• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Community
  • 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
      • C
        • Syntax-for-tools
          • Formalized-subset
          • Mapping-to-language-definition
          • Input-files
          • Compilation-database
          • Printer
          • Output-files
          • Abstract-syntax-operations
          • Implementation-environments
          • Abstract-syntax
          • Concrete-syntax
          • Disambiguation
          • Validation
          • Gcc-builtins
          • Preprocessing
          • Parsing
            • Parser
              • Parse-exprs/decls/stmts
              • Parser-states
                • Parstate
                • Token
                  • Token-fix
                  • Token-case
                  • Tokenp
                  • Token-equiv
                  • Token-string
                  • Token-punctuator
                  • Token-keyword
                  • Token-ident
                  • Token-const
                  • Token-kind
                • Parstate$
                • Position
                • To-parstate$
                • Token-option
                • Init-parstate
                • Span
                • Char+position
                • Token+span
                • Token-punctuatorp
                • Span-join
                • Token-keywordp
                • Position-inc-line
                • Position-inc-column
                • Parsize
                • Parstate->bytes
                • Parstate->chars-length
                • Update-parstate->token
                • Update-parstate->char
                • To-parstate$-tokens-unread
                • To-parstate$-chars-unread
                • To-parstate$-tokens-read
                • Update-parstate->tokens-unread
                • Update-parstate->tokens-read
                • Update-parstate->tokens-length
                • Update-parstate->chars-unread
                • Update-parstate->chars-read
                • To-parstate$-chars-read
                • Parstate->token
                • Parstate->char
                • Char+position-list
                • Update-parstate->version
                • Update-parstate->size
                • Update-parstate->position
                • Update-parstate->chars-length
                • Update-parstate->bytes
                • Token+span-list
                • Parstate->gcc
                • Parstate-fix
                • Parstate->tokens-unread
                • Parstate->chars-unread
                • Irr-position
                • Token-list
                • Position-init
                • Parstate->version
                • Parstate->tokens-read
                • Parstate->tokens-length
                • Parstate->size
                • Parstate->position
                • Parstate->chars-read
                • Irr-token
                • Irr-span
              • Parse-external-declaration
              • Parse-cast-expression
              • Parse-expression-or-type-name
              • Parse-postfix-expression
              • Lexer
              • Parse-primary-expression
              • Token-unary-expression-start-p
              • Parse-declaration-specifier
              • Parse-declaration-specifiers
              • Parse-unary-expression-or-parenthesized-type-name
              • Parse-asm-name-specifier
              • Parse-specifier/qualifier
              • Parse-expression-rest
              • Token-type-specifier-keyword-p
              • Parse-fileset
              • Parse-*-external-declaration
              • Parse-declarator-or-abstract-declarator
              • Parse-asm-goto-labels
              • Parse-asm-clobbers
              • Parse-translation-unit
              • Parse-*-label-declaration
              • Token-postfix-expression-rest-start-p
              • Parse-?-asm-name-specifier
              • Parse-*-comma-identifier
              • Parse-postfix-expression-rest
              • Parse-expression
              • Make-expr-unary-with-preinc/predec-ops
              • Parse-*-stringlit
              • Parse-statement
              • Token-struct-declaration-start-p
              • Parse-*-attribute-specifier
              • Parse-initializer-list
              • Parse-file
              • Parse-pointer
              • Parse-label-declaration
              • Parse-array/function-declarator
              • Token-type-qualifier-p
              • Parse-*-asm-qualifier
              • Parse-parameter-declaration
              • Parse-attribute-name
              • Parse-argument-expressions
              • Make-expr-cast/add-or-cast/sub-ambig
              • Parse-struct-or-union-specifier
              • Parse-declaration-or-statement
              • Parse-assignment-expression
              • Parse-asm-clobber
              • Token-specifier/qualifier-start-p
              • Token-primary-expression-start-p
              • Token-function-specifier-p
              • Token-expression-start-p
              • Parse-*-increment/decrement
              • Parse-direct-abstract-declarator
              • Parse-compound-statement
              • Token-to-type-specifier-keyword
              • Parse-unary-expression
              • Parse-argument-expressions-rest
              • Parse-generic-associations-rest
              • Parse-conditional-expression
              • Parse-fileset-loop
              • Parse-direct-abstract-declarator-rest
              • Token-designation?-initializer-start-p
              • Token-declaration-specifier-start-p
              • Parse-designator-list
              • Token-abstract-declarator-start-p
              • Parse-?-asm-output-operands
              • Parse-?-asm-input-operands
              • Parse-struct-declaration
              • Parse-specifier-qualifier-list
              • Parse-parameter-declaration-list
              • Parse-constant-expression
              • Token-type-specifier-start-p
              • Token-type-qualifier-or-attribute-specifier-start-p
              • Parse-static-assert-declaration
              • Parse-direct-declarator
              • Parse-declaration
              • Parse-attribute-parameters
              • Token-unary-operator-p
              • Token-to-unary-operator
              • Token-to-type-qualifier
              • Token-storage-class-specifier-p
              • Token-initializer-start-p
              • Token-direct-abstract-declarator-start-p
              • Token-declarator-start-p
              • Parse-initializer
              • Parse-direct-declarator-rest
              • Token-to-storage-class-specifier
              • Token-to-assignment-operator
              • Token-to-asm-qualifier
              • Token-struct-declarator-start-p
              • Token-direct-declarator-start-p
              • Token-assignment-operator-p
              • Parse-type-qualifier-and-attribute-specifier-list
              • Parse-enumerator-list
              • Parse-designation?-initializer
              • Parse-compound-literal
              • Parse-block-item
              • Token-type-name-start-p
              • Token-to-function-specifier
              • Token-preinc/predec-operator-p
              • Token-multiplicative-operator-p
              • Token-designator-start-p
              • Token-designation-start-p
              • Parse-generic-association
              • Parse-declaration-list
              • Parse-attribute-specifier
              • Parse-asm-output-operands
              • Token-to-relational-operator
              • Token-to-preinc/predec-operator
              • Token-to-multiplicative-operator
              • Token-relational-operator-p
              • Token-equality-operator-p
              • Token-asm-qualifier-p
              • Token-additive-operator-p
              • Parse-asm-statement
              • Parse-asm-input-operands
              • Token-to-equality-operator
              • Token-to-additive-operator
              • Token-shift-operator-p
              • Parser-messages
              • Parse-type-name
              • Parse-struct-declarator-list
              • Parse-struct-declaration-list
              • Parse-relational-expression-rest
              • Parse-multiplicative-expression-rest
              • Parse-logical-or-expression-rest
              • Parse-logical-and-expression-rest
              • Parse-inclusive-or-expression-rest
              • Parse-exclusive-or-expression-rest
              • Parse-equality-expression-rest
              • Parse-array/function-abstract-declarator
              • Parse-additive-expression-rest
              • Token-to-shift-operator
              • Parse-struct-declarator
              • Parse-shift-expression-rest
              • Parse-member-designor
              • Parse-init-declarator-list
              • Parse-init-declarator
              • Parse-designator
              • Parse-and-expression-rest
              • Parse-alignment-specifier
              • Reader
              • Parse-shift-expression
              • Parse-relational-expression
              • Parse-multiplicative-expression
              • Parse-logical-or-expression
              • Parse-logical-and-expression
              • Parse-inclusive-or-expression
              • Parse-exclusive-or-expression
              • Parse-equality-expression
              • Parse-enum-specifier
              • Parse-block-item-list
              • Parse-attribute-list
              • Parse-and-expression
              • Parse-additive-expression
              • Parse-abstract-declarator
              • Parse-member-designor-rest
              • Parse-declarator
              • Parse-attribute
              • Parse-type-qualifier-or-attribute-specifier
              • Parse-enumerator
              • Parse-asm-output-operand
              • Parse-asm-input-operand
        • Atc
        • Transformation-tools
        • Language
        • Representation
        • Insertion-sort
        • Pack
      • Soft
      • Bv
      • Imp-language
      • Ethereum
      • Event-macros
      • Java
      • Riscv
      • Bitcoin
      • Zcash
      • Yul
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Cryptography
      • Number-theory
      • Axe
      • Lists-light
      • Builtins
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Token

Token-fix

Fixing function for token structures.

Signature

(token-fix x) → new-x

Arguments

x — Guard (tokenp x).

Returns

new-x — Type (tokenp new-x).

Definitions and Theorems

Function: token-fix$inline

(defun token-fix$inline (x)
  (declare (xargs :guard (tokenp x)))
  (mbe :logic
       (case (token-kind x)
         (:keyword (b* ((unwrap (acl2::str-fix (cdr x))))
                     (cons :keyword unwrap)))
         (:ident (b* ((unwrap (ident-fix (cdr x))))
                   (cons :ident unwrap)))
         (:const (b* ((unwrap (const-fix (cdr x))))
                   (cons :const unwrap)))
         (:string (b* ((unwrap (stringlit-fix (cdr x))))
                    (cons :string unwrap)))
         (:punctuator (b* ((unwrap (acl2::str-fix (cdr x))))
                        (cons :punctuator unwrap))))
       :exec x))

Theorem: tokenp-of-token-fix

(defthm tokenp-of-token-fix
  (b* ((new-x (token-fix$inline x)))
    (tokenp new-x))
  :rule-classes :rewrite)

Theorem: token-fix-when-tokenp

(defthm token-fix-when-tokenp
  (implies (tokenp x)
           (equal (token-fix x) x)))

Function: token-equiv$inline

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

Theorem: token-equiv-is-an-equivalence

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

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

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

Theorem: token-fix-under-token-equiv

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

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

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

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

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

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

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

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

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

Theorem: token-kind$inline-of-token-fix-x

(defthm token-kind$inline-of-token-fix-x
  (equal (token-kind$inline (token-fix x))
         (token-kind$inline x)))

Theorem: token-kind$inline-token-equiv-congruence-on-x

(defthm token-kind$inline-token-equiv-congruence-on-x
  (implies (token-equiv x x-equiv)
           (equal (token-kind$inline x)
                  (token-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-token-fix

(defthm consp-of-token-fix
  (consp (token-fix x))
  :rule-classes :type-prescription)

Theorem: token-fix$inline-of-token-fix-x

(defthm token-fix$inline-of-token-fix-x
  (equal (token-fix$inline (token-fix x))
         (token-fix$inline x)))

Theorem: token-fix$inline-token-equiv-congruence-on-x

(defthm token-fix$inline-token-equiv-congruence-on-x
  (implies (token-equiv x x-equiv)
           (equal (token-fix$inline x)
                  (token-fix$inline x-equiv)))
  :rule-classes :congruence)