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• Proof-generation

Gen-initer-single-thm

Generate a theorem for the transformation of a single initializer.

Signature

(gen-initer-single-thm old new vartys const-new thm-index hints) 
  → 
(mv thm-event thm-name updated-thm-index)

Arguments

old — Guard (initerp old).

new — Guard (initerp 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-initer-single-thm

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

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

Theorem: symbolp-of-gen-initer-single-thm.thm-name

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

Theorem: posp-of-gen-initer-single-thm.updated-thm-index

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

Theorem: gen-initer-single-thm-of-initer-fix-old

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

Theorem: gen-initer-single-thm-initer-equiv-congruence-on-old

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

Theorem: gen-initer-single-thm-of-initer-fix-new

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

Theorem: gen-initer-single-thm-initer-equiv-congruence-on-new

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