summaryrefslogtreecommitdiffstats
path: root/cring.scm
blob: 6f33027faca8f5459082ce39115d3fa22371d2b0 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
;;;"cring.scm" Extend Scheme numerics to any commutative ring.
;Copyright (C) 1997, 1998, 2001 Aubrey Jaffer
;
;Permission to copy this software, to modify it, to redistribute it,
;to distribute modified versions, and to use it for any purpose is
;granted, subject to the following restrictions and understandings.
;
;1.  Any copy made of this software must include this copyright notice
;in full.
;
;2.  I have made no warranty or representation that the operation of
;this software will be error-free, and I am under no obligation to
;provide any services, by way of maintenance, update, or otherwise.
;
;3.  In conjunction with products arising from the use of this
;material, there shall be no use of my name in any advertising,
;promotional, or sales literature without prior written consent in
;each case.

(require 'common-list-functions)
(require 'relational-database)
(require 'databases)
(require 'sort)

(define number^ expt)
(define number* *)
(define number+ +)
(define number- -)
(define number/ /)
(define number0? zero?)
(define (zero? x) (and (number? x) (number0? x)))
;;(define (sign x) (if (positive? x) 1 (if (negative? x) -1 0)))

(define cring:db (create-database #f 'alist-table))
;@
(define (make-ruleset . rules)
  (define name #f)
  (cond ((and (not (null? rules)) (symbol? (car rules)))
	 (set! name (car rules))
	 (set! rules (cdr rules)))
	(else (set! name (gentemp))))
  (define-tables cring:db
    (list name
	  '((op symbol)
	    (sub-op1 symbol)
	    (sub-op2 symbol))
	  '((reduction expression))
	  rules))
  (let ((table ((cring:db 'open-table) name #t)))
    (and table
	 (list (table 'get 'reduction)
	       (table 'row:update)
	       table))))
;@
(define *ruleset* (make-ruleset 'default))
(define (cring:define-rule . args)
  (if *ruleset*
      ((cadr *ruleset*) args)
      (slib:warn "No ruleset in *ruleset*")))
;@
(define (combined-rulesets . rulesets)
  (define name #f)
  (cond ((symbol? (car rulesets))
	 (set! name (car rulesets))
	 (set! rulesets (cdr rulesets)))
	(else (set! name (gentemp))))
  (apply make-ruleset name
	 (apply append
		(map (lambda (ruleset) (((caddr ruleset) 'row:retrieve*)))
		     rulesets))))

;;; Distribute * over + (and -)
;@
(define distribute*
  (make-ruleset
   'distribute*
   `(* + identity
       ,(lambda (exp1 exp2)
	  ;;(print 'distributing '* '+ exp1 exp2 '==>)
	  (apply + (map (lambda (trm) (* trm exp2)) (cdr exp1)))))
   `(* - identity
       ,(lambda (exp1 exp2)
	  ;;(print 'distributing '* '- exp1 exp2 '==>)
	  (apply - (map (lambda (trm) (* trm exp2)) (cdr exp1)))))))

;;; Distribute / over + (and -)
;@
(define distribute/
  (make-ruleset
   'distribute/
   `(/ + identity
       ,(lambda (exp1 exp2)
	  ;;(print 'distributing '/ '+ exp1 exp2 '==>)
	  (apply + (map (lambda (trm) (/ trm exp2)) (cdr exp1)))))
   `(/ - identity
       ,(lambda (exp1 exp2)
	  ;;(print 'distributing '/ '- exp1 exp2 '==>)
	  (apply - (map (lambda (trm) (/ trm exp2)) (cdr exp1)))))))

(define (symbol-alpha? sym)
  (char-alphabetic? (string-ref (symbol->string sym) 0)))
(define (expression-< x y)
  (cond ((and (number? x) (number? y)) (> x y))	;want negatives last
	((number? x) #t)
	((number? y) #f)
	((and (symbol? x) (symbol? y))
	 (cond ((eqv? (symbol-alpha? x) (symbol-alpha? y))
		(string<? (symbol->string x) (symbol->string y)))
	       (else (symbol-alpha? x))))
	((symbol? x) #t)
	((symbol? y) #f)
	((null? x) #t)
	((null? y) #f)
	((expression-< (car x) (car y)) #t)
	((expression-< (car y) (car x)) #f)
	(else (expression-< (cdr x) (cdr y)))))
(define (expression-sort seq) (sort! seq expression-<))

(define is-term-op? (lambda (term op) (and (pair? term) (eq? op (car term)))))

;; To convert to CR internal form, NUMBER-op all the `numbers' in the
;; argument list and remove them from the argument list.  Collect the
;; remaining arguments into equivalence classes, keeping track of the
;; number of arguments in each class.  The returned list is thus:
;; (<numeric> (<expression1> . <exp1>) ...)

;;; Converts * argument list to CR internal form
(define (cr*-args->fcts args)
  ;;(print (cons 'cr*-args->fcts args) '==>)
  (let loop ((args args) (pow 1) (nums 1) (arg_exps '()))
    ;;(print (list 'loop args pow nums denoms arg_exps) '==>)
    (cond ((null? args) (cons nums arg_exps))
	  ((number? (car args))
	   (let ((num^pow (number^ (car args) (abs pow))))
	     (if (negative? pow)
		 (loop (cdr args) pow (number/ (number* num^pow nums))
		       arg_exps)
		 (loop (cdr args) pow (number* num^pow nums) arg_exps))))
	  ;; Associative Rule
	  ((is-term-op? (car args) '*) (loop (append (cdar args) (cdr args))
					     pow nums arg_exps))
	  ;; Do singlet -
	  ((and (is-term-op? (car args) '-) (= 2 (length (car args))))
	   ;;(print 'got-here (car args))
	   (set! arg_exps (loop (cdar args) pow (number- nums) arg_exps))
	   (loop (cdr args) pow
		 (car arg_exps)
		 (cdr arg_exps)))
	  ((and (is-term-op? (car args) '/) (= 2 (length (car args))))
	   ;; Do singlet /
	   ;;(print 'got-here=cr+ (car args))
	   (set! arg_exps (loop (cdar args) (number- pow) nums arg_exps))
	   (loop (cdr args) pow
		 (car arg_exps)
		 (cdr arg_exps)))
	  ((is-term-op? (car args) '/)
	   ;; Do multi-arg /
	   ;;(print 'doing '/ (cddar args) (number- pow))
	   (set! arg_exps
		 (loop (cddar args) (number- pow) nums arg_exps))
	   ;;(print 'finishing '/ (cons (cadar args) (cdr args)) pow)
	   (loop (cons (cadar args) (cdr args))
		 pow
		 (car arg_exps)
		 (cdr arg_exps)))
	  ;; Pull out numeric exponents as powers
	  ((and (is-term-op? (car args) '^)
		(= 3 (length (car args)))
		(number? (caddar args)))
	   (set! arg_exps (loop (list (cadar args))
				(number* pow (caddar args))
				nums
				arg_exps))
	   (loop (cdr args) pow (car arg_exps) (cdr arg_exps)))
	  ;; combine with same terms
	  ((assoc (car args) arg_exps)
	   => (lambda (pair) (set-cdr! pair (number+ pow (cdr pair)))
		      (loop (cdr args) pow nums arg_exps)))
	  ;; Add new term to arg_exps
	  (else (loop (cdr args) pow nums
		      (cons (cons (car args) pow) arg_exps))))))

;;; Converts + argument list to CR internal form
(define (cr+-args->trms args)
  (let loop ((args args) (cof 1) (numbers 0) (arg_exps '()))
    (cond ((null? args) (cons numbers arg_exps))
	  ((number? (car args))
	   (loop (cdr args)
		 cof
		 (number+ (number* (car args) cof) numbers)
		 arg_exps))
	  ;; Associative Rule
	  ((is-term-op? (car args) '+) (loop (append (cdar args) (cdr args))
					     cof
					     numbers
					     arg_exps))
	  ;; Idempotent singlet *
	  ((and (is-term-op? (car args) '*) (= 2 (length (car args))))
	   (loop (cons (cadar args) (cdr args))
		 cof
		 numbers
		 arg_exps))
	  ((and (is-term-op? (car args) '-) (= 2 (length (car args))))
	   ;; Do singlet -
	   (set! arg_exps (loop (cdar args) (number- cof) numbers arg_exps))
	   (loop (cdr args) cof (car arg_exps) (cdr arg_exps)))
	  ;; Pull out numeric factors as coefficients
	  ((and (is-term-op? (car args) '*) (some number? (cdar args)))
	   ;;(print 'got-here (car args) '=> (cons '* (remove-if number? (cdar args))))
	   (set! arg_exps
		 (loop (list (cons '* (remove-if number? (cdar args))))
		       (apply number* cof (remove-if-not number? (cdar args)))
		       numbers
		       arg_exps))
	   (loop (cdr args) cof (car arg_exps) (cdr arg_exps)))
	  ((is-term-op? (car args) '-)
	   ;; Do multi-arg -
	   (set! arg_exps (loop (cddar args) (number- cof) numbers arg_exps))
	   (loop (cons (cadar args) (cdr args))
		 cof
		 (car arg_exps)
		 (cdr arg_exps)))
	  ;; combine with same terms
	  ((assoc (car args) arg_exps)
	   => (lambda (pair) (set-cdr! pair (number+ cof (cdr pair)))
		      (loop (cdr args) cof numbers arg_exps)))
	  ;; Add new term to arg_exps
	  (else (loop (cdr args) cof numbers
		      (cons (cons (car args) cof) arg_exps))))))

;;; Converts + or * internal form to Scheme expression
(define (cr-terms->form op ident inv-op higher-op res_cofs)
  (define (negative-cof? fct_cof)
    (negative? (cdr fct_cof)))
  (define (finish exprs)
    (if (null? exprs) ident
	(if (null? (cdr exprs))
	    (car exprs)
	    (cons op exprs))))
  (define (do-terms sign fct_cofs)
    (expression-sort
     (map (lambda (fct_cof)
	    (define cof (number* sign (cdr fct_cof)))
	    (cond ((eqv? 1 cof) (car fct_cof))
		  ((number? (car fct_cof)) (number* cof (car fct_cof)))
		  ((is-term-op? (car fct_cof) higher-op)
		   (if (eq? higher-op '^)
		       (list '^ (cadar fct_cof) (* cof (caddar fct_cof)))
		       (cons higher-op (cons cof (cdar fct_cof)))))
		  ((eqv? -1 cof) (list inv-op (car fct_cof)))
		  (else (list higher-op (car fct_cof) cof))))
	  fct_cofs)))
  (let* ((all_cofs (remove-if (lambda (fct_cof)
				(or (zero? (cdr fct_cof))
				    (eqv? ident (car fct_cof))))
			      res_cofs))
	 (cofs (map cdr all_cofs))
	 (some-positive? (some positive? cofs)))
    ;;(print op 'positive? some-positive? 'negative? (some negative? cofs) all_cofs)
    (cond ((and some-positive? (some negative? cofs))
	   (append (list inv-op
			 (finish (do-terms
				  1 (remove-if negative-cof? all_cofs))))
		   (do-terms -1 (remove-if-not negative-cof? all_cofs))))
	  (some-positive? (finish (do-terms 1 all_cofs)))
	  ((not (some negative? cofs)) ident)
	  (else (list inv-op (finish (do-terms -1 all_cofs)))))))

(define (* . args)
  (cond
   ((null? args) 1)
   ;;This next line is commented out so ^ will collapse numerical expressions.
   ;;((null? (cdr args)) (car args))
   (else
    (let ((in (cr*-args->fcts args)))
      (cond
       ((zero? (car in)) 0)
       (else
	(if (null? (cdr in))
	    (set-cdr! in (list (cons 1 1))))
	(let* ((num #f)
	       (ans (cr-terms->form
		     '* 1 '/ '^
		     (apply
		      (lambda (numeric red_cofs res_cofs)
			(set! num numeric)
			(append
			 ;;(list (cons (abs numeric) 1))
			 red_cofs
			 res_cofs))
		      (cr1 '* number* '^ '/ (car in) (cdr in))))))
	  (cond ((number0? (+ -1 num)) ans)
		((number? ans) (number* num ans))
		((number0? (+ 1 num))
		 (if (and (list? ans) (= 2 (length ans)) (eq? '- (car ans)))
		     (cadr ans)
		     (list '- ans)))
		((not (pair? ans)) (list '* num ans))
		(else
		 (case (car ans)
		   ((*) (append (list '* num) (cdr ans)))
		   ((+) (apply + (map (lambda (mon) (* num mon)) (cdr ans))))
		   ((-) (apply - (map (lambda (mon) (* num mon)) (cdr ans))))
		   (else (list '* num ans))))))))))))

(define (+ . args)
  (cond ((null? args) 0)
	;;((null? (cdr args)) (car args))
	(else
	 (let ((in (cr+-args->trms args)))
	   (if (null? (cdr in))
	       (car in)
	       (cr-terms->form
		'+ 0 '- '*
		(apply (lambda (numeric red_cofs res_cofs)
			 (append
			  (list (if (and (number? numeric)
					 (negative? numeric))
				    (cons (abs numeric) -1)
				    (cons numeric 1)))
			  red_cofs
			  res_cofs))
		       (cr1 '+ number+ '* '- (car in) (cdr in)))))))))

(define (- arg1 . args)
  (if (null? args)
      (if (number? arg1) (number- arg1)
	  (* -1 arg1)			;(list '- arg1)
	  )
      (+ arg1 (* -1 (apply + args)))))

;;(print `(/ ,arg1 ,@args) '=> )
(define (/ arg1 . args)
  (if (null? args)
      (^ arg1 -1)
      (* arg1 (^ (apply * args) -1))))

(define (^ arg1 arg2)
  (cond ((and (number? arg2) (integer? arg2))
	 (* (list '^ arg1 arg2)))
	(else (list '^ arg1 arg2))))

;; TRY-EACH-PAIR-ONCE algorithm.  I think this does the minimum
;; number of rule lookups given no information about how to sort
;; terms.

;; Pick equivalence classes one at a time and move them into the
;; result set of equivalence classes by searching for rules to
;; multiply an element of the chosen class by itself (if multiple) and
;; the element of each class already in the result group.  Each
;; (multiplicative) term resulting from rule application would be put
;; in the result class, if that class exists; or put in an argument
;; class if not.

(define (cr1 op number-op hop inv-op numeric in)
  (define red_pows '())
  (define res_pows '())
  (define (cring:apply-rule->terms exp1 exp2) ;(display op)
    (let ((ans (cring:apply-rule op exp1 exp2)))
      (cond ((not ans) #f)
	    ((number? ans) (list ans))
	    (else (list (cons ans 1))))))
  (define (cring:apply-inv-rule->terms exp1 exp2) ;(display inv-op)
    (let ((ans (cring:apply-rule inv-op exp1 exp2)))
      (cond ((not ans) #f)
	    ((number? ans) (list ans))
	    (else (list (cons ans 1))))))
  (let loop_arg_pow_s ((arg (caar in)) (pow (cdar in)) (arg_pows (cdr in)))
    (define (arg-loop arg_pows)
      (cond ((not (null? arg_pows))
	     (loop_arg_pow_s (caar arg_pows) (cdar arg_pows) (cdr arg_pows)))
	    (else (list numeric red_pows res_pows)))) ; Actually return!
    (define (merge-res tmp_pows multiplicity)
      (cond ((null? tmp_pows))
	    ((number? (car tmp_pows))
	     (do ((m (number+ -1 (abs multiplicity)) (number+ -1 m))
		  (n numeric (number-op n (abs (car tmp_pows)))))
		 ((negative? m) (set! numeric n)))
	     (merge-res (cdr tmp_pows) multiplicity))
	    ((or (assoc (car tmp_pows) res_pows)
		 (assoc (car tmp_pows) arg_pows))
	     => (lambda (pair)
		  (set-cdr! pair (number+
				  pow (number-op multiplicity (cdar tmp_pows))))
		  (merge-res (cdr tmp_pows) multiplicity)))
	    ((assoc (car tmp_pows) red_pows)
	     => (lambda (pair)
		  (set! arg_pows
			(cons (cons (caar tmp_pows)
				    (number+
				     (cdr pair)
				     (number* multiplicity (cdar tmp_pows))))
			      arg_pows))
		  (set-cdr! pair 0)
		  (merge-res (cdr tmp_pows) multiplicity)))
	    (else (set! arg_pows
			(cons (cons (caar tmp_pows)
				    (number* multiplicity (cdar tmp_pows)))
			      arg_pows))
		  (merge-res (cdr tmp_pows) multiplicity))))
    (define (try-fct_pow fct_pow)
      ;;(print 'try-fct_pow fct_pow op 'arg arg 'pow pow)
      (cond ((or (zero? (cdr fct_pow)) (number? (car fct_pow))) #f)
	    ((not (and (number? pow) (number? (cdr fct_pow))
		       (integer? pow)	;(integer? (cdr fct_pow))
		       ))
	     #f)
	    ;;((zero? pow) (slib:error "Don't try exp-0 terms") #f)
	    ;;((or (number? arg) (number? (car fct_pow)))
	    ;; (slib:error 'found-number arg fct_pow) #f)
	    ((and (positive? pow) (positive? (cdr fct_pow))
		  (or (cring:apply-rule->terms arg (car fct_pow))
		      (cring:apply-rule->terms (car fct_pow) arg)))
	     => (lambda (terms)
		  ;;(print op op terms)
		  (let ((multiplicity (min pow (cdr fct_pow))))
		    (set-cdr! fct_pow (number- (cdr fct_pow) multiplicity))
		    (set! pow (number- pow multiplicity))
		    (merge-res terms multiplicity))))
	    ((and (negative? pow) (negative? (cdr fct_pow))
		  (or (cring:apply-rule->terms arg (car fct_pow))
		      (cring:apply-rule->terms (car fct_pow) arg)))
	     => (lambda (terms)
		  ;;(print inv-op inv-op terms)
		  (let ((multiplicity (max pow (cdr fct_pow))))
		    (set-cdr! fct_pow (number+ (cdr fct_pow) multiplicity))
		    (set! pow (number+ pow multiplicity))
		    (merge-res terms multiplicity))))
	    ((and (positive? pow) (negative? (cdr fct_pow))
		  (cring:apply-inv-rule->terms arg (car fct_pow)))
	     => (lambda (terms)
		  ;;(print op inv-op terms)
		  (let ((multiplicity (min pow (number- (cdr fct_pow)))))
		    (set-cdr! fct_pow (number+ (cdr fct_pow) multiplicity))
		    (set! pow (number- pow multiplicity))
		    (merge-res terms multiplicity))))
	    ((and (negative? pow) (positive? (cdr fct_pow))
		  (cring:apply-inv-rule->terms (car fct_pow) arg))
	     => (lambda (terms)
		  ;;(print inv-op op terms)
		  (let ((multiplicity (max (number- pow) (cdr fct_pow))))
		    (set-cdr! fct_pow (number- (cdr fct_pow) multiplicity))
		    (set! pow (number+ pow multiplicity))
		    (merge-res terms multiplicity))))
	    (else #f)))
    ;;(print op numeric 'arg arg 'pow pow 'arg_pows arg_pows 'red_pows red_pows 'res_pows res_pows)
    ;;(trace arg-loop cring:apply-rule->terms merge-res try-fct_pow) (set! *qp-width* 333)
    (cond ((or (zero? pow) (eqv? 1 arg)) ;(number? arg) arg seems to always be 1
	   (arg-loop arg_pows))
	  ((assoc arg res_pows) => (lambda (pair)
				     (set-cdr! pair (number+ pow (cdr pair)))
				     (arg-loop arg_pows)))
	  ((and (> (abs pow) 1) (cring:apply-rule->terms arg arg))
	   => (lambda (terms)
		(merge-res terms (quotient pow 2))
		(if (odd? pow)
		    (loop_arg_pow_s arg 1 arg_pows)
		    (arg-loop arg_pows))))
	  ((or (some try-fct_pow res_pows) (some try-fct_pow arg_pows))
	   (loop_arg_pow_s arg pow arg_pows))
	  (else (set! res_pows (cons (cons arg pow) res_pows))
		(arg-loop arg_pows)))))

(define (cring:try-rule op sop1 sop2 exp1 exp2)
  (and *ruleset*
       (let ((rule ((car *ruleset*) op sop1 sop2)))
	 (and rule (rule exp1 exp2)))))

(define (cring:apply-rule op exp1 exp2)
  (and (pair? exp1)
       (or (and (pair? exp2)
		(cring:try-rule op (car exp1) (car exp2) exp1 exp2))
	   (cring:try-rule op (car exp1) 'identity exp1 exp2))))

;;(begin (trace cr-terms->form) (set! *qp-width* 333))