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• Alias-norm.lisp

Aliases-add-pair

Signature

(aliases-add-pair x y aliases) → aliases1

Arguments

x — Guard (lhs-p x).

y — Guard (lhs-p y).

aliases — Guard (aliases-normorderedp aliases).

Returns

aliases1 — Type (aliases-normorderedp aliases1).

Definitions and Theorems

Function: aliases-add-pair

(defun aliases-add-pair (x y aliases)
 (declare (xargs :stobjs (aliases)))
 (declare (xargs :guard (and (lhs-p x)
                             (lhs-p y)
                             (aliases-normorderedp aliases))))
 (declare
   (xargs :guard (and (svarlist-boundedp (lhs-vars x)
                                         (aliass-length aliases))
                      (svarlist-boundedp (lhs-vars y)
                                         (aliass-length aliases)))))
 (let ((__function__ 'aliases-add-pair))
   (declare (ignorable __function__))
   (b* (((when (zp (aliass-length aliases)))
         (aliases-bound-fix aliases))
        (xcanon (lhs-alias-canonicalize-top x aliases))
        (ycanon (lhs-alias-canonicalize-top y aliases))
        (aliases (lhs-pairs-set-aliases xcanon ycanon aliases))
        ((mv & aliases)
         (lhs-alias-canonicalize-replace-top x aliases))
        ((mv & aliases)
         (lhs-alias-canonicalize-replace-top y aliases)))
     aliases)))

Theorem: aliases-normorderedp-of-aliases-add-pair

(defthm aliases-normorderedp-of-aliases-add-pair
  (b* ((aliases1 (aliases-add-pair x y aliases)))
    (aliases-normorderedp aliases1))
  :rule-classes :rewrite)

Theorem: aliases-add-pair-of-lhs-fix-x

(defthm aliases-add-pair-of-lhs-fix-x
  (equal (aliases-add-pair (lhs-fix x) y aliases)
         (aliases-add-pair x y aliases)))

Theorem: aliases-add-pair-lhs-equiv-congruence-on-x

(defthm aliases-add-pair-lhs-equiv-congruence-on-x
  (implies (lhs-equiv x x-equiv)
           (equal (aliases-add-pair x y aliases)
                  (aliases-add-pair x-equiv y aliases)))
  :rule-classes :congruence)

Theorem: aliases-add-pair-of-lhs-fix-y

(defthm aliases-add-pair-of-lhs-fix-y
  (equal (aliases-add-pair x (lhs-fix y) aliases)
         (aliases-add-pair x y aliases)))

Theorem: aliases-add-pair-lhs-equiv-congruence-on-y

(defthm aliases-add-pair-lhs-equiv-congruence-on-y
  (implies (lhs-equiv y y-equiv)
           (equal (aliases-add-pair x y aliases)
                  (aliases-add-pair x y-equiv aliases)))
  :rule-classes :congruence)

Theorem: aliases-add-pair-of-aliases-bound-fix-aliases

(defthm aliases-add-pair-of-aliases-bound-fix-aliases
  (equal (aliases-add-pair x y (aliases-bound-fix aliases))
         (aliases-add-pair x y aliases)))

Theorem: aliases-add-pair-aliases-equiv-congruence-on-aliases

(defthm aliases-add-pair-aliases-equiv-congruence-on-aliases
  (implies (aliases-equiv aliases aliases-equiv)
           (equal (aliases-add-pair x y aliases)
                  (aliases-add-pair x y aliases-equiv)))
  :rule-classes :congruence)

Theorem: len-of-aliases-add-pair

(defthm len-of-aliases-add-pair
  (implies (and (svarlist-boundedp (lhs-vars x)
                                   (len aliases))
                (svarlist-boundedp (lhs-vars y)
                                   (len aliases)))
           (equal (len (aliases-add-pair x y aliases))
                  (len aliases))))