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• Proof-generation

Gen-block-item-thm

Generate a theorem for the transformation of a block item.

Signature

(gen-block-item-thm old new vartys-pre 
                    vartys-post const-new thm-index hints) 
 
  → 
(mv thm-event thm-name updated-thm-index)

Arguments

old — Guard (block-itemp old).

new — Guard (block-itemp 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).

Definitions and Theorems

Function: gen-block-item-thm

(defun gen-block-item-thm
       (old new vartys-pre
            vartys-post const-new thm-index hints)
 (declare (xargs :guard (and (block-itemp old)
                             (block-itemp 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 (block-item-unambp old)
                             (block-item-annop old)
                             (block-item-unambp new)
                             (block-item-annop new))))
 (let ((__function__ 'gen-block-item-thm))
  (declare (ignorable __function__))
  (b*
   ((old (block-item-fix old))
    (new (block-item-fix new))
    ((unless (block-item-formalp old))
     (raise "Internal error: ~x0 is not in the formalized subset."
            old)
     (mv '(_) nil 1))
    ((unless (block-item-formalp new))
     (raise "Internal error: ~x0 is not in the formalized subset."
            new)
     (mv '(_) nil 1))
    (types (block-item-types old))
    ((unless (equal (block-item-types new) types))
     (raise
      "Internal error: ~
                the types ~x0 of the new block item ~x1 differ from ~
                the types ~x2 of the old block item ~x3."
      (block-item-types new)
      new types old)
     (mv '(_) nil 1))
    (vars-pre (gen-var-assertions vartys-pre 'compst))
    (vars-post (gen-var-assertions vartys-post 'old-compst))
    ((mv & old-item) (ldm-block-item old))
    ((mv & new-item) (ldm-block-item new))
    ((mv & ctypes)
     (ldm-type-option-set types))
    (formula
     (cons
      'b*
      (cons
       (cons
        (cons 'old-item
              (cons (cons 'quote (cons old-item 'nil))
                    'nil))
        (cons
          (cons 'new-item
                (cons (cons 'quote (cons new-item 'nil))
                      'nil))
          '(((mv old-sval old-compst)
             (c::exec-block-item old-item compst old-fenv limit))
            ((mv new-sval new-compst)
             (c::exec-block-item new-item 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-block-item-thm.thm-event

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

Theorem: symbolp-of-gen-block-item-thm.thm-name

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

Theorem: posp-of-gen-block-item-thm.updated-thm-index

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

Theorem: gen-block-item-thm-of-block-item-fix-old

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

Theorem: gen-block-item-thm-block-item-equiv-congruence-on-old

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

Theorem: gen-block-item-thm-of-block-item-fix-new

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

Theorem: gen-block-item-thm-block-item-equiv-congruence-on-new

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