• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Acre
    • Milawa
    • Smtlink
    • Aleobft
    • 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
    • Java
    • Taspi
    • Bitcoin
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Riscv
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
      • Primitive-functions
      • Translated-terms
      • Values
      • Evaluation
      • Program-equivalence
      • Functions
      • Packages
      • Programs
      • Interpreter
      • Evaluation-states
        • Eval-state
        • Frame
          • Frame-fix
          • Frame-equiv
          • Make-frame
          • Frame->binding
          • Change-frame
          • Frame->term
          • Framep
        • Binding
        • Stack
    • 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

• Frame

Frame-fix

Fixing function for frame structures.

Signature

(frame-fix x) → new-x

Arguments

x — Guard (framep x).

Returns

new-x — Type (framep new-x).

Definitions and Theorems

Function: frame-fix$inline

(defun frame-fix$inline (x)
  (declare (xargs :guard (framep x)))
  (let ((__function__ 'frame-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((term (tterm-fix (std::da-nth 0 (cdr x))))
              (binding (binding-fix (std::da-nth 1 (cdr x)))))
           (cons :frame (list term binding)))
         :exec x)))

Theorem: framep-of-frame-fix

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

Theorem: frame-fix-when-framep

(defthm frame-fix-when-framep
  (implies (framep x)
           (equal (frame-fix x) x)))

Function: frame-equiv$inline

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

Theorem: frame-equiv-is-an-equivalence

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

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

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

Theorem: frame-fix-under-frame-equiv

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

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

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

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

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

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

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

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

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