• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • C
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • Java
    • Taspi
    • Bitcoin
    • Riscv
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
      • Parser-output-to-values
      • Values
        • Value/valuelist/member/memberlist
        • Value-option
          • Value-option-fix
          • Value-option-case
          • Value-option-equiv
          • Value-option-some
          • Value-option-none
          • Value-optionp
        • Irr-value
        • Irr-member
      • Syntax
      • Patbind-pattern
      • Operations
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
    • Where-do-i-place-my-book
    • Axe
    • Bigmems
    • Builtins
    • Execloader
    • Aleo
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Value-option

Value-option-fix

Fixing function for value-option structures.

Signature

(value-option-fix x) → new-x

Arguments

x — Guard (value-optionp x).

Returns

new-x — Type (value-optionp new-x).

Definitions and Theorems

Function: value-option-fix$inline

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

Theorem: value-optionp-of-value-option-fix

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

Theorem: value-option-fix-when-value-optionp

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

Function: value-option-equiv$inline

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

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

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

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

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

Theorem: value-option-fix-under-value-option-equiv

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

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

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

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

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

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

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

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

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