE) {
                isl_stream_error(s, tok2, "expecting constant value");
                goto error;
        }

        isl_int_pow_ui(tok->u.v, tok->u.v, isl_int_get_ui(tok2->u.v));

        isl_token_free(tok2);
        return tok;
error:
        isl_token_free(tok);
        isl_token_free(tok2);
        return NULL;
}

/* Read an isl_val from "s".
 *
 * The following token sequences are recognized
 *
 *      "infty"         ->      infty
 *      "-" "infty"     ->      -infty
 *      "NaN"           ->      NaN
 *      n "/" d         ->      n/d
 *      v               ->      v
 *
 * where n, d and v are integer constants.
 */
__isl_give isl_val *isl_stream_read_val(__isl_keep isl_stream *s)
{
        struct isl_token *tok = NULL;
        struct isl_token *tok2 = NULL;
        isl_val *val;

        tok = next_token(s);
        if (!tok) {
                isl_stream_error(s, NULL, "unexpected EOF");
                goto error;
        }
        if (tok->type == ISL_TOKEN_INFTY) {
                isl_token_free(tok);
                return isl_val_infty(s->ctx);
        }
        if (tok->type == '-' &&
            isl_stream_eat_if_available(s, ISL_TOKEN_INFTY)) {
                isl_token_free(tok);
                return isl_val_neginfty(s->ctx);
        }
        if (tok->type == ISL_TOKEN_NAN) {
                isl_token_free(tok);
                return isl_val_nan(s->ctx);
        }
        if (tok->type != ISL_TOKEN_VALUE) {
                isl_stream_error(s, tok, "expecting value");
                goto error;
        }

        if (isl_stream_eat_if_available(s, '/')) {
                tok2 = next_token(s);
                if (!tok2) {
                        isl_stream_error(s, NULL, "unexpected EOF");
                        goto error;
                }
                if (tok2->type != ISL_TOKEN_VALUE) {
                        isl_stream_error(s, tok2, "expecting value");
                        goto error;
                }
                val = isl_val_rat_from_isl_int(s->ctx, tok->u.v, tok2->u.v);
                val = isl_val_normalize(val);
        } else {
                val = isl_val_int_from_isl_int(s->ctx, tok->u.v);
        }

        isl_token_free(tok);
        isl_token_free(tok2);
        return val;
error:
        isl_token_free(tok);
        isl_token_free(tok2);
        return NULL;
}

/* Read an isl_val from "str".
 */
__isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx, const char *str)
{
        isl_val *val;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        val = isl_stream_read_val(s);
        isl_stream_free(s);
        return val;
}

/* Perform an integer division on *f and
 * an integer value read from the stream.
 */
static isl_stat int_div_by_cst(__isl_keep isl_stream *s, isl_int *f)
{
        struct isl_token *tok;

        tok = next_token(s);
        if (!tok || tok->type != ISL_TOKEN_VALUE) {
                isl_stream_error(s, tok, "expecting constant value");
                goto error;
        }

        isl_int_fdiv_q(*f, *f, tok->u.v);

        isl_token_free(tok);

        return isl_stat_ok;
error:
        isl_token_free(tok);
        return isl_stat_error;
}

static isl_stat accept_cst_factor(__isl_keep isl_stream *s, isl_int *f)
{
        struct isl_token *tok;

        tok = next_token(s);
        if (!tok || tok->type != ISL_TOKEN_VALUE) {
                isl_stream_error(s, tok, "expecting constant value");
                goto error;
        }

        isl_int_mul(*f, *f, tok->u.v);

        isl_token_free(tok);

        if (isl_stream_eat_if_available(s, '*'))
                return accept_cst_factor(s, f);

        return isl_stat_ok;
error:
        isl_token_free(tok);
        return isl_stat_error;
}

/* Given an affine expression aff, return an affine expression
 * for aff % d, with d the next token on the stream, which is
 * assumed to be a constant.
 *
 * We introduce an integer division q = [aff/d] and the result
 * is set to aff - d q.
 */
static __isl_give isl_pw_aff *affine_mod(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_pw_aff *aff)
{
        struct isl_token *tok;
        isl_pw_aff *q;

        tok = next_token(s);
        if (!tok || tok->type != ISL_TOKEN_VALUE) {
                isl_stream_error(s, tok, "expecting constant value");
                goto error;
        }

        q = isl_pw_aff_copy(aff);
        q = isl_pw_aff_scale_down(q, tok->u.v);
        q = isl_pw_aff_floor(q);
        q = isl_pw_aff_scale(q, tok->u.v);

        aff = isl_pw_aff_sub(aff, q);

        isl_token_free(tok);
        return aff;
error:
        isl_pw_aff_free(aff);
        isl_token_free(tok);
        return NULL;
}

static __isl_give isl_pw_aff *accept_affine(__isl_keep isl_stream *s,
        __isl_take isl_space *space, struct vars *v);
static __isl_give isl_pw_aff_list *accept_affine_list(__isl_keep isl_stream *s,
        __isl_take isl_space *space, struct vars *v);

static __isl_give isl_pw_aff *accept_minmax(__isl_keep isl_stream *s,
        __isl_take isl_space *space, struct vars *v)
{
        struct isl_token *tok;
        isl_pw_aff_list *list = NULL;
        int min;

        tok = isl_stream_next_token(s);
        if (!tok)
                goto error;
        min = tok->type == ISL_TOKEN_MIN;
        isl_token_free(tok);

        if (isl_stream_eat(s, '('))
                goto error;

        list = accept_affine_list(s, isl_space_copy(space), v);
        if (!list)
                goto error;

        if (isl_stream_eat(s, ')'))
                goto error;

        isl_space_free(space);
        return min ? isl_pw_aff_list_min(list) : isl_pw_aff_list_max(list);
error:
        isl_space_free(space);
        isl_pw_aff_list_free(list);
        return NULL;
}

/* Is "tok" the start of an integer division?
 */
static int is_start_of_div(struct isl_token *tok)
{
        if (!tok)
                return 0;
        if (tok->type == '[')
                return 1;
        if (tok->type == ISL_TOKEN_FLOOR)
                return 1;
        if (tok->type == ISL_TOKEN_CEIL)
                return 1;
        if (tok->type == ISL_TOKEN_FLOORD)
                return 1;
        if (tok->type == ISL_TOKEN_CEILD)
                return 1;
        return 0;
}

/* Read an integer division from "s" and return it as an isl_pw_aff.
 *
 * The integer division can be of the form
 *
 *      [<affine expression>]
 *      floor(<affine expression>)
 *      ceil(<affine expression>)
 *      floord(<affine expression>,<denominator>)
 *      ceild(<affine expression>,<denominator>)
 */
static __isl_give isl_pw_aff *accept_div(__isl_keep isl_stream *s,
        __isl_take isl_space *space, struct vars *v)
{
        struct isl_token *tok;
        int f = 0;
        int c = 0;
        int extra = 0;
        isl_pw_aff *pwaff = NULL;

        if (isl_stream_eat_if_available(s, ISL_TOKEN_FLOORD))
                extra = f = 1;
        else if (isl_stream_eat_if_available(s, ISL_TOKEN_CEILD))
                extra = c = 1;
        else if (isl_stream_eat_if_available(s, ISL_TOKEN_FLOOR))
                f = 1;
        else if (isl_stream_eat_if_available(s, ISL_TOKEN_CEIL))
                c = 1;
        if (f || c) {
                if (isl_stream_eat(s, '('))
                        goto error;
        } else {
                if (isl_stream_eat(s, '['))
                        goto error;
        }

        pwaff = accept_affine(s, isl_space_copy(space), v);

        if (extra) {
                if (isl_stream_eat(s, ','))
                        goto error;

                tok = next_token(s);
                if (!tok)
                        goto error;
                if (tok->type != ISL_TOKEN_VALUE) {
                        isl_stream_error(s, tok, "expected denominator");
                        isl_stream_push_token(s, tok);
                        goto error;
                }
                pwaff = isl_pw_aff_scale_down(pwaff,  tok->u.v);
                isl_token_free(tok);
        }

        if (c)
                pwaff = isl_pw_aff_ceil(pwaff);
        else
                pwaff = isl_pw_aff_floor(pwaff);

        if (f || c) {
                if (isl_stream_eat(s, ')'))
                        goto error;
        } else {
                if (isl_stream_eat(s, ']'))
                        goto error;
        }

        isl_space_free(space);
        return pwaff;
error:
        isl_space_free(space);
        isl_pw_aff_free(pwaff);
        return NULL;
}

/* Divide "pa" by an integer constant read from the stream.
 */
static __isl_give isl_pw_aff *pw_aff_div_by_cst(__isl_keep isl_stream *s,
        __isl_take isl_pw_aff *pa)
{
        isl_int f;
        isl_int_init(f);
        isl_int_set_si(f, 1);
        if (accept_cst_factor(s, &f) < 0)
                pa = isl_pw_aff_free(pa);
        pa = isl_pw_aff_scale_down(pa, f);
        isl_int_clear(f);

        return pa;
}

static __isl_give isl_pw_aff *accept_affine_factor(__isl_keep isl_stream *s,
        __isl_take isl_space *space, struct vars *v)
{
        struct isl_token *tok = NULL;
        isl_pw_aff *res = NULL;

        tok = next_token(s);
        if (!tok) {
                isl_stream_error(s, NULL, "unexpected EOF");
                goto error;
        }

        if (tok->type == ISL_TOKEN_AFF) {
                res = isl_pw_aff_copy(tok->u.pwaff);
                isl_token_free(tok);
        } else if (tok->type == ISL_TOKEN_IDENT) {
                int n = v->n;
                int pos = vars_pos(v, tok->u.s, -1);
                isl_aff *aff;

                if (pos < 0)
                        goto error;
                if (pos >= n) {
                        vars_drop(v, v->n - n);
                        isl_stream_error(s, tok, "unknown identifier");
                        goto error;
                }

                aff = isl_aff_zero_on_domain(isl_local_space_from_space(isl_space_copy(space)));
                if (!aff)
                        goto error;
                aff->v = isl_vec_set_element_si(aff->v, 2 + pos, 1);
                if (!aff->v)
                        aff = isl_aff_free(aff);
                res = isl_pw_aff_from_aff(aff);
                isl_token_free(tok);
        } else if (tok->type == ISL_TOKEN_VALUE) {
                if (isl_stream_eat_if_available(s, '*')) {
                        res = accept_affine_factor(s, isl_space_copy(space), v);
                        res = isl_pw_aff_scale(res, tok->u.v);
                } else {
                        isl_local_space *ls;
                        isl_aff *aff;
                        ls = isl_local_space_from_space(isl_space_copy(space));
                        aff = isl_aff_zero_on_domain(ls);
                        aff = isl_aff_add_constant(aff, tok->u.v);
                        res = isl_pw_aff_from_aff(aff);
                }
                isl_token_free(tok);
        } else if (tok->type == '(') {
                isl_token_free(tok);
                tok = NULL;
                res = accept_affine(s, isl_space_copy(space), v);
                if (!res)
                        goto error;
                if (isl_stream_eat(s, ')'))
                        goto error;
        } else if (is_start_of_div(tok)) {
                isl_stream_push_token(s, tok);
                tok = NULL;
                res = accept_div(s, isl_space_copy(space), v);
        } else if (tok->type == ISL_TOKEN_MIN || tok->type == ISL_TOKEN_MAX) {
                isl_stream_push_token(s, tok);
                tok = NULL;
                res = accept_minmax(s, isl_space_copy(space), v);
        } else {
                isl_stream_error(s, tok, "expecting factor");
                goto error;
        }
        if (isl_stream_eat_if_available(s, '%') ||
            isl_stream_eat_if_available(s, ISL_TOKEN_MOD)) {
                isl_space_free(space);
                return affine_mod(s, v, res);
        }
        if (isl_stream_eat_if_available(s, '*')) {
                isl_int f;
                isl_int_init(f);
                isl_int_set_si(f, 1);
                if (accept_cst_factor(s, &f) < 0) {
                        isl_int_clear(f);
                        goto error2;
                }
                res = isl_pw_aff_scale(res, f);
                isl_int_clear(f);
        }
        if (isl_stream_eat_if_available(s, '/'))
                res = pw_aff_div_by_cst(s, res);
        if (isl_stream_eat_if_available(s, ISL_TOKEN_INT_DIV))
                res = isl_pw_aff_floor(pw_aff_div_by_cst(s, res));

        isl_space_free(space);
        return res;
error:
        isl_token_free(tok);
error2:
        isl_pw_aff_free(res);
        isl_space_free(space);
        return NULL;
}

static __isl_give isl_pw_aff *add_cst(__isl_take isl_pw_aff *pwaff, isl_int v)
{
        isl_aff *aff;
        isl_space *space;

        space = isl_pw_aff_get_domain_space(pwaff);
        aff = isl_aff_zero_on_domain(isl_local_space_from_space(space));
        aff = isl_aff_add_constant(aff, v);

        return isl_pw_aff_add(pwaff, isl_pw_aff_from_aff(aff));
}

/* Return a piecewise affine expression defined on the specified domain
 * that represents NaN.
 */
static __isl_give isl_pw_aff *nan_on_domain(__isl_keep isl_space *space)
{
        return isl_pw_aff_nan_on_domain_space(isl_space_copy(space));
}

static __isl_give isl_pw_aff *accept_affine(__isl_keep isl_stream *s,
        __isl_take isl_space *space, struct vars *v)
{
        struct isl_token *tok = NULL;
        isl_local_space *ls;
        isl_pw_aff *res;
        int sign = 1;

        ls = isl_local_space_from_space(isl_space_copy(space));
        res = isl_pw_aff_from_aff(isl_aff_zero_on_domain(ls));
        if (!res)
                goto error;

        for (;;) {
                tok = next_token(s);
                if (!tok) {
                        isl_stream_error(s, NULL, "unexpected EOF");
                        goto error;
                }
                if (tok->type == '-') {
                        sign = -sign;
                        isl_token_free(tok);
                        continue;
                }
                if (tok->type == '(' || is_start_of_div(tok) ||
                    tok->type == ISL_TOKEN_MIN || tok->type == ISL_TOKEN_MAX ||
                    tok->type == ISL_TOKEN_IDENT ||
                    tok->type == ISL_TOKEN_AFF) {
                        isl_pw_aff *term;
                        isl_stream_push_token(s, tok);
                        tok = NULL;
                        term = accept_affine_factor(s,
                                                    isl_space_copy(space), v);
                        if (sign < 0)
                                res = isl_pw_aff_sub(res, term);
                        else
                                res = isl_pw_aff_add(res, term);
                        if (!res)
                                goto error;
                        sign = 1;
                } else if (tok->type == ISL_TOKEN_VALUE) {
                        if (sign < 0)
                                isl_int_neg(tok->u.v, tok->u.v);
                        if (isl_stream_eat_if_available(s, '*') ||
                            isl_stream_next_token_is(s, ISL_TOKEN_IDENT)) {
                                isl_pw_aff *term;
                                term = accept_affine_factor(s,
                                                    isl_space_copy(space), v);
                                term = isl_pw_aff_scale(term, tok->u.v);
                                res = isl_pw_aff_add(res, term);
                                if (!res)
                                        goto error;
                        } else {
                                if (isl_stream_eat_if_available(s,
                                                        ISL_TOKEN_INT_DIV) &&
                                    int_div_by_cst(s, &tok->u.v) < 0)
                                        goto error;
                                res = add_cst(res, tok->u.v);
                        }
                        sign = 1;
                } else if (tok->type == ISL_TOKEN_NAN) {
                        res = isl_pw_aff_add(res, nan_on_domain(space));
                } else {
                        isl_stream_error(s, tok, "unexpected isl_token");
                        isl_stream_push_token(s, tok);
                        isl_pw_aff_free(res);
                        isl_space_free(space);
                        return NULL;
                }
                isl_token_free(tok);

                tok = next_token(s);
                if (tok && tok->type == '-') {
                        sign = -sign;
                        isl_token_free(tok);
                } else if (tok && tok->type == '+') {
                        /* nothing */
                        isl_token_free(tok);
                } else if (tok && tok->type == ISL_TOKEN_VALUE &&
                           isl_int_is_neg(tok->u.v)) {
                        isl_stream_push_token(s, tok);
                } else {
                        if (tok)
                                isl_stream_push_token(s, tok);
                        break;
                }
        }

        isl_space_free(space);
        return res;
error:
        isl_space_free(space);
        isl_token_free(tok);
        isl_pw_aff_free(res);
        return NULL;
}

/* Is "type" the type of a comparison operator between lists
 * of affine expressions?
 */
static int is_list_comparator_type(int type)
{
        switch (type) {
        case ISL_TOKEN_LEX_LT:
        case ISL_TOKEN_LEX_GT:
        case ISL_TOKEN_LEX_LE:
        case ISL_TOKEN_LEX_GE:
                return 1;
        default:
                return 0;
        }
}

static int is_comparator(struct isl_token *tok)
{
        if (!tok)
                return 0;
        if (is_list_comparator_type(tok->type))
                return 1;

        switch (tok->type) {
        case ISL_TOKEN_LT:
        case ISL_TOKEN_GT:
        case ISL_TOKEN_LE:
        case ISL_TOKEN_GE:
        case ISL_TOKEN_NE:
        case '=':
                return 1;
        default:
                return 0;
        }
}

static __isl_give isl_map *read_formula(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_map *map, int rational);
static __isl_give isl_pw_aff *accept_extended_affine(__isl_keep isl_stream *s,
        __isl_take isl_space *space, struct vars *v, int rational);

/* Accept a ternary operator, given the first argument.
 */
static __isl_give isl_pw_aff *accept_ternary(__isl_keep isl_stream *s,
        __isl_take isl_map *cond, struct vars *v, int rational)
{
        isl_space *space;
        isl_pw_aff *pwaff1 = NULL, *pwaff2 = NULL, *pa_cond;

        if (!cond)
                return NULL;

        if (isl_stream_eat(s, '?'))
                goto error;

        space = isl_space_wrap(isl_map_get_space(cond));
        pwaff1 = accept_extended_affine(s, space, v, rational);
        if (!pwaff1)
                goto error;

        if (isl_stream_eat(s, ':'))
                goto error;

        space = isl_pw_aff_get_domain_space(pwaff1);
        pwaff2 = accept_extended_affine(s, space, v, rational);
        if (!pwaff2)
                goto error;

        pa_cond = isl_set_indicator_function(isl_map_wrap(cond));
        return isl_pw_aff_cond(pa_cond, pwaff1, pwaff2);
error:
        isl_map_free(cond);
        isl_pw_aff_free(pwaff1);
        isl_pw_aff_free(pwaff2);
        return NULL;
}

/* Set *line and *col to those of the next token, if any.
 */
static void set_current_line_col(__isl_keep isl_stream *s, int *line, int *col)
{
        struct isl_token *tok;

        tok = isl_stream_next_token(s);
        if (!tok)
                return;

        *line = tok->line;
        *col = tok->col;
        isl_stream_push_token(s, tok);
}

/* Push a token encapsulating "pa" onto "s", with the given
 * line and column.
 */
static isl_stat push_aff(__isl_keep isl_stream *s, int line, int col,
        __isl_take isl_pw_aff *pa)
{
        struct isl_token *tok;

        tok = isl_token_new(s->ctx, line, col, 0);
        if (!tok)
                goto error;
        tok->type = ISL_TOKEN_AFF;
        tok->u.pwaff = pa;
        isl_stream_push_token(s, tok);

        return isl_stat_ok;
error:
        isl_pw_aff_free(pa);
        return isl_stat_error;
}

/* Is the next token a comparison operator?
 */
static int next_is_comparator(__isl_keep isl_stream *s)
{
        int is_comp;
        struct isl_token *tok;

        tok = isl_stream_next_token(s);
        if (!tok)
                return 0;

        is_comp = is_comparator(tok);
        isl_stream_push_token(s, tok);

        return is_comp;
}

/* Accept an affine expression that may involve ternary operators.
 * We first read an affine expression.
 * If it is not followed by a comparison operator, we simply return it.
 * Otherwise, we assume the affine expression is part of the first
 * argument of a ternary operator and try to parse that.
 */
static __isl_give isl_pw_aff *accept_extended_affine(__isl_keep isl_stream *s,
        __isl_take isl_space *space, struct vars *v, int rational)
{
        isl_map *cond;
        isl_pw_aff *pwaff;
        int line = -1, col = -1;

        set_current_line_col(s, &line, &col);

        pwaff = accept_affine(s, space, v);
        if (rational)
                pwaff = isl_pw_aff_set_rational(pwaff);
        if (!pwaff)
                return NULL;
        if (!next_is_comparator(s))
                return pwaff;

        space = isl_pw_aff_get_domain_space(pwaff);
        cond = isl_map_universe(isl_space_unwrap(space));

        if (push_aff(s, line, col, pwaff) < 0)
                cond = isl_map_free(cond);
        if (!cond)
                return NULL;

        cond = read_formula(s, v, cond, rational);

        return accept_ternary(s, cond, v, rational);
}

static __isl_give isl_map *read_var_def(__isl_keep isl_stream *s,
        __isl_take isl_map *map, enum isl_dim_type type, struct vars *v,
        int rational)
{
        isl_pw_aff *def;
        isl_size pos;
        isl_map *def_map;

        if (type == isl_dim_param)
                pos = isl_map_dim(map, isl_dim_param);
        else {
                pos = isl_map_dim(map, isl_dim_in);
                if (type == isl_dim_out) {
                        isl_size n_out = isl_map_dim(map, isl_dim_out);
                        if (pos < 0 || n_out < 0)
                                return isl_map_free(map);
                        pos += n_out;
                }
                type = isl_dim_in;
        }
        if (pos < 0)
                return isl_map_free(map);
        --pos;

        def = accept_extended_affine(s, isl_space_wrap(isl_map_get_space(map)),
                                        v, rational);
        def_map = isl_map_from_pw_aff(def);
        def_map = isl_map_equate(def_map, type, pos, isl_dim_out, 0);
        def_map = isl_set_unwrap(isl_map_domain(def_map));

        map = isl_map_intersect(map, def_map);

        return map;
}

static __isl_give isl_pw_aff_list *accept_affine_list(__isl_keep isl_stream *s,
        __isl_take isl_space *space, struct vars *v)
{
        isl_pw_aff *pwaff;
        isl_pw_aff_list *list;
        struct isl_token *tok = NULL;

        pwaff = accept_affine(s, isl_space_copy(space), v);
        list = isl_pw_aff_list_from_pw_aff(pwaff);
        if (!list)
                goto error;

        for (;;) {
                tok = isl_stream_next_token(s);
                if (!tok) {
                        isl_stream_error(s, NULL, "unexpected EOF");
                        goto error;
                }
                if (tok->type != ',') {
                        isl_stream_push_token(s, tok);
                        break;
                }
                isl_token_free(tok);

                pwaff = accept_affine(s, isl_space_copy(space), v);
                list = isl_pw_aff_list_concat(list,
                                isl_pw_aff_list_from_pw_aff(pwaff));
                if (!list)
                        goto error;
        }

        isl_space_free(space);
        return list;
error:
        isl_space_free(space);
        isl_pw_aff_list_free(list);
        return NULL;
}

static __isl_give isl_map *read_defined_var_list(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_map *map, int rational)
{
        struct isl_token *tok;

        while ((tok = isl_stream_next_token(s)) != NULL) {
                int p;
                int n = v->n;

                if (tok->type != ISL_TOKEN_IDENT)
                        break;

                p = vars_pos(v, tok->u.s, -1);
                if (p < 0)
                        goto error;
                if (p < n) {
                        isl_stream_error(s, tok, "expecting unique identifier");
                        goto error;
                }

                map = isl_map_add_dims(map, isl_dim_out, 1);

                isl_token_free(tok);
                tok = isl_stream_next_token(s);
                if (tok && tok->type == '=') {
                        isl_token_free(tok);
                        map = read_var_def(s, map, isl_dim_out, v, rational);
                        tok = isl_stream_next_token(s);
                }

                if (!tok || tok->type != ',')
                        break;

                isl_token_free(tok);
        }
        if (tok)
                isl_stream_push_token(s, tok);

        return map;
error:
        isl_token_free(tok);
        isl_map_free(map);
        return NULL;
}

static int next_is_tuple(__isl_keep isl_stream *s)
{
        struct isl_token *tok;
        int is_tuple;

        tok = isl_stream_next_token(s);
        if (!tok)
                return 0;
        if (tok->type == '[') {
                isl_stream_push_token(s, tok);
                return 1;
        }
        if (tok->type != ISL_TOKEN_IDENT && !tok->is_keyword) {
                isl_stream_push_token(s, tok);
                return 0;
        }

        is_tuple = isl_stream_next_token_is(s, '[');

        isl_stream_push_token(s, tok);

        return is_tuple;
}

/* Does the next token mark the end of a tuple element?
 */
static int next_is_end_tuple_element(__isl_keep isl_stream *s)
{
        return isl_stream_next_token_is(s, ',') ||
            isl_stream_next_token_is(s, ']');
}

/* Is the next token one that necessarily forms the start of a condition?
 */
static int next_is_condition_start(__isl_keep isl_stream *s)
{
        return isl_stream_next_token_is(s, ISL_TOKEN_EXISTS) ||
            isl_stream_next_token_is(s, ISL_TOKEN_NOT) ||
            isl_stream_next_token_is(s, ISL_TOKEN_TRUE) ||
            isl_stream_next_token_is(s, ISL_TOKEN_FALSE) ||
            isl_stream_next_token_is(s, ISL_TOKEN_MAP);
}

/* Is "pa" an expression in term of earlier dimensions?
 * The alternative is that the dimension is defined to be equal to itself,
 * meaning that it has a universe domain and an expression that depends
 * on itself.  "i" is the position of the expression in a sequence
 * of "n" expressions.  The final dimensions of "pa" correspond to
 * these "n" expressions.
 */
static isl_bool pw_aff_is_expr(__isl_keep isl_pw_aff *pa, int i, int n)
{
        isl_aff *aff;

        if (!pa)
                return isl_bool_error;
        if (pa->n != 1)
                return isl_bool_true;
        if (!isl_set_plain_is_universe(pa->p[0].set))
                return isl_bool_true;

        aff = pa->p[0].aff;
        if (isl_int_is_zero(aff->v->el[aff->v->size - n + i]))
                return isl_bool_true;
        return isl_bool_false;
}

/* Does the tuple contain any dimensions that are defined
 * in terms of earlier dimensions?
 */
static isl_bool tuple_has_expr(__isl_keep isl_multi_pw_aff *tuple)
{
        int i;
        isl_size n;
        isl_bool has_expr = isl_bool_false;
        isl_pw_aff *pa;

        n = isl_multi_pw_aff_dim(tuple, isl_dim_out);
        if (n < 0)
                return isl_bool_error;
        for (i = 0; i < n; ++i) {
                pa = isl_multi_pw_aff_get_pw_aff(tuple, i);
                has_expr = pw_aff_is_expr(pa, i, n);
                isl_pw_aff_free(pa);
                if (has_expr < 0 || has_expr)
                        break;
        }

        return has_expr;
}

/* Set the name of dimension "pos" in "space" to "name".
 * During printing, we add primes if the same name appears more than once
 * to distinguish the occurrences.  Here, we remove those primes from "name"
 * before setting the name of the dimension.
 */
static __isl_give isl_space *space_set_dim_name(__isl_take isl_space *space,
        int pos, char *name)
{
        char *prime;

        if (!name)
                return space;

        prime = strchr(name, '\'');
        if (prime)
                *prime = '\0';
        space = isl_space_set_dim_name(space, isl_dim_out, pos, name);
        if (prime)
                *prime = '\'';

        return space;
}

/* Construct an isl_pw_aff defined on a "space" (with v->n variables)
 * that is equal to the last of those variables.
 */
static __isl_give isl_pw_aff *identity_tuple_el_on_space(
        __isl_take isl_space *space, struct vars *v)
{
        isl_aff *aff;

        aff = isl_aff_zero_on_domain(isl_local_space_from_space(space));
        aff = isl_aff_add_coefficient_si(aff, isl_dim_in, v->n - 1, 1);
        return isl_pw_aff_from_aff(aff);
}

/* Construct an isl_pw_aff defined on the domain space of "pa"
 * that is equal to the last variable in "v".
 *
 * That is, if D is the domain space of "pa", then construct
 *
 *      D[..., i] -> i.
 */
static __isl_give isl_pw_aff *init_range(__isl_keep isl_pw_aff *pa,
        struct vars *v)
{
        isl_space *space;

        space = isl_pw_aff_get_domain_space(pa);
        return identity_tuple_el_on_space(space, v);
}

/* Impose the lower bound "lower" on the variable represented by "range_pa".
 *
 * In particular, "range_pa" is of the form
 *
 *      D[..., i] -> i : C
 *
 * with D also the domains space of "lower' and "C" some constraints.
 *
 * Return the expression
 *
 *      D[..., i] -> i : C and i >= lower
 */
static __isl_give isl_pw_aff *set_lower(__isl_take isl_pw_aff *range_pa,
        __isl_take isl_pw_aff *lower)
{
        isl_set *range;

        range = isl_pw_aff_ge_set(isl_pw_aff_copy(range_pa), lower);
        return isl_pw_aff_intersect_domain(range_pa, range);
}

/* Impose the upper bound "upper" on the variable represented by "range_pa".
 *
 * In particular, "range_pa" is of the form
 *
 *      D[..., i] -> i : C
 *
 * with D also the domains space of "upper' and "C" some constraints.
 *
 * Return the expression
 *
 *      D[..., i] -> i : C and i <= upper
 */
static __isl_give isl_pw_aff *set_upper(__isl_take isl_pw_aff *range_pa,
        __isl_take isl_pw_aff *upper)
{
        isl_set *range;

        range = isl_pw_aff_le_set(isl_pw_aff_copy(range_pa), upper);
        return isl_pw_aff_intersect_domain(range_pa, range);
}

/* Construct a piecewise affine expression corresponding
 * to the last variable in "v" that is greater than or equal to "pa".
 *
 * In particular, if D is the domain space of "pa",
 * then construct the expression
 *
 *      D[..., i] -> i,
 *
 * impose lower bound "pa" and return
 *
 *      D[..., i] -> i : i >= pa
 */
static __isl_give isl_pw_aff *construct_lower(__isl_take isl_pw_aff *pa,
        struct vars *v)
{
        return set_lower(init_range(pa, v), pa);
}

/* Construct a piecewise affine expression corresponding
 * to the last variable in "v" that is smaller than or equal to "pa".
 *
 * In particular, if D is the domain space of "pa",
 * then construct the expression
 *
 *      D[..., i] -> i,
 *
 * impose lower bound "pa" and return
 *
 *      D[..., i] -> i : i <= pa
 */
static __isl_give isl_pw_aff *construct_upper(__isl_take isl_pw_aff *pa,
        struct vars *v)
{
        return set_upper(init_range(pa, v), pa);
}

/* Construct a piecewise affine expression corresponding
 * to the last variable in "v" that ranges between "pa" and "pa2".
 *
 * In particular, if D is the domain space of "pa" (and "pa2"),
 * then construct the expression
 *
 *      D[..., i] -> i,
 *
 * impose lower bound "pa" and upper bound "pa2" and return
 *
 *      D[..., i] -> i : pa <= i <= pa2
 */
static __isl_give isl_pw_aff *construct_range(__isl_take isl_pw_aff *pa,
        __isl_take isl_pw_aff *pa2, struct vars *v)
{
        return set_upper(set_lower(init_range(pa, v), pa), pa2);
}

static int resolve_paren_expr(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_map *map, int rational);

/* Given that the (piecewise) affine expression "pa"
 * has just been parsed, followed by a colon,
 * continue parsing as part of a piecewise affine expression.
 *
 * In particular, check if the colon is followed by a condition.
 * If so, parse the conditions(a) on "pa" and include them in the domain.
 * Otherwise, if the colon is followed by another (piecewise) affine expression
 * then consider the two expressions as endpoints of a range of values and
 * return a piecewise affine expression that takes values in that range.
 * Note that an affine expression followed by a comparison operator
 * is considered to be part of a condition.
 * If the colon is not followed by anything (inside the tuple element),
 * then consider "pa" as a lower bound on a range of values without upper bound
 * and return a piecewise affine expression that takes values in that range.
 */
static __isl_give isl_pw_aff *update_piecewise_affine_colon(
        __isl_take isl_pw_aff *pa, __isl_keep isl_stream *s,
        struct vars *v, int rational)
{
        isl_space *dom_space;
        isl_map *map;

        dom_space = isl_pw_aff_get_domain_space(pa);
        map = isl_map_universe(isl_space_from_domain(dom_space));

        if (isl_stream_next_token_is(s, '('))
                if (resolve_paren_expr(s, v, isl_map_copy(map), rational))
                        goto error;
        if (next_is_end_tuple_element(s)) {
                isl_map_free(map);
                return construct_lower(pa, v);
        }
        if (!next_is_condition_start(s)) {
                int line = -1, col = -1;
                isl_space *space;
                isl_pw_aff *pa2;

                set_current_line_col(s, &line, &col);
                space = isl_space_wrap(isl_map_get_space(map));
                pa2 = accept_affine(s, space, v);
                if (rational)
                        pa2 = isl_pw_aff_set_rational(pa2);
                if (!next_is_comparator(s)) {
                        isl_map_free(map);
                        pa2 = isl_pw_aff_domain_factor_domain(pa2);
                        return construct_range(pa, pa2, v);
                }
                if (push_aff(s, line, col, pa2) < 0)
                        goto error;
        }

        map = read_formula(s, v, map, rational);
        pa = isl_pw_aff_intersect_domain(pa, isl_map_domain(map));

        return pa;
error:
        isl_map_free(map);
        isl_pw_aff_free(pa);
        return NULL;
}

/* Accept a piecewise affine expression.
 *
 * At the outer level, the piecewise affine expression may be of the form
 *
 *      aff1 : condition1; aff2 : conditions2; ...
 *
 * or one of
 *
 *      aff :
 *      aff1 : aff2
 *      : aff
 *      :
 *
 * or simply
 *
 *      aff
 *
 * each of the affine expressions may in turn include ternary operators.
 *
 * If the first token is a colon, then the expression must be
 * ":" or ": aff2", depending on whether anything follows the colon
 * inside the tuple element.
 * The first is considered to represent an arbitrary value.
 * The second is considered to represent a range of values
 * with the given upper bound and no lower bound.
 *
 * There may be parentheses around some subexpression of "aff1"
 * around "aff1" itself, around "aff1 : condition1" and/or
 * around the entire piecewise affine expression.
 * We therefore remove the opening parenthesis (if any) from the stream
 * in case the closing parenthesis follows the colon, but if the closing
 * parenthesis is the first thing in the stream after the parsed affine
 * expression, we push the parsed expression onto the stream and parse
 * again in case the parentheses enclose some subexpression of "aff1".
 */
static __isl_give isl_pw_aff *accept_piecewise_affine(__isl_keep isl_stream *s,
        __isl_take isl_space *space, struct vars *v, int rational)
{
        isl_pw_aff *res;
        isl_space *res_space;

        if (isl_stream_eat_if_available(s, ':')) {
                if (next_is_end_tuple_element(s))
                        return identity_tuple_el_on_space(space, v);
                else
                        return construct_upper(accept_affine(s, space, v), v);
        }

        res_space = isl_space_from_domain(isl_space_copy(space));
        res_space = isl_space_add_dims(res_space, isl_dim_out, 1);
        res = isl_pw_aff_empty(res_space);
        do {
                isl_pw_aff *pa;
                int seen_paren;
                int line = -1, col = -1;

                set_current_line_col(s, &line, &col);
                seen_paren = isl_stream_eat_if_available(s, '(');
                if (seen_paren)
                        pa = accept_piecewise_affine(s, isl_space_copy(space),
                                                        v, rational);
                else
                        pa = accept_extended_affine(s, isl_space_copy(space),
                                                        v, rational);
                if (seen_paren && isl_stream_eat_if_available(s, ')')) {
                        seen_paren = 0;
                        if (push_aff(s, line, col, pa) < 0)
                                goto error;
                        pa = accept_extended_affine(s, isl_space_copy(space),
                                                        v, rational);
                }
                if (isl_stream_eat_if_available(s, ':'))
                        pa = update_piecewise_affine_colon(pa, s, v, rational);

                res = isl_pw_aff_union_add(res, pa);

                if (seen_paren && isl_stream_eat(s, ')'))
                        goto error;
        } while (isl_stream_eat_if_available(s, ';'));

        isl_space_free(space);

        return res;
error:
        isl_space_free(space);
        return isl_pw_aff_free(res);
}

/* Read an affine expression from "s" for use in read_tuple.
 *
 * accept_extended_affine requires a wrapped space as input.
 * read_tuple on the other hand expects each isl_pw_aff
 * to have an anonymous space.  We therefore adjust the space
 * of the isl_pw_aff before returning it.
 */
static __isl_give isl_pw_aff *read_tuple_var_def(__isl_keep isl_stream *s,
        struct vars *v, int rational)
{
        isl_space *space;
        isl_pw_aff *def;

        space = isl_space_wrap(isl_space_alloc(s->ctx, 0, v->n, 0));

        def = accept_piecewise_affine(s, space, v, rational);
        def = isl_pw_aff_domain_factor_domain(def);

        return def;
}

/* Read a list of tuple elements by calling "read_el" on each of them and
 * return a space with the same number of set dimensions derived from
 * the parameter space "space" and possibly updated by "read_el".
 * The elements in the list are separated by either "," or "][".
 * If "comma" is set then only "," is allowed.
 */
static __isl_give isl_space *read_tuple_list(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_space *space, int rational, int comma,
        __isl_give isl_space *(*read_el)(__isl_keep isl_stream *s,
                struct vars *v, __isl_take isl_space *space, int rational,
                void *user),
        void *user)
{
        if (!space)
                return NULL;

        space = isl_space_set_from_params(space);

        if (isl_stream_next_token_is(s, ']'))
                return space;

        for (;;) {
                struct isl_token *tok;

                space = isl_space_add_dims(space, isl_dim_set, 1);

                space = read_el(s, v, space, rational, user);
                if (!space)
                        return NULL;

                tok = isl_stream_next_token(s);
                if (!comma && tok && tok->type == ']' &&
                    isl_stream_next_token_is(s, '[')) {
                        isl_token_free(tok);
                        tok = isl_stream_next_token(s);
                } else if (!tok || tok->type != ',') {
                        if (tok)
                                isl_stream_push_token(s, tok);
                        break;
                }

                isl_token_free(tok);
        }

        return space;
}

/* Read a tuple space from "s" derived from the parameter space "space".
 * Call "read_el" on each element in the tuples.
 */
static __isl_give isl_space *read_tuple_space(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_space *space, int rational, int comma,
        __isl_give isl_space *(*read_el)(__isl_keep isl_stream *s,
                struct vars *v, __isl_take isl_space *space, int rational,
                void *user),
        void *user)
{
        struct isl_token *tok;
        char *name = NULL;
        isl_space *res = NULL;

        tok = isl_stream_next_token(s);
        if (!tok)
                goto error;
        if (tok->type == ISL_TOKEN_IDENT || tok->is_keyword) {
                name = strdup(tok->u.s);
                isl_token_free(tok);
                if (!name)
                        goto error;
        } else
                isl_stream_push_token(s, tok);
        if (isl_stream_eat(s, '['))
                goto error;
        if (next_is_tuple(s)) {
                isl_space *out;
                res = read_tuple_space(s, v, isl_space_copy(space),
                                        rational, comma, read_el, user);
                if (isl_stream_eat(s, ISL_TOKEN_TO))
                        goto error;
                out = read_tuple_space(s, v, isl_space_copy(space),
                                        rational, comma, read_el, user);
                res = isl_space_product(res, out);
        } else
                res = read_tuple_list(s, v, isl_space_copy(space),
                                        rational, comma, read_el, user);
        if (isl_stream_eat(s, ']'))
                goto error;

        if (name) {
                res = isl_space_set_tuple_name(res, isl_dim_set, name);
                free(name);
        }

        isl_space_free(space);
        return res;
error:
        free(name);
        isl_space_free(res);
        isl_space_free(space);
        return NULL;
}

/* Construct an isl_pw_aff defined on a space with v->n variables
 * that is equal to the last of those variables.
 */
static __isl_give isl_pw_aff *identity_tuple_el(struct vars *v)
{
        isl_space *space;

        space = isl_space_set_alloc(v->ctx, 0, v->n);
        return identity_tuple_el_on_space(space, v);
}

/* This function is called for each element in a tuple inside read_tuple.
 * Add a new variable to "v" and construct a corresponding isl_pw_aff defined
 * over a space containing all variables in "v" defined so far.
 * The isl_pw_aff expresses the new variable in terms of earlier variables
 * if a definition is provided.  Otherwise, it is represented as being
 * equal to itself.
 * Add the isl_pw_aff to *list.
 * If the new variable was named, then adjust "space" accordingly and
 * return the updated space.
 */
static __isl_give isl_space *read_tuple_pw_aff_el(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_space *space, int rational, void *user)
{
        isl_pw_aff_list **list = (isl_pw_aff_list **) user;
        isl_pw_aff *pa;
        struct isl_token *tok;
        int new_name = 0;

        tok = next_token(s);
        if (!tok) {
                isl_stream_error(s, NULL, "unexpected EOF");
                return isl_space_free(space);
        }

        if (tok->type == ISL_TOKEN_IDENT) {
                int n = v->n;
                int p = vars_pos(v, tok->u.s, -1);
                if (p < 0)
                        goto error;
                new_name = p >= n;
        }

        if (tok->type == '*') {
                if (vars_add_anon(v) < 0)
                        goto error;
                isl_token_free(tok);
                pa = identity_tuple_el(v);
        } else if (new_name) {
                isl_size pos = isl_space_dim(space, isl_dim_out);
                if (pos < 0)
                        goto error;
                pos -= 1;
                space = space_set_dim_name(space, pos, v->v->name);
                isl_token_free(tok);
                if (isl_stream_eat_if_available(s, '='))
                        pa = read_tuple_var_def(s, v, rational);
                else
                        pa = identity_tuple_el(v);
        } else {
                isl_stream_push_token(s, tok);
                tok = NULL;
                if (vars_add_anon(v) < 0)
                        goto error;
                pa = read_tuple_var_def(s, v, rational);
        }

        *list = isl_pw_aff_list_add(*list, pa);
        if (!*list)
                return isl_space_free(space);

        return space;
error:
        isl_token_free(tok);
        return isl_space_free(space);
}

/* Read a tuple and represent it as an isl_multi_pw_aff.
 * The range space of the isl_multi_pw_aff is the space of the tuple.
 * The domain space is an anonymous space
 * with a dimension for each variable in the set of variables in "v",
 * including the variables in the range.
 * If a given dimension is not defined in terms of earlier dimensions in
 * the input, then the corresponding isl_pw_aff is set equal to one time
 * the variable corresponding to the dimension being defined.
 *
 * The elements in the tuple are collected in a list by read_tuple_pw_aff_el.
 * Each element in this list is defined over a space representing
 * the variables defined so far.  We need to adjust the earlier
 * elements to have as many variables in the domain as the final
 * element in the list.
 */
static __isl_give isl_multi_pw_aff *read_tuple(__isl_keep isl_stream *s,
        struct vars *v, int rational, int comma)
{
        int i;
        isl_size n;
        isl_space *space;
        isl_pw_aff_list *list;

        space = isl_space_params_alloc(v->ctx, 0);
        list = isl_pw_aff_list_alloc(s->ctx, 0);
        space = read_tuple_space(s, v, space, rational, comma,
                                &read_tuple_pw_aff_el, &list);
        n = isl_space_dim(space, isl_dim_set);
        if (n < 0)
                space = isl_space_free(space);
        for (i = 0; i + 1 < n; ++i) {
                isl_pw_aff *pa;

                pa = isl_pw_aff_list_get_pw_aff(list, i);
                pa = isl_pw_aff_add_dims(pa, isl_dim_in, n - (i + 1));
                list = isl_pw_aff_list_set_pw_aff(list, i, pa);
        }

        space = isl_space_from_range(space);
        space = isl_space_add_dims(space, isl_dim_in, v->n);
        return isl_multi_pw_aff_from_pw_aff_list(space, list);
}

/* Add the tuple represented by the isl_multi_pw_aff "tuple" to "map".
 * We first create the appropriate space in "map" based on the range
 * space of this isl_multi_pw_aff.  Then, we add equalities based
 * on the affine expressions.  These live in an anonymous space,
 * however, so we first need to reset the space to that of "map".
 */
static __isl_give isl_map *map_from_tuple(__isl_take isl_multi_pw_aff *tuple,
        __isl_take isl_map *map, enum isl_dim_type type, struct vars *v,
        int rational)
{
        int i;
        isl_size n;
        isl_ctx *ctx;
        isl_space *space = NULL;

        n = isl_multi_pw_aff_dim(tuple, isl_dim_out);
        if (!map || n < 0)
                goto error;
        ctx = isl_multi_pw_aff_get_ctx(tuple);
        space = isl_space_range(isl_multi_pw_aff_get_space(tuple));
        if (!space)
                goto error;

        if (type == isl_dim_param) {
                if (isl_space_has_tuple_name(space, isl_dim_set) ||
                    isl_space_is_wrapping(space)) {
                        isl_die(ctx, isl_error_invalid,
                                "parameter tuples cannot be named or nested",
                                goto error);
                }
                map = isl_map_add_dims(map, type, n);
                for (i = 0; i < n; ++i) {
                        isl_id *id;
                        if (!isl_space_has_dim_name(space, isl_dim_set, i))
                                isl_die(ctx, isl_error_invalid,
                                        "parameters must be named",
                                        goto error);
                        id = isl_space_get_dim_id(space, isl_dim_set, i);
                        map = isl_map_set_dim_id(map, isl_dim_param, i, id);
                }
        } else if (type == isl_dim_in) {
                isl_set *set;

                set = isl_set_universe(isl_space_copy(space));
                if (rational)
                        set = isl_set_set_rational(set);
                set = isl_set_intersect_params(set, isl_map_params(map));
                map = isl_map_from_domain(set);
        } else {
                isl_set *set;

                set = isl_set_universe(isl_space_copy(space));
                if (rational)
                        set = isl_set_set_rational(set);
                map = isl_map_from_domain_and_range(isl_map_domain(map), set);
        }

        for (i = 0; i < n; ++i) {
                isl_pw_aff *pa;
                isl_space *space;
                isl_aff *aff;
                isl_set *set;
                isl_map *map_i;

                pa = isl_multi_pw_aff_get_pw_aff(tuple, i);
                space = isl_pw_aff_get_domain_space(pa);
                aff = isl_aff_zero_on_domain(isl_local_space_from_space(space));
                aff = isl_aff_add_coefficient_si(aff,
                                                isl_dim_in, v->n - n + i, -1);
                pa = isl_pw_aff_add(pa, isl_pw_aff_from_aff(aff));
                if (rational)
                        pa = isl_pw_aff_set_rational(pa);
                set = isl_pw_aff_zero_set(pa);
                map_i = isl_map_from_range(set);
                map_i = isl_map_reset_space(map_i, isl_map_get_space(map));
                map = isl_map_intersect(map, map_i);
        }

        isl_space_free(space);
        isl_multi_pw_aff_free(tuple);
        return map;
error:
        isl_space_free(space);
        isl_multi_pw_aff_free(tuple);
        isl_map_free(map);
        return NULL;
}

/* Read a tuple from "s" and add it to "map".
 * The tuple is initially represented as an isl_multi_pw_aff and
 * then added to "map".
 */
static __isl_give isl_map *read_map_tuple(__isl_keep isl_stream *s,
        __isl_take isl_map *map, enum isl_dim_type type, struct vars *v,
        int rational, int comma)
{
        isl_multi_pw_aff *tuple;

        tuple = read_tuple(s, v, rational, comma);
        if (!tuple)
                return isl_map_free(map);

        return map_from_tuple(tuple, map, type, v, rational);
}

/* Given two equal-length lists of piecewise affine expression with the space
 * of "set" as domain, construct a set in the same space that expresses
 * that "left" and "right" satisfy the comparison "type".
 *
 * A space is constructed of the same dimension as the number of elements
 * in the two lists.  The comparison is then expressed in a map from
 * this space to itself and wrapped into a set.  Finally the two lists
 * of piecewise affine expressions are plugged into this set.
 *
 * Let S be the space of "set" and T the constructed space.
 * The lists are first changed into two isl_multi_pw_affs in S -> T and
 * then combined into an isl_multi_pw_aff in S -> [T -> T],
 * while the comparison is first expressed in T -> T, then [T -> T]
 * and finally in S.
 */
static __isl_give isl_set *list_cmp(__isl_keep isl_set *set, int type,
        __isl_take isl_pw_aff_list *left, __isl_take isl_pw_aff_list *right)
{
        isl_space *space;
        isl_size n;
        isl_multi_pw_aff *mpa1, *mpa2;

        n = isl_pw_aff_list_n_pw_aff(left);
        if (!set || n < 0 || !right)
                goto error;

        space = isl_set_get_space(set);
        space = isl_space_from_domain(space);
        space = isl_space_add_dims(space, isl_dim_out, n);
        mpa1 = isl_multi_pw_aff_from_pw_aff_list(isl_space_copy(space), left);
        mpa2 = isl_multi_pw_aff_from_pw_aff_list(isl_space_copy(space), right);
        mpa1 = isl_multi_pw_aff_range_product(mpa1, mpa2);

        space = isl_space_range(space);
        switch (type) {
        case ISL_TOKEN_LEX_LT:
                set = isl_map_wrap(isl_map_lex_lt(space));
                break;
        case ISL_TOKEN_LEX_GT:
                set = isl_map_wrap(isl_map_lex_gt(space));
                break;
        case ISL_TOKEN_LEX_LE:
                set = isl_map_wrap(isl_map_lex_le(space));
                break;
        case ISL_TOKEN_LEX_GE:
                set = isl_map_wrap(isl_map_lex_ge(space));
                break;
        default:
                isl_multi_pw_aff_free(mpa1);
                isl_space_free(space);
                isl_die(isl_set_get_ctx(set), isl_error_internal,
                        "unhandled list comparison type", return NULL);
        }
        set = isl_set_preimage_multi_pw_aff(set, mpa1);
        return set;
error:
        isl_pw_aff_list_free(left);
        isl_pw_aff_list_free(right);
        return NULL;
}

/* Construct constraints of the form
 *
 *      a op b
 *
 * where a is an element in "left", op is an operator of type "type" and
 * b is an element in "right", add the constraints to "set" and return
 * the result.
 * "rational" is set if the constraints should be treated as
 * a rational constraints.
 *
 * If "type" is the type of a comparison operator between lists
 * of affine expressions, then a single (compound) constraint
 * is constructed by list_cmp instead.
 */
static __isl_give isl_set *construct_constraints(
        __isl_take isl_set *set, int type,
        __isl_keep isl_pw_aff_list *left, __isl_keep isl_pw_aff_list *right,
        int rational)
{
        isl_set *cond;

        left = isl_pw_aff_list_copy(left);
        right = isl_pw_aff_list_copy(right);
        if (rational) {
                left = isl_pw_aff_list_set_rational(left);
                right = isl_pw_aff_list_set_rational(right);
        }
        if (is_list_comparator_type(type))
                cond = list_cmp(set, type, left, right);
        else if (type == ISL_TOKEN_LE)
                cond = isl_pw_aff_list_le_set(left, right);
        else if (type == ISL_TOKEN_GE)
                cond = isl_pw_aff_list_ge_set(left, right);
        else if (type == ISL_TOKEN_LT)
                cond = isl_pw_aff_list_lt_set(left, right);
        else if (type == ISL_TOKEN_GT)
                cond = isl_pw_aff_list_gt_set(left, right);
        else if (type == ISL_TOKEN_NE)
                cond = isl_pw_aff_list_ne_set(left, right);
        else
                cond = isl_pw_aff_list_eq_set(left, right);

        return isl_set_intersect(set, cond);
}

/* Read a constraint from "s", add it to "map" and return the result.
 * "v" contains a description of the identifiers parsed so far.
 * "rational" is set if the constraint should be treated as
 * a rational constraint.
 * The constraint read from "s" may be applied to multiple pairs
 * of affine expressions and may be chained.
 * In particular, a list of affine expressions is read, followed
 * by a comparison operator and another list of affine expressions.
 * The comparison operator is then applied to each pair of elements
 * in the two lists and the results are added to "map".
 * However, if the operator expects two lists of affine expressions,
 * then it is applied directly to those lists and the two lists
 * are required to have the same length.
 * If the next token is another comparison operator, then another
 * list of affine expressions is read and the process repeats.
 *
 * The processing is performed on a wrapped copy of "map" because
 * an affine expression cannot have a binary relation as domain.
 */
static __isl_give isl_map *add_constraint(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_map *map, int rational)
{
        struct isl_token *tok;
        int type;
        isl_pw_aff_list *list1 = NULL, *list2 = NULL;
        isl_size n1, n2;
        isl_set *set;

        set = isl_map_wrap(map);
        list1 = accept_affine_list(s, isl_set_get_space(set), v);
        if (!list1)
                goto error;
        tok = isl_stream_next_token(s);
        if (!is_comparator(tok)) {
                isl_stream_error(s, tok, "missing operator");
                if (tok)
                        isl_stream_push_token(s, tok);
                goto error;
        }
        type = tok->type;
        isl_token_free(tok);
        for (;;) {
                list2 = accept_affine_list(s, isl_set_get_space(set), v);
                n1 = isl_pw_aff_list_n_pw_aff(list1);
                n2 = isl_pw_aff_list_n_pw_aff(list2);
                if (n1 < 0 || n2 < 0)
                        goto error;
                if (is_list_comparator_type(type) && n1 != n2) {
                        isl_stream_error(s, NULL,
                                        "list arguments not of same size");
                        goto error;
                }

                set = construct_constraints(set, type, list1, list2, rational);
                isl_pw_aff_list_free(list1);
                list1 = list2;

                if (!next_is_comparator(s))
                        break;
                tok = isl_stream_next_token(s);
                type = tok->type;
                isl_token_free(tok);
        }
        isl_pw_aff_list_free(list1);

        return isl_set_unwrap(set);
error:
        isl_pw_aff_list_free(list1);
        isl_pw_aff_list_free(list2);
        isl_set_free(set);
        return NULL;
}

static __isl_give isl_map *read_exists(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_map *map, int rational)
{
        int n = v->n;
        int seen_paren = isl_stream_eat_if_available(s, '(');

        map = isl_map_from_domain(isl_map_wrap(map));
        map = read_defined_var_list(s, v, map, rational);

        if (isl_stream_eat(s, ':'))
                goto error;

        map = read_formula(s, v, map, rational);
        map = isl_set_unwrap(isl_map_domain(map));

        vars_drop(v, v->n - n);
        if (seen_paren && isl_stream_eat(s, ')'))
                goto error;

        return map;
error:
        isl_map_free(map);
        return NULL;
}

/* Parse an expression between parentheses and push the result
 * back on the stream.
 *
 * The parsed expression may be either an affine expression
 * or a condition.  The first type is pushed onto the stream
 * as an isl_pw_aff, while the second is pushed as an isl_map.
 *
 * If the initial token indicates the start of a condition,
 * we parse it as such.
 * Otherwise, we first parse an affine expression and push
 * that onto the stream.  If the affine expression covers the
 * entire expression between parentheses, we return.
 * Otherwise, we assume that the affine expression is the
 * start of a condition and continue parsing.
 */
static int resolve_paren_expr(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_map *map, int rational)
{
        struct isl_token *tok, *tok2;
        int has_paren;
        int line, col;
        isl_pw_aff *pwaff;

        tok = isl_stream_next_token(s);
        if (!tok || tok->type != '(')
                goto error;

        if (isl_stream_next_token_is(s, '('))
                if (resolve_paren_expr(s, v, isl_map_copy(map), rational))
                        goto error;

        if (next_is_condition_start(s)) {
                map = read_formula(s, v, map, rational);
                if (isl_stream_eat(s, ')'))
                        goto error;
                tok->type = ISL_TOKEN_MAP;
                tok->u.map = map;
                isl_stream_push_token(s, tok);
                return 0;
        }

        tok2 = isl_stream_next_token(s);
        if (!tok2)
                goto error;
        line = tok2->line;
        col = tok2->col;
        isl_stream_push_token(s, tok2);

        pwaff = accept_affine(s, isl_space_wrap(isl_map_get_space(map)), v);
        if (!pwaff)
                goto error;

        has_paren = isl_stream_eat_if_available(s, ')');

        if (push_aff(s, line, col, pwaff) < 0)
                goto error;

        if (has_paren) {
                isl_token_free(tok);
                isl_map_free(map);
                return 0;
        }

        map = read_formula(s, v, map, rational);
        if (isl_stream_eat(s, ')'))
                goto error;

        tok->type = ISL_TOKEN_MAP;
        tok->u.map = map;
        isl_stream_push_token(s, tok);

        return 0;
error:
        isl_token_free(tok);
        isl_map_free(map);
        return -1;
}

static __isl_give isl_map *read_conjunct(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_map *map, int rational)
{
        if (isl_stream_next_token_is(s, '('))
                if (resolve_paren_expr(s, v, isl_map_copy(map), rational))
                        goto error;

        if (isl_stream_next_token_is(s, ISL_TOKEN_MAP)) {
                struct isl_token *tok;
                tok = isl_stream_next_token(s);
                if (!tok)
                        goto error;
                isl_map_free(map);
                map = isl_map_copy(tok->u.map);
                isl_token_free(tok);
                return map;
        }

        if (isl_stream_eat_if_available(s, ISL_TOKEN_EXISTS))
                return read_exists(s, v, map, rational);

        if (isl_stream_eat_if_available(s, ISL_TOKEN_TRUE))
                return map;

        if (isl_stream_eat_if_available(s, ISL_TOKEN_FALSE)) {
                isl_space *space = isl_map_get_space(map);
                isl_map_free(map);
                return isl_map_empty(space);
        }
                
        return add_constraint(s, v, map, rational);
error:
        isl_map_free(map);
        return NULL;
}

static __isl_give isl_map *read_conjuncts(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_map *map, int rational)
{
        isl_map *res;
        int negate;

        negate = isl_stream_eat_if_available(s, ISL_TOKEN_NOT);
        res = read_conjunct(s, v, isl_map_copy(map), rational);
        if (negate)
                res = isl_map_subtract(isl_map_copy(map), res);

        while (res && isl_stream_eat_if_available(s, ISL_TOKEN_AND)) {
                isl_map *res_i;

                negate = isl_stream_eat_if_available(s, ISL_TOKEN_NOT);
                res_i = read_conjunct(s, v, isl_map_copy(map), rational);
                if (negate)
                        res = isl_map_subtract(res, res_i);
                else
                        res = isl_map_intersect(res, res_i);
        }

        isl_map_free(map);
        return res;
}

static __isl_give isl_map *read_disjuncts(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_map *map, int rational)
{
        isl_map *res;

        if (isl_stream_next_token_is(s, '}'))
                return map;

        res = read_conjuncts(s, v, isl_map_copy(map), rational);
        while (isl_stream_eat_if_available(s, ISL_TOKEN_OR)) {
                isl_map *res_i;

                res_i = read_conjuncts(s, v, isl_map_copy(map), rational);
                res = isl_map_union(res, res_i);
        }

        isl_map_free(map);
        return res;
}

/* Read a first order formula from "s", add the corresponding
 * constraints to "map" and return the result.
 *
 * In particular, read a formula of the form
 *
 *      a
 *
 * or
 *
 *      a implies b
 *
 * where a and b are disjunctions.
 *
 * In the first case, map is replaced by
 *
 *      map \cap { [..] : a }
 *
 * In the second case, it is replaced by
 *
 *      (map \setminus { [..] : a}) \cup (map \cap { [..] : b })
 */
static __isl_give isl_map *read_formula(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_map *map, int rational)
{
        isl_map *res;

        res = read_disjuncts(s, v, isl_map_copy(map), rational);

        if (isl_stream_eat_if_available(s, ISL_TOKEN_IMPLIES)) {
                isl_map *res2;

                res = isl_map_subtract(isl_map_copy(map), res);
                res2 = read_disjuncts(s, v, map, rational);
                res = isl_map_union(res, res2);
        } else
                isl_map_free(map);

        return res;
}

static isl_size polylib_pos_to_isl_pos(__isl_keep isl_basic_map *bmap, int pos)
{
        isl_size n_out, n_in, n_param, n_div;

        n_param = isl_basic_map_dim(bmap, isl_dim_param);
        n_in = isl_basic_map_dim(bmap, isl_dim_in);
        n_out = isl_basic_map_dim(bmap, isl_dim_out);
        n_div = isl_basic_map_dim(bmap, isl_dim_div);
        if (n_param < 0 || n_in < 0 || n_out < 0 || n_div < 0)
                return isl_size_error;

        if (pos < n_out)
                return 1 + n_param + n_in + pos;
        pos -= n_out;

        if (pos < n_in)
                return 1 + n_param + pos;
        pos -= n_in;

        if (pos < n_div)
                return 1 + n_param + n_in + n_out + pos;
        pos -= n_div;

        if (pos < n_param)
                return 1 + pos;

        return 0;
}

static __isl_give isl_basic_map *basic_map_read_polylib_constraint(
        __isl_keep isl_stream *s, __isl_take isl_basic_map *bmap)
{
        int j;
        struct isl_token *tok;
        int type;
        int k;
        isl_int *c;
        isl_size total;

        if (!bmap)
                return NULL;

        tok = isl_stream_next_token(s);
        if (!tok || tok->type != ISL_TOKEN_VALUE) {
                isl_stream_error(s, tok, "expecting coefficient");
                if (tok)
                        isl_stream_push_token(s, tok);
                goto error;
        }
        if (!tok->on_new_line) {
                isl_stream_error(s, tok, "coefficient should appear on new line");
                isl_stream_push_token(s, tok);
                goto error;
        }

        type = isl_int_get_si(tok->u.v);
        isl_token_free(tok);

        isl_assert(s->ctx, type == 0 || type == 1, goto error);
        if (type == 0) {
                k = isl_basic_map_alloc_equality(bmap);
                c = bmap->eq[k];
        } else {
                k = isl_basic_map_alloc_inequality(bmap);
                c = bmap->ineq[k];
        }
        if (k < 0)
                goto error;

        total = isl_basic_map_dim(bmap, isl_dim_all);
        if (total < 0)
                return isl_basic_map_free(bmap);
        for (j = 0; j < 1 + total; ++j) {
                isl_size pos;
                tok = isl_stream_next_token(s);
                if (!tok || tok->type != ISL_TOKEN_VALUE) {
                        isl_stream_error(s, tok, "expecting coefficient");
                        if (tok)
                                isl_stream_push_token(s, tok);
                        goto error;
                }
                if (tok->on_new_line) {
                        isl_stream_error(s, tok,
                                "coefficient should not appear on new line");
                        isl_stream_push_token(s, tok);
                        goto error;
                }
                pos = polylib_pos_to_isl_pos(bmap, j);
                if (pos >= 0)
                        isl_int_set(c[pos], tok->u.v);
                isl_token_free(tok);
                if (pos < 0)
                        return isl_basic_map_free(bmap);
        }

        return bmap;
error:
        isl_basic_map_free(bmap);
        return NULL;
}

static __isl_give isl_basic_map *basic_map_read_polylib(
        __isl_keep isl_stream *s)
{
        int i;
        struct isl_token *tok;
        struct isl_token *tok2;
        int n_row, n_col;
        int on_new_line;
        unsigned in = 0, out, local = 0;
        struct isl_basic_map *bmap = NULL;
        int nparam = 0;

        tok = isl_stream_next_token(s);
        if (!tok) {
                isl_stream_error(s, NULL, "unexpected EOF");
                return NULL;
        }
        tok2 = isl_stream_next_token(s);
        if (!tok2) {
                isl_token_free(tok);
                isl_stream_error(s, NULL, "unexpected EOF");
                return NULL;
        }
        if (tok->type != ISL_TOKEN_VALUE || tok2->type != ISL_TOKEN_VALUE) {
                isl_stream_push_token(s, tok2);
                isl_stream_push_token(s, tok);
                isl_stream_error(s, NULL,
                                 "expecting constraint matrix dimensions");
                return NULL;
        }
        n_row = isl_int_get_si(tok->u.v);
        n_col = isl_int_get_si(tok2->u.v);
        on_new_line = tok2->on_new_line;
        isl_token_free(tok2);
        isl_token_free(tok);
        isl_assert(s->ctx, !on_new_line, return NULL);
        isl_assert(s->ctx, n_row >= 0, return NULL);
        isl_assert(s->ctx, n_col >= 2 + nparam, return NULL);
        tok = isl_stream_next_token_on_same_line(s);
        if (tok) {
                if (tok->type != ISL_TOKEN_VALUE) {
                        isl_stream_error(s, tok,
                                    "expecting number of output dimensions");
                        isl_stream_push_token(s, tok);
                        goto error;
                }
                out = isl_int_get_si(tok->u.v);
                isl_token_free(tok);

                tok = isl_stream_next_token_on_same_line(s);
                if (!tok || tok->type != ISL_TOKEN_VALUE) {
                        isl_stream_error(s, tok,
                                    "expecting number of input dimensions");
                        if (tok)
                                isl_stream_push_token(s, tok);
                        goto error;
                }
                in = isl_int_get_si(tok->u.v);
                isl_token_free(tok);

                tok = isl_stream_next_token_on_same_line(s);
                if (!tok || tok->type != ISL_TOKEN_VALUE) {
                        isl_stream_error(s, tok,
                                    "expecting number of existentials");
                        if (tok)
                                isl_stream_push_token(s, tok);
                        goto error;
                }
                local = isl_int_get_si(tok->u.v);
                isl_token_free(tok);

                tok = isl_stream_next_token_on_same_line(s);
                if (!tok || tok->type != ISL_TOKEN_VALUE) {
                        isl_stream_error(s, tok,
                                    "expecting number of parameters");
                        if (tok)
                                isl_stream_push_token(s, tok);
                        goto error;
                }
                nparam = isl_int_get_si(tok->u.v);
                isl_token_free(tok);
                if (n_col != 1 + out + in + local + nparam + 1) {
                        isl_stream_error(s, NULL,
                                    "dimensions don't match");
                        goto error;
                }
        } else
                out = n_col - 2 - nparam;
        bmap = isl_basic_map_alloc(s->ctx, nparam, in, out, local, n_row, n_row);
        if (!bmap)
                return NULL;

        for (i = 0; i < local; ++i) {
                int k = isl_basic_map_alloc_div(bmap);
                if (k < 0)
                        goto error;
                isl_seq_clr(bmap->div[k], 1 + 1 + nparam + in + out + local);
        }

        for (i = 0; i < n_row; ++i)
                bmap = basic_map_read_polylib_constraint(s, bmap);

        tok = isl_stream_next_token_on_same_line(s);
        if (tok) {
                isl_stream_error(s, tok, "unexpected extra token on line");
                isl_stream_push_token(s, tok);
                goto error;
        }

        bmap = isl_basic_map_simplify(bmap);
        bmap = isl_basic_map_finalize(bmap);
        return bmap;
error:
        isl_basic_map_free(bmap);
        return NULL;
}

static __isl_give isl_map *map_read_polylib(__isl_keep isl_stream *s)
{
        struct isl_token *tok;
        struct isl_token *tok2;
        int i, n;
        struct isl_map *map;

        tok = isl_stream_next_token(s);
        if (!tok) {
                isl_stream_error(s, NULL, "unexpected EOF");
                return NULL;
        }
        tok2 = isl_stream_next_token_on_same_line(s);
        if (tok2 && tok2->type == ISL_TOKEN_VALUE) {
                isl_stream_push_token(s, tok2);
                isl_stream_push_token(s, tok);
                return isl_map_from_basic_map(basic_map_read_polylib(s));
        }
        if (tok2) {
                isl_stream_error(s, tok2, "unexpected token");
                isl_stream_push_token(s, tok2);
                isl_stream_push_token(s, tok);
                return NULL;
        }
        n = isl_int_get_si(tok->u.v);
        isl_token_free(tok);

        isl_assert(s->ctx, n >= 1, return NULL);

        map = isl_map_from_basic_map(basic_map_read_polylib(s));

        for (i = 1; map && i < n; ++i)
                map = isl_map_union(map,
                        isl_map_from_basic_map(basic_map_read_polylib(s)));

        return map;
}

static int optional_power(__isl_keep isl_stream *s)
{
        int pow;
        struct isl_token *tok;

        tok = isl_stream_next_token(s);
        if (!tok)
                return 1;
        if (tok->type != '^') {
                isl_stream_push_token(s, tok);
                return 1;
        }
        isl_token_free(tok);
        tok = isl_stream_next_token(s);
        if (!tok || tok->type != ISL_TOKEN_VALUE) {
                isl_stream_error(s, tok, "expecting exponent");
                if (tok)
                        isl_stream_push_token(s, tok);
                return 1;
        }
        pow = isl_int_get_si(tok->u.v);
        isl_token_free(tok);
        return pow;
}

static __isl_give isl_pw_qpolynomial *read_term(__isl_keep isl_stream *s,
        __isl_keep isl_map *map, struct vars *v);

static __isl_give isl_pw_qpolynomial *read_factor(__isl_keep isl_stream *s,
        __isl_keep isl_map *map, struct vars *v)
{
        isl_pw_qpolynomial *pwqp;
        struct isl_token *tok;

        tok = next_token(s);
        if (!tok) {
                isl_stream_error(s, NULL, "unexpected EOF");
                return NULL;
        }
        if (tok->type == '(') {
                int pow;

                isl_token_free(tok);
                pwqp = read_term(s, map, v);
                if (!pwqp)
                        return NULL;
                if (isl_stream_eat(s, ')'))
                        goto error;
                pow = optional_power(s);
                pwqp = isl_pw_qpolynomial_pow(pwqp, pow);
        } else if (tok->type == ISL_TOKEN_VALUE) {
                struct isl_token *tok2;
                isl_qpolynomial *qp;

                tok2 = isl_stream_next_token(s);
                if (tok2 && tok2->type == '/') {
                        isl_token_free(tok2);
                        tok2 = next_token(s);
                        if (!tok2 || tok2->type != ISL_TOKEN_VALUE) {
                                isl_stream_error(s, tok2, "expected denominator");
                                isl_token_free(tok);
                                isl_token_free(tok2);
                                return NULL;
                        }
                        qp = isl_qpolynomial_rat_cst_on_domain(isl_map_get_space(map),
                                                    tok->u.v, tok2->u.v);
                        isl_token_free(tok2);
                } else {
                        isl_stream_push_token(s, tok2);
                        qp = isl_qpolynomial_cst_on_domain(isl_map_get_space(map),
                                                tok->u.v);
                }
                isl_token_free(tok);
                pwqp = isl_pw_qpolynomial_from_qpolynomial(qp);
        } else if (tok->type == ISL_TOKEN_INFTY) {
                isl_qpolynomial *qp;
                isl_token_free(tok);
                qp = isl_qpolynomial_infty_on_domain(isl_map_get_space(map));
                pwqp = isl_pw_qpolynomial_from_qpolynomial(qp);
        } else if (tok->type == ISL_TOKEN_NAN) {
                isl_qpolynomial *qp;
                isl_token_free(tok);
                qp = isl_qpolynomial_nan_on_domain(isl_map_get_space(map));
                pwqp = isl_pw_qpolynomial_from_qpolynomial(qp);
        } else if (tok->type == ISL_TOKEN_IDENT) {
                int n = v->n;
                int pos = vars_pos(v, tok->u.s, -1);
                int pow;
                isl_qpolynomial *qp;
                if (pos < 0) {
                        isl_token_free(tok);
                        return NULL;
                }
                if (pos >= n) {
                        vars_drop(v, v->n - n);
                        isl_stream_error(s, tok, "unknown identifier");
                        isl_token_free(tok);
                        return NULL;
                }
                isl_token_free(tok);
                pow = optional_power(s);
                qp = isl_qpolynomial_var_pow_on_domain(isl_map_get_space(map), pos, pow);
                pwqp = isl_pw_qpolynomial_from_qpolynomial(qp);
        } else if (is_start_of_div(tok)) {
                isl_pw_aff *pwaff;
                int pow;

                isl_stream_push_token(s, tok);
                pwaff = accept_div(s, isl_map_get_space(map), v);
                pow = optional_power(s);
                pwqp = isl_pw_qpolynomial_from_pw_aff(pwaff);
                pwqp = isl_pw_qpolynomial_pow(pwqp, pow);
        } else if (tok->type == '-') {
                isl_token_free(tok);
                pwqp = read_factor(s, map, v);
                pwqp = isl_pw_qpolynomial_neg(pwqp);
        } else {
                isl_stream_error(s, tok, "unexpected isl_token");
                isl_stream_push_token(s, tok);
                return NULL;
        }

        if (isl_stream_eat_if_available(s, '*') ||
            isl_stream_next_token_is(s, ISL_TOKEN_IDENT)) {
                isl_pw_qpolynomial *pwqp2;

                pwqp2 = read_factor(s, map, v);
                pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp2);
        }

        return pwqp;
error:
        isl_pw_qpolynomial_free(pwqp);
        return NULL;
}

static __isl_give isl_pw_qpolynomial *read_term(__isl_keep isl_stream *s,
        __isl_keep isl_map *map, struct vars *v)
{
        struct isl_token *tok;
        isl_pw_qpolynomial *pwqp;

        pwqp = read_factor(s, map, v);

        for (;;) {
                tok = next_token(s);
                if (!tok)
                        return pwqp;

                if (tok->type == '+') {
                        isl_pw_qpolynomial *pwqp2;

                        isl_token_free(tok);
                        pwqp2 = read_factor(s, map, v);
                        pwqp = isl_pw_qpolynomial_add(pwqp, pwqp2);
                } else if (tok->type == '-') {
                        isl_pw_qpolynomial *pwqp2;

                        isl_token_free(tok);
                        pwqp2 = read_factor(s, map, v);
                        pwqp = isl_pw_qpolynomial_sub(pwqp, pwqp2);
                } else if (tok->type == ISL_TOKEN_VALUE &&
                            isl_int_is_neg(tok->u.v)) {
                        isl_pw_qpolynomial *pwqp2;

                        isl_stream_push_token(s, tok);
                        pwqp2 = read_factor(s, map, v);
                        pwqp = isl_pw_qpolynomial_add(pwqp, pwqp2);
                } else {
                        isl_stream_push_token(s, tok);
                        break;
                }
        }

        return pwqp;
}

static __isl_give isl_map *read_optional_formula(__isl_keep isl_stream *s,
        __isl_take isl_map *map, struct vars *v, int rational)
{
        struct isl_token *tok;

        tok = isl_stream_next_token(s);
        if (!tok) {
                isl_stream_error(s, NULL, "unexpected EOF");
                goto error;
        }
        if (tok->type == ':' ||
            (tok->type == ISL_TOKEN_OR && !strcmp(tok->u.s, "|"))) {
                isl_token_free(tok);
                map = read_formula(s, v, map, rational);
        } else
                isl_stream_push_token(s, tok);

        return map;
error:
        isl_map_free(map);
        return NULL;
}

static struct isl_obj obj_read_poly(__isl_keep isl_stream *s,
        __isl_take isl_map *map, struct vars *v, int n)
{
        struct isl_obj obj = { isl_obj_pw_qpolynomial, NULL };
        isl_pw_qpolynomial *pwqp;
        struct isl_set *set;

        pwqp = read_term(s, map, v);
        map = read_optional_formula(s, map, v, 0);
        set = isl_map_range(map);

        pwqp = isl_pw_qpolynomial_intersect_domain(pwqp, set);

        vars_drop(v, v->n - n);

        obj.v = pwqp;
        return obj;
}

static struct isl_obj obj_read_poly_or_fold(__isl_keep isl_stream *s,
        __isl_take isl_set *set, struct vars *v, int n)
{
        int min, max;
        struct isl_obj obj = { isl_obj_pw_qpolynomial_fold, NULL };
        isl_pw_qpolynomial *pwqp;
        isl_pw_qpolynomial_fold *pwf = NULL;
        enum isl_fold fold;

        max = isl_stream_eat_if_available(s, ISL_TOKEN_MAX);
        min = !max && isl_stream_eat_if_available(s, ISL_TOKEN_MIN);
        if (!min && !max)
                return obj_read_poly(s, set, v, n);
        fold = max ? isl_fold_max : isl_fold_min;

        if (isl_stream_eat(s, '('))
                goto error;

        pwqp = read_term(s, set, v);
        pwf = isl_pw_qpolynomial_fold_from_pw_qpolynomial(fold, pwqp);

        while (isl_stream_eat_if_available(s, ',')) {
                isl_pw_qpolynomial_fold *pwf_i;
                pwqp = read_term(s, set, v);
                pwf_i = isl_pw_qpolynomial_fold_from_pw_qpolynomial(fold, pwqp);
                pwf = isl_pw_qpolynomial_fold_fold(pwf, pwf_i);
        }

        if (isl_stream_eat(s, ')'))
                goto error;

        set = read_optional_formula(s, set, v, 0);
        pwf = isl_pw_qpolynomial_fold_intersect_domain(pwf, set);

        vars_drop(v, v->n - n);

        obj.v = pwf;
        return obj;
error:
        isl_set_free(set);
        isl_pw_qpolynomial_fold_free(pwf);
        obj.type = isl_obj_none;
        return obj;
}

static int is_rational(__isl_keep isl_stream *s)
{
        struct isl_token *tok;

        tok = isl_stream_next_token(s);
        if (!tok)
                return 0;
        if (tok->type == ISL_TOKEN_RAT && isl_stream_next_token_is(s, ':')) {
                isl_token_free(tok);
                isl_stream_eat(s, ':');
                return 1;
        }

        isl_stream_push_token(s, tok);

        return 0;
}

static struct isl_obj obj_read_body(__isl_keep isl_stream *s,
        __isl_take isl_map *map, struct vars *v)
{
        struct isl_token *tok;
        struct isl_obj obj = { isl_obj_set, NULL };
        int n = v->n;
        int rational;

        rational = is_rational(s);
        if (rational)
                map = isl_map_set_rational(map);

        if (isl_stream_next_token_is(s, ':')) {
                obj.type = isl_obj_set;
                obj.v = read_optional_formula(s, map, v, rational);
                return obj;
        }

        if (!next_is_tuple(s))
                return obj_read_poly_or_fold(s, map, v, n);

        map = read_map_tuple(s, map, isl_dim_in, v, rational, 0);
        if (!map)
                goto error;
        tok = isl_stream_next_token(s);
        if (!tok)
                goto error;
        if (tok->type == ISL_TOKEN_TO) {
                obj.type = isl_obj_map;
                isl_token_free(tok);
                if (!next_is_tuple(s)) {
                        isl_set *set = isl_map_domain(map);
                        return obj_read_poly_or_fold(s, set, v, n);
                }
                map = read_map_tuple(s, map, isl_dim_out, v, rational, 0);
                if (!map)
                        goto error;
        } else {
                map = isl_map_domain(map);
                isl_stream_push_token(s, tok);
        }

        map = read_optional_formula(s, map, v, rational);

        vars_drop(v, v->n - n);

        obj.v = map;
        return obj;
error:
        isl_map_free(map);
        obj.type = isl_obj_none;
        return obj;
}

static struct isl_obj to_union(isl_ctx *ctx, struct isl_obj obj)
{
        if (obj.type == isl_obj_map) {
                obj.v = isl_union_map_from_map(obj.v);
                obj.type = isl_obj_union_map;
        } else if (obj.type == isl_obj_set) {
                obj.v = isl_union_set_from_set(obj.v);
                obj.type = isl_obj_union_set;
        } else if (obj.type == isl_obj_pw_qpolynomial) {
                obj.v = isl_union_pw_qpolynomial_from_pw_qpolynomial(obj.v);
                obj.type = isl_obj_union_pw_qpolynomial;
        } else if (obj.type == isl_obj_pw_qpolynomial_fold) {
                obj.v = isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold(obj.v);
                obj.type = isl_obj_union_pw_qpolynomial_fold;
        } else
                isl_assert(ctx, 0, goto error);
        return obj;
error:
        obj.type->free(obj.v);
        obj.type = isl_obj_none;
        return obj;
}

static struct isl_obj obj_add(__isl_keep isl_stream *s,
        struct isl_obj obj1, struct isl_obj obj2)
{
        if (obj2.type == isl_obj_none || !obj2.v)
                goto error;
        if (obj1.type == isl_obj_set && obj2.type == isl_obj_union_set)
                obj1 = to_union(s->ctx, obj1);
        if (obj1.type == isl_obj_union_set && obj2.type == isl_obj_set)
                obj2 = to_union(s->ctx, obj2);
        if (obj1.type == isl_obj_map && obj2.type == isl_obj_union_map)
                obj1 = to_union(s->ctx, obj1);
        if (obj1.type == isl_obj_union_map && obj2.type == isl_obj_map)
                obj2 = to_union(s->ctx, obj2);
        if (obj1.type == isl_obj_pw_qpolynomial &&
            obj2.type == isl_obj_union_pw_qpolynomial)
                obj1 = to_union(s->ctx, obj1);
        if (obj1.type == isl_obj_union_pw_qpolynomial &&
            obj2.type == isl_obj_pw_qpolynomial)
                obj2 = to_union(s->ctx, obj2);
        if (obj1.type == isl_obj_pw_qpolynomial_fold &&
            obj2.type == isl_obj_union_pw_qpolynomial_fold)
                obj1 = to_union(s->ctx, obj1);
        if (obj1.type == isl_obj_union_pw_qpolynomial_fold &&
            obj2.type == isl_obj_pw_qpolynomial_fold)
                obj2 = to_union(s->ctx, obj2);
        if (obj1.type != obj2.type) {
                isl_stream_error(s, NULL,
                                "attempt to combine incompatible objects");
                goto error;
        }
        if (!obj1.type->add)
                isl_die(s->ctx, isl_error_internal,
                        "combination not supported on object type", goto error);
        if (obj1.type == isl_obj_map && !isl_map_has_equal_space(obj1.v, obj2.v)) {
                obj1 = to_union(s->ctx, obj1);
                obj2 = to_union(s->ctx, obj2);
        }
        if (obj1.type == isl_obj_set && !isl_set_has_equal_space(obj1.v, obj2.v)) {
                obj1 = to_union(s->ctx, obj1);
                obj2 = to_union(s->ctx, obj2);
        }
        if (obj1.type == isl_obj_pw_qpolynomial &&
            !isl_pw_qpolynomial_has_equal_space(obj1.v, obj2.v)) {
                obj1 = to_union(s->ctx, obj1);
                obj2 = to_union(s->ctx, obj2);
        }
        if (obj1.type == isl_obj_pw_qpolynomial_fold &&
            !isl_pw_qpolynomial_fold_has_equal_space(obj1.v, obj2.v)) {
                obj1 = to_union(s->ctx, obj1);
                obj2 = to_union(s->ctx, obj2);
        }
        obj1.v = obj1.type->add(obj1.v, obj2.v);
        return obj1;
error:
        obj1.type->free(obj1.v);
        obj2.type->free(obj2.v);
        obj1.type = isl_obj_none;
        obj1.v = NULL;
        return obj1;
}

/* Are the first two tokens on "s", "domain" (either as a string
 * or as an identifier) followed by ":"?
 */
static int next_is_domain_colon(__isl_keep isl_stream *s)
{
        struct isl_token *tok;
        char *name;
        int res;

        tok = isl_stream_next_token(s);
        if (!tok)
                return 0;
        if (tok->type != ISL_TOKEN_IDENT && tok->type != ISL_TOKEN_STRING) {
                isl_stream_push_token(s, tok);
                return 0;
        }

        name = isl_token_get_str(s->ctx, tok);
        res = !strcmp(name, "domain") && isl_stream_next_token_is(s, ':');
        free(name);

        isl_stream_push_token(s, tok);

        return res;
}

/* Do the first tokens on "s" look like a schedule?
 *
 * The root of a schedule is always a domain node, so the first thing
 * we expect in the stream is a domain key, i.e., "domain" followed
 * by ":".  If the schedule was printed in YAML flow style, then
 * we additionally expect a "{" to open the outer mapping.
 */
static int next_is_schedule(__isl_keep isl_stream *s)
{
        struct isl_token *tok;
        int is_schedule;

        tok = isl_stream_next_token(s);
        if (!tok)
                return 0;
        if (tok->type != '{') {
                isl_stream_push_token(s, tok);
                return next_is_domain_colon(s);
        }

        is_schedule = next_is_domain_colon(s);
        isl_stream_push_token(s, tok);

        return is_schedule;
}

/* Read an isl_schedule from "s" and store it in an isl_obj.
 */
static struct isl_obj schedule_read(__isl_keep isl_stream *s)
{
        struct isl_obj obj;

        obj.type = isl_obj_schedule;
        obj.v = isl_stream_read_schedule(s);

        return obj;
}

/* Read a disjunction of object bodies from "s".
 * That is, read the inside of the braces, but not the braces themselves.
 * "v" contains a description of the identifiers parsed so far.
 * "map" contains information about the parameters.
 */
static struct isl_obj obj_read_disjuncts(__isl_keep isl_stream *s,
        struct vars *v, __isl_keep isl_map *map)
{
        struct isl_obj obj = { isl_obj_set, NULL };

        if (isl_stream_next_token_is(s, '}')) {
                obj.type = isl_obj_union_set;
                obj.v = isl_union_set_empty(isl_map_get_space(map));
                return obj;
        }

        for (;;) {
                struct isl_obj o;
                o = obj_read_body(s, isl_map_copy(map), v);
                if (!obj.v)
                        obj = o;
                else
                        obj = obj_add(s, obj, o);
                if (obj.type == isl_obj_none || !obj.v)
                        return obj;
                if (!isl_stream_eat_if_available(s, ';'))
                        break;
                if (isl_stream_next_token_is(s, '}'))
                        break;
        }

        return obj;
}

static struct isl_obj obj_read(__isl_keep isl_stream *s)
{
        isl_map *map = NULL;
        struct isl_token *tok;
        struct vars *v = NULL;
        struct isl_obj obj = { isl_obj_set, NULL };

        if (next_is_schedule(s))
                return schedule_read(s);

        tok = next_token(s);
        if (!tok) {
                isl_stream_error(s, NULL, "unexpected EOF");
                goto error;
        }
        if (tok->type == ISL_TOKEN_VALUE) {
                struct isl_token *tok2;
                struct isl_map *map;

                tok2 = isl_stream_next_token(s);
                if (!tok2 || tok2->type != ISL_TOKEN_VALUE ||
                    isl_int_is_neg(tok2->u.v)) {
                        if (tok2)
                                isl_stream_push_token(s, tok2);
                        obj.type = isl_obj_val;
                        obj.v = isl_val_int_from_isl_int(s->ctx, tok->u.v);
                        isl_token_free(tok);
                        return obj;
                }
                isl_stream_push_token(s, tok2);
                isl_stream_push_token(s, tok);
                map = map_read_polylib(s);
                if (!map)
                        goto error;
                if (isl_map_may_be_set(map))
                        obj.v = isl_map_range(map);
                else {
                        obj.type = isl_obj_map;
                        obj.v = map;
                }
                return obj;
        }
        v = vars_new(s->ctx);
        if (!v) {
                isl_stream_push_token(s, tok);
                goto error;
        }
        map = isl_map_universe(isl_space_params_alloc(s->ctx, 0));
        if (tok->type == '[') {
                isl_stream_push_token(s, tok);
                map = read_map_tuple(s, map, isl_dim_param, v, 0, 0);
                if (!map)
                        goto error;
                tok = isl_stream_next_token(s);
                if (!tok || tok->type != ISL_TOKEN_TO) {
                        isl_stream_error(s, tok, "expecting '->'");
                        if (tok)
                                isl_stream_push_token(s, tok);
                        goto error;
                }
                isl_token_free(tok);
                tok = isl_stream_next_token(s);
        }
        if (!tok || tok->type != '{') {
                isl_stream_error(s, tok, "expecting '{'");
                if (tok)
                        isl_stream_push_token(s, tok);
                goto error;
        }
        isl_token_free(tok);

        tok = isl_stream_next_token(s);
        if (!tok)
                ;
        else if (tok->type == ISL_TOKEN_IDENT && !strcmp(tok->u.s, "Sym")) {
                isl_token_free(tok);
                if (isl_stream_eat(s, '='))
                        goto error;
                map = read_map_tuple(s, map, isl_dim_param, v, 0, 1);
                if (!map)
                        goto error;
        } else
                isl_stream_push_token(s, tok);

        obj = obj_read_disjuncts(s, v, map);
        if (obj.type == isl_obj_none || !obj.v)
                goto error;

        tok = isl_stream_next_token(s);
        if (tok && tok->type == '}') {
                isl_token_free(tok);
        } else {
                isl_stream_error(s, tok, "unexpected isl_token");
                if (tok)
                        isl_token_free(tok);
                goto error;
        }

        vars_free(v);
        isl_map_free(map);

        return obj;
error:
        isl_map_free(map);
        obj.type->free(obj.v);
        if (v)
                vars_free(v);
        obj.v = NULL;
        return obj;
}

struct isl_obj isl_stream_read_obj(__isl_keep isl_stream *s)
{
        return obj_read(s);
}

__isl_give isl_map *isl_stream_read_map(__isl_keep isl_stream *s)
{
        struct isl_obj obj;

        obj = obj_read(s);
        if (obj.v)
                isl_assert(s->ctx, obj.type == isl_obj_map ||
                                   obj.type == isl_obj_set, goto error);
        
        if (obj.type == isl_obj_set)
                obj.v = isl_map_from_range(obj.v);

        return obj.v;
error:
        obj.type->free(obj.v);
        return NULL;
}

__isl_give isl_set *isl_stream_read_set(__isl_keep isl_stream *s)
{
        struct isl_obj obj;

        obj = obj_read(s);
        if (obj.v) {
                if (obj.type == isl_obj_map && isl_map_may_be_set(obj.v)) {
                        obj.v = isl_map_range(obj.v);
                        obj.type = isl_obj_set;
                }
                isl_assert(s->ctx, obj.type == isl_obj_set, goto error);
        }

        return obj.v;
error:
        obj.type->free(obj.v);
        return NULL;
}

__isl_give isl_union_map *isl_stream_read_union_map(__isl_keep isl_stream *s)
{
        struct isl_obj obj;

        obj = obj_read(s);
        if (obj.type == isl_obj_map) {
                obj.type = isl_obj_union_map;
                obj.v = isl_union_map_from_map(obj.v);
        }
        if (obj.type == isl_obj_set) {
                obj.type = isl_obj_union_set;
                obj.v = isl_union_set_from_set(obj.v);
        }
        if (obj.v && obj.type == isl_obj_union_set &&
            isl_union_set_is_empty(obj.v))
                obj.type = isl_obj_union_map;
        if (obj.v && obj.type != isl_obj_union_map)
                isl_die(s->ctx, isl_error_invalid, "invalid input", goto error);

        return obj.v;
error:
        obj.type->free(obj.v);
        return NULL;
}

/* Extract an isl_union_set from "obj".
 * This only works if the object was detected as either a set
 * (in which case it is converted to a union set) or a union set.
 */
static __isl_give isl_union_set *extract_union_set(isl_ctx *ctx,
        struct isl_obj obj)
{
        if (obj.type == isl_obj_set) {
                obj.type = isl_obj_union_set;
                obj.v = isl_union_set_from_set(obj.v);
        }
        if (obj.v)
                isl_assert(ctx, obj.type == isl_obj_union_set, goto error);

        return obj.v;
error:
        obj.type->free(obj.v);
        return NULL;
}

/* Read an isl_union_set from "s".
 * First read a generic object and then try and extract
 * an isl_union_set from that.
 */
__isl_give isl_union_set *isl_stream_read_union_set(__isl_keep isl_stream *s)
{
        struct isl_obj obj;

        obj = obj_read(s);
        return extract_union_set(s->ctx, obj);
}

static __isl_give isl_basic_map *basic_map_read(__isl_keep isl_stream *s)
{
        struct isl_obj obj;
        struct isl_map *map;
        struct isl_basic_map *bmap;

        obj = obj_read(s);
        if (obj.v && (obj.type != isl_obj_map && obj.type != isl_obj_set))
                isl_die(s->ctx, isl_error_invalid, "not a (basic) set or map",
                        goto error);
        map = obj.v;
        if (!map)
                return NULL;

        if (map->n > 1)
                isl_die(s->ctx, isl_error_invalid,
                        "set or map description involves "
                        "more than one disjunct", goto error);

        if (map->n == 0)
                bmap = isl_basic_map_empty(isl_map_get_space(map));
        else
                bmap = isl_basic_map_copy(map->p[0]);

        isl_map_free(map);

        return bmap;
error:
        obj.type->free(obj.v);
        return NULL;
}

static __isl_give isl_basic_set *basic_set_read(__isl_keep isl_stream *s)
{
        isl_basic_map *bmap;
        bmap = basic_map_read(s);
        if (!bmap)
                return NULL;
        if (!isl_basic_map_may_be_set(bmap))
                isl_die(s->ctx, isl_error_invalid,
                        "input is not a set", goto error);
        return isl_basic_map_range(bmap);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

__isl_give isl_basic_map *isl_basic_map_read_from_file(isl_ctx *ctx,
        FILE *input)
{
        struct isl_basic_map *bmap;
        isl_stream *s = isl_stream_new_file(ctx, input);
        if (!s)
                return NULL;
        bmap = basic_map_read(s);
        isl_stream_free(s);
        return bmap;
}

__isl_give isl_basic_set *isl_basic_set_read_from_file(isl_ctx *ctx,
        FILE *input)
{
        isl_basic_set *bset;
        isl_stream *s = isl_stream_new_file(ctx, input);
        if (!s)
                return NULL;
        bset = basic_set_read(s);
        isl_stream_free(s);
        return bset;
}

__isl_give isl_basic_map *isl_basic_map_read_from_str(isl_ctx *ctx,
        const char *str)
{
        struct isl_basic_map *bmap;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        bmap = basic_map_read(s);
        isl_stream_free(s);
        return bmap;
}

__isl_give isl_basic_set *isl_basic_set_read_from_str(isl_ctx *ctx,
        const char *str)
{
        isl_basic_set *bset;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        bset = basic_set_read(s);
        isl_stream_free(s);
        return bset;
}

__isl_give isl_map *isl_map_read_from_file(struct isl_ctx *ctx,
        FILE *input)
{
        struct isl_map *map;
        isl_stream *s = isl_stream_new_file(ctx, input);
        if (!s)
                return NULL;
        map = isl_stream_read_map(s);
        isl_stream_free(s);
        return map;
}

__isl_give isl_map *isl_map_read_from_str(struct isl_ctx *ctx,
        const char *str)
{
        struct isl_map *map;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        map = isl_stream_read_map(s);
        isl_stream_free(s);
        return map;
}

__isl_give isl_set *isl_set_read_from_file(struct isl_ctx *ctx,
        FILE *input)
{
        isl_set *set;
        isl_stream *s = isl_stream_new_file(ctx, input);
        if (!s)
                return NULL;
        set = isl_stream_read_set(s);
        isl_stream_free(s);
        return set;
}

__isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx, const char *str)
{
        isl_set *set;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        set = isl_stream_read_set(s);
        isl_stream_free(s);
        return set;
}

__isl_give isl_union_map *isl_union_map_read_from_file(isl_ctx *ctx,
        FILE *input)
{
        isl_union_map *umap;
        isl_stream *s = isl_stream_new_file(ctx, input);
        if (!s)
                return NULL;
        umap = isl_stream_read_union_map(s);
        isl_stream_free(s);
        return umap;
}

__isl_give isl_union_map *isl_union_map_read_from_str(struct isl_ctx *ctx,
                const char *str)
{
        isl_union_map *umap;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        umap = isl_stream_read_union_map(s);
        isl_stream_free(s);
        return umap;
}

__isl_give isl_union_set *isl_union_set_read_from_file(isl_ctx *ctx,
        FILE *input)
{
        isl_union_set *uset;
        isl_stream *s = isl_stream_new_file(ctx, input);
        if (!s)
                return NULL;
        uset = isl_stream_read_union_set(s);
        isl_stream_free(s);
        return uset;
}

__isl_give isl_union_set *isl_union_set_read_from_str(struct isl_ctx *ctx,
                const char *str)
{
        isl_union_set *uset;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        uset = isl_stream_read_union_set(s);
        isl_stream_free(s);
        return uset;
}

static __isl_give isl_vec *isl_vec_read_polylib(__isl_keep isl_stream *s)
{
        struct isl_vec *vec = NULL;
        struct isl_token *tok;
        unsigned size;
        int j;

        tok = isl_stream_next_token(s);
        if (!tok || tok->type != ISL_TOKEN_VALUE) {
                isl_stream_error(s, tok, "expecting vector length");
                goto error;
        }

        size = isl_int_get_si(tok->u.v);
        isl_token_free(tok);

        vec = isl_vec_alloc(s->ctx, size);

        for (j = 0; j < size; ++j) {
                tok = isl_stream_next_token(s);
                if (!tok || tok->type != ISL_TOKEN_VALUE) {
                        isl_stream_error(s, tok, "expecting constant value");
                        goto error;
                }
                isl_int_set(vec->el[j], tok->u.v);
                isl_token_free(tok);
        }

        return vec;
error:
        isl_token_free(tok);
        isl_vec_free(vec);
        return NULL;
}

static __isl_give isl_vec *vec_read(__isl_keep isl_stream *s)
{
        return isl_vec_read_polylib(s);
}

__isl_give isl_vec *isl_vec_read_from_file(isl_ctx *ctx, FILE *input)
{
        isl_vec *v;
        isl_stream *s = isl_stream_new_file(ctx, input);
        if (!s)
                return NULL;
        v = vec_read(s);
        isl_stream_free(s);
        return v;
}

__isl_give isl_pw_qpolynomial *isl_stream_read_pw_qpolynomial(
        __isl_keep isl_stream *s)
{
        struct isl_obj obj;

        obj = obj_read(s);
        if (obj.v)
                isl_assert(s->ctx, obj.type == isl_obj_pw_qpolynomial,
                           goto error);

        return obj.v;
error:
        obj.type->free(obj.v);
        return NULL;
}

__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_read_from_str(isl_ctx *ctx,
                const char *str)
{
        isl_pw_qpolynomial *pwqp;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        pwqp = isl_stream_read_pw_qpolynomial(s);
        isl_stream_free(s);
        return pwqp;
}

__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_read_from_file(isl_ctx *ctx,
                FILE *input)
{
        isl_pw_qpolynomial *pwqp;
        isl_stream *s = isl_stream_new_file(ctx, input);
        if (!s)
                return NULL;
        pwqp = isl_stream_read_pw_qpolynomial(s);
        isl_stream_free(s);
        return pwqp;
}

/* Read an isl_pw_qpolynomial_fold from "s".
 * First read a generic object and
 * then check that it is an isl_pw_qpolynomial_fold.
 */
__isl_give isl_pw_qpolynomial_fold *isl_stream_read_pw_qpolynomial_fold(
        __isl_keep isl_stream *s)
{
        struct isl_obj obj;

        obj = obj_read(s);
        if (obj.v && obj.type != isl_obj_pw_qpolynomial_fold)
                isl_die(s->ctx, isl_error_invalid, "invalid input", goto error);

        return obj.v;
error:
        obj.type->free(obj.v);
        return NULL;
}

/* Read an isl_pw_qpolynomial_fold from "str".
 */
__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_read_from_str(
        isl_ctx *ctx, const char *str)
{
        isl_pw_qpolynomial_fold *pwqp;
        isl_stream *s;

        s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        pwqp = isl_stream_read_pw_qpolynomial_fold(s);
        isl_stream_free(s);

        return pwqp;
}

/* Is the next token an identifier not in "v"?
 */
static int next_is_fresh_ident(__isl_keep isl_stream *s, struct vars *v)
{
        int n = v->n;
        int fresh;
        struct isl_token *tok;

        tok = isl_stream_next_token(s);
        if (!tok)
                return 0;
        fresh = tok->type == ISL_TOKEN_IDENT && vars_pos(v, tok->u.s, -1) >= n;
        isl_stream_push_token(s, tok);

        vars_drop(v, v->n - n);

        return fresh;
}

/* First read the domain of the affine expression, which may be
 * a parameter space or a set.
 * The tricky part is that we don't know if the domain is a set or not,
 * so when we are trying to read the domain, we may actually be reading
 * the affine expression itself (defined on a parameter domains)
 * If the tuple we are reading is named, we assume it's the domain.
 * Also, if inside the tuple, the first thing we find is a nested tuple
 * or a new identifier, we again assume it's the domain.
 * Finally, if the tuple is empty, then it must be the domain
 * since it does not contain an affine expression.
 * Otherwise, we assume we are reading an affine expression.
 */
static __isl_give isl_set *read_aff_domain(__isl_keep isl_stream *s,
        __isl_take isl_set *dom, struct vars *v)
{
        struct isl_token *tok, *tok2;
        int is_empty;

        tok = isl_stream_next_token(s);
        if (tok && (tok->type == ISL_TOKEN_IDENT || tok->is_keyword)) {
                isl_stream_push_token(s, tok);
                return read_map_tuple(s, dom, isl_dim_set, v, 0, 0);
        }
        if (!tok || tok->type != '[') {
                isl_stream_error(s, tok, "expecting '['");
                goto error;
        }
        tok2 = isl_stream_next_token(s);
        is_empty = tok2 && tok2->type == ']';
        if (tok2)
                isl_stream_push_token(s, tok2);
        if (is_empty || next_is_tuple(s) || next_is_fresh_ident(s, v)) {
                isl_stream_push_token(s, tok);
                dom = read_map_tuple(s, dom, isl_dim_set, v, 0, 0);
        } else
                isl_stream_push_token(s, tok);

        return dom;
error:
        if (tok)
                isl_stream_push_token(s, tok);
        isl_set_free(dom);
        return NULL;
}

/* Read an affine expression from "s".
 */
__isl_give isl_aff *isl_stream_read_aff(__isl_keep isl_stream *s)
{
        isl_aff *aff;
        isl_multi_aff *ma;
        isl_size dim;

        ma = isl_stream_read_multi_aff(s);
        dim = isl_multi_aff_dim(ma, isl_dim_out);
        if (dim < 0)
                goto error;
        if (dim != 1)
                isl_die(s->ctx, isl_error_invalid,
                        "expecting single affine expression",
                        goto error);

        aff = isl_multi_aff_get_aff(ma, 0);
        isl_multi_aff_free(ma);
        return aff;
error:
        isl_multi_aff_free(ma);
        return NULL;
}

/* Read a piecewise affine expression from "s" with domain (space) "dom".
 */
static __isl_give isl_pw_aff *read_pw_aff_with_dom(__isl_keep isl_stream *s,
        __isl_take isl_set *dom, struct vars *v)
{
        isl_pw_aff *pwaff = NULL;

        if (!isl_set_is_params(dom) && isl_stream_eat(s, ISL_TOKEN_TO))
                goto error;

        if (isl_stream_eat(s, '['))
                goto error;

        pwaff = accept_affine(s, isl_set_get_space(dom), v);

        if (isl_stream_eat(s, ']'))
                goto error;

        dom = read_optional_formula(s, dom, v, 0);
        pwaff = isl_pw_aff_intersect_domain(pwaff, dom);

        return pwaff;
error:
        isl_set_free(dom);
        isl_pw_aff_free(pwaff);
        return NULL;
}

__isl_give isl_pw_aff *isl_stream_read_pw_aff(__isl_keep isl_stream *s)
{
        struct vars *v;
        isl_set *dom = NULL;
        isl_set *aff_dom;
        isl_pw_aff *pa = NULL;
        int n;

        v = vars_new(s->ctx);
        if (!v)
                return NULL;

        dom = isl_set_universe(isl_space_params_alloc(s->ctx, 0));
        if (next_is_tuple(s)) {
                dom = read_map_tuple(s, dom, isl_dim_param, v, 1, 0);
                if (isl_stream_eat(s, ISL_TOKEN_TO))
                        goto error;
        }
        if (isl_stream_eat(s, '{'))
                goto error;

        n = v->n;
        aff_dom = read_aff_domain(s, isl_set_copy(dom), v);
        pa = read_pw_aff_with_dom(s, aff_dom, v);
        vars_drop(v, v->n - n);

        while (isl_stream_eat_if_available(s, ';')) {
                isl_pw_aff *pa_i;

                n = v->n;
                aff_dom = read_aff_domain(s, isl_set_copy(dom), v);
                pa_i = read_pw_aff_with_dom(s, aff_dom, v);
                vars_drop(v, v->n - n);

                pa = isl_pw_aff_union_add(pa, pa_i);
        }

        if (isl_stream_eat(s, '}'))
                goto error;

        vars_free(v);
        isl_set_free(dom);
        return pa;
error:
        vars_free(v);
        isl_set_free(dom);
        isl_pw_aff_free(pa);
        return NULL;
}

__isl_give isl_aff *isl_aff_read_from_str(isl_ctx *ctx, const char *str)
{
        isl_aff *aff;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        aff = isl_stream_read_aff(s);
        isl_stream_free(s);
        return aff;
}

__isl_give isl_pw_aff *isl_pw_aff_read_from_str(isl_ctx *ctx, const char *str)
{
        isl_pw_aff *pa;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        pa = isl_stream_read_pw_aff(s);
        isl_stream_free(s);
        return pa;
}

/* Extract an isl_multi_pw_aff with domain space "dom_space"
 * from a tuple "tuple" read by read_tuple.
 *
 * Note that the function read_tuple accepts tuples where some output or
 * set dimensions are defined in terms of other output or set dimensions
 * since this function is also used to read maps.  As a special case,
 * read_tuple also accept dimensions that are defined in terms of themselves
 * (i.e., that are not defined).
 * These cases are not allowed when extracting an isl_multi_pw_aff so check
 * that the definitions of the output/set dimensions do not involve any
 * output/set dimensions.
 * Finally, drop the output dimensions from the domain of the result
 * of read_tuple (which is of the form [input, output] -> [output],
 * with anonymous domain) and reset the space.
 */
static __isl_give isl_multi_pw_aff *extract_mpa_from_tuple(
        __isl_take isl_space *dom_space, __isl_keep isl_multi_pw_aff *tuple)
{
        int i;
        isl_size dim, n;
        isl_space *space;
        isl_multi_pw_aff *mpa;

        n = isl_multi_pw_aff_dim(tuple, isl_dim_out);
        dim = isl_space_dim(dom_space, isl_dim_all);
        if (n < 0 || dim < 0)
                dom_space = isl_space_free(dom_space);
        space = isl_space_range(isl_multi_pw_aff_get_space(tuple));
        space = isl_space_align_params(space, isl_space_copy(dom_space));
        if (!isl_space_is_params(dom_space))
                space = isl_space_map_from_domain_and_range(
                                isl_space_copy(dom_space), space);
        isl_space_free(dom_space);
        mpa = isl_multi_pw_aff_alloc(space);

        for (i = 0; i < n; ++i) {
                isl_pw_aff *pa;
                pa = isl_multi_pw_aff_get_pw_aff(tuple, i);
                if (!pa)
                        return isl_multi_pw_aff_free(mpa);
                if (isl_pw_aff_involves_dims(pa, isl_dim_in, dim, i + 1)) {
                        isl_ctx *ctx = isl_pw_aff_get_ctx(pa);
                        isl_pw_aff_free(pa);
                        isl_die(ctx, isl_error_invalid,
                                "not an affine expression",
                                return isl_multi_pw_aff_free(mpa));
                }
                pa = isl_pw_aff_drop_dims(pa, isl_dim_in, dim, n);
                space = isl_multi_pw_aff_get_domain_space(mpa);
                pa = isl_pw_aff_reset_domain_space(pa, space);
                mpa = isl_multi_pw_aff_set_pw_aff(mpa, i, pa);
        }

        return mpa;
}

/* Read a tuple of affine expressions, together with optional constraints
 * on the domain from "s".  "dom" represents the initial constraints
 * on the domain.
 *
 * The isl_multi_aff may live in either a set or a map space.
 * First read the first tuple and check if it is followed by a "->".
 * If so, convert the tuple into the domain of the isl_multi_pw_aff and
 * read in the next tuple.  This tuple (or the first tuple if it was
 * not followed by a "->") is then converted into an isl_multi_pw_aff
 * through a call to extract_mpa_from_tuple.
 * The result is converted to an isl_pw_multi_aff and
 * its domain is intersected with the domain.
 *
 * Note that the last tuple may introduce new identifiers,
 * but these cannot be referenced in the description of the domain.
 */
static __isl_give isl_pw_multi_aff *read_conditional_multi_aff(
        __isl_keep isl_stream *s, __isl_take isl_set *dom, struct vars *v)
{
        isl_multi_pw_aff *tuple;
        isl_multi_pw_aff *mpa;
        isl_pw_multi_aff *pma;
        int n = v->n;
        int n_dom;

        n_dom = v->n;
        tuple = read_tuple(s, v, 0, 0);
        if (!tuple)
                goto error;
        if (isl_stream_eat_if_available(s, ISL_TOKEN_TO)) {
                isl_map *map = map_from_tuple(tuple, dom, isl_dim_in, v, 0);
                dom = isl_map_domain(map);
                n_dom = v->n;
                tuple = read_tuple(s, v, 0, 0);
                if (!tuple)
                        goto error;
        }
        mpa = extract_mpa_from_tuple(isl_set_get_space(dom), tuple);
        isl_multi_pw_aff_free(tuple);
        if (!mpa)
                dom = isl_set_free(dom);

        vars_drop(v, v->n - n_dom);
        dom = read_optional_formula(s, dom, v, 0);

        vars_drop(v, v->n - n);

        pma = isl_pw_multi_aff_from_multi_pw_aff(mpa);
        pma = isl_pw_multi_aff_intersect_domain(pma, dom);

        return pma;
error:
        isl_set_free(dom);
        return NULL;
}

/* Read an isl_union_pw_multi_aff from "s".
 *
 * In particular, first read the parameters and then read a sequence
 * of zero or more tuples of affine expressions with optional conditions and
 * add them up.
 */
__isl_give isl_union_pw_multi_aff *isl_stream_read_union_pw_multi_aff(
        __isl_keep isl_stream *s)
{
        struct vars *v;
        isl_set *dom;
        isl_union_pw_multi_aff *upma = NULL;

        v = vars_new(s->ctx);
        if (!v)
                return NULL;

        dom = isl_set_universe(isl_space_params_alloc(s->ctx, 0));
        if (next_is_tuple(s)) {
                dom = read_map_tuple(s, dom, isl_dim_param, v, 1, 0);
                if (isl_stream_eat(s, ISL_TOKEN_TO))
                        goto error;
        }
        if (isl_stream_eat(s, '{'))
                goto error;

        upma = isl_union_pw_multi_aff_empty(isl_set_get_space(dom));

        do {
                isl_pw_multi_aff *pma;
                isl_union_pw_multi_aff *upma2;

                if (isl_stream_next_token_is(s, '}'))
                        break;

                pma = read_conditional_multi_aff(s, isl_set_copy(dom), v);
                upma2 = isl_union_pw_multi_aff_from_pw_multi_aff(pma);
                upma = isl_union_pw_multi_aff_union_add(upma, upma2);
                if (!upma)
                        goto error;
        } while (isl_stream_eat_if_available(s, ';'));

        if (isl_stream_eat(s, '}'))
                goto error;

        isl_set_free(dom);
        vars_free(v);
        return upma;
error:
        isl_union_pw_multi_aff_free(upma);
        isl_set_free(dom);
        vars_free(v);
        return NULL;
}

/* Read an isl_pw_multi_aff from "s".
 *
 * Read a more generic isl_union_pw_multi_aff first and
 * then check that the result lives in a single space.
 */
__isl_give isl_pw_multi_aff *isl_stream_read_pw_multi_aff(
        __isl_keep isl_stream *s)
{
        isl_bool single_space;
        isl_union_pw_multi_aff *upma;

        upma = isl_stream_read_union_pw_multi_aff(s);
        single_space = isl_union_pw_multi_aff_isa_pw_multi_aff(upma);
        if (single_space < 0)
                upma = isl_union_pw_multi_aff_free(upma);
        else if (!single_space)
                isl_die(s->ctx, isl_error_invalid,
                        "expecting expression in single space",
                        upma = isl_union_pw_multi_aff_free(upma));
        return isl_union_pw_multi_aff_as_pw_multi_aff(upma);
}

__isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(isl_ctx *ctx,
        const char *str)
{
        isl_pw_multi_aff *pma;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        pma = isl_stream_read_pw_multi_aff(s);
        isl_stream_free(s);
        return pma;
}

/* Read an isl_union_pw_multi_aff from "str".
 */
__isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_read_from_str(
        isl_ctx *ctx, const char *str)
{
        isl_union_pw_multi_aff *upma;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        upma = isl_stream_read_union_pw_multi_aff(s);
        isl_stream_free(s);
        return upma;
}

/* Assuming "pa" represents a single affine expression defined on a universe
 * domain, extract this affine expression.
 */
static __isl_give isl_aff *aff_from_pw_aff(__isl_take isl_pw_aff *pa)
{
        isl_aff *aff;

        if (!pa)
                return NULL;
        if (pa->n != 1)
                isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid,
                        "expecting single affine expression",
                        goto error);
        if (!isl_set_plain_is_universe(pa->p[0].set))
                isl_die(isl_pw_aff_get_ctx(pa), isl_error_invalid,
                        "expecting universe domain",
                        goto error);

        aff = isl_aff_copy(pa->p[0].aff);
        isl_pw_aff_free(pa);
        return aff;
error:
        isl_pw_aff_free(pa);
        return NULL;
}

#undef BASE
#define BASE val

#include <isl_multi_read_no_explicit_domain_templ.c>

#undef BASE
#define BASE id

#include <isl_multi_read_no_explicit_domain_templ.c>

/* Read a multi-affine expression from "s".
 * If the multi-affine expression has a domain, then the tuple
 * representing this domain cannot involve any affine expressions.
 * The tuple representing the actual expressions needs to consist
 * of only affine expressions.  Moreover, these expressions can
 * only depend on parameters and input dimensions and not on other
 * output dimensions.
 */
__isl_give isl_multi_aff *isl_stream_read_multi_aff(__isl_keep isl_stream *s)
{
        struct vars *v;
        isl_set *dom = NULL;
        isl_multi_pw_aff *tuple = NULL;
        int i;
        isl_size dim, n;
        isl_space *space, *dom_space;
        isl_multi_aff *ma = NULL;

        v = vars_new(s->ctx);
        if (!v)
                return NULL;

        dom = isl_set_universe(isl_space_params_alloc(s->ctx, 0));
        if (next_is_tuple(s)) {
                dom = read_map_tuple(s, dom, isl_dim_param, v, 1, 0);
                if (isl_stream_eat(s, ISL_TOKEN_TO))
                        goto error;
        }
        if (!isl_set_plain_is_universe(dom))
                isl_die(s->ctx, isl_error_invalid,
                        "expecting universe parameter domain", goto error);
        if (isl_stream_eat(s, '{'))
                goto error;

        tuple = read_tuple(s, v, 0, 0);
        if (!tuple)
                goto error;
        if (isl_stream_eat_if_available(s, ISL_TOKEN_TO)) {
                isl_set *set;
                isl_space *space;
                isl_bool has_expr;

                has_expr = tuple_has_expr(tuple);
                if (has_expr < 0)
                        goto error;
                if (has_expr)
                        isl_die(s->ctx, isl_error_invalid,
                                "expecting universe domain", goto error);
                space = isl_space_range(isl_multi_pw_aff_get_space(tuple));
                set = isl_set_universe(space);
                dom = isl_set_intersect_params(set, dom);
                isl_multi_pw_aff_free(tuple);
                tuple = read_tuple(s, v, 0, 0);
                if (!tuple)
                        goto error;
        }

        if (isl_stream_eat(s, '}'))
                goto error;

        n = isl_multi_pw_aff_dim(tuple, isl_dim_out);
        dim = isl_set_dim(dom, isl_dim_all);
        if (n < 0 || dim < 0)
                goto error;
        dom_space = isl_set_get_space(dom);
        space = isl_space_range(isl_multi_pw_aff_get_space(tuple));
        space = isl_space_align_params(space, isl_space_copy(dom_space));
        if (!isl_space_is_params(dom_space))
                space = isl_space_map_from_domain_and_range(
                                isl_space_copy(dom_space), space);
        isl_space_free(dom_space);
        ma = isl_multi_aff_alloc(space);

        for (i = 0; i < n; ++i) {
                isl_pw_aff *pa;
                isl_aff *aff;
                pa = isl_multi_pw_aff_get_pw_aff(tuple, i);
                aff = aff_from_pw_aff(pa);
                if (!aff)
                        goto error;
                if (isl_aff_involves_dims(aff, isl_dim_in, dim, i + 1)) {
                        isl_aff_free(aff);
                        isl_die(s->ctx, isl_error_invalid,
                                "not an affine expression", goto error);
                }
                aff = isl_aff_drop_dims(aff, isl_dim_in, dim, n);
                space = isl_multi_aff_get_domain_space(ma);
                aff = isl_aff_reset_domain_space(aff, space);
                ma = isl_multi_aff_set_aff(ma, i, aff);
        }

        isl_multi_pw_aff_free(tuple);
        vars_free(v);
        isl_set_free(dom);
        return ma;
error:
        isl_multi_pw_aff_free(tuple);
        vars_free(v);
        isl_set_free(dom);
        isl_multi_aff_free(ma);
        return NULL;
}

__isl_give isl_multi_aff *isl_multi_aff_read_from_str(isl_ctx *ctx,
        const char *str)
{
        isl_multi_aff *maff;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        maff = isl_stream_read_multi_aff(s);
        isl_stream_free(s);
        return maff;
}

/* Read an isl_multi_pw_aff from "s".
 *
 * The input format is similar to that of map, except that any conditions
 * on the domains should be specified inside the tuple since each
 * piecewise affine expression may have a different domain.
 * However, additional, shared conditions can also be specified.
 * This is especially useful for setting the explicit domain
 * of a zero-dimensional isl_multi_pw_aff.
 *
 * Since we do not know in advance if the isl_multi_pw_aff lives
 * in a set or a map space, we first read the first tuple and check
 * if it is followed by a "->".  If so, we convert the tuple into
 * the domain of the isl_multi_pw_aff and read in the next tuple.
 * This tuple (or the first tuple if it was not followed by a "->")
 * is then converted into the isl_multi_pw_aff through a call
 * to extract_mpa_from_tuple and the domain of the result
 * is intersected with the domain.
 *
 * Note that the last tuple may introduce new identifiers,
 * but these cannot be referenced in the description of the domain.
 */
__isl_give isl_multi_pw_aff *isl_stream_read_multi_pw_aff(
        __isl_keep isl_stream *s)
{
        int n_dom;
        struct vars *v;
        isl_set *dom = NULL;
        isl_multi_pw_aff *tuple = NULL;
        isl_multi_pw_aff *mpa = NULL;

        v = vars_new(s->ctx);
        if (!v)
                return NULL;

        dom = isl_set_universe(isl_space_params_alloc(s->ctx, 0));
        if (next_is_tuple(s)) {
                dom = read_map_tuple(s, dom, isl_dim_param, v, 1, 0);
                if (isl_stream_eat(s, ISL_TOKEN_TO))
                        goto error;
        }
        if (isl_stream_eat(s, '{'))
                goto error;

        n_dom = v->n;
        tuple = read_tuple(s, v, 0, 0);
        if (!tuple)
                goto error;
        if (isl_stream_eat_if_available(s, ISL_TOKEN_TO)) {
                isl_map *map = map_from_tuple(tuple, dom, isl_dim_in, v, 0);
                dom = isl_map_domain(map);
                n_dom = v->n;
                tuple = read_tuple(s, v, 0, 0);
                if (!tuple)
                        goto error;
        }

        vars_drop(v, v->n - n_dom);
        if (isl_stream_eat_if_available(s, ':'))
                dom = read_formula(s, v, dom, 0);

        if (isl_stream_eat(s, '}'))
                goto error;

        mpa = extract_mpa_from_tuple(isl_set_get_space(dom), tuple);

        isl_multi_pw_aff_free(tuple);
        vars_free(v);
        mpa = isl_multi_pw_aff_intersect_domain(mpa, dom);
        return mpa;
error:
        isl_multi_pw_aff_free(tuple);
        vars_free(v);
        isl_set_free(dom);
        isl_multi_pw_aff_free(mpa);
        return NULL;
}

/* Read an isl_multi_pw_aff from "str".
 */
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(isl_ctx *ctx,
        const char *str)
{
        isl_multi_pw_aff *mpa;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        mpa = isl_stream_read_multi_pw_aff(s);
        isl_stream_free(s);
        return mpa;
}

/* Read the body of an isl_union_pw_aff from "s" with parameter domain "dom".
 */
static __isl_give isl_union_pw_aff *read_union_pw_aff_with_dom(
        __isl_keep isl_stream *s, __isl_take isl_set *dom, struct vars *v)
{
        isl_pw_aff *pa;
        isl_union_pw_aff *upa = NULL;
        isl_set *aff_dom;
        int n;

        n = v->n;
        aff_dom = read_aff_domain(s, isl_set_copy(dom), v);
        pa = read_pw_aff_with_dom(s, aff_dom, v);
        vars_drop(v, v->n - n);

        upa = isl_union_pw_aff_from_pw_aff(pa);

        while (isl_stream_eat_if_available(s, ';')) {
                isl_pw_aff *pa_i;
                isl_union_pw_aff *upa_i;

                n = v->n;
                aff_dom = read_aff_domain(s, isl_set_copy(dom), v);
                pa_i = read_pw_aff_with_dom(s, aff_dom, v);
                vars_drop(v, v->n - n);

                upa_i = isl_union_pw_aff_from_pw_aff(pa_i);
                upa = isl_union_pw_aff_union_add(upa, upa_i);
        }

        isl_set_free(dom);
        return upa;
}

/* Read an isl_union_pw_aff from "s".
 *
 * First check if there are any paramters, then read in the opening brace
 * and use read_union_pw_aff_with_dom to read in the body of
 * the isl_union_pw_aff.  Finally, read the closing brace.
 */
__isl_give isl_union_pw_aff *isl_stream_read_union_pw_aff(
        __isl_keep isl_stream *s)
{
        struct vars *v;
        isl_set *dom;
        isl_union_pw_aff *upa = NULL;

        v = vars_new(s->ctx);
        if (!v)
                return NULL;

        dom = isl_set_universe(isl_space_params_alloc(s->ctx, 0));
        if (next_is_tuple(s)) {
                dom = read_map_tuple(s, dom, isl_dim_param, v, 1, 0);
                if (isl_stream_eat(s, ISL_TOKEN_TO))
                        goto error;
        }
        if (isl_stream_eat(s, '{'))
                goto error;

        upa = read_union_pw_aff_with_dom(s, isl_set_copy(dom), v);

        if (isl_stream_eat(s, '}'))
                goto error;

        vars_free(v);
        isl_set_free(dom);
        return upa;
error:
        vars_free(v);
        isl_set_free(dom);
        isl_union_pw_aff_free(upa);
        return NULL;
}

/* Read an isl_union_pw_aff from "str".
 */
__isl_give isl_union_pw_aff *isl_union_pw_aff_read_from_str(isl_ctx *ctx,
        const char *str)
{
        isl_union_pw_aff *upa;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        upa = isl_stream_read_union_pw_aff(s);
        isl_stream_free(s);
        return upa;
}

/* This function is called for each element in a tuple inside
 * isl_stream_read_multi_union_pw_aff.
 *
 * Read a '{', the union piecewise affine expression body and a '}' and
 * add the isl_union_pw_aff to *list.
 */
static __isl_give isl_space *read_union_pw_aff_el(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_space *space, int rational, void *user)
{
        isl_set *dom;
        isl_union_pw_aff *upa;
        isl_union_pw_aff_list **list = (isl_union_pw_aff_list **) user;

        dom = isl_set_universe(isl_space_params(isl_space_copy(space)));
        if (isl_stream_eat(s, '{'))
                goto error;
        upa = read_union_pw_aff_with_dom(s, dom, v);
        *list = isl_union_pw_aff_list_add(*list, upa);
        if (isl_stream_eat(s, '}'))
                return isl_space_free(space);
        if (!*list)
                return isl_space_free(space);
        return space;
error:
        isl_set_free(dom);
        return isl_space_free(space);
}

/* Do the next tokens in "s" correspond to an empty tuple?
 * In particular, does the stream start with a '[', followed by a ']',
 * not followed by a "->"?
 */
static int next_is_empty_tuple(__isl_keep isl_stream *s)
{
        struct isl_token *tok, *tok2, *tok3;
        int is_empty_tuple = 0;

        tok = isl_stream_next_token(s);
        if (!tok)
                return 0;
        if (tok->type != '[') {
                isl_stream_push_token(s, tok);
                return 0;
        }

        tok2 = isl_stream_next_token(s);
        if (tok2 && tok2->type == ']') {
                tok3 = isl_stream_next_token(s);
                is_empty_tuple = !tok || tok->type != ISL_TOKEN_TO;
                if (tok3)
                        isl_stream_push_token(s, tok3);
        }
        if (tok2)
                isl_stream_push_token(s, tok2);
        isl_stream_push_token(s, tok);

        return is_empty_tuple;
}

/* Do the next tokens in "s" correspond to a tuple of parameters?
 * In particular, does the stream start with a '[' that is not
 * followed by a '{' or a nested tuple?
 */
static int next_is_param_tuple(__isl_keep isl_stream *s)
{
        struct isl_token *tok, *tok2;
        int is_tuple;

        tok = isl_stream_next_token(s);
        if (!tok)
                return 0;
        if (tok->type != '[' || next_is_tuple(s)) {
                isl_stream_push_token(s, tok);
                return 0;
        }

        tok2 = isl_stream_next_token(s);
        is_tuple = tok2 && tok2->type != '{';
        if (tok2)
                isl_stream_push_token(s, tok2);
        isl_stream_push_token(s, tok);

        return is_tuple;
}

/* Read the core of a body of an isl_multi_union_pw_aff from "s",
 * i.e., everything except the parameter specification and
 * without shared domain constraints.
 * "v" contains a description of the identifiers parsed so far.
 * The parameters, if any, are specified by "space".
 *
 * The body is of the form
 *
 *      [{ [..] : ... ; [..] : ... }, { [..] : ... ; [..] : ... }]
 *
 * Read the tuple, collecting the individual isl_union_pw_aff
 * elements in a list and construct the result from the tuple space and
 * the list.
 */
static __isl_give isl_multi_union_pw_aff *read_multi_union_pw_aff_body_core(
        __isl_keep isl_stream *s, struct vars *v, __isl_take isl_space *space)
{
        isl_union_pw_aff_list *list;
        isl_multi_union_pw_aff *mupa;

        list = isl_union_pw_aff_list_alloc(s->ctx, 0);
        space = read_tuple_space(s, v, space, 1, 0,
                                &read_union_pw_aff_el, &list);
        mupa = isl_multi_union_pw_aff_from_union_pw_aff_list(space, list);

        return mupa;
}

/* Read the body of an isl_union_set from "s",
 * i.e., everything except the parameter specification.
 * "v" contains a description of the identifiers parsed so far.
 * The parameters, if any, are specified by "space".
 *
 * First read a generic disjunction of object bodies and then try and extract
 * an isl_union_set from that.
 */
static __isl_give isl_union_set *read_union_set_body(__isl_keep isl_stream *s,
        struct vars *v, __isl_take isl_space *space)
{
        struct isl_obj obj = { isl_obj_set, NULL };
        isl_map *map;

        map = isl_set_universe(space);
        if (isl_stream_eat(s, '{') < 0)
                goto error;
        obj = obj_read_disjuncts(s, v, map);
        if (isl_stream_eat(s, '}') < 0)
                goto error;
        isl_map_free(map);

        return extract_union_set(s->ctx, obj);
error:
        obj.type->free(obj.v);
        isl_map_free(map);
        return NULL;
}

/* Read the body of an isl_multi_union_pw_aff from "s",
 * i.e., everything except the parameter specification.
 * "v" contains a description of the identifiers parsed so far.
 * The parameters, if any, are specified by "space".
 *
 * In particular, handle the special case with shared domain constraints.
 * These are specified as
 *
 *      ([...] : ...)
 *
 * and are especially useful for setting the explicit domain
 * of a zero-dimensional isl_multi_union_pw_aff.
 * The core isl_multi_union_pw_aff body ([...]) is read by
 * read_multi_union_pw_aff_body_core.
 */
static __isl_give isl_multi_union_pw_aff *read_multi_union_pw_aff_body(
        __isl_keep isl_stream *s, struct vars *v, __isl_take isl_space *space)
{
        isl_multi_union_pw_aff *mupa;

        if (!isl_stream_next_token_is(s, '('))
                return read_multi_union_pw_aff_body_core(s, v, space);

        if (isl_stream_eat(s, '(') < 0)
                goto error;
        mupa = read_multi_union_pw_aff_body_core(s, v, isl_space_copy(space));
        if (isl_stream_eat_if_available(s, ':')) {
                isl_union_set *dom;

                dom = read_union_set_body(s, v, space);
                mupa = isl_multi_union_pw_aff_intersect_domain(mupa, dom);
        } else {
                isl_space_free(space);
        }
        if (isl_stream_eat(s, ')') < 0)
                return isl_multi_union_pw_aff_free(mupa);

        return mupa;
error:
        isl_space_free(space);
        return NULL;
}

/* Read an isl_multi_union_pw_aff from "s".
 *
 * The input has the form
 *
 *      [{ [..] : ... ; [..] : ... }, { [..] : ... ; [..] : ... }]
 *
 * or
 *
 *      [..] -> [{ [..] : ... ; [..] : ... }, { [..] : ... ; [..] : ... }]
 *
 * Additionally, a shared domain may be specified as
 *
 *      ([..] : ...)
 *
 * or
 *
 *      [..] -> ([..] : ...)
 *
 * The first case is handled by the caller, the second case
 * is handled by read_multi_union_pw_aff_body.
 *
 * We first check for the special case of an empty tuple "[]".
 * Then we check if there are any parameters.
 * Finally, read the tuple and construct the result.
 */
static __isl_give isl_multi_union_pw_aff *read_multi_union_pw_aff_core(
        __isl_keep isl_stream *s)
{
        struct vars *v;
        isl_set *dom = NULL;
        isl_space *space;
        isl_multi_union_pw_aff *mupa = NULL;

        if (next_is_empty_tuple(s)) {
                if (isl_stream_eat(s, '['))
                        return NULL;
                if (isl_stream_eat(s, ']'))
                        return NULL;
                space = isl_space_set_alloc(s->ctx, 0, 0);
                return isl_multi_union_pw_aff_zero(space);
        }

        v = vars_new(s->ctx);
        if (!v)
                return NULL;

        dom = isl_set_universe(isl_space_params_alloc(s->ctx, 0));
        if (next_is_param_tuple(s)) {
                dom = read_map_tuple(s, dom, isl_dim_param, v, 1, 0);
                if (isl_stream_eat(s, ISL_TOKEN_TO))
                        goto error;
        }
        space = isl_set_get_space(dom);
        isl_set_free(dom);
        mupa = read_multi_union_pw_aff_body(s, v, space);

        vars_free(v);

        return mupa;
error:
        vars_free(v);
        isl_set_free(dom);
        isl_multi_union_pw_aff_free(mupa);
        return NULL;
}

/* Read an isl_multi_union_pw_aff from "s".
 *
 * In particular, handle the special case with shared domain constraints.
 * These are specified as
 *
 *      ([...] : ...)
 *
 * and are especially useful for setting the explicit domain
 * of a zero-dimensional isl_multi_union_pw_aff.
 * The core isl_multi_union_pw_aff ([...]) is read by
 * read_multi_union_pw_aff_core.
 */
__isl_give isl_multi_union_pw_aff *isl_stream_read_multi_union_pw_aff(
        __isl_keep isl_stream *s)
{
        isl_multi_union_pw_aff *mupa;

        if (!isl_stream_next_token_is(s, '('))
                return read_multi_union_pw_aff_core(s);

        if (isl_stream_eat(s, '(') < 0)
                return NULL;
        mupa = read_multi_union_pw_aff_core(s);
        if (isl_stream_eat_if_available(s, ':')) {
                isl_union_set *dom;

                dom = isl_stream_read_union_set(s);
                mupa = isl_multi_union_pw_aff_intersect_domain(mupa, dom);
        }
        if (isl_stream_eat(s, ')') < 0)
                return isl_multi_union_pw_aff_free(mupa);
        return mupa;
}

/* Read an isl_multi_union_pw_aff from "str".
 */
__isl_give isl_multi_union_pw_aff *isl_multi_union_pw_aff_read_from_str(
        isl_ctx *ctx, const char *str)
{
        isl_multi_union_pw_aff *mupa;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        mupa = isl_stream_read_multi_union_pw_aff(s);
        isl_stream_free(s);
        return mupa;
}

__isl_give isl_union_pw_qpolynomial *isl_stream_read_union_pw_qpolynomial(
        __isl_keep isl_stream *s)
{
        struct isl_obj obj;

        obj = obj_read(s);
        if (obj.type == isl_obj_pw_qpolynomial) {
                obj.type = isl_obj_union_pw_qpolynomial;
                obj.v = isl_union_pw_qpolynomial_from_pw_qpolynomial(obj.v);
        }
        if (obj.v)
                isl_assert(s->ctx, obj.type == isl_obj_union_pw_qpolynomial,
                           goto error);

        return obj.v;
error:
        obj.type->free(obj.v);
        return NULL;
}

__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_read_from_str(
        isl_ctx *ctx, const char *str)
{
        isl_union_pw_qpolynomial *upwqp;
        isl_stream *s = isl_stream_new_str(ctx, str);
        if (!s)
                return NULL;
        upwqp = isl_stream_read_union_pw_qpolynomial(s);
        isl_stream_free(s);
        return upwqp;
}