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; Written by J Moore, 6/13/01
; License: A 3-clause BSD license. See the LICENSE file distributed with ACL2.
(in-package "ACL2")
; All the "terms" encountered in this work are untranslated. We nevertheless
; explore them. We will always check that they are "deft terms" which means
; they are
; <dterm> ::= <atom> -- variables, constants, unquoted evgs like 3 and "abc" |
; (quote x) |
; (sym <dterm> ... <dterm>)
(defmacro enable-disable (a b)
`(set-difference-theories (enable ,@a) ',b))
(mutual-recursion
(defun undeft-termp (x)
(declare (xargs :mode :program))
(cond
((atom x) nil)
((not (true-listp x))
`(er soft 'deft
"Untranslated terms encountered by DEFT must be true-lists, but ~p0 ~
is not."
',x))
((eq (car x) 'quote)
(cond ((= (length x) 2) nil)
(t `(er soft 'deft
"QUOTEd terms such as ~p0 must have length 2."
',x))))
((or (not (symbolp (car x)))
(member-eq (car x) '(cond let let*)))
; We list above some commonly used macros that violate the syntax of
; <dterm> above.
`(er soft 'deft
"We do not permit ~p0 as a function symbol."
',(car x)))
(t (undeft-termp-lst (cdr x)))))
(defun undeft-termp-lst (lst)
(declare (xargs :mode :program))
(cond
((atom lst) t)
(t (or (undeft-termp (car lst))
(undeft-termp-lst (cdr lst)))))))
(mutual-recursion
(defun dterm-all-vars (dterm vars)
(declare (xargs :mode :program))
(cond
((atom dterm)
(cond ((and (symbolp dterm)
(eq (legal-variable-or-constant-namep dterm) 'variable))
(add-to-set-eq dterm vars))
(t vars)))
((eq (car dterm) 'quote) vars)
(t (dterm-all-vars-lst (cdr dterm) vars))))
(defun dterm-all-vars-lst (lst vars)
(declare (xargs :mode :program))
(cond ((atom lst) vars)
(t (dterm-all-vars-lst (cdr lst)
(dterm-all-vars (car lst) vars))))))
(mutual-recursion
(defun dterm-sublis (alist dterm)
; This function knows how to substitute both for vars and exprs.
(declare (xargs :mode :program))
(let ((pair (assoc-equal dterm alist)))
(cond
(pair (cdr pair))
((atom dterm) dterm)
((eq (car dterm) 'quote) dterm)
(t (cons (car dterm) (dterm-sublis-lst alist (cdr dterm)))))))
(defun dterm-sublis-lst (alist lst)
(declare (xargs :mode :program))
(cond ((null lst) nil)
(t (cons (dterm-sublis alist (car lst))
(dterm-sublis-lst alist (cdr lst)))))))
(defun dterm-sublis-subst-to-alist (alist subst)
(declare (xargs :mode :program))
(cond ((null subst) nil)
(t (cons (cons (caar subst) (dterm-sublis alist (cadr (car subst))))
(dterm-sublis-subst-to-alist alist (cdr subst))))))
(defun dterm-sublis-subst (alist subst)
(declare (xargs :mode :program))
(let ((alist2 (dterm-sublis-subst-to-alist alist subst)))
(pairlis$ (strip-cars alist2)
(pairlis$ (strip-cdrs alist2) nil))))
(defun assoc-keys-other-than (lst alist)
(declare (xargs :mode :program))
(cond ((null alist) nil)
((member-eq (caar alist) lst) (assoc-keys-other-than lst (cdr alist)))
(t (cons (caar alist) (assoc-keys-other-than lst (cdr alist))))))
(defun dterm-sublis-into-lmi (alist lmi)
(declare (xargs :mode :program))
(cond
((atom lmi) lmi)
((eq (car lmi) :instance)
(list* :instance (dterm-sublis-into-lmi alist (cadr lmi))
(dterm-sublis-subst alist (cddr lmi))))
(t lmi)))
(defun dterm-sublis-into-use-hint (alist lst)
(declare (xargs :mode :program))
(cond
((null lst) nil)
(t
(cons (dterm-sublis-into-lmi alist (car lst))
(dterm-sublis-into-use-hint alist (cdr lst))))))
(defun convert-keyword-alist-to-alist (bindings keyword-alist)
(declare (xargs :mode :program))
(cond ((atom keyword-alist) nil)
(t (cons (cons (car keyword-alist)
(cond ((eq (car keyword-alist) :use)
(cond ((and (consp (cadr keyword-alist))
(eq (car (cadr keyword-alist)) :instance))
(dterm-sublis-into-lmi bindings (cadr keyword-alist)))
(t (dterm-sublis-into-use-hint bindings
(cadr keyword-alist)))))
(t (cadr keyword-alist))))
(convert-keyword-alist-to-alist bindings (cddr keyword-alist))))))
(defun negate-dterm (dterm)
(declare (xargs :mode :program))
(cond ((equal dterm t) nil)
((equal dterm nil) t)
((and (consp dterm)
(eq (car dterm) 'not))
(cadr dterm))
(t (list 'not dterm))))
(defun conjoin-dterms (dterm1 dterm2)
(declare (xargs :mode :program))
(cond ((equal dterm1 nil) nil)
((equal dterm2 nil) nil)
((equal dterm1 t) dterm2)
((equal dterm2 t) dterm1)
(t (let ((lst1 (case-match dterm1
(('and . terms)
terms)
(& (list dterm1))))
(lst2 (case-match dterm2
(('and . terms)
terms)
(& (list dterm2)))))
(cons 'and (append lst1 lst2))))))
(defun implicate-dterms (dhyp dconcl)
(declare (xargs :mode :program))
(cond ((eq dhyp t) dconcl)
(t (case-match dconcl
(('implies hyps concl)
(list 'implies
(conjoin-dterms hyps dhyp)
concl))
(& (list 'implies dhyp dconcl))))))
(defun dterm-hyp (dterm)
(declare (xargs :mode :program))
(case-match dterm
(('implies hyp &) hyp)
(& t)))
(defun dterm-concl (dterm)
(declare (xargs :mode :program))
(case-match dterm
(('implies & concl) concl)
(& dterm)))
(defun apply-proof-step (dhyp1 dterm)
(declare (xargs :mode :program))
(let ((dhyp2 (dterm-hyp dterm))
(dconcl (dterm-concl dterm)))
(case-match dhyp1
(('equal lhs rhs)
(let ((dconcl2 (dterm-sublis (list (cons lhs rhs)) dconcl)))
(cond ((equal dconcl2 dconcl)
(implicate-dterms (conjoin-dterms dhyp2 dhyp1) dconcl))
(t (implicate-dterms dhyp2 dconcl2)))))
(& (implicate-dterms (conjoin-dterms dhyp2 dhyp1) dconcl)))))
(defun pairlis1 (x1 lst)
; Make an alist pairing x1 with each element of lst.
(declare (xargs :mode :program))
(cond ((null lst) nil)
(t (cons (cons x1 (car lst))
(pairlis1 x1 (cdr lst))))))
(defun generalization-phrasep (all-vars bindings phrase new-hyps alist)
; We parse phrase into repetitions of
; `expr TO var'
; `expr TO var WHERE hyp' ;;; hyp is `about' var but must be proved of `expr'
; possibly separated by `and'.
; We return (mv er-form new-hyps alist), where new-hyps is a list of hyps
; (about the exprs, not the vars) to be proved and alist is a substitution
; mapping the vars to the exprs.
(declare (xargs :mode :program))
(cond
((atom phrase)
(mv nil
(dterm-sublis-lst alist (reverse new-hyps))
(reverse alist)))
((keywordp (car phrase))
(mv `(er soft 'deft
"It is illegal to put a hint inside a generalization step. The ~
usual intent is to aid the proof of a restriction on some ~
variable, as in (GENERALIZE expr TO var WHERE (p var) ~p0...). ~
The proper way to achieve this is to OBSERVE that expr has the ~
desired property before its generalization to var, as in ~
(OBSERVE (p expr) ~p0 ...) (GENERALIZE expr TO ar)."
',(car phrase))
nil nil))
((eq (car phrase) 'and)
(generalization-phrasep all-vars bindings (cdr phrase) new-hyps alist))
((and (consp (cdr phrase))
(eq (cadr phrase) 'to)
(consp (cddr phrase))
(symbolp (caddr phrase))
(not (member-eq (caddr phrase) all-vars)))
(let* ((expr (dterm-sublis bindings (car phrase)))
(var (caddr phrase))
(hyp (if (and (consp (cdddr phrase))
(eq (cadddr phrase) 'where)
(car (cddddr phrase)))
(dterm-sublis bindings (car (cddddr phrase)))
nil))
(phrase1 (if hyp (cdr (cddddr phrase)) (cdddr phrase))))
(generalization-phrasep (cons var all-vars) bindings phrase1
(if hyp (cons hyp new-hyps) new-hyps)
(cons (cons var expr) alist))))
(t (mv `(er soft 'deft
"Illegal GENERALIZATION step. We expected to see repetitions ~
of the phrases `expr TO var' or `expr TO var WHERE ~
restriction', possibly separated by `and', where var is a ~
variable not previously involved in the problem; ~p0 cannot be ~
parsed that way."
',phrase)
nil nil))))
(mutual-recursion
(defun translate-proof1 (dname dterm proof addr bindings
revents otherwise-term xhyp cnames
use-hint consider-dterm thm-pair)
(declare (xargs :mode :program))
(cond
((null proof)
(mv-let (er-form event addr1)
(deft-fn dname
dterm
addr
bindings
`((:use . ,(revappend cnames (reverse use-hint)))
(:in-theory . 'nil))
nil
:default
nil)
(cond
(er-form (mv er-form nil nil))
(t (mv nil
(cons event revents)
addr1)))))
(t
(let ((proof-step (car proof)))
(case-match
proof-step
(('case test . subproof)
(let* ((case-name (packn `(* ,addr)))
(test (if (eq test 'otherwise)
otherwise-term
(dterm-sublis bindings test)))
(case-dterm (implicate-dterms test dterm)))
(mv-let
(er-form revents1 addr1)
(translate-proof1
case-name
case-dterm
(if (member-equal subproof '((easy)(trivial)))
nil
subproof)
(1+ addr)
bindings
revents t
(dterm-hyp case-dterm)
nil use-hint nil nil)
(cond
(er-form (mv er-form nil nil))
(t (translate-proof1
dname
dterm
(cdr proof)
addr1
bindings
revents1
(conjoin-dterms
otherwise-term
(negate-dterm test))
xhyp
(cons case-name cnames)
use-hint nil nil))))))
(('let var & expr)
(translate-proof1
dname dterm (cdr proof) addr
(cons (cons var (dterm-sublis bindings expr)) bindings)
revents otherwise-term xhyp cnames use-hint consider-dterm
thm-pair))
(('Theorem dthm . h-alist)
(let* ((theorem-name (packn `(* ,addr)))
(pass-bindings-downp (and (consp h-alist)
(eq (car h-alist) :pass-bindings-downp)))
(h-alist (if pass-bindings-downp (cdr h-alist) h-alist)))
(mv-let
(er-form event addr1)
(deft-fn theorem-name dthm (1+ addr)
(if pass-bindings-downp bindings nil)
(convert-keyword-alist-to-alist bindings h-alist)
nil
:default
nil)
(cond
(er-form (mv er-form nil nil))
(t (translate-proof1
dname
dterm
(cdr proof)
addr1
bindings
(cons event revents)
otherwise-term
xhyp
cnames
use-hint
nil
(cons theorem-name dthm)))))))
(('Instantiate-just-proved-theorem . rest)
(translate-proof1 dname dterm
(cons (cons 'Instantiate rest) (cdr proof))
addr bindings revents otherwise-term xhyp cnames use-hint
consider-dterm thm-pair))
(('Instantiate . subst)
(cond
(thm-pair
(let* ((alist (dterm-sublis-subst-to-alist bindings subst))
(subst (pairlis$ (strip-cars alist)
(pairlis$ (strip-cdrs alist) nil)))
(dthm-inst (dterm-sublis alist (cdr thm-pair))))
(translate-proof1
dname
dterm
(cdr proof)
addr
bindings
revents
otherwise-term
(conjoin-dterms xhyp dthm-inst)
cnames
(cons `(:instance ,(car thm-pair)
,@subst)
use-hint)
nil
thm-pair)))
(t (mv `(er soft 'deft
"It is illegal to use INSTANTIATE except when it ~
immediately follows THEOREM or another INSTANTIATE.")
nil nil))))
(('Generalize . generalization-phrase)
(mv-let
(er-form new-hyps alist)
(generalization-phrasep
(dterm-all-vars dterm nil)
bindings generalization-phrase nil nil)
(cond
(er-form (mv er-form nil nil))
(t
(translate-proof1
dname dterm
`(,@(pairlis1 'Observe (pairlis-x2 new-hyps nil))
(Theorem
,(dterm-sublis
(pairlis$ (strip-cdrs alist) (strip-cars alist))
(implicate-dterms
(cond ((null new-hyps) xhyp)
((null (cdr new-hyps))
(conjoin-dterms xhyp (car new-hyps)))
(t (conjoin-dterms xhyp (cons 'and new-hyps))))
(dterm-concl dterm)))
:pass-bindings-downp
:proof ,(cdr proof))
(Instantiate
,@(pairlis$ (strip-cars alist)
(pairlis-x2 (strip-cdrs alist) nil))))
addr bindings revents otherwise-term xhyp cnames use-hint
consider-dterm thm-pair)))))
(('So-it-suffices-to-prove . rest)
(translate-proof1 dname dterm
(cons (cons 'so rest) (cdr proof))
addr bindings revents otherwise-term xhyp cnames use-hint
consider-dterm thm-pair))
(('So new-dterm)
(let ((new-dterm (dterm-sublis bindings new-dterm))
(goal-name-suff (packn `(* ,addr -sufficient)))
(goal-name (packn `(* ,addr))))
(mv-let (er-form event addr1)
(deft-fn goal-name-suff
(implicate-dterms new-dterm dterm)
(+ 2 addr)
bindings
`((:use . ,(revappend cnames (reverse use-hint)))
(:in-theory . 'nil))
nil
:default
nil)
(cond
(er-form (mv er-form nil nil))
(t (mv-let
(er-form revents addr2)
(translate-proof1
goal-name
new-dterm
(cdr proof)
addr1
bindings
(cons event revents)
otherwise-term
(dterm-hyp new-dterm)
nil nil nil nil)
(cond
(er-form (mv er-form nil nil))
(t
(mv-let (er-form event addr3)
(deft-fn dname
dterm
addr2
bindings
`((:use . (,goal-name-suff
,goal-name))
(:in-theory . 'nil))
nil
:default
nil)
(cond
(er-form (mv er-form nil nil))
(t (mv nil
(cons event revents)
addr3))))))))))))
(('Observe obs-dterm . h-alist)
(let* ((obs-dterm (dterm-sublis bindings obs-dterm))
(step-name (packn `(* ,addr)))
; See translate-proof2 for an explanation of this next part.
(pass-consider-dtermp
(and (consp h-alist)
(eq (car h-alist) :pass-consider-dtermp)))
(h-alist (if pass-consider-dtermp (cdr h-alist) h-alist)))
(mv-let
(er-form event addr1)
(deft-fn step-name
(implicate-dterms xhyp obs-dterm)
(1+ addr)
bindings
(convert-keyword-alist-to-alist bindings h-alist)
nil
:default
nil)
(cond
(er-form (mv er-form nil nil))
(t (translate-proof1
dname dterm
(cdr proof)
addr1
bindings
(cons event revents)
otherwise-term
(conjoin-dterms xhyp obs-dterm)
cnames
(cons step-name use-hint)
(if pass-consider-dtermp consider-dterm nil)
nil))))))
(('consider dterm1)
(translate-proof1
dname dterm (cdr proof) addr bindings
revents otherwise-term xhyp cnames use-hint
(dterm-sublis bindings dterm1)
nil))
(('= dterm1 . h-alist)
(translate-proof2 '= 'equal dterm1 h-alist
dname dterm proof addr bindings revents
otherwise-term xhyp cnames use-hint
consider-dterm thm-pair))
(('<-> dterm1 . h-alist)
(translate-proof2 '<-> 'iff dterm1 h-alist
dname dterm proof addr bindings revents
otherwise-term xhyp cnames use-hint
consider-dterm thm-pair))
(('-> dterm1 . h-alist)
(translate-proof2 '-> 'implies dterm1 h-alist
dname dterm proof addr bindings revents
otherwise-term xhyp cnames use-hint
consider-dterm thm-pair))
(('< dterm1 . h-alist)
(translate-proof2 '< '< dterm1 h-alist
dname dterm proof addr bindings revents
otherwise-term xhyp cnames use-hint
consider-dterm thm-pair))
(('<= dterm1 . h-alist)
(translate-proof2 '<= '<= dterm1 h-alist
dname dterm proof addr bindings revents
otherwise-term xhyp cnames use-hint
consider-dterm thm-pair))
(('> dterm1 . h-alist)
(translate-proof2 '> '> dterm1 h-alist
dname dterm proof addr bindings revents
otherwise-term xhyp cnames use-hint
consider-dterm thm-pair))
(('>= dterm1 . h-alist)
(translate-proof2 '>= '>= dterm1 h-alist
dname dterm proof addr bindings revents
otherwise-term xhyp cnames use-hint
consider-dterm thm-pair))
(& (mv `(er soft 'deft
"Unrecognized proof step, ~p0."
',proof-step)
nil nil)))))))
(defun translate-proof2 (symbol fn dterm1 h-alist
dname dterm proof addr bindings revents
otherwise-term xhyp cnames use-hint
consider-dterm thm-pair)
(declare (xargs :mode :program))
(declare (ignore thm-pair))
(cond
(consider-dterm
(let ((dterm1 (dterm-sublis bindings dterm1)))
(translate-proof1
dname dterm
; The :pass-consider-dtermp hack allows us to invoke Observe but tell it to pass
; the consider-dterm unchanged. Normally, Observe nulls out the
; consider-dterm. We pass in the instantiated dterm1 as the new consider-dterm
; and arrange for it to be passed on.
(cons `(Observe (,fn ,consider-dterm ,dterm1)
:pass-consider-dtermp . ,h-alist)
(cdr proof))
addr
bindings revents otherwise-term xhyp cnames use-hint
dterm1
nil)))
(t (mv `(er soft 'deft
"The ~p0 relation, as in (~p0 ~p1 ...), may be used only immediately after CONSIDER ~
or another ~p0 or similar relation."
',symbol
',dterm1)
nil nil))))
(defun translate-proof
(name dterm proof addr bindings rule-classes otf-flg doc)
(declare (xargs :mode :program))
(mv-let (er-form revents addr)
(translate-proof1 name
dterm
proof
addr
bindings
nil t
(dterm-hyp dterm)
nil nil nil nil)
(cond
(er-form (mv er-form nil nil))
(t (let* (
; The first element of revents -- the last to be generated -- is
; of the form (defthm name dterm :rule-classes nil :hints hints ...)
; and we are merely interested in the hints.
(hints (cadr (assoc-keyword :hints (cdddr (car revents)))))
(main
`(defthm ,name ,dterm
,@(and doc `(:doc ,doc))
,@(and (not (eq otf-flg :default))
`(:otf-flg ,otf-flg))
,@(and (not (eq rule-classes :default))
`(:rule-classes ,rule-classes))
,@(and hints
`(:hints ,hints))))
(local-events (reverse (cdr revents))))
(cond
((null local-events)
(mv nil main addr))
((null (cdr local-events))
(mv nil
`(encapsulate nil (local ,(car local-events)) ,main)
addr))
(t (mv nil
`(encapsulate nil
(local (encapsulate nil ,@local-events))
,main)
addr))))))))
(defun deft-fn (name term addr bindings h-alist rule-classes otf-flg doc)
(declare (xargs :mode :program))
(let ((proof (cdr (assoc-eq :proof h-alist))))
(cond
(proof
(let ((bad (assoc-keys-other-than '(:proof) h-alist)))
(cond
(bad
(mv `(er soft 'deft
"It is illegal to supply both a :PROOF hint and any other ~
proof-time advice. You supplied ~&1."
',bad)
nil nil))
(t (translate-proof name term
proof
addr
bindings
rule-classes otf-flg doc)))))
(t (let ((bad (assoc-keys-other-than
'(:proof ;;; if it was provided, it was nil
:in-theory
:enable
:disable
:use
:expand
:cases
:induct
:by
:restrict
:do-not
:do-not-induct
:hints)
h-alist))
(in-theory (cdr (assoc :in-theory h-alist)))
(enable (cdr (assoc :enable h-alist)))
(disable (cdr (assoc :disable h-alist)))
(use (cdr (assoc :use h-alist)))
(expand (cdr (assoc :expand h-alist)))
(cases (cdr (assoc :cases h-alist)))
(induct (cdr (assoc :induct h-alist)))
(by (cdr (assoc :by h-alist)))
(restrict (cdr (assoc :restrict h-alist)))
(do-not (cdr (assoc :do-not h-alist)))
(do-not-induct (cdr (assoc :do-not-induct h-alist)))
(hints (cdr (assoc :hints h-alist))))
(cond
(bad
(mv `(er soft 'deft
"Unrecognized keyword argument~#0~[~/s~], ~&0."
',(reverse bad))
nil nil))
((and (or (assoc-equal "Goal" hints)
(assoc-equal "goal" hints))
(or in-theory enable disable use expand cases induct by
restrict do-not do-not-induct))
(mv '(er soft 'deft
"It is not permitted to supply both a :HINTS argument for ~
\"Goal\" and any of :IN-THEORY, :ENABLE, :DISABLE, :USE, ~
:EXPAND, :CASES, :INDUCT, :RESTRICT, :BY, :DO-NOT, or ~
:DO-NOT-INDUCT (which are implicitly for \"Goal\") ~
because DEFT does not know how to combine hints.")
nil nil))
((and in-theory
(or enable disable))
(mv '(er soft 'deft
"It is not permitted to supply both an :IN-THEORY ~
argument and either of :ENABLE or :DISABLE, because DEFT ~
does not know how to combine theory hints.")
nil nil))
(t (mv
nil
`(defthm ,name ,term
,@(and doc `(:doc ,doc))
,@(and (not (eq otf-flg :default)) `(:otf-flg ,otf-flg))
,@(and (not (eq rule-classes :default))
`(:rule-classes ,rule-classes))
,@(and hints
(not (or in-theory enable disable
use expand cases restrict
induct by do-not do-not-induct))
`(:hints ,hints))
,@(and (or in-theory enable disable use expand cases
restrict induct by do-not do-not-induct)
`(:hints
(("Goal"
,@(and in-theory `(:in-theory ,in-theory))
,@(and (or enable disable)
`(:in-theory
(enable-disable
(,@(cond
((null enable) nil)
((or (atom enable)
(keywordp (car enable)))
(list enable))
(t enable)))
(,@(cond
((null disable) nil)
((or (atom disable)
(keywordp (car disable)))
(list disable))
(t disable))))))
,@(and use `(:use ,use))
,@(and expand `(:expand ,expand))
,@(and cases `(:cases ,cases))
,@(and restrict `(:restrict ,restrict))
,@(and induct `(:induct ,induct))
,@(and by `(:by ,by))
,@(and do-not `(:do-not ,do-not))
,@(and do-not-induct
`(:do-not-induct ,do-not-induct)))
,@hints))))
addr))))))))
)
(defun delete-null-cdrs (alist)
(declare (xargs :mode :program))
(cond ((atom alist) nil)
((null (cdar alist)) (delete-null-cdrs (cdr alist)))
(t (cons (car alist) (delete-null-cdrs (cdr alist))))))
(defmacro dft (&whole event-form name term
&key proof
doc
(rule-classes ':default)
(otf-flg ':default)
in-theory enable disable
use expand cases induct by restrict
do-not do-not-induct hints)
(declare (ignore event-form))
(mv-let (er-form event addr)
(deft-fn name term
1
nil
(delete-null-cdrs
`((:proof . ,proof)
(:in-theory . ,in-theory)
(:enable . ,enable)
(:disable . ,disable)
(:use . ,use)
(:expand . ,expand)
(:cases . ,cases)
(:induct . ,induct)
(:by . ,by)
(:restrict . ,restrict)
(:do-not . ,do-not)
(:do-not-induct . ,do-not-induct)
(:hints . ,hints)))
rule-classes
otf-flg
doc)
(declare (ignore addr))
(cond (er-form er-form)
(t event))))
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