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Proof-generation

Gen-stmt-thm

Generate a theorem for the transformation of a statement.

Signature
(gen-stmt-thm old new vartys const-new thm-index hints) → (mv thm-event thm-name updated-thm-index)
Arguments: old — Guard (stmtp old).; new — Guard (stmtp 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).

Definitions and Theorems

Function: gen-stmt-thm

(defun gen-stmt-thm (old new vartys const-new thm-index hints)
 (declare (xargs :guard (and (stmtp old)
                             (stmtp new)
                             (c::ident-type-mapp vartys)
                             (symbolp const-new)
                             (posp thm-index)
                             (true-listp hints))))
 (declare (xargs :guard (and (stmt-unambp old)
                             (stmt-annop old)
                             (stmt-unambp new)
                             (stmt-annop new))))
 (let ((__function__ 'gen-stmt-thm))
  (declare (ignorable __function__))
  (b*
   ((old (stmt-fix old))
    (new (stmt-fix new))
    ((unless (stmt-formalp old))
     (raise "Internal error: ~x0 is not in the formalized subset."
            old)
     (mv '(_) nil 1))
    ((unless (stmt-formalp new))
     (raise "Internal error: ~x0 is not in the formalized subset."
            new)
     (mv '(_) nil 1))
    (types (stmt-types old))
    ((unless (equal (stmt-types new) types))
     (raise
      "Internal error: ~
                the types ~x0 of the new statement ~x1 differ from ~
                the types ~x2 of the old statement ~x3."
      (stmt-types new)
      new types old)
     (mv '(_) nil 1))
    (vars-pre (gen-var-assertions vartys 'compst))
    (vars-post (gen-var-assertions vartys 'old-compst))
    ((mv & old-stmt) (ldm-stmt old))
    ((mv & new-stmt) (ldm-stmt new))
    ((mv & ctypes)
     (ldm-type-option-set types))
    (formula
     (cons
      'b*
      (cons
       (cons
          (cons 'old-stmt
                (cons (cons 'quote (cons old-stmt 'nil))
                      'nil))
          (cons (cons 'new-stmt
                      (cons (cons 'quote (cons new-stmt 'nil))
                            'nil))
                '(((mv old-sval old-compst)
                   (c::exec-stmt old-stmt compst old-fenv limit))
                  ((mv new-sval new-compst)
                   (c::exec-stmt new-stmt compst new-fenv limit)))))
       (cons
        (cons
         'implies
         (cons
          (cons 'and
                (cons '(> (c::compustate-frames-number compst)
                          0)
                      (append vars-pre
                              '((not (c::errorp old-sval))))))
          (cons
           (cons
            'and
            (cons
             '(not (c::errorp new-sval))
             (cons
              '(equal old-sval new-sval)
              (cons
               '(equal old-compst new-compst)
               (cons
                (cons 'in
                      (cons '(c::type-option-of-stmt-value old-sval)
                            (cons (cons 'quote (cons ctypes 'nil))
                                  'nil)))
                vars-post)))))
           '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-stmt-thm.thm-event

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

Theorem: symbolp-of-gen-stmt-thm.thm-name

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

Theorem: posp-of-gen-stmt-thm.updated-thm-index

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

Theorem: gen-stmt-thm-of-stmt-fix-old

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

Theorem: gen-stmt-thm-stmt-equiv-congruence-on-old

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

Theorem: gen-stmt-thm-of-stmt-fix-new

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

Theorem: gen-stmt-thm-stmt-equiv-congruence-on-new

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