• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
      • Crypto-hdwallet
      • Apt
      • Error-checking
      • Fty-extensions
      • Isar
      • Kestrel-utilities
      • Soft
      • Bv
      • Imp-language
      • C
      • Event-macros
      • Java
      • Bitcoin
      • Ethereum
      • Yul
        • Transformations
        • Language
          • Abstract-syntax
          • Dynamic-semantics
            • Exec
            • Find-fun
            • Init-local
            • Mode
            • Write-vars-values
            • Add-vars-values
            • Add-funs
            • Eoutcome
            • Soutcome
            • Ensure-funscope-disjoint
            • Write-var-value
            • Restrict-vars
            • Add-var-value
            • Funinfo
            • Exec-top-block
            • Values
            • Cstate
            • Funinfo+funenv
            • Read-vars-values
            • Read-var-value
            • Funenv
            • Funscope-for-fundefs
            • Exec-path
            • Path-to-var
            • Funinfo+funenv-result
            • Exec-literal
            • Soutcome-result
            • Mode-set-result
            • Funscope-result
            • Funinfo-result
            • Funenv-result
            • Eoutcome-result
            • Cstate-result
            • Paths-to-vars
            • Funinfo-for-fundef
            • Literal-evaluation
            • Lstate
            • Funscope
              • Funscopep
              • Funscope-fix
              • Funscope-equiv
            • Mode-set
          • Concrete-syntax
          • Static-soundness
          • Static-semantics
          • Errors
        • Yul-json
      • Zcash
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Number-theory
      • Cryptography
      • Lists-light
      • Builtins
      • Axe
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Funscope

Funscope-fix

(funscope-fix x) is a usual ACL2::fty omap fixing function.

Signature

(funscope-fix x) → *

Arguments

x — Guard (funscopep x).

Definitions and Theorems

Function: funscope-fix

(defun funscope-fix (x)
  (declare (xargs :guard (funscopep x)))
  (mbe :logic (if (funscopep x) x nil)
       :exec x))

Theorem: funscopep-of-funscope-fix

(defthm funscopep-of-funscope-fix
  (funscopep (funscope-fix x)))

Theorem: funscope-fix-when-funscopep

(defthm funscope-fix-when-funscopep
  (implies (funscopep x)
           (equal (funscope-fix x) x)))

Theorem: emptyp-funscope-fix

(defthm emptyp-funscope-fix
  (implies (or (omap::emptyp x)
               (not (funscopep x)))
           (omap::emptyp (funscope-fix x))))

Theorem: emptyp-of-funscope-fix-to-not-funscope-or-emptyp

(defthm emptyp-of-funscope-fix-to-not-funscope-or-emptyp
  (equal (omap::emptyp (funscope-fix x))
         (or (not (funscopep x))
             (omap::emptyp x))))

Function: funscope-equiv$inline

(defun funscope-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (funscopep acl2::x)
                              (funscopep acl2::y))))
  (equal (funscope-fix acl2::x)
         (funscope-fix acl2::y)))

Theorem: funscope-equiv-is-an-equivalence

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

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

(defthm funscope-equiv-implies-equal-funscope-fix-1
  (implies (funscope-equiv acl2::x x-equiv)
           (equal (funscope-fix acl2::x)
                  (funscope-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: funscope-fix-under-funscope-equiv

(defthm funscope-fix-under-funscope-equiv
  (funscope-equiv (funscope-fix acl2::x)
                  acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

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

(defthm equal-of-funscope-fix-1-forward-to-funscope-equiv
  (implies (equal (funscope-fix acl2::x) acl2::y)
           (funscope-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm equal-of-funscope-fix-2-forward-to-funscope-equiv
  (implies (equal acl2::x (funscope-fix acl2::y))
           (funscope-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm funscope-equiv-of-funscope-fix-1-forward
  (implies (funscope-equiv (funscope-fix acl2::x)
                           acl2::y)
           (funscope-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm funscope-equiv-of-funscope-fix-2-forward
  (implies (funscope-equiv acl2::x (funscope-fix acl2::y))
           (funscope-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)