• 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
          • Disambiguator
          • Abstract-syntax
          • Parser
            • Parse-exprs/decls/stmts
            • Check-full-ppnumber
            • Read-char
            • Parstate
            • Lex-identifier/keyword
            • Lex-oct-iconst-/-dec-fconst
            • Lex-lexeme
            • Parse-external-declaration
            • Parse-cast-expression
            • Lex-isuffix-if-present
            • Parse-expression-or-type-name
            • Parse-postfix-expression
            • Lex-hex-iconst/fconst
            • Lex-dec-iconst/fconst
            • Lex-block-comment
            • Lex-escape-sequence
            • Read-token
            • Token
            • Lex-*-hexadecimal-digit
            • Lex-*-c-char
            • Lex-*-s-char
            • Parse-specifier/qualifier
            • Lex-*-digit
            • Lex-line-comment
            • Char-to-msg
            • Parse-primary-expression
            • Parse-declaration-specifier
            • Lex-iconst/fconst
            • Parse-external-declaration-list
            • Parse-declaration-specifiers
            • Lex-dec-expo-if-present
            • Init-parstate
            • Reread-to-token
            • Parse-asm-name-specifier
            • Lex-character-constant
            • Parse-expression-rest
            • Parstate$
            • Lex-dec-fconst
            • Token-unary-expression-start-p
            • Parse-declarator-or-abstract-declarator
            • Parse-asm-goto-labels
            • Parse-asm-clobbers
            • Lex-stringlit
            • Lex-non-octal-digit
            • Position
              • Positionp
              • Position-fix
              • Position-equiv
              • Make-position
              • Change-position
              • Position->line
              • Position->column
            • Lexeme
            • Lex-fsuffix-if-present
            • Lex-hexadecimal-digit
            • Token-type-specifier-keyword-p
            • Parse-translation-unit
            • Token-postfix-expression-rest-start-p
            • To-parstate$
            • Parse-?-asm-name-specifier
            • Parse-postfix-expression-rest
            • Parse-expression
            • Lex-sign-if-present
            • Lex-dec-expo
            • Lex-bin-expo
            • Unread-to-token
            • Parse-*-stringlit
            • Parse-statement
            • Parse-fileset
            • Make-expr-unary-with-preinc/predec-ops
            • Token-option
            • Lexeme-option
            • Token-struct-declaration-start-p
            • Parse-*-attribute-specifier
            • Parse-initializer-list
            • Parse-file
            • Parse-pointer
            • Parse-array/function-declarator
            • Unread-chars
            • Span
            • Read-stringlit
            • Lex-hex-quad
            • Unread-tokens
            • Token-type-qualifier-p
            • Read-identifier
            • Parse-*-asm-qualifier
            • Unread-char
            • Parse-attribute-name
            • Parse-argument-expressions
            • Make-expr-cast/add-or-cast/sub-ambig
            • Read-punctuator
            • Parse-struct-or-union-specifier
            • Parse-assignment-expression
            • Parse-asm-clobber
            • Token-specifier/qualifier-start-p
            • Token-primary-expression-start-p
            • Token-function-specifier-p
            • Reterr-msg
            • Read-keyword
            • Parse-*-increment/decrement
            • Parse-direct-abstract-declarator
            • Parse-declaration-or-statement
            • Char+position
            • Unread-token
            • Token+span
            • Token-expression-start-p
            • Update-parstate->tokens-unread
            • Update-parstate->chars-unread
            • Token-to-msg
            • Update-parstate->tokens-read
            • Update-parstate->tokens-length
            • Update-parstate->position
            • Update-parstate->chars-read
            • Parse-parameter-declaration
            • Parse-argument-expressions-rest
            • Update-parstate->chars-length
            • Token-to-type-specifier-keyword
            • Update-parstate->bytes
            • Parse-unary-expression
            • Parse-generic-associations-rest
            • Parse-conditional-expression
            • Update-parstate->size
            • Update-parstate->gcc
            • Parsize
            • Parse-direct-abstract-declarator-rest
            • Token-declaration-specifier-start-p
            • Parse-designator-list
            • Token-designation?-initializer-start-p
            • 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-fileset-loop
            • 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-punctuatorp
            • Token-direct-abstract-declarator-start-p
            • Token-declarator-start-p
            • Parse-direct-declarator-rest
            • Token-to-storage-class-specifier
            • Token-to-assignment-operator
            • Token-to-asm-qualifier
            • Token-struct-declarator-start-p
            • Token-keywordp
            • Token-initializer-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
            • Parstate->tokens-unread
            • Parstate->chars-unread
            • Parstate->bytes
            • Parse-initializer
            • 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
            • Span-join
            • Parstate->tokens-read
            • Parstate->tokens-length
            • Parstate->size
            • Parstate->chars-read
            • Parstate->chars-length
            • Parse-asm-statement
            • Parse-asm-input-operands
            • Update-parstate->token
            • Update-parstate->char
            • Token-to-equality-operator
            • Token-to-additive-operator
            • Token-shift-operator-p
            • To-parstate$-tokens-unread
            • To-parstate$-chars-unread
            • Position-inc-line
            • Position-inc-column
            • Parstate->gcc
            • 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
            • To-parstate$-tokens-read
            • Parse-struct-declarator
            • Parse-shift-expression-rest
            • Parse-member-designor
            • Parse-init-declarator-list
            • Parse-init-declarator
            • Parse-and-expression-rest
            • Parse-alignment-specifier
            • To-parstate$-chars-read
            • Position-to-msg
            • Parstate->token
            • Parstate->char
            • 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
            • Char+position-list
            • Token+span-list
            • Span-to-msg
            • Parstate-fix
            • Parse-member-designor-rest
            • Position-init
            • Parstate->position
            • Parse-designator
            • Parse-declarator
            • Parse-attribute
            • Irr-token
            • Irr-span
            • Irr-position
            • Irr-lexeme
            • Token-list
            • Parse-type-qualifier-or-attribute-specifier
            • Parse-enumerator
            • Parse-asm-output-operand
            • Parse-asm-input-operand
          • Validator
          • Printer
          • Formalized-subset
          • Mapping-to-language-definition
          • Defpred
          • Output-files
          • Input-files
          • Abstract-syntax-operations
          • Implementation-environments
          • Concrete-syntax
          • Unambiguity
          • Preprocessing
          • Abstraction-mapping
          • Annotation
        • Atc
        • Language
        • 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

• Position

Position-fix

Fixing function for position structures.

Signature

(position-fix x) → new-x

Arguments

x — Guard (positionp x).

Returns

new-x — Type (positionp new-x).

Definitions and Theorems

Function: position-fix$inline

(defun position-fix$inline (x)
  (declare (xargs :guard (positionp x)))
  (let ((__function__ 'position-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((line (acl2::pos-fix (cdr (std::da-nth 0 x))))
              (column (nfix (cdr (std::da-nth 1 x)))))
           (list (cons 'line line)
                 (cons 'column column)))
         :exec x)))

Theorem: positionp-of-position-fix

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

Theorem: position-fix-when-positionp

(defthm position-fix-when-positionp
  (implies (positionp x)
           (equal (position-fix x) x)))

Function: position-equiv$inline

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

Theorem: position-equiv-is-an-equivalence

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

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

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

Theorem: position-fix-under-position-equiv

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

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

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

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

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

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

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

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

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