• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Community
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
    • Sv
      • Svex-stvs
      • Svex-decomposition-methodology
      • Sv-versus-esim
      • Svex-decomp
      • Svex-compose-dfs
      • Svex-compilation
      • Moddb
      • Svmods
      • Svstmt
      • Sv-tutorial
      • Expressions
        • Rewriting
        • Svex
        • Bit-blasting
        • Functions
        • 4vmask
          • Svex-argmasks
          • 4vmask-p
          • 4vmask-subsumes
          • 4veclist-mask
          • 4vec-mask-to-zero
          • 4vec-mask
          • 4vmasklist-subsumes
          • 4vmask-union
          • 4vec-mask?
          • 4vmask-equiv
          • 4vmask-fix
          • 4vmask-alist
            • 4vmask-alist-p
            • 4vmask-alist-fix
            • 4vmask-acons
            • 4vmask-assoc
            • 4vmask-alist-equiv
          • 4veclist-mask?
          • 4vmasklist
          • 4vmask-empty
        • Why-infinite-width
        • Svex-vars
        • Evaluation
        • Values
      • Symbolic-test-vector
      • Vl-to-svex
    • Fgl
    • Vwsim
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• 4vmask-alist

4vmask-acons

Extend a slow 4vmask-alist with a new binding.

Signature

(4vmask-acons var mask alist) → extended-alist

Arguments

var — Variable to bind.
    Guard (svar-p var).

mask — Mask to bind it to.
    Guard (4vmask-p mask).

alist — Initial alist to extend.
    Guard (4vmask-alist-p alist).

Returns

extended-alist — Type (4vmask-alist-p extended-alist).

Definitions and Theorems

Function: 4vmask-acons

(defun 4vmask-acons (var mask alist)
  (declare (xargs :guard (and (svar-p var)
                              (4vmask-p mask)
                              (4vmask-alist-p alist))))
  (let ((__function__ '4vmask-acons))
    (declare (ignorable __function__))
    (mbe :logic (cons (cons (svar-fix var) (4vmask-fix mask))
                      (4vmask-alist-fix alist))
         :exec (acons var mask alist))))

Theorem: 4vmask-alist-p-of-4vmask-acons

(defthm 4vmask-alist-p-of-4vmask-acons
  (b* ((extended-alist (4vmask-acons var mask alist)))
    (4vmask-alist-p extended-alist))
  :rule-classes :rewrite)

Theorem: 4vmask-acons-of-svar-fix-var

(defthm 4vmask-acons-of-svar-fix-var
  (equal (4vmask-acons (svar-fix var) mask alist)
         (4vmask-acons var mask alist)))

Theorem: 4vmask-acons-svar-equiv-congruence-on-var

(defthm 4vmask-acons-svar-equiv-congruence-on-var
  (implies (svar-equiv var var-equiv)
           (equal (4vmask-acons var mask alist)
                  (4vmask-acons var-equiv mask alist)))
  :rule-classes :congruence)

Theorem: 4vmask-acons-of-4vmask-fix-mask

(defthm 4vmask-acons-of-4vmask-fix-mask
  (equal (4vmask-acons var (4vmask-fix mask)
                       alist)
         (4vmask-acons var mask alist)))

Theorem: 4vmask-acons-4vmask-equiv-congruence-on-mask

(defthm 4vmask-acons-4vmask-equiv-congruence-on-mask
  (implies (4vmask-equiv mask mask-equiv)
           (equal (4vmask-acons var mask alist)
                  (4vmask-acons var mask-equiv alist)))
  :rule-classes :congruence)

Theorem: 4vmask-acons-of-4vmask-alist-fix-alist

(defthm 4vmask-acons-of-4vmask-alist-fix-alist
  (equal (4vmask-acons var mask (4vmask-alist-fix alist))
         (4vmask-acons var mask alist)))

Theorem: 4vmask-acons-4vmask-alist-equiv-congruence-on-alist

(defthm 4vmask-acons-4vmask-alist-equiv-congruence-on-alist
  (implies (4vmask-alist-equiv alist alist-equiv)
           (equal (4vmask-acons var mask alist)
                  (4vmask-acons var mask alist-equiv)))
  :rule-classes :congruence)

Theorem: 4vmask-assoc-of-4vmask-acons

(defthm 4vmask-assoc-of-4vmask-acons
  (equal (4vmask-assoc j (4vmask-acons k v x))
         (if (svar-equiv j k)
             (4vmask-fix v)
           (4vmask-assoc j x))))