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• Advanced-equivalence-checking-with-fgl

Replace-equal-with-top-level-equal-rec

Signature

(replace-equal-with-top-level-equal-rec x) → new-x

Arguments

x — Guard (pseudo-termp x).

Returns

new-x — Type (pseudo-termp new-x).

Definitions and Theorems

Function: replace-equal-with-top-level-equal-rec

(defun
 replace-equal-with-top-level-equal-rec
 (x)
 (declare (xargs :guard (pseudo-termp x)))
 (let
  ((__function__ 'replace-equal-with-top-level-equal-rec))
  (declare (ignorable __function__))
  (pseudo-term-case
   x
   :fncall
   (cond
    ((eq x.fn 'equal)
     (pseudo-term-fncall 'top-level-equal
                         x.args))
    ((eq x.fn 'implies)
     (pseudo-term-fncall
      'implies
      (list
         (first x.args)
         (replace-equal-with-top-level-equal-rec (second x.args)))))
    ((eq x.fn 'if)
     (if
      (equal (third x.args) ''nil)
      (pseudo-term-fncall
       'if
       (list
            (replace-equal-with-top-level-equal-rec (first x.args))
            (replace-equal-with-top-level-equal-rec (second x.args))
            ''nil))
      (pseudo-term-fncall
       'if
       (list
         (first x.args)
         (replace-equal-with-top-level-equal-rec (second x.args))
         (replace-equal-with-top-level-equal-rec (third x.args))))))
    ((eq x.fn 'return-last)
     (pseudo-term-fncall
      'return-last
      (list
          (first x.args)
          (second x.args)
          (replace-equal-with-top-level-equal-rec (third x.args)))))
    (t (pseudo-term-fix x)))
   :lambda (pseudo-term-lambda
                x.formals
                (replace-equal-with-top-level-equal-rec x.body)
                x.args)
   :otherwise (pseudo-term-fix x))))

Theorem: pseudo-termp-of-replace-equal-with-top-level-equal-rec

(defthm pseudo-termp-of-replace-equal-with-top-level-equal-rec
        (b* ((new-x (replace-equal-with-top-level-equal-rec x)))
            (pseudo-termp new-x))
        :rule-classes :rewrite)

Theorem: replace-equal-with-top-level-equal-rec-correct

(defthm
    replace-equal-with-top-level-equal-rec-correct
    (equal (repl-equal-ev (replace-equal-with-top-level-equal-rec x)
                          a)
           (repl-equal-ev x a)))