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Svex-varmasks->a4env-rec

Signature

(svex-varmasks->a4env-rec vars masks boolmasks nextvar acc) 
  → 
(mv err a4env nextvar1)

Arguments

vars — Guard (svarlist-p vars).

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

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

nextvar — Guard (natp nextvar).

acc — Guard (nat-bool-a4env-p! acc).

Returns

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

a4env — Type (nat-bool-a4env-p! a4env), given (nat-bool-a4env-p! acc).

nextvar1 — Type (equal nextvar1 (+ (nfix nextvar) (svex-maskbits-for-vars vars masks boolmasks))) .

Definitions and Theorems

Function: svex-varmasks->a4env-rec

(defun svex-varmasks->a4env-rec (vars masks boolmasks nextvar acc)
  (declare (xargs :guard (and (svarlist-p vars)
                              (svex-mask-alist-p masks)
                              (svar-boolmasks-p boolmasks)
                              (natp nextvar)
                              (nat-bool-a4env-p! acc))))
  (let ((__function__ 'svex-varmasks->a4env-rec))
    (declare (ignorable __function__))
    (b* ((acc (svex-a4vec-env-fix acc))
         ((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))
         (a4vec (4vmask-to-a4vec mask boolmask nextvar))
         (nextvar (+ (lnfix nextvar)
                     (4vmask-to-a4vec-varcount mask boolmask))))
      (svex-varmasks->a4env-rec
           (cdr vars)
           masks boolmasks nextvar
           (cons (cons (svar-fix (car vars)) a4vec)
                 acc)))))

Theorem: return-type-of-svex-varmasks->a4env-rec.err

(defthm return-type-of-svex-varmasks->a4env-rec.err
 (b* (((mv ?err ?a4env ?nextvar1)
       (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)))
   (iff err
        (not (svex-maskbits-ok vars masks))))
 :rule-classes :rewrite)

Theorem: nat-bool-a4env-p!-of-svex-varmasks->a4env-rec.a4env

(defthm nat-bool-a4env-p!-of-svex-varmasks->a4env-rec.a4env
 (implies
   (nat-bool-a4env-p! acc)
   (b*
     (((mv ?err ?a4env ?nextvar1)
       (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)))
     (nat-bool-a4env-p! a4env)))
 :rule-classes :rewrite)

Theorem: return-type-of-svex-varmasks->a4env-rec.nextvar1

(defthm return-type-of-svex-varmasks->a4env-rec.nextvar1
 (b* (((mv ?err ?a4env ?nextvar1)
       (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)))
   (equal nextvar1
          (+ (nfix nextvar)
             (svex-maskbits-for-vars vars masks boolmasks))))
 :rule-classes :rewrite)

Theorem: svex-varmasks->a4env-rec-accumulator-elim

(defthm svex-varmasks->a4env-rec-accumulator-elim
 (implies
   (syntaxp (not (equal acc ''nil)))
   (b*
     (((mv err1 a4env1 nextvar1)
       (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc))
      ((mv err2 a4env2 nextvar2)
       (svex-varmasks->a4env-rec vars masks boolmasks nextvar nil)))
     (and (equal err1 err2)
          (equal a4env1
                 (append a4env2 (svex-a4vec-env-fix acc)))
          (equal nextvar1 nextvar2)))))

Theorem: member-vars-of-svex-varmasks->a4env-rec

(defthm member-vars-of-svex-varmasks->a4env-rec
 (iff
  (member
   v
   (nat-bool-a4env-vars
    (mv-nth
      1
      (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc))))
  (or (member v (nat-bool-a4env-vars acc))
      (and (natp v)
           (<= (nfix nextvar) v)
           (< v
              (+ (nfix nextvar)
                 (svex-maskbits-for-vars vars masks boolmasks)))))))

Theorem: svex-varmasks->a4env-rec-lower-bounds

(defthm svex-varmasks->a4env-rec-lower-bounds
 (implies
  (and (nat-bool-a4env-lower-boundp bound acc)
       (<= (nfix bound) (nfix nextvar)))
  (nat-bool-a4env-lower-boundp
   bound
   (mv-nth
     1
     (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)))))

Theorem: svex-varmasks->a4env-rec-upper-bounds

(defthm svex-varmasks->a4env-rec-upper-bounds
 (implies
  (and (nat-bool-a4env-upper-boundp bound acc)
       (<= (+ (nfix nextvar)
              (svex-maskbits-for-vars vars masks boolmasks))
           (nfix bound)))
  (nat-bool-a4env-upper-boundp
   bound
   (mv-nth
     1
     (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)))))

Theorem: key-exists-in-svex-varmasks->a4env-rec

(defthm key-exists-in-svex-varmasks->a4env-rec
 (b* (((mv ?err ?a4env ?nextvar1)
       (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)))
   (implies
        (not err)
        (iff (hons-assoc-equal v a4env)
             (or (member v (svarlist-fix vars))
                 (hons-assoc-equal v (svex-a4vec-env-fix acc)))))))

Theorem: alist-keys-of-svex-varmasks->a4env-rec

(defthm alist-keys-of-svex-varmasks->a4env-rec
 (b* (((mv ?err ?a4env ?nextvar1)
       (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)))
  (implies (not err)
           (equal (alist-keys a4env)
                  (append (rev (svarlist-fix vars))
                          (alist-keys (svex-a4vec-env-fix acc)))))))

Theorem: svex-varmasks->a4env-rec-of-svarlist-fix-vars

(defthm svex-varmasks->a4env-rec-of-svarlist-fix-vars
  (equal
       (svex-varmasks->a4env-rec (svarlist-fix vars)
                                 masks boolmasks nextvar acc)
       (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)))

Theorem: svex-varmasks->a4env-rec-svarlist-equiv-congruence-on-vars

(defthm svex-varmasks->a4env-rec-svarlist-equiv-congruence-on-vars
 (implies
  (svarlist-equiv vars vars-equiv)
  (equal (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)
         (svex-varmasks->a4env-rec vars-equiv
                                   masks boolmasks nextvar acc)))
 :rule-classes :congruence)

Theorem: svex-varmasks->a4env-rec-of-svex-mask-alist-fix-masks

(defthm svex-varmasks->a4env-rec-of-svex-mask-alist-fix-masks
  (equal
       (svex-varmasks->a4env-rec vars (svex-mask-alist-fix masks)
                                 boolmasks nextvar acc)
       (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)))

Theorem: svex-varmasks->a4env-rec-svex-mask-alist-equiv-congruence-on-masks

(defthm
 svex-varmasks->a4env-rec-svex-mask-alist-equiv-congruence-on-masks
 (implies
  (svex-mask-alist-equiv masks masks-equiv)
  (equal
      (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)
      (svex-varmasks->a4env-rec vars
                                masks-equiv boolmasks nextvar acc)))
 :rule-classes :congruence)

Theorem: svex-varmasks->a4env-rec-of-svar-boolmasks-fix-boolmasks

(defthm svex-varmasks->a4env-rec-of-svar-boolmasks-fix-boolmasks
 (equal
      (svex-varmasks->a4env-rec vars
                                masks (svar-boolmasks-fix boolmasks)
                                nextvar acc)
      (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)))

Theorem: svex-varmasks->a4env-rec-svar-boolmasks-equiv-congruence-on-boolmasks

(defthm
 svex-varmasks->a4env-rec-svar-boolmasks-equiv-congruence-on-boolmasks
 (implies
  (svar-boolmasks-equiv boolmasks boolmasks-equiv)
  (equal
      (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)
      (svex-varmasks->a4env-rec vars
                                masks boolmasks-equiv nextvar acc)))
 :rule-classes :congruence)

Theorem: svex-varmasks->a4env-rec-of-nfix-nextvar

(defthm svex-varmasks->a4env-rec-of-nfix-nextvar
  (equal
       (svex-varmasks->a4env-rec vars masks boolmasks (nfix nextvar)
                                 acc)
       (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)))

Theorem: svex-varmasks->a4env-rec-nat-equiv-congruence-on-nextvar

(defthm svex-varmasks->a4env-rec-nat-equiv-congruence-on-nextvar
 (implies
  (nat-equiv nextvar nextvar-equiv)
  (equal
      (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)
      (svex-varmasks->a4env-rec vars
                                masks boolmasks nextvar-equiv acc)))
 :rule-classes :congruence)

Theorem: svex-varmasks->a4env-rec-of-svex-a4vec-env-fix-acc

(defthm svex-varmasks->a4env-rec-of-svex-a4vec-env-fix-acc
  (equal
       (svex-varmasks->a4env-rec vars masks boolmasks
                                 nextvar (svex-a4vec-env-fix acc))
       (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)))

Theorem: svex-varmasks->a4env-rec-svex-a4vec-env-equiv-congruence-on-acc

(defthm
    svex-varmasks->a4env-rec-svex-a4vec-env-equiv-congruence-on-acc
 (implies
  (svex-a4vec-env-equiv acc acc-equiv)
  (equal
      (svex-varmasks->a4env-rec vars masks boolmasks nextvar acc)
      (svex-varmasks->a4env-rec vars
                                masks boolmasks nextvar acc-equiv)))
 :rule-classes :congruence)