• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Aleobft
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • C
      • Syntax-for-tools
      • Atc
      • Language
        • Abstract-syntax
        • Integer-ranges
        • Dynamic-semantics
        • Static-semantics
        • Grammar
        • Integer-formats
        • Types
        • Portable-ascii-identifiers
        • Values
        • Integer-operations
        • Implementation-environments
          • Schar-format
          • Uchar-format
          • Signed-format
          • Ienv->schar-min
          • Ienv
          • Char-format
            • Char-format-fix
            • Char-format-equiv
            • Make-char-format
            • Char-format->signedp
            • Change-char-format
            • Char-formatp
          • Ienv->uchar-max
          • Ienv->char-min
          • Ienv->char-bits
          • Ienv->schar-max
          • Ienv->char-max
        • Computation-states
        • Object-designators
        • Operations
        • Errors
        • Tag-environments
        • Function-environments
        • Character-sets
        • Flexible-array-member-removal
        • Arithmetic-operations
        • Pointer-operations
        • Bytes
        • Keywords
        • Real-operations
        • Array-operations
        • Scalar-operations
        • Structure-operations
      • Representation
      • Transformation-tools
      • Pack
    • Java
    • Taspi
    • Bitcoin
    • Riscv
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
    • Where-do-i-place-my-book
    • Bigmems
    • Builtins
    • Axe
    • Execloader
    • Solidity
    • Leo
    • Paco
    • Concurrent-programs
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Char-format

Char-format-fix

Fixing function for char-format structures.

Signature

(char-format-fix x) → new-x

Arguments

x — Guard (char-formatp x).

Returns

new-x — Type (char-formatp new-x).

Definitions and Theorems

Function: char-format-fix$inline

(defun char-format-fix$inline (x)
  (declare (xargs :guard (char-formatp x)))
  (let ((__function__ 'char-format-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((signedp (acl2::bool-fix (cdr (std::da-nth 0 x)))))
           (list (cons 'signedp signedp)))
         :exec x)))

Theorem: char-formatp-of-char-format-fix

(defthm char-formatp-of-char-format-fix
  (b* ((new-x (char-format-fix$inline x)))
    (char-formatp new-x))
  :rule-classes :rewrite)

Theorem: char-format-fix-when-char-formatp

(defthm char-format-fix-when-char-formatp
  (implies (char-formatp x)
           (equal (char-format-fix x) x)))

Function: char-format-equiv$inline

(defun char-format-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (char-formatp acl2::x)
                              (char-formatp acl2::y))))
  (equal (char-format-fix acl2::x)
         (char-format-fix acl2::y)))

Theorem: char-format-equiv-is-an-equivalence

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

Theorem: char-format-equiv-implies-equal-char-format-fix-1

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

Theorem: char-format-fix-under-char-format-equiv

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

Theorem: equal-of-char-format-fix-1-forward-to-char-format-equiv

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

Theorem: equal-of-char-format-fix-2-forward-to-char-format-equiv

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

Theorem: char-format-equiv-of-char-format-fix-1-forward

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

Theorem: char-format-equiv-of-char-format-fix-2-forward

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