src/nisimp.lisp

   1 ;;; -*-  Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*- ;;;;
   2 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
   3 ;;;     The data in this file contains enhancements.                   ;;;;;
   4 ;;;                                                                    ;;;;;
   5 ;;;  Copyright (c) 1984,1987 by William Schelter,University of Texas   ;;;;;
   6 ;;;     All rights reserved                                            ;;;;;
   7 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
   8 ;;;     (c) Copyright 1982 Massachusetts Institute of Technology         ;;;
   9 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
  10
  11 (in-package :maxima)
  12
  13 (macsyma-module nisimp)
  14
  15 ;;;programs for the LET LETSIMP LETRULES and REMLET commands
  16 ;;;these programs use the names LETSIMPTREE and LETRULES on the
  17 ;;;property list of atoms
  18 ;;;except for the top level programs all program names have the prefix NIS
  19
  20 (declare-top (special nistree nisrules nisflag))
  21
  22 (defmvar $letvarsimp nil)
  23
  24 (defmvar $letrat nil
  25   nil
  26   :properties ((evflag t)))
  27
  28 (defmvar $default_let_rule_package '$default_let_rule_package
  29   "The name of the default rule package used by `let' and `letsimp'")
  30
  31 (putprop '$default_let_rule_package 'let-rule-setter 'assign)
  32
  33 (defmvar $current_let_rule_package '$default_let_rule_package
  34   "The name of the current rule package used by `let' and `letsimp'")
  35
  36 (putprop '$current_let_rule_package 'let-rule-setter 'assign)
  37
  38 (defmvar $let_rule_packages '((mlist) $default_let_rule_package)
  39   "The names of the various let rule simplification packages")
  40
  41 (putprop '$let_rule_packages 'let-rule-setter 'assign)
  42
  43 (setq nisrules nil nistree nil)
  44
  45 (defun let-rule-setter (var val)
  46   (cond ((eq var '$default_let_rule_package)
  47          (merror (intl:gettext "assignment: cannot assign to default_let_rule_package.")))
  48         ((and (eq var '$current_let_rule_package)
  49               (not (memalike val (cdr $let_rule_packages))))
  50          (merror (intl:gettext "assignment: ~M is not a rule package.") val))
  51         ((eq var '$let_rule_packages)
  52          (merror (intl:gettext "assignment: cannot assign to let_rule_packages.~%assignment: call 'let' to create let rule packages.")))))
  53
  54 (defmspec $let (l) (setq l (cdr l))
  55           (if (null (cdr l)) (wna-err '$let))
  56           ;;LET([PATTERN,REPL,PRED,ARG1,...,ARGN],NAME)
  57           (prog (pattern pat replacement treename text $ratfac)
  58              ;;LET(PATTERN,REPL,PRED,ARG1,...,ARGN)
  59              (cond ((atom (car l))
  60                     (setq treename $current_let_rule_package))
  61                    ((eq 'mlist (caaar l))
  62                     (setq treename (cadr l))
  63                     (if (not (symbolp treename))
  64                         (improper-arg-err treename '$let))
  65                     (setq l (cdar l)))
  66                    (t (setq treename $current_let_rule_package)))
  67              (let ((nistree (mget treename 'letsimptree))
  68                    (nisrules (mget treename 'letrules)))
  69                (setq pat (strip-lineinfo (meval (car l))))
  70                (setq replacement (cdr l))
  71                (setq pattern (cond ((atom pat) (list pat))
  72                                    ((eq (caar pat) 'mtimes)
  73                                     (cdr pat))
  74                                    (t (list pat))))
  75                (setq nistree (nislet nistree pattern replacement))
  76                (cond (treename (mputprop treename
  77                                          nistree
  78                                          'letsimptree)
  79                                (add2lnc treename $let_rule_packages)))
  80                (nonsymchk (caddr l) '$let)
  81                (setq text
  82                      (append (list '(mtext) pat '| --> | )
  83                              (cond ((cddr l)
  84                                     (list (cadr l)
  85                                           '#.(intern (format nil " ~A " 'where))
  86                                           (cons (list (caddr l))
  87                                                 (cdddr l))))
  88                                    (t replacement))))
  89                (setq nisrules (append (list text) nisrules))
  90                (cond (treename (mputprop treename
  91                                          nisrules
  92                                          'letrules)))
  93                (return text))))
  94
  95 (defun nislet (tree list function)
  96   (prog (permlist)
  97      (setq permlist (nispermutations list))
  98      step (cond ((eq nil permlist) (return tree)))
  99      (setq tree (nistreebuilder tree (car permlist) function))
 100      (setq permlist (cdr permlist))
 101      (go step)))
 102
 103 (defun nispermutations (llist)
 104   (cond
 105     ((null (cdr llist)) (list llist))
 106     (t
 107      (prog (permlist a)
 108       step (setq permlist
 109                  (append
 110                   (nisaddon (car llist)
 111                             (nispermutations (append a (cdr llist))))
 112                   permlist))
 113       (if (null (cdr llist)) (return permlist))
 114       (push (car llist) a)
 115       (setq llist (cdr llist))
 116       (go step)))))
 117
 118 (defun nisaddon (x llist)
 119   (if llist (cons (cons x (car llist)) (nisaddon x (cdr llist)))))
 120
 121 (defun nistreebuilder (tree perm function)
 122   (cond ((null perm) (cons (list function) tree))
 123         ((null tree)
 124          (list (cons (car perm)
 125                      (nistreebuilder nil (cdr perm) function))))
 126         ((equal (car perm) (caar tree))
 127          (nisswcar tree
 128                    (nisswcdr (car tree)
 129                              (nistreebuilder (cdar tree)
 130                                              (cdr perm)
 131                                              function))))
 132         (t (nisswcdr tree
 133                      (nistreebuilder (cdr tree)
 134                                      perm
 135                                      function)))))
 136
 137 (defun nisswcar (x y)
 138   (cons y (cdr x)))
 139
 140 (defun nisswcdr (x y)
 141   (cons (car x) y))
 142
 143 (defmspec $remlet (x)
 144   (setq x (cdr x))
 145   ;; REMLET(PROD,NAME) REMLET(PROD) REMLET() REMLET(FALSE,NAME)
 146   (prog (pattern text treename)
 147      (cond ((cddr x) (wna-err '$remlet))
 148            ((null (cdr x)) (setq treename $current_let_rule_package))
 149            (t (setq treename (cadr x))
 150               (if (not (symbolp treename))
 151                   (improper-arg-err treename '$remlet))))
 152      (setq pattern (strip-lineinfo (meval (car x))))
 153      (when (or (not pattern) (eq '$all pattern))
 154        (setq nisrules nil nistree nil)
 155        (unless (eq treename '$default_let_rule_package)
 156          (setq $let_rule_packages (delete treename $let_rule_packages :count 1 :test #'eq)))
 157        (go a))
 158      (setq nistree (mget treename 'letsimptree))
 159      (if (setq text (nisremlet pattern)) (return text))
 160      (if nistree
 161          (setq nisrules
 162                (nistreelister (mget treename 'letrules) pattern))
 163          (setq nisrules nil))
 164      a    (mputprop treename nistree 'letsimptree)
 165      (mputprop treename nisrules 'letrules)
 166      (return '$done)))
 167
 168 (defun nistreelister (llist pattern)
 169   (prog (x)
 170    a    (if (alike1 pattern (cadar llist)) (return (append x (cdr llist))))
 171    (setq x (append x (list (car llist))) llist (cdr llist))
 172    (go a)))
 173
 174 (defun nisremlet (pat)
 175   (prog (llist permlist x)
 176      (setq llist (if (mtimesp pat) (cdr pat) (ncons pat)))
 177      (setq nisflag t x nistree)
 178      (setq permlist (nispermutations llist))
 179      step (when (null permlist) (setq nistree x) (return nil))
 180      (setq x (nistreetrimmer (car permlist) x))
 181      (if (null nisflag) (merror (intl:gettext "remlet: no rule found: ~M") pat))
 182      (setq permlist (cdr permlist))
 183      (go step)))
 184
 185 (defun nistreetrimmer (perm tree)
 186   (cond ((null perm)
 187          (cond ((null tree) (setq nisflag nil))
 188                ((null (cdar tree))
 189                 (setq nisflag (caar tree)) (cdr tree))
 190                (t (nisswcdr tree (nistreetrimmer nil (cdr tree))))))
 191         ((null tree) (setq nisflag nil))
 192         ((equal (car perm) (caar tree))
 193          (prog (x)
 194             (setq x (nistreetrimmer (cdr perm) (cdar tree)))
 195             (if (null x) (return (cdr tree)))
 196             (return (nisswcar tree (nisswcdr (car tree) x)))))
 197         (t (nisswcdr tree (nistreetrimmer perm (cdr tree))))))
 198
 199 (defmspec $letrules (name)
 200   (setq name (cdr name))                ;LETRULES(NAME)
 201   (let ((treename (if name (car name) $current_let_rule_package)))
 202     (if (not (symbolp treename)) (improper-arg-err treename '$letrules))
 203     (setq nistree (mget treename 'letsimptree)
 204           nisrules (mget treename 'letrules))
 205     (apply #'$disp nisrules)))
 206
 207 (defmspec $letsimp (form)               ;letsimp(expr,tree1,...,treen)
 208   (setq form (cdr form))
 209   (let* ((expr (strip-lineinfo (meval (pop form))))
 210          (sw ($ratp expr))
 211          $ratfac)
 212     (progv (unless sw '(varlist genvar))
 213         (unless sw (list varlist genvar))
 214       (when (and sw (member 'trunc (cdar expr) :test #'eq))
 215         (setq expr ($taytorat expr)))
 216       (dolist (rulepackage (or form (list $current_let_rule_package))
 217                (if sw (ratf expr) expr))
 218         (unless (symbolp rulepackage)
 219           (improper-arg-err rulepackage '$letsimp))
 220         (when (setq nistree (mget rulepackage 'letsimptree))
 221           ;; Whereas nisletsimp returns an expression in general
 222           ;; representation, the original expr might be in CRE form.
 223           ;; Regardless, we use ratf to make sure varlist and genvar
 224           ;; know of expr's kernels.
 225           (setq expr (nisletsimp (if (atom expr)
 226                                      expr
 227                                      (ratf expr)))))))))
 228
 229 (defun nisletsimp (e)
 230   (let (x)
 231     (cond ((mnump e) e)
 232           ((or (and (atom e) (setq x (ncons e)))
 233                (and (eq (caar e) 'mtimes) (setq x (cdr e))))
 234            (setq x (nisnewlist x))
 235            (if x (nisletsimp ($ratexpand (cons '(mtimes) x))) e))
 236           ((member (caar e) '(mplus mequal mlist $matrix) :test #'eq)
 237            (cons (if (eq (caar e) 'mplus) '(mplus) (car e))
 238                  (mapcar #'nisletsimp (cdr e))))
 239           ((or (eq (caar e) 'mrat)
 240                (and (eq (caar e) 'mquotient) (setq e (ratf e))))
 241            (nisletsimprat e))
 242           (t ;; A kernel (= product of 1 element)
 243            (setq x (nisnewlist (ncons e)))
 244            (if x (nisletsimp ($ratexpand (cons '(mtimes) x))) e)))))
 245
 246 (defun nisletsimprat (e)
 247   (let ((num (cadr e)) (denom (cddr e)) $ratexpand)
 248     (if $letvarsimp (setq varlist (mapcar #'nisletsimp varlist)))
 249     (let (($ratexpand t))
 250       ; Construct new CREs based on the numerator and denominator
 251       ; of E and disrep them in the VARLIST and GENVAR context from
 252       ; E.
 253       ;
 254       ; NISLETSIMP can change VARLIST and GENVAR, so the order of
 255       ; the PDIS and NISLETSIMP forms matter here.  PDISing and
 256       ; NISLETSIMPing the numerator before moving on to the
 257       ; denominator is not correct.
 258       (let ((varlist (mrat-varlist e))
 259             (genvar (mrat-genvar e)))
 260         (setq num (pdis num)
 261               denom (pdis denom)))
 262       (setq num (nisletsimp num)
 263             denom (nisletsimp denom)))
 264     (setq e (list '(mquotient) num denom))
 265     (if $letrat (nisletsimp ($ratexpand e)) e)))
 266
 267 (defun nisnewlist (llist)
 268   (let ((x (nissearch llist nistree nil))) (if x (nisreplace llist x))))
 269
 270 (defun nissearch (x y z)
 271   (cond ((null y) nil)
 272         ((nisinnernull y) (nisfix (nisinnernull y) z))
 273         ((null x) nil)
 274         (t (prog (xx yy path bind)
 275               (setq yy y)
 276               a    (setq xx x)
 277               b    (cond ((and (setq bind (nismatch (car xx)
 278                                                     (caar yy)
 279                                                     z))
 280                                (setq path
 281                                      (nissearch (cdr xx)
 282                                                 (cdar yy)
 283                                                 (cdr bind))))
 284                           (return (cons (car bind) path))))
 285               (setq xx (cdr xx))
 286               (cond (xx (go b)))
 287               (setq yy (cdr yy))
 288               (cond ((null yy) (return nil)))
 289               (go a)))))
 290
 291 (defun nisinnernull (x)
 292   (cond ((null x) nil)
 293         ((null (cdar x)) (caar x))
 294         (t (nisinnernull (cdr x)))))
 295
 296 (defun nisfix (funperd argasslist)
 297   (prog (function args bindings perd flag)
 298      (if (not argasslist) (return (car funperd)))
 299      (setq argasslist (nisnumberpicker argasslist))
 300      (setq args (maplist 'caar argasslist))
 301      (setq bindings (maplist 'cdar argasslist))
 302      (mbinding (args bindings)
 303                (setq function (car funperd))
 304                (if (setq perd (cdr funperd))
 305                    (if (not (meval perd)) (setq flag t)))
 306                (if (null flag) (setq function (meval function))))
 307      (return (if flag nil (list function)))))
 308
 309 (defun nisnumberpicker (x)
 310   (cond ((null x) nil)
 311         ((or (not (symbolp (caar x)))
 312              (kindp (caar x) '$constant))
 313          ;; Skip over numbers and constants
 314          (nisnumberpicker (cdr x)))
 315         (t (nisswcdr x (nisnumberpicker (cdr x))))))
 316
 317 (defun nismatch (a b c)
 318   (prog (x y newexpt)
 319      (setq x (nisextract a))
 320      (setq y (nisextract b))
 321      (cond
 322        ((listp (cadr y))
 323         (cond ((and (listp (cadr x))
 324                     (equal (car x) (car y))
 325                     (setq c (cons (cons (car x) (car y)) c))
 326                     (setq c (nisargschecker (cadr x)
 327                                             (cadr y)
 328                                             c))
 329                     (setq newexpt (nisexpocheck (cddr x)
 330                                                 (cddr y)
 331                                                 c)))
 332                (cond ((equal '(rat) (car newexpt))
 333                       (return (cons (cons a (nisbuild x newexpt))
 334                                     c)))
 335                      (t (return (cons (cons a '(dummy 0 (0 0)))
 336                                       newexpt)))))
 337               (t (return nil)))))
 338      (cond ((and (setq c (nisargmatch (niskernel a) (car y) c))
 339                  (setq newexpt (nisexpocheck (cddr x)
 340                                              (cddr y)
 341                                              c)))
 342             (cond ((equal '(rat) (car newexpt))
 343                    (return (cons (cons a (nisbuild x newexpt))
 344                                  c)))
 345                   (t (return (cons (cons a '(dummy 0 (0 0)))
 346                                    newexpt))))))
 347      (return nil)))
 348
 349 (defun niskernel (a)
 350   (if (mexptp a) (cadr a) a))
 351
 352 (defun nisextract (x)
 353   (cond ((or (atom x) (eq (caar x) 'rat))
 354          (cons x (cons t 1)))
 355         ((eq 'mexpt (caar x))
 356          (cond ((atom (cadr x))
 357                 (cons (cadr x) (cons t (caddr x))))
 358                (t (cons (if (member 'array (cdaadr x) :test #'eq)
 359                             (list (caaadr x) 'array)
 360                             (caaadr x))
 361                         (cons (cdadr x) (caddr x))))))
 362         (t (cons (if (member 'array (cdar x) :test #'eq)
 363                      (list (caar x) 'array)
 364                      (caar x))
 365                  (cons (cdr x) 1)))))
 366
 367 (defun nisargschecker (listargs treeargs argasslist)
 368   (prog (c)
 369      (cond ((and listargs treeargs) (go check))
 370            ((or listargs treeargs) (return nil))
 371            (t (return argasslist)))
 372      check(setq c (nisargmatch (car listargs)
 373                                (car treeargs)
 374                                argasslist))
 375      (cond (c (return (nisargschecker (cdr listargs)
 376                                       (cdr treeargs)
 377                                       c)))
 378            (t (return nil)))))
 379
 380 (defun nisexpocheck (listpower treepower argasslist)
 381   (prog (p q r s a b xx)
 382      (cond ((atom treepower)
 383             (cond ((numberp treepower)
 384                    (prog2 (setq r treepower s 1) (go math)))
 385                   (t (return (nisargmatch listpower
 386                                           treepower
 387                                           argasslist))))))
 388      (setq r (cadr treepower) s (caddr treepower))
 389      (if (not (numberp s)) (return nil))
 390      math (cond ((numberp listpower) (setq p listpower q 1))
 391                 ((atom listpower) (return nil))
 392                 ((eq 'rat (caar listpower))
 393                  (setq p (cadr listpower) q (caddr listpower)))
 394                 (t (return nil)))
 395      (setq xx (* (* q s) (- (* p s) (* q r))))
 396      (setq a (< (* r s) 0))
 397      (setq b (< xx 0))
 398      (cond ((or (not (or a b)) (and a (or b (equal 0 xx))))
 399             (return (list '(rat) xx (* q s)))))
 400      (return nil)))
 401
 402 (defun nisargmatch (x y c)
 403   (prog (w)
 404      (setq w c)
 405      up   (if (null w) (go down))
 406      (cond ((eq (caar w) y)
 407             (cond ((alike1 (cdar w) x) (return c))
 408                   (t (return nil)))))
 409      (setq w (cdr w))
 410      (go up)
 411      down (setq w (mget y 'matchdeclare))
 412      (cond ((null w) (if (equal x y) (go out) (return nil)))
 413            ((member (car w) '($true t) :test #'eq) (go out))
 414            ((and (atom (car w))
 415                  (meval (cons (ncons (car w))
 416                               (append (cdr w) (list x)))))
 417             (go out))
 418            ((and (not (atom (car w)))
 419                  (not (atom (caar w)))
 420                  (atom (caaar w))
 421          ; If we arrive here, (CAR W) is a Maxima expression like ((FOO) ...)
 422          ; If (CAR W) is a Maxima lambda expression, evaluate it via MFUNCALL.
 423          ; Otherwise, append X and call MEVAL.
 424          ; Note that "otherwise" includes Maxima lambda expressions with missing arguments;
 425          ; in that case the expression is ((MQAPPLY) ((LAMBDA) ...)) and MEVAL is the way to go.
 426                  (if (eq (caaar w) 'lambda)
 427            (mfuncall (car w) x)
 428            (meval (append (car w) (list x)))))
 429             (go out))
 430            (t (return nil)))
 431      out  (return (cons (cons y x) c))))
 432
 433 (defun nisbuild (x newexpt)
 434   (list '(mexpt)
 435         (if (listp (cadr x))
 436             (cons (if (symbolp (car x)) (ncons (car x)) (car x))
 437                   (cadr x))
 438             (car x))
 439         newexpt))
 440
 441 (defun nisreplace (llist asslist)
 442   (cond ((eq (cdr asslist) nil) (cons (car asslist) llist))
 443         ((equal (car llist) (caar asslist))
 444          (cond ((equal 0 (cadar (cdddar asslist)))
 445                 (nisreplace (cdr llist) (cdr asslist)))
 446                (t (cons (cdar asslist)
 447                         (nisreplace (cdr llist) (cdr asslist))))))
 448         (t (cons (car llist) (nisreplace (cdr llist) asslist)))))