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• Svex-focused-equivalence-checking

Svex-mask-env-common-constants

FGL binder to find common constants (under a set of masks) in two symbolic SVEX environments.

Signature

(svex-mask-env-common-constants ans masks env1 env2) 
  → 
const-env

Arguments

ans — Guard (svex-env-p ans).

masks — Guard (svex-mask-alist-p masks).

env1 — Guard (svex-env-p env1).

env2 — Guard (svex-env-p env2).

Definitions and Theorems

Function: svex-mask-env-common-constants

(defun svex-mask-env-common-constants (ans masks env1 env2)
 (declare (xargs :guard (and (svex-env-p ans)
                             (svex-mask-alist-p masks)
                             (svex-env-p env1)
                             (svex-env-p env2))))
 (let ((__function__ 'svex-mask-env-common-constants))
  (declare (ignorable __function__))
  (let ((ans (svex-env-fix ans)))
    (if
     (and (ec-call (svex-envs-agree-on-masks masks (append ans env1)
                                             env1))
          (ec-call (svex-envs-agree-on-masks masks (append ans env2)
                                             env2)))
     ans
     nil))))

Theorem: svex-env-common-constants-correct

(defthm svex-env-common-constants-correct
  (b* ((?const-env
            (svex-mask-env-common-constants ans masks env1 env2)))
    (and (svex-envs-agree-on-masks masks (append const-env env1)
                                   env1)
         (svex-envs-agree-on-masks masks (append const-env env2)
                                   env2))))

Theorem: svexlist-eval-of-svex-mask-env-common-constants

(defthm svexlist-eval-of-svex-mask-env-common-constants
  (b* ((masks (svexlist-mask-alist x))
       (?const-env
            (svex-mask-env-common-constants ans masks env1 env2)))
    (and (equal (svexlist-eval x (append const-env env1))
                (svexlist-eval x env1))
         (equal (svexlist-eval x (append const-env env2))
                (svexlist-eval x env2)))))

Theorem: svex-mask-env-common-constants-of-svex-env-fix-ans

(defthm svex-mask-env-common-constants-of-svex-env-fix-ans
  (equal (svex-mask-env-common-constants (svex-env-fix ans)
                                         masks env1 env2)
         (svex-mask-env-common-constants ans masks env1 env2)))

Theorem: svex-mask-env-common-constants-svex-env-equiv-congruence-on-ans

(defthm
    svex-mask-env-common-constants-svex-env-equiv-congruence-on-ans
 (implies
   (svex-env-equiv ans ans-equiv)
   (equal
        (svex-mask-env-common-constants ans masks env1 env2)
        (svex-mask-env-common-constants ans-equiv masks env1 env2)))
 :rule-classes :congruence)

Theorem: svex-mask-env-common-constants-of-svex-env-fix-env1

(defthm svex-mask-env-common-constants-of-svex-env-fix-env1
  (equal
       (svex-mask-env-common-constants ans masks (svex-env-fix env1)
                                       env2)
       (svex-mask-env-common-constants ans masks env1 env2)))

Theorem: svex-mask-env-common-constants-svex-env-equiv-congruence-on-env1

(defthm
   svex-mask-env-common-constants-svex-env-equiv-congruence-on-env1
 (implies
   (svex-env-equiv env1 env1-equiv)
   (equal
        (svex-mask-env-common-constants ans masks env1 env2)
        (svex-mask-env-common-constants ans masks env1-equiv env2)))
 :rule-classes :congruence)

Theorem: svex-mask-env-common-constants-of-svex-env-fix-env2

(defthm svex-mask-env-common-constants-of-svex-env-fix-env2
  (equal (svex-mask-env-common-constants
              ans masks env1 (svex-env-fix env2))
         (svex-mask-env-common-constants ans masks env1 env2)))

Theorem: svex-mask-env-common-constants-svex-env-equiv-congruence-on-env2

(defthm
   svex-mask-env-common-constants-svex-env-equiv-congruence-on-env2
 (implies
   (svex-env-equiv env2 env2-equiv)
   (equal
        (svex-mask-env-common-constants ans masks env1 env2)
        (svex-mask-env-common-constants ans masks env1 env2-equiv)))
 :rule-classes :congruence)