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• Alias-norm.lisp

Lhs-alias-canonicalize-top

Signature

(lhs-alias-canonicalize-top x aliases) → xx

Arguments

x — Guard (lhs-p x).

aliases — Guard (aliases-normorderedp aliases).

Returns

xx — Type (and (lhs-p xx) (implies (svarlist-boundedp (lhs-vars x) (len aliases)) (svarlist-boundedp (lhs-vars xx) (len aliases)))) .

Definitions and Theorems

Function: lhs-alias-canonicalize-top

(defun lhs-alias-canonicalize-top (x aliases)
 (declare (xargs :stobjs (aliases)))
 (declare (xargs :guard (and (lhs-p x)
                             (aliases-normorderedp aliases))))
 (declare
      (xargs :guard (svarlist-boundedp (lhs-vars x)
                                       (aliass-length aliases))))
 (let ((__function__ 'lhs-alias-canonicalize-top))
  (declare (ignorable __function__))
  (b* (((mv first rest) (lhs-decomp x))
       ((unless first) nil)
       ((lhrange first) first))
    (lhatom-case
         first.atom :z
         (lhs-cons first
                   (lhs-alias-canonicalize-top rest aliases))
         :var
         (b* ((idx (svar-index first.atom.name)))
           (lhs-concat
                first.w
                (lhs-alias-canonicalize
                     (lhs-rsh first.atom.rsh (getalias idx aliases))
                     idx first.w first.atom.rsh aliases)
                (lhs-alias-canonicalize-top rest aliases)))))))

Theorem: return-type-of-lhs-alias-canonicalize-top

(defthm return-type-of-lhs-alias-canonicalize-top
  (b* ((xx (lhs-alias-canonicalize-top x aliases)))
    (and (lhs-p xx)
         (implies (svarlist-boundedp (lhs-vars x)
                                     (len aliases))
                  (svarlist-boundedp (lhs-vars xx)
                                     (len aliases)))))
  :rule-classes :rewrite)

Theorem: lhs-alias-canonicalize-top-of-lhs-fix-x

(defthm lhs-alias-canonicalize-top-of-lhs-fix-x
  (equal (lhs-alias-canonicalize-top (lhs-fix x)
                                     aliases)
         (lhs-alias-canonicalize-top x aliases)))

Theorem: lhs-alias-canonicalize-top-lhs-equiv-congruence-on-x

(defthm lhs-alias-canonicalize-top-lhs-equiv-congruence-on-x
  (implies (lhs-equiv x x-equiv)
           (equal (lhs-alias-canonicalize-top x aliases)
                  (lhs-alias-canonicalize-top x-equiv aliases)))
  :rule-classes :congruence)

Theorem: lhs-alias-canonicalize-top-of-aliases-bound-fix-aliases

(defthm lhs-alias-canonicalize-top-of-aliases-bound-fix-aliases
  (equal (lhs-alias-canonicalize-top x (aliases-bound-fix aliases))
         (lhs-alias-canonicalize-top x aliases)))

Theorem: lhs-alias-canonicalize-top-aliases-equiv-congruence-on-aliases

(defthm
     lhs-alias-canonicalize-top-aliases-equiv-congruence-on-aliases
  (implies (aliases-equiv aliases aliases-equiv)
           (equal (lhs-alias-canonicalize-top x aliases)
                  (lhs-alias-canonicalize-top x aliases-equiv)))
  :rule-classes :congruence)