• Top
  • Documentation
  • Books
  • Recursion-and-induction
  • Boolean-reasoning
  • Debugging
  • Projects
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
    • Sv
      • Svex-stvs
      • Svex-fixpoint-decomposition-methodology
      • Sv-versus-esim
      • Svex-decomp
      • Svex-compose-dfs
      • Moddb
      • Svex-compilation
      • Svmods
      • Svstmt
      • Sv-tutorial
      • Expressions
        • Rewriting
        • Svex
          • Svar
            • Svar-p
            • Svar-fix
            • Make-svar
            • Svar-equiv
            • Svar->override-test
            • Svar->override-val
            • Svar->nonblocking
            • Change-svar
            • Svar->delay
            • Svarlist
            • Svar->name
            • Svar-map
            • Svar-alist
          • Least-fixpoint
          • Svex-p
          • Svex-select
          • Svex-alist
          • Svex-equiv
          • Svexlist
          • Svex-call
          • Fnsym
          • Svex-quote
          • Svex-var
          • Svcall-rw
          • Svcall
          • Svex-kind
          • Svcall*
          • Svex-fix
          • Svex-count
          • Svex-1z
          • Svex-1x
          • Svex-z
          • Svex-x
        • Bit-blasting
        • Functions
        • 4vmask
        • Why-infinite-width
        • Svex-vars
        • Evaluation
        • Values
      • Symbolic-test-vector
      • Vl-to-svex
    • Fgl
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Testing-utilities
  • Math

• Svar

Svar-fix

Fixing function for svar structures.

Signature

(svar-fix x) → new-x

Arguments

x — Guard (svar-p x).

Returns

new-x — Type (svar-p new-x).

Definitions and Theorems

Function: svar-fix$inline

(defun
 svar-fix$inline (x)
 (declare (xargs :guard (svar-p x)))
 (let
  ((__function__ 'svar-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((name (if (atom x) x (cadr x)))
     (delay (nfix (if (atom x)
                      0
                      (if (< (cddr x) 0)
                          (logtail 3 (lognot (cddr x)))
                          (cddr x)))))
     (nonblocking
          (bool-fix (if (atom x)
                        nil
                        (let ((bits (cddr x)))
                             (and (< bits 0) (logbitp 2 bits))))))
     (override-test
          (bool-fix (if (atom x)
                        nil
                        (let ((bits (cddr x)))
                             (and (< bits 0) (logbitp 0 bits))))))
     (override-val
          (bool-fix (if (atom x)
                        nil
                        (let ((bits (cddr x)))
                             (and (< bits 0) (logbitp 1 bits)))))))
    (if
     (and (or (stringp name)
              (and (symbolp name)
                   (not (booleanp name))))
          (not nonblocking)
          (not override-test)
          (not override-val)
          (eql delay 0))
     name
     (hons
          :var (hons name
                     (if (or nonblocking override-test override-val)
                         (acl2::loglist* (bool->bit override-test)
                                         (bool->bit override-val)
                                         (bool->bit nonblocking)
                                         (lognot delay))
                         delay)))))
   :exec x)))

Theorem: svar-p-of-svar-fix

(defthm svar-p-of-svar-fix
        (b* ((new-x (svar-fix$inline x)))
            (svar-p new-x))
        :rule-classes :rewrite)

Theorem: svar-fix-when-svar-p

(defthm svar-fix-when-svar-p
        (implies (svar-p x)
                 (equal (svar-fix x) x)))

Function: svar-equiv$inline

(defun svar-equiv$inline (x y)
       (declare (xargs :guard (and (svar-p x) (svar-p y))))
       (equal (svar-fix x) (svar-fix y)))

Theorem: svar-equiv-is-an-equivalence

(defthm svar-equiv-is-an-equivalence
        (and (booleanp (svar-equiv x y))
             (svar-equiv x x)
             (implies (svar-equiv x y)
                      (svar-equiv y x))
             (implies (and (svar-equiv x y) (svar-equiv y z))
                      (svar-equiv x z)))
        :rule-classes (:equivalence))

Theorem: svar-equiv-implies-equal-svar-fix-1

(defthm svar-equiv-implies-equal-svar-fix-1
        (implies (svar-equiv x x-equiv)
                 (equal (svar-fix x) (svar-fix x-equiv)))
        :rule-classes (:congruence))

Theorem: svar-fix-under-svar-equiv

(defthm svar-fix-under-svar-equiv
        (svar-equiv (svar-fix x) x)
        :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-svar-fix-1-forward-to-svar-equiv

(defthm equal-of-svar-fix-1-forward-to-svar-equiv
        (implies (equal (svar-fix x) y)
                 (svar-equiv x y))
        :rule-classes :forward-chaining)

Theorem: equal-of-svar-fix-2-forward-to-svar-equiv

(defthm equal-of-svar-fix-2-forward-to-svar-equiv
        (implies (equal x (svar-fix y))
                 (svar-equiv x y))
        :rule-classes :forward-chaining)

Theorem: svar-equiv-of-svar-fix-1-forward

(defthm svar-equiv-of-svar-fix-1-forward
        (implies (svar-equiv (svar-fix x) y)
                 (svar-equiv x y))
        :rule-classes :forward-chaining)

Theorem: svar-equiv-of-svar-fix-2-forward

(defthm svar-equiv-of-svar-fix-2-forward
        (implies (svar-equiv x (svar-fix y))
                 (svar-equiv x y))
        :rule-classes :forward-chaining)