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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 | ; Copyright (C) 2006 University of Texas at Austin
; This program is free software; you can redistribute it and/or modify
; it under the terms of the GNU General Public License as published by
; the Free Software Foundation; either version 2 of the License, or
; (at your option) any later version.
; This program is distributed in the hope that it will be useful,
; but WITHOUT ANY WARRANTY; without even the implied warranty of
; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
; GNU General Public License for more details.
; You should have received a copy of the GNU General Public License
; along with this program; if not, write to the Free Software
; Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
; Written by: Matt Kaufmann
; email: Kaufmann@cs.utexas.edu
; Department of Computer Science
; University of Texas at Austin
; Austin, TX 78701 U.S.A.
; October, 2006
; In a nutshell:
; If you submit (bash term), then the result is a list of goals to which ACL2
; can simplify term when attempting to prove it. (In particular, if the result
; is nil, then ACL2 can prove term.) More accurately: (bash term) returns (mv
; nil val state), where: val is a list of terms, in untranslated (user-level)
; form, whose provability implies the provability of the input term. If ACL2
; cannot simplify the input term (e.g., if there is a translation error), then
; it prints a warning and returns (mv nil input-term state).
; More details:
; This book defines a utility similar to the proof-checker's bash command, but
; for use in the top-level loop. The input term can be a user-level term,
; i.e., it need not be translated. Thus this bash utility is given a term, and
; it returns an error triple (mv nil termlist state) where if no error occurs
; in the process, then termlist is the list of goals that ACL2 would get stuck
; on, if you were to attempt to prove the given term with only simplification,
; i.e., with a "Goal" hint of :do-not '(generalize eliminate-destructors
; fertilize eliminate-irrelevance) and with induction turned off. Bash does
; all the normal simplification stuff, including forward chaining. Use :hints
; to specify hints using the same syntax as for thm and defthm. Use a non-nil
; value of :verbose if you want output, including the proof attempt. The
; keyword values are not evaluated, so :hints could be of the form (("Goal
; ...)) but not '(("Goal" ...)).
; This book also includes a functional (non-macro) version of bash, bash-fn.
; At the end is a variant contributed by Dave Greve, bash-term-to-dnf, that
; returns a list of goals (implicitly conjoined) where each goal has the form
; (lit1 lit2 ... litk), for which the goal is equivalent to the negation of the
; conjunction of the liti.
; Examples:
#|
ACL2 !>(bash (equal (append x y) (append (car (cons x a)) z)))
((EQUAL (APPEND X Y) (APPEND X Z)))
ACL2 !>(bash (equal (car (cons x y)) x))
NIL
ACL2 !>(bash (implies (true-listp x) (equal (append x y) zzz))
:hints (("Goal" :expand ((true-listp x)
(true-listp (cdr x))
(append x y)))))
((EQUAL Y ZZZ)
(IMPLIES (AND (CONSP X)
(CONSP (CDR X))
(TRUE-LISTP (CDDR X)))
(EQUAL (LIST* (CAR X)
(CADR X)
(APPEND (CDDR X) Y))
ZZZ))
(IMPLIES (AND (CONSP X) (NOT (CDR X)))
(EQUAL (CONS (CAR X) Y) ZZZ)))
ACL2 !>(bash-term-to-dnf
'(implies (true-listp x) (equal (append x y) zzz))
'(("Goal" :expand ((true-listp x)
(true-listp (cdr x))
(append x y))))
nil nil state)
(((EQUAL Y ZZZ))
((NOT (CONSP X))
(NOT (CONSP (CDR X)))
(NOT (TRUE-LISTP (CDDR X)))
(EQUAL (LIST* (CAR X)
(CADR X)
(APPEND (CDDR X) Y))
ZZZ))
((NOT (CONSP X))
(CDR X)
(EQUAL (CONS (CAR X) Y) ZZZ)))
ACL2 !>
.....
Here's how one might simplify hypotheses.
(defstub p1 (x) t)
(defstub p2 (x) t)
(defun p3 (x) (if (atom x) (p2 x) (p1 (car x))))
(include-book
"misc/bash" :dir :system)
Then:
ACL2 !>(bash (implies (and (p1 x) (p3 x))
(hide aaa)))
((IMPLIES (AND (P1 X) (CONSP X) (P1 (CAR X)))
(HIDE AAA))
(IMPLIES (AND (P1 X) (NOT (CONSP X)) (P2 X))
(HIDE AAA)))
ACL2 !>
Here's how to do what I think you may want to do.
(defun strip-lastcar (lst)
(if (atom lst)
lst
(cons (butlast (car lst) 1)
(strip-lastcar (cdr lst)))))
Then:
ACL2 !>(er-let* ((clauses (bash-term-to-dnf
'(implies (and (p1 x) (p3 x))
(hide aaa))
nil nil t state)))
(mv nil (strip-lastcar clauses) state))
(((NOT (P1 X))
(NOT (CONSP X))
(NOT (P1 (CAR X))))
((NOT (P1 X)) (CONSP X) (NOT (P2 X))))
ACL2 !>
|# ; |
(in-package "ACL2")
(program)
(set-state-ok t)
(defun simplify-with-prover (form hints ctx state)
; This is patterned after (define-pc-primitive prove ...).
(let ((wrld (w state))
(ens (ens state))
(name-tree 'bash))
(er-let*
((thints (translate-hints
name-tree
; Keep the following in sync with the definition of the proof-checker :bash
; command.
(append
*bash-skip-forcing-round-hints*
(add-string-val-pair-to-string-val-alist
"Goal"
:do-not
(list 'quote '(generalize eliminate-destructors fertilize
eliminate-irrelevance))
(add-string-val-pair-to-string-val-alist
"Goal"
:do-not-induct
name-tree
hints))
(default-hints wrld))
ctx wrld state))
(tterm (translate form t t t ctx wrld state)))
(mv-let (erp ttree state)
(state-global-let*
((guard-checking-on nil)
(in-prove-flg t))
(pc-prove tterm form thints t ens wrld ctx state))
(cond (erp (mv t nil state))
(t (let ((clauses (unproved-pc-prove-terms ttree)))
(cond ((and (eql (length clauses) 1)
(eql (length (car clauses)) 1)
(eql (caar clauses) tterm))
(mv 'no-change nil state))
(t (value clauses))))))))))
(defun bash-fn (form hints verbose ctx state)
; Keep this in sync with bash-term-to-dnf.
(mv-let
(erp clauses state)
(cond (verbose
(simplify-with-prover form hints ctx state))
(t
(state-global-let*
((inhibit-output-lst *valid-output-names*))
(simplify-with-prover form hints ctx state))))
(cond
(erp
(pprogn
(warning$ ctx "bash"
"Unable to simplify the input term~@0"
(cond ((eq erp 'no-change)
".")
(t (msg " because an error occurred.~@0"
(cond
(verbose "")
(t " Try setting the verbose flag to t in ~
order to see what is going on."))))))
(value (list form))))
(t
(value (prettyify-clause-lst clauses (let*-abstractionp state) (w state)))))))
(defmacro bash (term &key verbose hints)
`(bash-fn ',term ',hints ',verbose 'bash state))
; Dave Greve has contributed the following (only slightly modified here), to
; create a variant bash-term-to-dnf of bash-fn. This example may suggest other
; variants; feel free to contribute yours to Matt Kaufmann,
; kaufmann@cs.utexas.edu.
(defun goals-to-cnf (goals)
(cond ((endp goals) nil)
(t (cons (append (access goal (car goals) :hyps)
(list (dumb-negate-lit (access goal (car goals)
:conc))))
(goals-to-cnf (cdr goals))))))
(defun untranslate-lst-lst (list iff-flg wrld)
(cond
((endp list)
nil)
(t (cons (untranslate-lst (car list) iff-flg wrld)
(untranslate-lst-lst (cdr list) iff-flg wrld)))))
(defun bash-term-to-dnf (form hints verbose untranslate-flg state)
; Keep this in sync with bash-fn.
(let ((ctx 'bash-term-to-dnf))
(mv-let
(erp clauses state)
(cond (verbose
(simplify-with-prover form hints ctx state))
(t
(state-global-let*
((gag-mode nil set-gag-mode-fn)
(inhibit-output-lst *valid-output-names*)
(print-clause-ids nil))
(simplify-with-prover form hints ctx state))))
(cond
(erp
(cond ((eq verbose :all)
(pprogn
(warning$ ctx "bash"
"Unable to simplify the input term~@0"
(cond ((eq erp 'no-change)
".")
(t (msg " because an error occurred.~@0"
(cond
(verbose "")
(t " Try setting the verbose flag to ~
t in order to see what is going ~
on."))))))
(value (list (list form)))))
(t
(value (list (list form))))))
(untranslate-flg
(value (untranslate-lst-lst clauses t (w state))))
(t
(value clauses))))))
;; When we call bash with hints we may modify the enabled structure.
;; If we do this inside of a computed hint it may result in slow array
;; access warnings. By wrapping the outermost state modifying call
;; with preserve-pspv you can protect the state.
(defmacro preserve-pspv (call &key (pspv 'pspv))
`(let ((pspv ,pspv))
(let* ((old-ens (access rewrite-constant
(access prove-spec-var pspv :rewrite-constant)
:current-enabled-structure))
(old-name (access enabled-structure old-ens :array-name)))
(mv-let (err val state) ,call
(let ((ens (compress1 old-name (access enabled-structure old-ens :theory-array))))
(declare (ignore ens))
(mv err val state))))))
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