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