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• Alias-norm.lisp

Lhs-alias-norm

Signature

(lhs-alias-norm x aliases) → xx

Arguments

x — Guard (lhs-p x).

Returns

xx — Type (lhs-p xx).

Definitions and Theorems

Function: lhs-alias-norm

(defun lhs-alias-norm (x aliases)
 (declare (xargs :stobjs (aliases)))
 (declare (xargs :guard (lhs-p x)))
 (declare
      (xargs :guard (svarlist-boundedp (lhs-vars x)
                                       (aliass-length aliases))))
 (let ((__function__ 'lhs-alias-norm))
  (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-norm rest aliases))
      :var
      (b* ((idx (svar-index first.atom.name)))
        (lhs-concat first.w
                    (lhs-rsh first.atom.rsh (get-alias idx aliases))
                    (lhs-alias-norm rest aliases)))))))

Theorem: lhs-p-of-lhs-alias-norm

(defthm lhs-p-of-lhs-alias-norm
  (b* ((xx (lhs-alias-norm x aliases)))
    (lhs-p xx))
  :rule-classes :rewrite)

Theorem: lhs-alias-norm-of-lhs-fix-x

(defthm lhs-alias-norm-of-lhs-fix-x
  (equal (lhs-alias-norm (lhs-fix x) aliases)
         (lhs-alias-norm x aliases)))

Theorem: lhs-alias-norm-lhs-equiv-congruence-on-x

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

Theorem: lhs-alias-norm-of-lhslist-fix-aliases

(defthm lhs-alias-norm-of-lhslist-fix-aliases
  (equal (lhs-alias-norm x (lhslist-fix aliases))
         (lhs-alias-norm x aliases)))

Theorem: lhs-alias-norm-lhslist-equiv-congruence-on-aliases

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

Theorem: vars-of-lhs-alias-norm

(defthm vars-of-lhs-alias-norm
  (implies (not (member v (aliases-vars aliases)))
           (not (member v
                        (lhs-vars (lhs-alias-norm x aliases))))))