• 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
      • Set
      • Soft
      • C
      • Bv
      • Imp-language
      • Event-macros
      • Java
      • Bitcoin
      • Ethereum
      • Yul
      • Zcash
      • ACL2-programming-language
        • Primitive-functions
        • Translated-terms
        • Values
        • Evaluation
        • Program-equivalence
        • Functions
          • Function
          • Function-lookup
          • Function-option
            • Function-option-fix
            • Function-option-case
            • Function-option-equiv
            • Function-option-some
            • Function-option-none
            • Function-optionp
          • Lift-function
          • Lift-function-list
          • Function-set
        • Packages
        • Programs
        • Interpreter
        • Evaluation-states
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Cryptography
      • Number-theory
      • Lists-light
      • Axe
      • Builtins
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Function-option

Function-option-fix

Fixing function for function-option structures.

Signature

(function-option-fix x) → new-x

Arguments

x — Guard (function-optionp x).

Returns

new-x — Type (function-optionp new-x).

Definitions and Theorems

Function: function-option-fix$inline

(defun function-option-fix$inline (x)
  (declare (xargs :guard (function-optionp x)))
  (let ((__function__ 'function-option-fix))
    (declare (ignorable __function__))
    (mbe :logic (cond ((not x) nil)
                      (t (b* ((fty::val (function-fix x)))
                           fty::val)))
         :exec x)))

Theorem: function-optionp-of-function-option-fix

(defthm function-optionp-of-function-option-fix
  (b* ((new-x (function-option-fix$inline x)))
    (function-optionp new-x))
  :rule-classes :rewrite)

Theorem: function-option-fix-when-function-optionp

(defthm function-option-fix-when-function-optionp
  (implies (function-optionp x)
           (equal (function-option-fix x) x)))

Function: function-option-equiv$inline

(defun function-option-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (function-optionp acl2::x)
                              (function-optionp acl2::y))))
  (equal (function-option-fix acl2::x)
         (function-option-fix acl2::y)))

Theorem: function-option-equiv-is-an-equivalence

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

Theorem: function-option-equiv-implies-equal-function-option-fix-1

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

Theorem: function-option-fix-under-function-option-equiv

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

Theorem: equal-of-function-option-fix-1-forward-to-function-option-equiv

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

Theorem: equal-of-function-option-fix-2-forward-to-function-option-equiv

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

Theorem: function-option-equiv-of-function-option-fix-1-forward

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

Theorem: function-option-equiv-of-function-option-fix-2-forward

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