• 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
        • Syntax-for-tools
        • Atc
        • Language
          • Abstract-syntax
          • Integer-ranges
          • Dynamic-semantics
          • Static-semantics
          • Grammar
          • Integer-formats
          • Types
          • Portable-ascii-identifiers
          • Values
          • Integer-operations
          • Computation-states
          • Object-designators
          • Implementation-environments
            • Schar-format
              • Schar-format-fix
              • Schar-format-equiv
              • Make-schar-format
              • Schar-format->signed
              • Schar-format->trap
              • Change-schar-format
              • Schar-formatp
            • Uchar-format
            • Signed-format
            • Ienv->schar-min
            • Ienv
            • Ienv->uchar-max
            • Ienv->char-bits
            • Ienv->schar-max
          • 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
      • Event-macros
      • Java
      • Bitcoin
      • Ethereum
      • Yul
      • 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

• Schar-format

Schar-format-fix

Fixing function for schar-format structures.

Signature

(schar-format-fix x) → new-x

Arguments

x — Guard (schar-formatp x).

Returns

new-x — Type (schar-formatp new-x).

Definitions and Theorems

Function: schar-format-fix$inline

(defun schar-format-fix$inline (x)
  (declare (xargs :guard (schar-formatp x)))
  (let ((__function__ 'schar-format-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((signed (signed-format-fix (cdr (std::da-nth 0 x))))
              (trap (acl2::bool-fix (cdr (std::da-nth 1 x)))))
           (list (cons 'signed signed)
                 (cons 'trap trap)))
         :exec x)))

Theorem: schar-formatp-of-schar-format-fix

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

Theorem: schar-format-fix-when-schar-formatp

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

Function: schar-format-equiv$inline

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

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

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

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

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

Theorem: schar-format-fix-under-schar-format-equiv

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

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

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

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

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

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

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

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

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