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Proof-generation

Gen-declon-thm

Generate a theorem for the transformation of a declaration.

Signature
(gen-declon-thm old new vartys-pre vartys-post const-new thm-index hints) → (mv thm-event thm-name updated-thm-index)
Arguments: old — Guard (declonp old).; new — Guard (declonp new).; vartys-pre — Guard (c::ident-type-mapp vartys-pre).; vartys-post — Guard (c::ident-type-mapp vartys-post).; 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).

The declarations must be of objects in blocks.

Definitions and Theorems

Function: gen-declon-thm

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

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

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

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

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

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

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

(defthm gen-declon-thm-of-declon-fix-old
  (equal (gen-declon-thm (declon-fix old)
                         new vartys-pre
                         vartys-post const-new thm-index hints)
         (gen-declon-thm old new vartys-pre
                         vartys-post const-new thm-index hints)))

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

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

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

(defthm gen-declon-thm-of-declon-fix-new
  (equal (gen-declon-thm old (declon-fix new)
                         vartys-pre
                         vartys-post const-new thm-index hints)
         (gen-declon-thm old new vartys-pre
                         vartys-post const-new thm-index hints)))

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

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