• 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
      • Set
      • Soft
      • C
      • Bv
      • Imp-language
      • Event-macros
      • Java
      • Bitcoin
      • Ethereum
      • Yul
        • Transformations
        • Language
          • Abstract-syntax
          • Dynamic-semantics
          • Concrete-syntax
          • Static-soundness
          • Static-semantics
            • Static-safety-checking
              • Check-safe-statements/blocks/cases/fundefs
              • Check-safe-expressions
              • Check-safe-fundef-list
              • Check-safe-variable-multi
              • Check-safe-variable-single
              • Check-safe-assign-multi
              • Check-safe-assign-single
              • Check-safe-path
              • Check-safe-extends-varset
              • Vars+modes
                • Vars+modes-fix
                • Vars+modes-equiv
                • Make-vars+modes
                • Vars+modes->vars
                • Vars+modes->modes
                • Change-vars+modes
                • Vars+modes-p
              • Add-vars
              • Add-var
              • Add-funtypes
              • Check-safe-literal
              • Funtype
              • Get-funtype
              • Check-var
              • Check-safe-top-block
              • Check-safe-path-list
              • Vars+modes-result
              • Funtype-result
              • Funtable-result
              • Funtable-for-fundefs
              • Funtype-for-fundef
              • Funtable
            • Static-shadowing-checking
            • Mode-set-result
            • Literal-evaluation
            • Static-identifier-checking
            • Static-safety-checking-evm
            • Mode-set
            • Modes
          • Errors
        • Yul-json
      • Zcash
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Cryptography
      • Number-theory
      • Lists-light
      • Axe
      • Builtins
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Vars+modes

Vars+modes-fix

Fixing function for vars+modes structures.

Signature

(vars+modes-fix x) → new-x

Arguments

x — Guard (vars+modes-p x).

Returns

new-x — Type (vars+modes-p new-x).

Definitions and Theorems

Function: vars+modes-fix$inline

(defun vars+modes-fix$inline (x)
 (declare (xargs :guard (vars+modes-p x)))
 (let ((__function__ 'vars+modes-fix))
  (declare (ignorable __function__))
  (mbe
      :logic
      (b* ((vars (identifier-set-fix (cdr (std::da-nth 0 (cdr x)))))
           (modes (mode-set-fix (cdr (std::da-nth 1 (cdr x))))))
        (cons :vars+modes (list (cons 'vars vars)
                                (cons 'modes modes))))
      :exec x)))

Theorem: vars+modes-p-of-vars+modes-fix

(defthm vars+modes-p-of-vars+modes-fix
  (b* ((new-x (vars+modes-fix$inline x)))
    (vars+modes-p new-x))
  :rule-classes :rewrite)

Theorem: vars+modes-fix-when-vars+modes-p

(defthm vars+modes-fix-when-vars+modes-p
  (implies (vars+modes-p x)
           (equal (vars+modes-fix x) x)))

Function: vars+modes-equiv$inline

(defun vars+modes-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (vars+modes-p acl2::x)
                              (vars+modes-p acl2::y))))
  (equal (vars+modes-fix acl2::x)
         (vars+modes-fix acl2::y)))

Theorem: vars+modes-equiv-is-an-equivalence

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

Theorem: vars+modes-equiv-implies-equal-vars+modes-fix-1

(defthm vars+modes-equiv-implies-equal-vars+modes-fix-1
  (implies (vars+modes-equiv acl2::x x-equiv)
           (equal (vars+modes-fix acl2::x)
                  (vars+modes-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: vars+modes-fix-under-vars+modes-equiv

(defthm vars+modes-fix-under-vars+modes-equiv
  (vars+modes-equiv (vars+modes-fix acl2::x)
                    acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-vars+modes-fix-1-forward-to-vars+modes-equiv

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

Theorem: equal-of-vars+modes-fix-2-forward-to-vars+modes-equiv

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

Theorem: vars+modes-equiv-of-vars+modes-fix-1-forward

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

Theorem: vars+modes-equiv-of-vars+modes-fix-2-forward

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