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Svex-varmasks/env->aig-env-rec

Signature

(svex-varmasks/env->aig-env-rec 
     vars masks boolmasks env nextvar acc) 
 
  → 
(mv err env nextvar1)

Arguments

vars — Guard (svarlist-p vars).

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

boolmasks — Guard (svar-boolmasks-p boolmasks).

env — look up variables in env to get 4vecs to assign -- symbolic.
    Guard (svex-env-p env).

nextvar — Guard (natp nextvar).

acc — aig environment accumulator.

Returns

err — some mask was negative.
    Type (implies (svex-mask-alist-p masks) (iff err (not (svex-maskbits-ok vars masks)))) .

nextvar1 — Type (implies (and (svex-mask-alist-p masks) (svar-boolmasks-p boolmasks)) (equal nextvar1 (+ (nfix nextvar) (svex-maskbits-for-vars vars masks boolmasks)))) .

Definitions and Theorems

Function: svex-varmasks/env->aig-env-rec

(defun svex-varmasks/env->aig-env-rec
       (vars masks boolmasks env nextvar acc)
  (declare (xargs :guard (and (svarlist-p vars)
                              (svex-mask-alist-p masks)
                              (svar-boolmasks-p boolmasks)
                              (svex-env-p env)
                              (natp nextvar))))
  (let ((__function__ 'svex-varmasks/env->aig-env-rec))
    (declare (ignorable __function__))
    (b* (((when (atom vars))
          (mv nil acc (lnfix nextvar)))
         (mask (svex-mask-lookup (svex-var (car vars))
                                 masks))
         ((when (sparseint-< mask 0))
          (mv (msg "Negative mask: ~x0~%"
                   (svar-fix (car vars)))
              acc (lnfix nextvar)))
         (boolmask (svar-boolmasks-lookup (car vars)
                                          boolmasks))
         (4vec (4vec-fix (svex-env-lookup (svar-fix (car vars))
                                          env)))
         (env-part (4vmask-to-a4vec-env mask boolmask 4vec nextvar))
         (nextvar (+ (lnfix nextvar)
                     (4vmask-to-a4vec-varcount mask boolmask))))
      (svex-varmasks/env->aig-env-rec
           (cdr vars)
           masks boolmasks
           env nextvar (append env-part acc)))))

Theorem: return-type-of-svex-varmasks/env->aig-env-rec.err

(defthm return-type-of-svex-varmasks/env->aig-env-rec.err
  (b* (((mv ?err ?env ?nextvar1)
        (svex-varmasks/env->aig-env-rec
             vars masks boolmasks env nextvar acc)))
    (implies (svex-mask-alist-p masks)
             (iff err
                  (not (svex-maskbits-ok vars masks)))))
  :rule-classes :rewrite)

Theorem: return-type-of-svex-varmasks/env->aig-env-rec.nextvar1

(defthm return-type-of-svex-varmasks/env->aig-env-rec.nextvar1
  (b* (((mv ?err ?env ?nextvar1)
        (svex-varmasks/env->aig-env-rec
             vars masks boolmasks env nextvar acc)))
    (implies
         (and (svex-mask-alist-p masks)
              (svar-boolmasks-p boolmasks))
         (equal nextvar1
                (+ (nfix nextvar)
                   (svex-maskbits-for-vars vars masks boolmasks)))))
  :rule-classes :rewrite)

Theorem: key-exists-in-svex-varmasks/env->aig-env-rec

(defthm key-exists-in-svex-varmasks/env->aig-env-rec
 (implies
  (and (svex-mask-alist-p masks)
       (svar-boolmasks-p boolmasks))
  (iff
   (hons-assoc-equal
        v
        (mv-nth 1
                (svex-varmasks/env->aig-env-rec
                     vars masks boolmasks env nextvar acc)))
   (or
     (hons-assoc-equal v acc)
     (and (natp v)
          (<= (nfix nextvar) v)
          (< v
             (+ (nfix nextvar)
                (svex-maskbits-for-vars vars masks boolmasks))))))))

Theorem: svex-varmasks/env->aig-env-accumulator-elim

(defthm svex-varmasks/env->aig-env-accumulator-elim
 (implies
  (syntaxp (not (equal acc ''nil)))
  (equal (mv-nth 1
                 (svex-varmasks/env->aig-env-rec
                      vars masks boolmasks env nextvar acc))
         (append (mv-nth 1
                         (svex-varmasks/env->aig-env-rec
                              vars masks boolmasks env nextvar nil))
                 acc))))

Theorem: 4vmask-to-a4vec-vars-subset-of-keys

(defthm 4vmask-to-a4vec-vars-subset-of-keys
 (subsetp-equal
      (nat-bool-a4vec-vars (4vmask-to-a4vec mask boolmask nextvar))
      (alist-keys (4vmask-to-a4vec-env mask boolmask val nextvar))))

Theorem: member-nat-bool-a4vec-vars-of-lookup-when-upper-bounded

(defthm member-nat-bool-a4vec-vars-of-lookup-when-upper-bounded
 (implies
  (and (nat-bool-a4env-p a4acc)
       (nat-bool-a4env-upper-boundp nextvar a4acc)
       (<= (nfix nextvar) k))
  (not
     (member
          k
          (nat-bool-a4vec-vars (cdr (hons-assoc-equal v a4acc)))))))

Theorem: 4vmask-to-a4vec-env-vars-not-intersect-when-upper-bounded

(defthm 4vmask-to-a4vec-env-vars-not-intersect-when-upper-bounded
 (implies
  (and (nat-bool-a4env-p a4acc)
       (double-rewrite (nat-bool-a4env-upper-boundp nextvar a4acc)))
  (not
   (intersectp
    (nat-bool-a4vec-vars (cdr (hons-assoc-equal v a4acc)))
    (alist-keys (4vmask-to-a4vec-env mask boolmask val nextvar))))))

Theorem: svex-env-boolmasks-ok-necc

(defthm svex-env-boolmasks-ok-necc
  (implies (svex-env-boolmasks-ok env boolmasks)
           (4vec-boolmaskp (svex-env-lookup v env)
                           (svar-boolmasks-lookup v boolmasks))))

Theorem: svex-env-boolmasks-ok-witnessing-witness-rule-correct

(defthm svex-env-boolmasks-ok-witnessing-witness-rule-correct
 (implies
  (not
      ((lambda (v boolmasks env)
         (not (4vec-boolmaskp (svex-env-lookup v env)
                              (svar-boolmasks-lookup v boolmasks))))
       (svex-env-boolmasks-ok-witness env boolmasks)
       boolmasks env))
  (svex-env-boolmasks-ok env boolmasks))
 :rule-classes nil)

Theorem: svex-env-boolmasks-ok-instancing-instance-rule-correct

(defthm svex-env-boolmasks-ok-instancing-instance-rule-correct
 (implies (not (4vec-boolmaskp (svex-env-lookup v env)
                               (svar-boolmasks-lookup v boolmasks)))
          (not (svex-env-boolmasks-ok env boolmasks)))
 :rule-classes nil)

Theorem: eval-svex-varmasks->a4env-rec-with-env

(defthm eval-svex-varmasks->a4env-rec-with-env
  (b* (((mv err a4env ?nextvar1)
        (svex-varmasks->a4env-rec vars masks boolmasks nextvar nil))
       ((mv ?err1 env ?nextvar1)
        (svex-varmasks/env->aig-env-rec
             vars
             (svex-mask-alist-extract-vars masks)
             boolmasks goalenv nextvar nil)))
    (implies (and (not err)
                  (svex-mask-alist-p masks)
                  (svar-boolmasks-p boolmasks)
                  (svex-env-boolmasks-ok goalenv boolmasks))
             (svex-envs-mask-equiv-on-vars
                  vars
                  masks (svex-a4vec-env-eval a4env env)
                  goalenv))))

Theorem: svex-varmasks/env->aig-env-rec-of-svarlist-fix-vars

(defthm svex-varmasks/env->aig-env-rec-of-svarlist-fix-vars
 (equal
    (svex-varmasks/env->aig-env-rec (svarlist-fix vars)
                                    masks boolmasks env nextvar acc)
    (svex-varmasks/env->aig-env-rec
         vars masks boolmasks env nextvar acc)))

Theorem: svex-varmasks/env->aig-env-rec-svarlist-equiv-congruence-on-vars

(defthm
   svex-varmasks/env->aig-env-rec-svarlist-equiv-congruence-on-vars
  (implies (svarlist-equiv vars vars-equiv)
           (equal (svex-varmasks/env->aig-env-rec
                       vars masks boolmasks env nextvar acc)
                  (svex-varmasks/env->aig-env-rec
                       vars-equiv
                       masks boolmasks env nextvar acc)))
  :rule-classes :congruence)

Theorem: svex-varmasks/env->aig-env-rec-of-svex-mask-alist-fix-masks

(defthm svex-varmasks/env->aig-env-rec-of-svex-mask-alist-fix-masks
 (equal
    (svex-varmasks/env->aig-env-rec vars (svex-mask-alist-fix masks)
                                    boolmasks env nextvar acc)
    (svex-varmasks/env->aig-env-rec
         vars masks boolmasks env nextvar acc)))

Theorem: svex-varmasks/env->aig-env-rec-svex-mask-alist-equiv-congruence-on-masks

(defthm
 svex-varmasks/env->aig-env-rec-svex-mask-alist-equiv-congruence-on-masks
 (implies (svex-mask-alist-equiv masks masks-equiv)
          (equal (svex-varmasks/env->aig-env-rec
                      vars masks boolmasks env nextvar acc)
                 (svex-varmasks/env->aig-env-rec
                      vars
                      masks-equiv boolmasks env nextvar acc)))
 :rule-classes :congruence)

Theorem: svex-varmasks/env->aig-env-rec-of-svar-boolmasks-fix-boolmasks

(defthm
     svex-varmasks/env->aig-env-rec-of-svar-boolmasks-fix-boolmasks
  (equal (svex-varmasks/env->aig-env-rec
              vars
              masks (svar-boolmasks-fix boolmasks)
              env nextvar acc)
         (svex-varmasks/env->aig-env-rec
              vars masks boolmasks env nextvar acc)))

Theorem: svex-varmasks/env->aig-env-rec-svar-boolmasks-equiv-congruence-on-boolmasks

(defthm
 svex-varmasks/env->aig-env-rec-svar-boolmasks-equiv-congruence-on-boolmasks
 (implies (svar-boolmasks-equiv boolmasks boolmasks-equiv)
          (equal (svex-varmasks/env->aig-env-rec
                      vars masks boolmasks env nextvar acc)
                 (svex-varmasks/env->aig-env-rec
                      vars
                      masks boolmasks-equiv env nextvar acc)))
 :rule-classes :congruence)

Theorem: svex-varmasks/env->aig-env-rec-of-svex-env-fix-env

(defthm svex-varmasks/env->aig-env-rec-of-svex-env-fix-env
  (equal (svex-varmasks/env->aig-env-rec
              vars masks boolmasks (svex-env-fix env)
              nextvar acc)
         (svex-varmasks/env->aig-env-rec
              vars masks boolmasks env nextvar acc)))

Theorem: svex-varmasks/env->aig-env-rec-svex-env-equiv-congruence-on-env

(defthm
    svex-varmasks/env->aig-env-rec-svex-env-equiv-congruence-on-env
  (implies (svex-env-equiv env env-equiv)
           (equal (svex-varmasks/env->aig-env-rec
                       vars masks boolmasks env nextvar acc)
                  (svex-varmasks/env->aig-env-rec
                       vars
                       masks boolmasks env-equiv nextvar acc)))
  :rule-classes :congruence)

Theorem: svex-varmasks/env->aig-env-rec-of-nfix-nextvar

(defthm svex-varmasks/env->aig-env-rec-of-nfix-nextvar
  (equal (svex-varmasks/env->aig-env-rec
              vars masks boolmasks env (nfix nextvar)
              acc)
         (svex-varmasks/env->aig-env-rec
              vars masks boolmasks env nextvar acc)))

Theorem: svex-varmasks/env->aig-env-rec-nat-equiv-congruence-on-nextvar

(defthm
     svex-varmasks/env->aig-env-rec-nat-equiv-congruence-on-nextvar
  (implies (nat-equiv nextvar nextvar-equiv)
           (equal (svex-varmasks/env->aig-env-rec
                       vars masks boolmasks env nextvar acc)
                  (svex-varmasks/env->aig-env-rec
                       vars
                       masks boolmasks env nextvar-equiv acc)))
  :rule-classes :congruence)