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• Alias-norm.lisp

Aliases-finish-canonicalize

Signature

(aliases-finish-canonicalize n aliases) → aliases1

Arguments

n — Guard (natp n).

aliases — Guard (aliases-normorderedp aliases).

Returns

aliases1 — Type (aliases-normorderedp aliases1).

Definitions and Theorems

Function: aliases-finish-canonicalize

(defun aliases-finish-canonicalize (n aliases)
 (declare (xargs :stobjs (aliases)))
 (declare (xargs :guard (and (natp n)
                             (aliases-normorderedp aliases))))
 (declare (xargs :guard (<= n (aliass-length aliases))))
 (let ((__function__ 'aliases-finish-canonicalize))
   (declare (ignorable __function__))
   (b* (((when (mbe :logic (zp (- (aliass-length aliases) (nfix n)))
                    :exec (eql (aliass-length aliases) n)))
         (aliases-bound-fix aliases))
        (lhs (getalias n aliases))
        (canon (lhs-alias-canonicalize lhs n (lhs-width lhs)
                                       0 aliases))
        (aliases (setalias n canon aliases)))
     (aliases-finish-canonicalize (1+ (lnfix n))
                                  aliases))))

Theorem: aliases-normorderedp-of-aliases-finish-canonicalize

(defthm aliases-normorderedp-of-aliases-finish-canonicalize
  (b* ((aliases1 (aliases-finish-canonicalize n aliases)))
    (aliases-normorderedp aliases1))
  :rule-classes :rewrite)

Theorem: aliases-finish-canonicalize-of-nfix-n

(defthm aliases-finish-canonicalize-of-nfix-n
  (equal (aliases-finish-canonicalize (nfix n)
                                      aliases)
         (aliases-finish-canonicalize n aliases)))

Theorem: aliases-finish-canonicalize-nat-equiv-congruence-on-n

(defthm aliases-finish-canonicalize-nat-equiv-congruence-on-n
  (implies (nat-equiv n n-equiv)
           (equal (aliases-finish-canonicalize n aliases)
                  (aliases-finish-canonicalize n-equiv aliases)))
  :rule-classes :congruence)

Theorem: aliases-finish-canonicalize-of-aliases-bound-fix-aliases

(defthm aliases-finish-canonicalize-of-aliases-bound-fix-aliases
  (equal (aliases-finish-canonicalize n (aliases-bound-fix aliases))
         (aliases-finish-canonicalize n aliases)))

Theorem: aliases-finish-canonicalize-aliases-equiv-congruence-on-aliases

(defthm
    aliases-finish-canonicalize-aliases-equiv-congruence-on-aliases
  (implies (aliases-equiv aliases aliases-equiv)
           (equal (aliases-finish-canonicalize n aliases)
                  (aliases-finish-canonicalize n aliases-equiv)))
  :rule-classes :congruence)

Theorem: len-of-aliases-finish-canonicalize

(defthm len-of-aliases-finish-canonicalize
  (equal (len (aliases-finish-canonicalize n aliases))
         (len aliases)))