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• Compile.lisp

Svex-override-lhrange

Signature

(svex-override-lhrange x override-test offset override-val assigns) 
  → 
assigns1

Arguments

x — Guard (lhrange-p x).

override-test — Guard (svex-p override-test).

offset — Guard (natp offset).

override-val — Guard (svex-p override-val).

assigns — Guard (svex-alist-p assigns).

Returns

assigns1 — Type (svex-alist-p assigns1).

Definitions and Theorems

Function: svex-override-lhrange

(defun svex-override-lhrange (x override-test
                                offset override-val assigns)
  (declare (xargs :guard (and (lhrange-p x)
                              (svex-p override-test)
                              (natp offset)
                              (svex-p override-val)
                              (svex-alist-p assigns))))
  (let ((__function__ 'svex-override-lhrange))
    (declare (ignorable __function__))
    (b* (((lhrange x) x)
         ((when (eq (lhatom-kind x.atom) :z))
          (svex-alist-fix assigns))
         ((lhatom-var x.atom) x.atom)
         (expr (or (svex-fastlookup x.atom.name assigns)
                   (svex-quote (4vec-z))))
         (last (svex-rsh (+ x.atom.rsh x.w) expr))
         (mid (svex-call '?*
                         (list (svex-zerox 1 override-test)
                               (svex-rsh offset override-val)
                               (svex-rsh x.atom.rsh expr))))
         (newexpr (svex-concat x.atom.rsh
                               expr (svex-concat x.w mid last))))
      (hons-acons x.atom.name
                  newexpr (svex-alist-fix assigns)))))

Theorem: svex-alist-p-of-svex-override-lhrange

(defthm svex-alist-p-of-svex-override-lhrange
  (b*
    ((assigns1 (svex-override-lhrange x override-test
                                      offset override-val assigns)))
    (svex-alist-p assigns1))
  :rule-classes :rewrite)

Theorem: vars-of-svex-override-lhrange

(defthm vars-of-svex-override-lhrange
  (b*
    ((assigns1 (svex-override-lhrange x override-test
                                      offset override-val assigns)))
    (implies (and (not (member v (svex-alist-vars assigns)))
                  (not (member v (svex-vars override-test)))
                  (not (member v (svex-vars override-val))))
             (not (member v (svex-alist-vars assigns1)))))
  :rule-classes :rewrite)

Theorem: lookup-of-svex-override-lhrange

(defthm lookup-of-svex-override-lhrange
  (b*
    ((assigns1 (svex-override-lhrange x override-test
                                      offset override-val assigns)))
    (implies (and (not (member v (lhatom-vars (lhrange->atom x))))
                  (not (svex-lookup v assigns))
                  (svar-p v))
             (not (svex-lookup v assigns1))))
  :rule-classes :rewrite)

Theorem: svex-override-lhrange-of-lhrange-fix-x

(defthm svex-override-lhrange-of-lhrange-fix-x
  (equal (svex-override-lhrange (lhrange-fix x)
                                override-test
                                offset override-val assigns)
         (svex-override-lhrange x override-test
                                offset override-val assigns)))

Theorem: svex-override-lhrange-lhrange-equiv-congruence-on-x

(defthm svex-override-lhrange-lhrange-equiv-congruence-on-x
  (implies
       (lhrange-equiv x x-equiv)
       (equal (svex-override-lhrange x override-test
                                     offset override-val assigns)
              (svex-override-lhrange x-equiv override-test
                                     offset override-val assigns)))
  :rule-classes :congruence)

Theorem: svex-override-lhrange-of-svex-fix-override-test

(defthm svex-override-lhrange-of-svex-fix-override-test
  (equal (svex-override-lhrange x (svex-fix override-test)
                                offset override-val assigns)
         (svex-override-lhrange x override-test
                                offset override-val assigns)))

Theorem: svex-override-lhrange-svex-equiv-congruence-on-override-test

(defthm svex-override-lhrange-svex-equiv-congruence-on-override-test
  (implies
       (svex-equiv override-test override-test-equiv)
       (equal (svex-override-lhrange x override-test
                                     offset override-val assigns)
              (svex-override-lhrange x override-test-equiv
                                     offset override-val assigns)))
  :rule-classes :congruence)

Theorem: svex-override-lhrange-of-nfix-offset

(defthm svex-override-lhrange-of-nfix-offset
  (equal (svex-override-lhrange x override-test (nfix offset)
                                override-val assigns)
         (svex-override-lhrange x override-test
                                offset override-val assigns)))

Theorem: svex-override-lhrange-nat-equiv-congruence-on-offset

(defthm svex-override-lhrange-nat-equiv-congruence-on-offset
 (implies
  (nat-equiv offset offset-equiv)
  (equal (svex-override-lhrange x override-test
                                offset override-val assigns)
         (svex-override-lhrange x override-test
                                offset-equiv override-val assigns)))
 :rule-classes :congruence)

Theorem: svex-override-lhrange-of-svex-fix-override-val

(defthm svex-override-lhrange-of-svex-fix-override-val
  (equal (svex-override-lhrange x override-test
                                offset (svex-fix override-val)
                                assigns)
         (svex-override-lhrange x override-test
                                offset override-val assigns)))

Theorem: svex-override-lhrange-svex-equiv-congruence-on-override-val

(defthm svex-override-lhrange-svex-equiv-congruence-on-override-val
 (implies
  (svex-equiv override-val override-val-equiv)
  (equal (svex-override-lhrange x override-test
                                offset override-val assigns)
         (svex-override-lhrange x override-test
                                offset override-val-equiv assigns)))
 :rule-classes :congruence)

Theorem: svex-override-lhrange-of-svex-alist-fix-assigns

(defthm svex-override-lhrange-of-svex-alist-fix-assigns
  (equal
       (svex-override-lhrange x override-test offset
                              override-val (svex-alist-fix assigns))
       (svex-override-lhrange x override-test
                              offset override-val assigns)))

Theorem: svex-override-lhrange-svex-alist-equiv-congruence-on-assigns

(defthm svex-override-lhrange-svex-alist-equiv-congruence-on-assigns
 (implies
  (svex-alist-equiv assigns assigns-equiv)
  (equal (svex-override-lhrange x override-test
                                offset override-val assigns)
         (svex-override-lhrange x override-test
                                offset override-val assigns-equiv)))
 :rule-classes :congruence)