; expander.lisp  --  symbolic expansion utilities for ACL2
; Copyright (C) 1997  Computational Logic, Inc.

; This book 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 book 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 book; if not, write to the Free Software
; Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.

; Originally written by Matt Kaufmann at Computational Logic, Inc.
; Although some attempt has been made to bring it up to date with ACL2
; Release 2.0, this file should be viewed as a set of routines that
; may prove useful in using ACL2 but _not_ as code that can be trusted
; to the extent that the ACL2 system prover may be trusted.

; For ACL2 3.0, removed symsim-for-value (not clear that it's been used for a
; long time).  And, we allow symsim to return multiple clauses.

; Top-level routines (only the first two have reasonable documentation):

; SYMSIM: See :doc string

; DEFTHM?: See :doc string

; TOOL1-FN: Takes a list of hypotheses and some hints and returns a simplified
; version, as a list of clauses.  Also returns a list of all runes used and a
; list of assumptions generated by forcing.

; TOOL2-FN: Takes a term and a list of hypotheses, together with some
; hints, and returns a term that is the result of rewriting the term
; under those hypotheses, using those hints.  Note that the hypotheses
; are used to build a context, using forward chaining and probably
; linear arithmetic as well, but are not simplified.  This tool also
; sends back a list of runes.

; Changes by Daron Vroon on June 4, 2007:

; TOOL1-FN and TOOL2-FN have now each been split into 2 functions: a
; "front end" that calculates the ctx, ens, and wrld to use, along
; with some other calculations, and a "back end" that uses the ctx,
; ens, and wrld to do what the original function did. The
; functionality of TOOL1-FN and TOOL2-FN have not been changed, and
; users of these functions should notice no difference.

; Splitting these functions in two allowed for the definition of two
; new functions, TOOL1-FN0 and TOOL2-FN0. These perform the same task
; as TOOL1-FN and TOOL2-FN, respectively, with one difference: the
; user must supply the ctx, ens, and wrld. This is helpful to people
; who want to simplify expressions in the midst of making other
; changes that require a modified world or a user-defined ctx.

; To certify this book:
; (certify-book "expander").

(in-package "ACL2")

; The following deflabel is placed here primarily to provide a section in which
; to hang documentation.
(deflabel expander :doc
 ":Doc-Section Expander

  routines for simplifying terms~/

  The routines provided by the expander can be useful in generating
  theorems and simplifying expressions, under given assumptions.~/

  They were developed rather in a hurry and should be used without
  expecting the usual standards of care present in development of ACL2
  code.  Once these routines are used to generate theorems for you,
  you should check the theorems directly with ACL2.~/")

; We know what we are doing when using state:
(set-state-ok t)

(encapsulate
 ((hidden-expander-function (x) t))
 (logic)
 (local (defun hidden-expander-function (x) x)))

(defun silly-rec-fn-for-rewrite* (x)
  (if (consp x)
      (silly-rec-fn-for-rewrite* (cdr x))
    x))

(verify-guards silly-rec-fn-for-rewrite*)

(program)

(defconst *valid-output-names-except-error*
  (set-difference-eq *valid-output-names* '(error)))

(defmacro tool1 (hyps &key hints (prove-assumptions 't) inhibit-output)
  `(er-progn (tool1-fn ',hyps state ',hints ',prove-assumptions
                       ',inhibit-output
                       t t)
             (value :invisible)))

(defun pop-clauses (pool)
  (mv-let (signal pool-lst cl-set hint-settings pop-history new-pool)
          (pop-clause1 pool nil)
          (declare (ignore pool-lst hint-settings pop-history))
          (cond
           ((or (eq signal 'win) (eq signal 'lose))
            (mv signal cl-set))
           (t
            (mv-let (signal rest-clauses)
                    (pop-clauses new-pool)
                    (cond
                     ((eq signal 'win) (mv 'win (append cl-set rest-clauses)))
                     (t (mv signal nil))))))))

(defun prove-loop1-clauses (pool-lst clauses pspv hints ens wrld ctx state)

; Based on prove-loop1, except returns (mv erp ttree clauses pairs
; new-pspv state), where pairs is a list of pairs (assumnotes
; . clause), suitable for the third argument of prove-loop1 starting
; with forcing round 1.

  (mv-let (erp pspv jppl-flg state)
          (waterfall 0 pool-lst clauses pspv hints ens wrld ctx state)
          (declare (ignore jppl-flg))
          (cond
           (erp (mv t nil nil nil nil state))
           (t
            (mv-let
             (signal new-clauses)
             (pop-clauses (access prove-spec-var pspv :pool))
             (cond
              ((eq signal 'lose)
               (mv t nil nil nil nil state))
              (t
               (mv-let
                (pairs new-pspv state)

; Forcing round...

                (process-assumptions 0 pspv wrld state)
                (mv-let
                 (erp ttree state)
                 (accumulate-ttree-into-state
                  (access prove-spec-var new-pspv :tag-tree)
                  state)
                 (assert$
                  (null erp)
                  (mv nil ttree new-clauses pairs new-pspv
                      state)))))))))))

(defun prove-loop-clauses (clauses pspv hints ens wrld ctx state)

; We either cause an error or return a ttree.  If the ttree contains
; :byes, the proof attempt has technically failed, although it has
; succeeded modulo the :byes.

  (pprogn
   (increment-timer 'other-time state)
   (mv-let (erp ttree new-clauses pairs new-pspv state)
           (prove-loop1-clauses nil
                                clauses
                                pspv
                                hints ens wrld ctx state)
           (pprogn
            (increment-timer 'prove-time state)
            (cond
             (erp (mv erp nil nil nil nil state))
             (t (mv nil ttree new-clauses pairs new-pspv state)))))))

(defun prove-clauses (term pspv hints ens wrld ctx state)

; Adapted from prove.

  (prog2$
   (initialize-brr-stack state)
   (mv-let (erp ttree1 clauses pairs new-pspv state)
           (prove-loop-clauses (list (list term))
                               (change prove-spec-var pspv
                                       :user-supplied-term term
                                       :orig-hints hints)
                               hints ens wrld ctx state)
           (cond
            (erp (mv t nil nil nil nil state))
            (t
             (mv-let
              (erp val state)
              (chk-assumption-free-ttree ttree1 ctx state)
              (declare (ignore val))
              (cond
               (erp (mv t nil nil nil nil state))
               (t (pprogn
                   (cond
                    ((tagged-object :bye ttree1)
                     (let ((byes (reverse (tagged-objects :bye ttree1
                                                          nil))))
                       (pprogn

; The use of ~*1 below instead of just ~&1 forces each of the defthm
; forms to come out on a new line indented 5 spaces.  As is already
; known with ~&1, it can tend to scatter the items randomly -- some on
; the left margin and others indented -- depending on where each item
; fits flat on the line first offered.

                        (io? prove nil state
                             (wrld byes)
                             (fms "To complete this proof you should try to ~
                                   admit the following ~
                                   event~#0~[~/s~]~|~%~*1~%See the discussion ~
                                   of :by hints in :DOC hints regarding the ~
                                   name~#0~[~/s~] displayed above."
                                  (list (cons #\0 byes)
                                        (cons #\1
                                              (list ""
                                                    "~|~     ~q*."
                                                    "~|~     ~q*,~|and~|"
                                                    "~|~     ~q*,~|~%" 
                                                   
                                                    (make-defthm-forms-for-byes
                                                     byes wrld))))
                                  (proofs-co state)
                                  state
                                  nil))
                        state)))
                    (t state))
                   (mv erp ttree1 clauses pairs
                       (change prove-spec-var new-pspv
                               :pool nil)
                       state))))))))))

(defun chk-for-hidden-expander-function1 (cl)
  (let ((term (car (last cl))))
    (case-match term
                (('hide ('hidden-expander-function &))
                 term)
                (t
                 (er hard 'chk-for-hidden-expander-function1
                     "Expected clause to end with hidden call of ~
                      HIDDEN-EXPANDER-FUNCTION, but instead clause is ~p0."
                     cl)))))

(defun chk-for-hidden-expander-function (clauses)
  (cond ((null clauses) nil)
        (t (and (chk-for-hidden-expander-function1 (car clauses))
                (chk-for-hidden-expander-function (cdr clauses))))))

(defun untranslate-clause-lst (cl-lst wrld)
  (cond
   ((null cl-lst)
    nil)
   (t
    (cons (prettyify-clause1 (car cl-lst) wrld)
          (untranslate-clause-lst (cdr cl-lst) wrld)))))

(defun tool1-print (print-flg runes clauses state)
  (cond
   (print-flg
    (fms "~%***OUTPUT OF TOOL1***~%~%Tag tree:~%  ~p0~%~%List of simplified ~
          hypotheses:~%  ~p1~|~%"
         (list (cons #\0 runes)
               (cons #\1
                     (untranslate-clause-lst clauses (w state))))
         *standard-co* state nil))
   (t state)))

(defun hide-special-hyps (lst)
  "We do this stuff so that equalities and SYNP hyps won't be thrown out.
   Perhaps what we really need is a hyp simplifier with less aggressive
   heuristics." 
  (cond
   ((null lst) nil)
   (t (let ((hyp (car lst)))
        (let ((new-hyp
               (case-match hyp
                 (('equal x y)
                  (let ((x1 (if (variablep x)
                                (list 'hide x)
                              x))
                        (y1 (if (variablep y)
                                (list 'hide y)
                              y)))
                    (list 'equal x1 y1)))
                 (('synp . x) (list 'hide (cons 'synp x)))
                 (& hyp))))
          (cons new-hyp (hide-special-hyps (cdr lst))))))))

(defun fix-special-hyps (lst)
  (cond
   ((null lst) nil)
   (t (let ((hyp (car lst)))
        (let ((new-hyp
               (case-match hyp
                           (('not ('equal ('hide x) ('hide y)))
                            (list 'not (list 'equal x y)))
                           (('not ('equal ('hide x) y))
                            (list 'not (list 'equal x y)))
                           (('not ('equal y ('hide x)))
                            (list 'not (list 'equal y x)))
                           (('not ('hide ('synp . x)))
                            (list 'not (cons 'synp x)))
                           (& hyp))))
          (cons new-hyp (fix-special-hyps (cdr lst))))))))

(defun remove-hidden-terms (cl-set)
  (cond
   ((null cl-set)
    nil)
   (t (cons (fix-special-hyps (butlast (car cl-set) 1))
            (remove-hidden-terms (cdr cl-set))))))

(defun add-key-val-pair-to-key-val-alist (key key1 val alist)
  ;; adapted from ACL2 function add-to-set-equal-in-alist
  (cond ((null alist) (list (list key key1 val)))
        ((equal key (caar alist))
         (cons (list* key key1 val (cdar alist))
               (cdr alist)))
        (t (cons (car alist)
                 (add-key-val-pair-to-key-val-alist key key1 val (cdr
                                                                  alist))))))

(defun remove-hidden-expander-term-from-cl (cl)
  (cond ((endp cl) nil)
        (t (let ((term (car cl)))
             (case-match term
               (('HIDE ('HIDDEN-EXPANDER-FUNCTION &))
                (cdr cl))
               (& (cons (car cl)
                        (remove-hidden-expander-term-from-cl (cdr cl)))))))))

(defun remove-hidden-expander-term-from-cl-list (cl-list)
  (cond ((endp cl-list)
         nil)
        (t (cons (remove-hidden-expander-term-from-cl (car cl-list))
                 (remove-hidden-expander-term-from-cl-list (cdr cl-list))))))

(defun get-assns (ttree remove-hidden)
  (cond (remove-hidden
         (remove-hidden-expander-term-from-cl-list
          (reverse (strip-cdrs (tagged-objects :bye ttree nil)))))
        (t
         (reverse (strip-cdrs (tagged-objects :bye ttree nil))))))

(defun tool1-fn1 (hyps ctx ens wrld state hints prove-assumptions inhibit-output
                       translate-flg print-flg)

; Returns error triple with value (list* runes clauses assumptions), where
; assumptions is nil if prove-assumptions is t (because they must be proved) or
; nil (because they are ignored).

  (er-let* ((hints (if (alistp hints)
                       (value (add-key-val-pair-to-key-val-alist
                               "Goal"
                               ;; only preprocess and simplify are allowed 
                               :do-not
                               (list 'quote '(generalize
                                              eliminate-destructors
                                              fertilize
                                              eliminate-irrelevance))
                               hints))
                     (er soft ctx
                         "The hints must be an alist, but ~p0 is not."
                         hints)))
            (thints (translate-hints 'tool1 hints ctx wrld state))
            (thyps0
             (if translate-flg
                 (translate-term-lst hyps t t t ctx wrld state)
               (value hyps)))
            (thyps
             (value (hide-special-hyps thyps0)))
            (vars
             (value (all-vars1-lst thyps nil)))
            (tconc
             (translate (list 'hide
                              (list 'hidden-expander-function
                                    (cons 'list vars)))
                        t t t  ctx wrld state))
            (tterm (value (implicate (conjoin thyps) tconc)))) 
           (mv-let
            (erp ttree clauses pairs new-pspv state)
            (prove-clauses tterm
                           (make-pspv ens wrld
                                      :displayed-goal
                                      (untranslate tterm t wrld)
                                      :otf-flg t)
                           thints ens wrld ctx state)
            (prog2$
             (chk-for-hidden-expander-function clauses)
             (cond
              (erp
               (mv erp nil state))
              (prove-assumptions
               (er-let* ((thints
                          (if (eq prove-assumptions t)
                              (value thints)
                            (translate-hints 'tool1
                                             *bash-skip-forcing-round-hints*
                                             ctx wrld state))))
                        (state-global-let*
                         ((inhibit-output-lst
                           (if (eq prove-assumptions t)
                               (@ inhibit-output-lst)
                             (if (eq inhibit-output :prove)
                                 (remove1-eq 'prove (@ inhibit-output-lst))
                               (@ inhibit-output-lst)))))
                         (er-let*
                          ((new-ttree
                            (prove-loop1 1 nil pairs new-pspv
                                         thints ens wrld ctx state)))
                          (let ((runes (all-runes-in-ttree
                                        new-ttree
                                        (all-runes-in-ttree ttree nil)))
                                (assumptions (get-assns new-ttree t)))
                            (pprogn
                             (tool1-print print-flg runes clauses state)
                             (value (list* runes
                                           (dumb-negate-lit-lst-lst
                                            (remove-hidden-terms clauses))
                                           assumptions))))))))
              (t (let ((runes (all-runes-in-ttree ttree nil)))
                   (pprogn
                    (tool1-print print-flg runes clauses state)
                    (value (list* runes
                                  (dumb-negate-lit-lst-lst
                                   (remove-hidden-terms clauses))
                                  nil))))))))))

(defun tool1-fn (hyps state hints prove-assumptions inhibit-output
                      translate-flg print-flg)

; Returns error triple with value (list* runes clauses assumptions), where
; assumptions is nil if prove-assumptions is t (because they must be proved) or
; nil (because they are ignored).

  (state-global-let*
   ((ld-skip-proofsp nil)
    (inhibit-output-lst
     (if inhibit-output
         (if (eq inhibit-output :prove)
             (union-eq '(proof-tree prove) (@ inhibit-output-lst))
           *valid-output-names-except-error*)
       (@ inhibit-output-lst))))
   (with-ctx-summarized
    "( TOOL1 ...)"
    (let ((wrld (w state))
          (ens (ens state)))
      (tool1-fn1 hyps ctx ens wrld state hints prove-assumptions inhibit-output
                      translate-flg print-flg)))))

(defun tool1-fn0 (hyps ctx ens wrld state hints prove-assumptions inhibit-output
                       translate-flg print-flg)

; same as tool1-fn, except the user must supply their own wrld, ens, and ctx.

  (state-global-let*
   ((ld-skip-proofsp nil)
    (inhibit-output-lst
     (if inhibit-output
         (if (eq inhibit-output :prove)
             (union-eq '(proof-tree prove) (@ inhibit-output-lst))
           *valid-output-names-except-error*)
       (@ inhibit-output-lst))))
   (tool1-fn1 hyps ctx ens wrld state hints prove-assumptions inhibit-output
              translate-flg print-flg)))

;;;;;;; Tool 2

(defmacro tool2 (term hyps
                      &key hints equiv (prove-assumptions 't) inhibit-output)
  `(tool2-fn ',term ',hyps ',equiv state ',hints ',prove-assumptions
             ',inhibit-output t t))

(defun tool2-print (print-flg runes rewritten-term state)
  (cond
   (print-flg
    (fms "~%***OUTPUT OF TOOL2***~%~%Tag tree:~%  ~p0~%~%Rewritten term:~% ~
          ~p1~|~%"
         (list (cons #\0 runes)
               (cons #\1 (untranslate rewritten-term nil (w state))))
         *standard-co* state nil))
   (t state)))

(defun expander-repeat-limit (state)
  (if (f-boundp-global 'expander-repeat-limit state)
      (f-get-global 'expander-repeat-limit state)
    3))

(defun rewrite* (term hyps ctx
                      repeat-limit
                      completed-iterations
                      ;; alist bkptr
                      ;; &extra formals
                      type-alist
                      ;; obj
                      geneqv wrld state
                      ;; fnstack ancestors
                      simplify-clause-pot-lst
                      rcnst gstack ttree)

; Rewrite term repeatedly, (- repeat-limit completed-iterations) times.  Note
; that hyps is T after the first time through.

  (mv-let (val new-ttree)
          (rewrite-entry (rewrite term nil 1)
                         :obj '?
                         :fnstack 
; We want to fool rewrite-fncall on lambdas.
                         '(silly-rec-fn-for-rewrite*)
                         :pre-dwp nil  ;; RBK:
                         :ancestors nil
                         :backchain-limit 500
                         :rdepth (rewrite-stack-limit wrld))
          (cond
           ((equal val term)
            (cond
             ((eq hyps t)
              (mv term ttree state))
             (t (er soft ctx
                    "The term~%  ~p0~%failed to rewrite to a new term under ~
                     hypotheses~%  ~p1."
                    (untranslate val nil wrld)
                    (untranslate-lst hyps t wrld)))))
           ((= repeat-limit completed-iterations)
            (pprogn
             (fms "OUT OF PATIENCE!  Completed ~n0 iterations."
                  (list (cons #\0 (list completed-iterations)))
                  *standard-co* state nil)
             (mv val new-ttree state)))
           (t (pprogn (if (eql completed-iterations 0)
                          state
                        (fms "NOTE:  Starting ~n0 repetition of rewrite.~%"
                             (list (cons #\0 (list (1+ completed-iterations))))
                             *standard-co* state nil))
                      (rewrite* val t ctx
                                repeat-limit
                                (1+ completed-iterations)
                                type-alist geneqv wrld state
                                simplify-clause-pot-lst rcnst gstack
                                new-ttree))))))

(defun tool2-fn1
  (term hyps equiv ctx ens wrld state thints prove-assumptions
        inhibit-output translate-flg print-flg)

; Returns error triple with value (list* runes rewritten-term assumptions).
; But assumptions is nil if prove-assumptions is nil (we don't collect them) or
; is t (we insist that all forced assumptions be proved).

  (let* ((saved-pspv (make-pspv ens wrld
                                :displayed-goal term ; from, e.g., thm-fn
                                :user-supplied-term term ;from, e.g., prove
                                :orig-hints thints))) ;from, e.g., prove
    (er-let*
     ((thyps (if translate-flg
                 (translate-term-lst hyps t t t ctx wrld state)
               (value hyps)))
      (tterm (if translate-flg
                 (translate term t t t ctx wrld state)
               (value term))))
     (mv-let                            ;from waterfall1
      (erp pair state)
      (find-applicable-hint-settings
       *initial-clause-id*
       (add-literal tterm (dumb-negate-lit-lst thyps) t)
       nil saved-pspv ctx
       thints thints wrld nil state)
      (cond
       (erp (silent-error state))
       (t
        (let ((hint-settings (car pair))
              (thints (cdr pair)))
          (pprogn
           (cond ((null hint-settings)
                  state)
                 (t (thanks-for-the-hint nil state))) ;BB
           (er-let* ((pspv (load-hint-settings-into-pspv
                            t hint-settings saved-pspv wrld ctx state)))
                    (cond
                     ((intersectp-eq
                       '(:do-not-induct :do-not :induct :use :cases :by)
                       (strip-cars hint-settings))
                      (er soft ctx
                          "It makes no sense for TOOL2 to be given hints ~
                                for \"Goal\" that include any of ~
                                :do-not-induct, :do-not,:induct, :use, ~
                                :cases, or :by.  The hint ~p0 is therefore ~
                                illegal."
                          (cons "Goal" hint-settings)))
                     (t
                      (pprogn
                       (initialize-proof-tree ;from waterfall
                        *initial-clause-id*
                        (list (list (implicate (conjoin thyps) tterm)))
                        ctx
                        state)
                       (let*            ;from simplify-clause1
                           ((current-clause (dumb-negate-lit-lst thyps))
                            (rcnst
                             (change rewrite-constant
                                     (access prove-spec-var pspv :rewrite-constant)
                                     :force-info
                                     (if (ffnnamep-lst 'if current-clause)
                                         'weak
                                       t)))
                            (pts 
                             ;; (current-clause-pts (enumerate-elements current-clause 0))
                             nil))
                         (mv-let        ;from simplify-clause1
                          (contradictionp type-alist fc-pair-lst)
                          (forward-chain current-clause
                                         pts
                                         (access rewrite-constant
                                                 rcnst :force-info)
                                         nil wrld ens
                                         (access rewrite-constant rcnst
                                                 :oncep-override)
                                         state)
                          (declare (ignore fc-pair-lst))
                          (cond
                           (contradictionp
                            (er soft ctx
                                "Contradiction found in hypotheses~%  ~
                                      ~p0~%using type-set reasoning!"
                                hyps))
                           (t
                            (mv-let     ;from simplify-clause1
                             (contradictionp simplify-clause-pot-lst)
                             (setup-simplify-clause-pot-lst current-clause
                                                            (pts-to-ttree-lst 
                                                             pts)
                                                            nil ; fc-pair-lst  ;; RBK:
                                                            type-alist
                                                            rcnst
                                                            wrld state)
                             (cond
                              (contradictionp
                               (er soft ctx
                                   "Contradiction found in hypotheses~%  ~
                                         ~p0~%using linear reasoning!"
                                   hyps))
                              (t

                                        ; We skip the call of process-equational-polys in simplify-clause1; I think
                                        ; that we can assume that by the time tool2 is called, that call wouldn't have
                                        ; any effect anyhow.  By the way, we skipped remove-trivial-equivalence
                                        ; earlier.

                                        ; Now we continue as in rewrite-clause.

                               (mv-let
                                (not-flg atm)
                                (strip-not tterm)
                                (let ((local-rcnst
                                       (change rewrite-constant rcnst
                                               :current-literal
                                               (make current-literal
                                                     :not-flg not-flg
                                                     :atm atm)))
                                      (gstack (initial-gstack 'simplify-clause
                                                              nil current-clause)))
                                  (mv-let
                                   (val ttree state)
                                   (rewrite* atm hyps ctx
                                             (expander-repeat-limit state)
                                             0
                                             type-alist
                                             (cadr (car (last (getprop
                                                               equiv
                                                               'congruences
                                                               nil
                                                               'current-acl2-world
                                                               wrld))))
                                             wrld state
                                             simplify-clause-pot-lst rcnst gstack
                                             nil)
                                   (cond
                                    ((equal val t)
                                     (mv t nil state))
                                    (t
                                     (mv-let
                                      (bad-ass ttree)
                                      (resume-suspended-assumption-rewriting
                                       ttree
                                       nil
                                       gstack
                                       simplify-clause-pot-lst
                                       local-rcnst
                                       wrld
                                       state)
                                      (cond
                                       (bad-ass
                                        (er soft ctx
                                            "Generated false assumption, ~
                                                  ~p0!  So, rewriting is ~
                                                  aborted, just as it would ~
                                                  be in the course of a ~
                                                  regular Acl2 proof."
                                            bad-ass))
                                       (t
                                        (let ((rewritten-term
                                               (if not-flg
                                                   (dumb-negate-lit val)
                                                 val)))
                                          (cond
                                           (prove-assumptions
                                            (mv-let
                                             (pairs pspv state)
                                             (process-assumptions
                                              0
                                              (change prove-spec-var saved-pspv
                                                      :tag-tree
                                                      (set-cl-ids-of-assumptions
                                                       ttree *initial-clause-id*))
                                              wrld state)
                                             (er-let*
                                              ((ttree
                                                (accumulate-ttree-into-state
                                                 (access prove-spec-var pspv :tag-tree)
                                                 state))
                                               (thints
                                                (if (eq prove-assumptions t)
                                                    (value thints)
                                                  (translate-hints 'tool2
                                                                   *bash-skip-forcing-round-hints*
                                                                   ctx wrld state))))
                                              (er-progn
                                               (state-global-let*
                                                ((inhibit-output-lst
                                                  (if (or (eq prove-assumptions t)
                                                          (eq inhibit-output t))
                                                      (@ inhibit-output-lst)
                                                    (if (eq inhibit-output
                                                            :prove)
                                                        (remove1-eq
                                                         'prove
                                                         (@ inhibit-output-lst))
                                                      (@ inhibit-output-lst)))))
                                                (er-let*
                                                 ((new-ttree
                                                   (prove-loop1 1 nil pairs pspv
                                                                thints ens wrld
                                                                ctx state)))
                                                 (let* ((runes
                                                         (all-runes-in-ttree
                                                          new-ttree
                                                          (all-runes-in-ttree
                                                           ttree nil)))
                                                        (byes (get-assns
                                                               new-ttree
                                                               nil))
                                                        (val (list* runes
                                                                    rewritten-term
                                                                    byes)))
                                                   (pprogn (tool2-print print-flg runes
                                                                        rewritten-term state)
                                                           (f-put-global 'tool2-error
                                                                         nil state)
                                                           (f-put-global
                                                            'tool2-result
                                                            val
                                                            state)
                                                           (value val)))))))))
                                           (t (let* ((runes (all-runes-in-ttree
                                                             ttree nil))
                                                     (val (list* runes
                                                                 rewritten-term
                                                                 nil)))
                                                (pprogn
                                                 (tool2-print print-flg runes
                                                              rewritten-term
                                                              state)
                                                 (f-put-global 'tool2-error
                                                               nil state)
                                                 (f-put-global
                                                  'tool2-result
                                                  val
                                                  state)
                                                 (value val)))))))))))))))))))))))))))))))))

(defun tool2-fn
  (term hyps equiv state hints prove-assumptions inhibit-output translate-flg
        print-flg)

; Returns error triple with value (list* runes rewritten-term assumptions).
; But assumptions is nil if prove-assumptions is nil (we don't collect them) or
; is t (we insist that all forced assumptions be proved).

  (let ((ctx 'TOOL2))
    (state-global-let*
     ((inhibit-output-lst
       (if inhibit-output
           (if (eq inhibit-output :prove)
               (union-eq '(proof-tree prove) (@ inhibit-output-lst))
             *valid-output-names-except-error*)
         (@ inhibit-output-lst))))
     (prog2$
      (initialize-brr-stack state)
      (er-let*
       ((wrld (value (w state)))
        (thints (translate-hints 'tool2 hints ctx wrld state)))
       (let ((ens (ens state)))
         (tool2-fn1 term hyps equiv ctx ens wrld state thints prove-assumptions
                    inhibit-output translate-flg print-flg)))))))

(defun tool2-fn0
  (term hyps equiv ctx ens wrld state hints prove-assumptions
        inhibit-output translate-flg print-flg)

; Same as tool2-fn, except the user must supply the ctx, ens, and wrld.

  (state-global-let*
   ((inhibit-output-lst
     (if inhibit-output
         (if (eq inhibit-output :prove)
             (union-eq '(proof-tree prove) (@ inhibit-output-lst))
           *valid-output-names-except-error*)
       (@ inhibit-output-lst))))
   (prog2$
    (initialize-brr-stack state)
    (er-let* 
     ((thints (translate-hints 'tool2 hints ctx wrld state)))
     (tool2-fn1 term hyps equiv ctx ens wrld state thints prove-assumptions
                inhibit-output translate-flg print-flg)))))

;;;;;;; Hooking them together

(defun tool2-fn-lst
  (term runes hyps-lst assns equiv state hints prove-assumptions inhibit-output
        print-flg)

; Returns the result of mapping tool2-fn over the list hyps-lst, pairing each
; result with the corresponding member of hyps-lst.  Assumes hyps-lst is
; already translated.  The value returned is actually a list of tuples
; (list* runes hyps rewritten-term assumptions).

  (cond
   ((null hyps-lst)
    (value nil))
   (t
    (mv-let
     (erp x state)
     (tool2-fn term (car hyps-lst) equiv state hints prove-assumptions
               inhibit-output nil print-flg)
     (cond
      (erp
       (tool2-fn-lst term runes (cdr hyps-lst) assns equiv state
                     hints prove-assumptions inhibit-output print-flg))
      (t
       (er-let*
        ((rst (tool2-fn-lst term runes (cdr hyps-lst) assns equiv
                            state
                            hints prove-assumptions inhibit-output print-flg)))
        (value (cons (list* (union-equal runes (car x))
                            (car hyps-lst)
                            (cadr x)
                            (union-equal assns (cddr x)))
                     rst)))))))))

(defun simplify-hyps
  (remaining-hyps rewritten-previous-hyps-rev runes assns equiv state hints
                  prove-assumptions inhibit-output print-flg)

; Returns the result of mapping tool2-fn over each hyp in remaining-hyps, where
; the hyps in rewritten-previous-hyps-rev and (cdr remaining-hyps) are assumed.
; Assumes all hyps are already translated.  The value returned is actually a
; list (list* runes (list rewritten-hyp-list) assumptions).

  (cond
   ((null remaining-hyps)
    (value (list* runes (list (reverse rewritten-previous-hyps-rev)) assns)))
   (t (er-let*
       ((x (tool2-fn (car remaining-hyps)
                     (revappend rewritten-previous-hyps-rev
                                (cdr remaining-hyps))
                     equiv state hints prove-assumptions
                     inhibit-output nil print-flg)))
       (simplify-hyps (cdr remaining-hyps)
                      (cons (cadr x) rewritten-previous-hyps-rev)
                      (union-equal (car x) runes)
                      (union-equal (cddr x) assns)
                      equiv state hints prove-assumptions inhibit-output
                      print-flg)))))

(defun tool-fn
  (term hyps simplify-hyps-p equiv state hints prove-assumptions inhibit-output
        print-flg ctx)

; Term and hyps are in translated form.  Returns a list of tuples
; (list* runes hyps rewritten-term assumptions).

  (er-let* ((runes-hyps-assns
             (cond
              ((eq simplify-hyps-p :no-split)
               (simplify-hyps hyps nil nil nil equiv state hints
                              prove-assumptions inhibit-output print-flg))
              ((eq simplify-hyps-p t)
               (tool1-fn hyps state hints prove-assumptions inhibit-output
                         nil print-flg))
              (simplify-hyps-p
                (value (er hard 'tool-fn
                           "Bad :simplify-hyps-p argument (should be ~v0): ~x1"
                           (list t nil :no-split)
                           simplify-hyps-p)))
              (t (value (list* nil (list hyps) nil))))))
           (cond
            ((null (cdr runes-hyps-assns))
             (er soft ctx
                 "It does not make sense to simplify the term ~p0, because the ~
                  hypothesis list ~p1 is contradictory."
                 (untranslate term nil (w state))
                 (untranslate-lst hyps t (w state))))
            (t
             (pprogn
              (cond (print-flg
                     (fms "***NOTE***:  Starting TOOL2.~%" nil *standard-co* state nil))
                    (t state))
              (er-let*
               ((x (tool2-fn-lst term
                                 (car runes-hyps-assns)
                                 (cadr runes-hyps-assns)
                                 (cddr runes-hyps-assns)
                                 equiv state hints prove-assumptions
                                 inhibit-output print-flg)))
               (cond
                ((not (= (length x) (length (cadr runes-hyps-assns))))
                 (er soft ctx
                     "Unable to successfully simplify term~%  ~p0~%and ~
                      hypotheses~%  ~p1 in every case generated."
                     (untranslate term nil (w state))
                     (untranslate-lst hyps t (w state))))
                (x (value x))
                (t (er soft ctx
                       "No theorems were suggested for term~%  ~p0~%and ~
                        hypotheses~%  ~p1.")))))))))

(defmacro defthm?
  (name term &key hints (prove-assumptions 't) (simplify-hyps-p 't) print-flg)

  ":Doc-Section Expander

  generate a theorem~/
  ~bv[]
  Example:
  (defthm? app-simplify
    (implies (true-listp x)
             (equal (append x y)
                    ?))
    :hints ((\"Goal\" :expand ((true-listp x)
                             (true-listp (cdr x))
                             (append x y))))
    ; show some output
    :print-flg t)
  ~ev[]~/

  General Forms:
  (DEFTHM? name
    (IMPLIES hyps (equiv term ?))
    :hints             hints
    :prove-assumptions prove-flg ; t or nil, default t
    :print-flg         print-flg ; t or nil, default nil
    :simplify-hyps-p   flg       ; t, nil, or :no-split; default t
  )

  (DEFTHM? name
    (equiv term ?)
    :hints             hints
    :prove-assumptions prove-flg ; t or nil, default t
    :print-flg         print-flg ; t or nil, default nil
    :simplify-hyps-p   flg       ; t, nil, or :no-split; default t
  )
  ~ev[]
  where ~c[name] is a new symbolic name (~pl[name]), ~c[term] is a
  term to be simplified assuming ~c[hyps] is true, and ~ilc[hints] is
  as described in its ~il[documentation].  The four keyword arguments
  above are all optional, and behave as you might expect.  In particular, set
  ~c[:simplify-hyps-p] to ~c[nil] if you do not want the ~c[hyps] to be
  simplified; otherwise, case splitting may occur in the course of their
  simplification.

  If the given ~c[term] cannot be simplified, then the event fails.
  Otherwise, the result is an ~ilc[encapsulate] event with one or more
  ~ilc[defthm] events of the form of the theorem, except with ~c[hyps]
  simplified (and even omitted if simplified to ~c[t]) and ~c[term]
  simplified under the assumption that ~c[hyps] is true.  The reason
  that there can be more than one ~ilc[defthm] event is that ~c[hyps] may
  simplify to an expression that generates a case split, for example
  if it simplifies to an ~ilc[if] expression that does not represent a
  conjunction.

  In general, simplification may generate assumptions because of
  ~ilc[force].  By default, an attempt is made to prove these
  assumptions, which must succeed or else this event fails.  However,
  if ~c[:prove-assumptions] is ~c[nil], then roughly speaking, no
  proof of forced hypotheses is attempted until after simplification
  is complete.  The documentation of :prove-assumptions is admittedly
  weak here; feel free to experiment.

  Also ~pl[symsim].

  Here are some examples, including the one above.  Try them out and
  see what happens.
  ~bv[]

  ; Doesn't simplify, so fails:
  (defthm? app-simplify
    (implies (true-listp x)
             (equal (append x y)
                    ?))
    :hints ((\"Goal\" :expand (true-listp x))))

  :pbt 0

  ; The following creates one event, but maybe we'd prefer cases to be
  ; broken out into separate events.  That comes next.
  (defthm? app-simplify
    (implies (true-listp x)
             (equal (append x y)
                    ?))
    :hints ((\"Goal\" :expand (append x y))))

  :pbt 0
  :pe :here
  :pe APP-SIMPLIFY
  :u

  (defthm? app-simplify
    (implies (true-listp x)
             (equal (append x y)
                    ?))
    :hints ((\"Goal\" :expand ((true-listp x)
                             (true-listp (cdr x))
                             (append x y))))
    ; show some extra output; this is optional
    :print-flg t)

  :pe :here
  :u
  ~ev[]~/"

  (let* ((form0
          `(defthm?-fn ',name ',term ',simplify-hyps-p ',hints
             ',prove-assumptions ',print-flg (w state) state))
         (form `(er-let* ((val ,form0))
                         (pprogn (f-put-global 'defthm?-result val state)
                                 (value :invisible)))))
                       
    `(state-global-let*
      ((defthm?-result nil))
      (er-progn (ld '(,form)
                    :ld-pre-eval-print nil
                    :ld-prompt nil)
                (value (f-get-global 'defthm?-result state))))))

; This is new in 8/97.  If we don't include executable counterparts of some
; functions, one of the examples in the documentation fails to simplify.
; Try the following.  If you define *adjust-hints-exec-theory* to be nil
; instead, the defthm? will still fail, but it will get more stuck in the
; final proof attempt than it should.
#|
(defthm true-listp-expand-append
  (implies (and (force (true-listp x))
                x)
           (equal (append x y)
                  (cons (car x) (append (cdr x) y)))))
(defthm? foo (implies (consp x) (equal (append X Y) ?))
  :prove-assumptions nil)
|#
(defconst *adjust-hints-exec-theory*
  '(definition-runes
     (union-eq '(iff) *expandable-boot-strap-non-rec-fns*)
     t
     world))

(defun adjust-hints-with-runes1 (hint runes)

; hint is an alternating list of keywords and hints, e.g.,
; (:expand (foo x) :in-theory *s-prop-theory*)

  (cond
   ((null hint)
    (list :in-theory
          (list 'union-theories
                *adjust-hints-exec-theory*
                (list 'quote runes))))
   ((eq (car hint) :in-theory)
    (list* :in-theory
           (list 'union-theories
                 *adjust-hints-exec-theory*
                 `(intersection-theories ',runes ,(cadr hint)))
           (cddr hint)))
   (t
    (list* (car hint)
           (cadr hint)
           (adjust-hints-with-runes1 (cddr hint) runes)))))

(defun adjust-hints-with-runes (hints runes top-goal-seen-p)

; We know that only runes were used in the proof, and we want to adjust hints
; correspondingly.

  (cond
   ((null hints)
    (if top-goal-seen-p
        nil
      `(("Goal" :in-theory (union-theories
                            ,*adjust-hints-exec-theory*
                            ',runes)))))
   (t (cons (cons (caar hints) (adjust-hints-with-runes1 (cdar hints) runes))
            (adjust-hints-with-runes (cdr hints) runes
                                     (or top-goal-seen-p
                                         (equal (caar hints) "Goal")))))))

(defconst *fake-runes*
  (list *fake-rune-for-anonymous-enabled-rule*
        *fake-rune-for-type-set*
        *fake-rune-for-linear*))

(defun defthm-?-fn-forms1-lst (name index x equiv lhs hints wrld)

; x is from the output of tool-fn:  a list of elements of the form
; (list* runes hyps rewritten-term assumptions)
; If there is only one lemma, it has the name <name>, else we create
; <name>$0, ... <name>$n etc.

  (cond
   ((null x)
    nil)
   (t (let ((runes (set-difference-equal (car (car x))
                                         *fake-runes*))
            (hyps (cadr (car x)))
            (rhs (caddr (car x)))
            (assumptions (cdddr (car x))))
        (cons `(defthm
                 ,(if (and (zerop index) (null (cdr x)))
                      name
                    (packn (list name '$ index)))
                 ,(untranslate (implicate (conjoin (append assumptions hyps))
                                          (fcons-term* equiv lhs rhs))
                               t wrld)
                 :hints ,(adjust-hints-with-runes hints runes nil))
              (defthm-?-fn-forms1-lst name (1+ index) (cdr x) equiv lhs hints wrld))))))

(defun defthm?-fn-forms
  (name form simplify-hyps-p hints prove-assumptions inhibit-output print-flg wrld state)
  (with-ctx-summarized
   (cons 'defthm? name)
   (er-let*
    ((tform (translate form t t t ctx wrld state)))
    (let* ((x (unprettyify tform))
           (hyps (car (car x)))
           (concl (cdr (car x))))
      (cond
       ((and (null (cdr x))
             (not (variablep concl))
             (not (fquotep concl))
             (variablep (fargn concl 2)))
        (cond
         ((equivalence-relationp (ffn-symb concl) wrld)
          (er-let*
           ((x (tool-fn (fargn concl 1) hyps simplify-hyps-p (ffn-symb concl)
                        state hints prove-assumptions inhibit-output print-flg
                        ctx)))
           (value (defthm-?-fn-forms1-lst name 0 x (ffn-symb concl)
                    (fargn concl 1) hints wrld))))
         (t (er soft ctx
                "The form supplied to DEFTHM? must be of the form ~p0 or ~p1, ~
                 where equiv is an equivalence relation.  However, ~p2 is not ~
                 an equivalence relation in the current world."
                '(implies hyps (equiv lhs var))
                '(equiv lhs var)
                (ffn-symb concl)))))
       (t (er soft ctx
              "The form supplied to DEFTHM? must be of the form ~p0 or ~p1,~
               where var is a variable.  But ~p2 is not of this form."
              '(implies hyps (equiv lhs var))
              '(equiv lhs var)
              form)))))))

(defun defthm?-fn
  (name term simplify-hyps-p hints prove-assumptions print-flg wrld state)
  (state-global-let*
   ((inhibit-output-lst
     (if (boundp-global 'defthm?-inhibit-output-lst state)
; Suggestion:  '(warning observation prove event summary proof-tree)
         (f-get-global 'defthm?-inhibit-output-lst state)
       (@ inhibit-output-lst))))
   (er-let* ((forms (defthm?-fn-forms name term simplify-hyps-p hints
                      prove-assumptions nil print-flg wrld state)))
            (er-progn (encapsulate-fn nil (cons '(logic) forms) state nil)
                      (value (list* 'encapsulate () forms))))))

(defmacro symsim
  (term hyps &key
        hints (prove-assumptions 'try) (inhibit-output 't) (simplify-hyps-p 't)
        print-flg)

  ":Doc-Section Expander

  simplify given term and hypotheses~/
  ~bv[]
  Example:

  (symsim (append x y)
          ((not (atom x)) (not (cdr x)))
          :hints ((\"Goal\" :expand
                   ((true-listp x)
                    (true-listp (cdr x))
                    (append x y)))))
  ~ev[]
  yields
  ~bv[]
  Simplified term:
    (CONS (CAR X) Y)
  Simplified hyps:
   ((CONSP X) (NOT (CDR X)))~/

  General Form:
  (symsim term hyps
          :hints             hints
          :inhibit-output    inhibit-flg ; t, :prove, or nil, default t
          :prove-assumptions prove-flg   ; t, nil, or (default) any other value
          :print-flg         print-flg   ; t or nil, default nil
          :simplify-hyps-p   flg         ; t, nil, or :no-split; default t
  )
  ~ev[]
  where ~c[term] is a term to be simplified assuming that each ~c[hyp]
  in the list ~c[hyps] is true, and ~ilc[hints] is as described in its
  ~il[documentation].  The keyword arguments above are all optional, and behave
  as you might expect.  In particular, set ~c[:simplify-hyps-p] to ~c[nil] if
  you do not want the ~c[hyps] to be simplified; otherwise, case splitting may
  occur in the course of their simplification.

  Prover output is inhibited if ~c[:inhibit-output] is ~c[t] (the default).
  Only proof output is inhibited if ~c[:inhibit-output] is ~c[:prover] (so for
  example, summaries and warnings are printed), and all prover output is shown
  if ~c[:inhibit-output] is ~c[nil].

  Also ~pl[defthm?], which has a related functionality and is a
  bit more thoroughly documented.  Here are some examples that should
  help give an idea of how ~c[symsim] works.  (The name, by the way,
  is short for \"symbolically simulate\".)  Try these, as well as the
  examples shown above.
  ~bv[]

  (symsim (append x y)
          nil
          :hints ((\"Goal\" :expand
                   ((true-listp x)
                    (append x y)
                    (append (cdr x) y)))))

  ; Generates three cases:
  (symsim (append x y)
          ((true-listp x))
          :hints ((\"Goal\" :expand
                   ((true-listp x)
                    (true-listp (cdr x))
                    (append x y)
                    (append (cdr x) y)))))

  ; Let's illustrate the role of FORCE.  The following rule
  ; forces append to open up, and comes into play below.
  (defthm true-listp-expand-append
    (implies (and (force (true-listp x))
                  x)
             (equal (append x y)
                    (cons (car x) (append (cdr x) y)))))

  ; Generates assumption forced by preceding rule.
  (symsim (append x y)
          ((not (atom x))))

  ; But now we fail; but why?  See next form.
  (symsim (append x y)
          ((consp x))
          :prove-assumptions t)

  ; Let's not inhibit output.  Then we can see the failed forcing round.
  (symsim (append x y)
          ((consp x))
          :prove-assumptions t
          :inhibit-output nil)

  ; As above, but doesn't deal with generated forced assumptions at all (just
  ; drops them on the floor).
  (symsim (append x y)
          ((consp x))
          :prove-assumptions nil)
  ~ev[]"

  `(symsim-fn ',term ',hyps ',simplify-hyps-p ',hints ',prove-assumptions
              ',inhibit-output ',print-flg (w state) state))

(defun symsim-fn-print-lst (tuples n total wrld state)
  (cond ((null tuples)
         (fms "========================================~%~%"
              (list (cons #\0 n))
              *standard-co* state nil))
        (t
         (let ((tuple (car tuples)))
           (pprogn
            (fms "========== Generated case #~x0 of ~x1 ==========~%"
                 (list (cons #\0 n)
                       (cons #\1 total))
                 *standard-co* state nil)
            (fms "Runes:~%  ~p0~%Simplified hyps:~% ~p1~%Simplified term:~%  ~p2~%Simplified ~
                  assumptions:~% ~p3~%"
                 (list (cons #\0 (car tuple))
                       (cons #\1 (untranslate-lst (cadr tuple) t wrld))
                       (cons #\2 (untranslate (caddr tuple) nil wrld))
                       (cons #\3 (prettyify-clause-lst
                                  (cdddr tuple)
                                  (let*-abstractionp state)
                                  wrld)))
                 *standard-co* state nil)
            (symsim-fn-print-lst (cdr tuples) (1+ n) total wrld state))))))

(defun symsim-fn (term hyps simplify-hyps-p hints prove-assumptions
                       inhibit-output print-flg wrld state)

; Returns a list of tuples of the form (list* runes hyps rewritten-term
; assumptions), after doing some appropriate printing.

  (er-let*
   ((tterm (translate term t t t 'top-level wrld state))
    (thyps (translate-term-lst hyps t t t 'top-level wrld state))
    (tuples-lst (tool-fn tterm thyps simplify-hyps-p 'equal state
                         hints prove-assumptions
                         inhibit-output
                         print-flg (cons 'symsim-fn term))))
   (pprogn (if print-flg
               (symsim-fn-print-lst tuples-lst 1 (length tuples-lst) wrld
                                    state)
             state)
           (value tuples-lst))))