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• Alias-norm.lisp

Canonicalize-alias-pairs

Signature

(canonicalize-alias-pairs pairs aliases) → aliases

Arguments

pairs — Guard (lhspairs-p pairs).

aliases — Guard (aliases-normorderedp aliases).

Returns

aliases — Type (aliases-normorderedp aliases).

Definitions and Theorems

Function: canonicalize-alias-pairs

(defun canonicalize-alias-pairs (pairs aliases)
  (declare (xargs :stobjs (aliases)))
  (declare (xargs :guard (and (lhspairs-p pairs)
                              (aliases-normorderedp aliases))))
  (declare
       (xargs :guard (svarlist-boundedp (lhspairs-vars pairs)
                                        (aliass-length aliases))))
  (let ((__function__ 'canonicalize-alias-pairs))
    (declare (ignorable __function__))
    (b* ((aliases (aliases-put-pairs pairs aliases)))
      (aliases-finish-canonicalize 0 aliases))))

Theorem: aliases-normorderedp-of-canonicalize-alias-pairs

(defthm aliases-normorderedp-of-canonicalize-alias-pairs
  (b* ((aliases (canonicalize-alias-pairs pairs aliases)))
    (aliases-normorderedp aliases))
  :rule-classes :rewrite)

Theorem: canonicalize-alias-pairs-of-lhspairs-fix-pairs

(defthm canonicalize-alias-pairs-of-lhspairs-fix-pairs
  (equal (canonicalize-alias-pairs (lhspairs-fix pairs)
                                   aliases)
         (canonicalize-alias-pairs pairs aliases)))

Theorem: canonicalize-alias-pairs-lhspairs-equiv-congruence-on-pairs

(defthm canonicalize-alias-pairs-lhspairs-equiv-congruence-on-pairs
  (implies (lhspairs-equiv pairs pairs-equiv)
           (equal (canonicalize-alias-pairs pairs aliases)
                  (canonicalize-alias-pairs pairs-equiv aliases)))
  :rule-classes :congruence)

Theorem: canonicalize-alias-pairs-of-aliases-bound-fix-aliases

(defthm canonicalize-alias-pairs-of-aliases-bound-fix-aliases
 (equal (canonicalize-alias-pairs pairs (aliases-bound-fix aliases))
        (canonicalize-alias-pairs pairs aliases)))

Theorem: canonicalize-alias-pairs-aliases-equiv-congruence-on-aliases

(defthm canonicalize-alias-pairs-aliases-equiv-congruence-on-aliases
  (implies (aliases-equiv aliases aliases-equiv)
           (equal (canonicalize-alias-pairs pairs aliases)
                  (canonicalize-alias-pairs pairs aliases-equiv)))
  :rule-classes :congruence)

Theorem: len-of-canonicalize-alias-pairs

(defthm len-of-canonicalize-alias-pairs
  (implies (svarlist-boundedp (lhspairs-vars pairs)
                              (len aliases))
           (equal (len (canonicalize-alias-pairs pairs aliases))
                  (len aliases))))