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Proof-generation

Gen-expr-pure-thm

Generate a theorem for the transformation of a pure expression.

Signature
(gen-expr-pure-thm old new vartys const-new thm-index hints) → (mv thm-event thm-name updated-thm-index)
Arguments: old — Guard (exprp old).; new — Guard (exprp new).; vartys — Guard (c::ident-type-mapp vartys).; const-new — Guard (symbolp const-new).; thm-index — Guard (posp thm-index).; hints — Guard (true-listp hints).
Returns: thm-event — Type (pseudo-event-formp thm-event).; thm-name — Type (symbolp thm-name).; updated-thm-index — Type (posp updated-thm-index).

We are in the process of transitioning theorem generation for expressions from this function to gen-expr-thm, while at the same time we are extending and generalizing our dynamic semantics of C. When that transition is completed, we will eliminate this function.

Definitions and Theorems

Function: gen-expr-pure-thm

(defun gen-expr-pure-thm (old new vartys const-new thm-index hints)
 (declare (xargs :guard (and (exprp old)
                             (exprp new)
                             (c::ident-type-mapp vartys)
                             (symbolp const-new)
                             (posp thm-index)
                             (true-listp hints))))
 (declare (xargs :guard (and (expr-unambp old)
                             (expr-annop old)
                             (expr-unambp new)
                             (expr-annop new))))
 (let ((__function__ 'gen-expr-pure-thm))
  (declare (ignorable __function__))
  (b*
   ((old (expr-fix old))
    (new (expr-fix new))
    ((unless (expr-pure-formalp old))
     (raise "Internal error: ~x0 is not in the formalized subset."
            old)
     (mv '(_) nil 1))
    ((unless (expr-pure-formalp new))
     (raise "Internal error: ~x0 is not in the formalized subset."
            new)
     (mv '(_) nil 1))
    (type (expr-type old))
    ((unless (equal (expr-type new) type))
     (raise
      "Internal error: ~
                the type ~x0 of the new expression ~x1 differs from ~
                the type ~x2 of the old expression ~x3."
      (expr-type new)
      new type old)
     (mv '(_) nil 1))
    ((unless (type-formalp type))
     (raise "Internal error: expression ~x0 has type ~x1."
            old type)
     (mv '(_) nil 1))
    ((mv & old-expr) (ldm-expr old))
    ((mv & new-expr) (ldm-expr new))
    ((mv & ctype) (ldm-type type))
    (vars-pre (gen-var-assertions vartys 'compst))
    (formula
     (cons
      'b*
      (cons
       (cons
            (cons 'old-expr
                  (cons (cons 'quote (cons old-expr 'nil))
                        'nil))
            (cons (cons 'new-expr
                        (cons (cons 'quote (cons new-expr 'nil))
                              'nil))
                  '((old-result (c::exec-expr-pure old-expr compst))
                    (new-result (c::exec-expr-pure new-expr compst))
                    (old-value (c::expr-value->value old-result))
                    (new-value (c::expr-value->value new-result)))))
       (cons
        (cons
         'implies
         (cons
          (cons 'and
                (append vars-pre
                        '((not (c::errorp old-result)))))
          (cons
           (cons
            'and
            (cons
             '(not (c::errorp new-result))
             (cons
              '(equal old-value new-value)
              (cons
                   (cons 'equal
                         (cons '(c::type-of-value old-value)
                               (cons (cons 'quote (cons ctype 'nil))
                                     'nil)))
                   'nil))))
           'nil)))
        'nil))))
    ((mv thm-name thm-index)
     (gen-thm-name const-new thm-index))
    (thm-event
     (cons
      'defrule
      (cons
           thm-name
           (cons formula
                 (cons ':rule-classes
                       (cons 'nil
                             (cons ':hints (cons hints 'nil)))))))))
   (mv thm-event thm-name thm-index))))

Theorem: pseudo-event-formp-of-gen-expr-pure-thm.thm-event

(defthm pseudo-event-formp-of-gen-expr-pure-thm.thm-event
  (b* (((mv ?thm-event ?thm-name ?updated-thm-index)
        (gen-expr-pure-thm old
                           new vartys const-new thm-index hints)))
    (pseudo-event-formp thm-event))
  :rule-classes :rewrite)

Theorem: symbolp-of-gen-expr-pure-thm.thm-name

(defthm symbolp-of-gen-expr-pure-thm.thm-name
  (b* (((mv ?thm-event ?thm-name ?updated-thm-index)
        (gen-expr-pure-thm old
                           new vartys const-new thm-index hints)))
    (symbolp thm-name))
  :rule-classes :rewrite)

Theorem: posp-of-gen-expr-pure-thm.updated-thm-index

(defthm posp-of-gen-expr-pure-thm.updated-thm-index
  (b* (((mv ?thm-event ?thm-name ?updated-thm-index)
        (gen-expr-pure-thm old
                           new vartys const-new thm-index hints)))
    (posp updated-thm-index))
  :rule-classes :rewrite)

Theorem: gen-expr-pure-thm-of-expr-fix-old

(defthm gen-expr-pure-thm-of-expr-fix-old
  (equal (gen-expr-pure-thm (expr-fix old)
                            new vartys const-new thm-index hints)
         (gen-expr-pure-thm old
                            new vartys const-new thm-index hints)))

Theorem: gen-expr-pure-thm-expr-equiv-congruence-on-old

(defthm gen-expr-pure-thm-expr-equiv-congruence-on-old
 (implies
   (c$::expr-equiv old old-equiv)
   (equal (gen-expr-pure-thm old
                             new vartys const-new thm-index hints)
          (gen-expr-pure-thm old-equiv
                             new vartys const-new thm-index hints)))
 :rule-classes :congruence)

Theorem: gen-expr-pure-thm-of-expr-fix-new

(defthm gen-expr-pure-thm-of-expr-fix-new
  (equal (gen-expr-pure-thm old (expr-fix new)
                            vartys const-new thm-index hints)
         (gen-expr-pure-thm old
                            new vartys const-new thm-index hints)))

Theorem: gen-expr-pure-thm-expr-equiv-congruence-on-new

(defthm gen-expr-pure-thm-expr-equiv-congruence-on-new
 (implies
     (c$::expr-equiv new new-equiv)
     (equal (gen-expr-pure-thm old
                               new vartys const-new thm-index hints)
            (gen-expr-pure-thm old new-equiv
                               vartys const-new thm-index hints)))
 :rule-classes :congruence)