• Top
  • Documentation
  • Books
  • Recursion-and-induction
  • Boolean-reasoning
  • Debugging
  • Projects
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
      • Crypto-hdwallet
      • Error-checking
      • Apt
      • Abnf
      • Fty-extensions
      • Isar
      • Kestrel-utilities
      • Prime-field-constraint-systems
      • Soft
      • Bv
      • Imp-language
      • Event-macros
      • Bitcoin
      • Ethereum
        • Mmp-trees
        • Semaphore
        • Database
          • Databasep
          • Database-fix
          • Database-equiv
        • Cryptography
        • Rlp
        • Transactions
        • Hex-prefix
        • Basics
        • Addresses
      • Yul
      • Zcash
      • ACL2-programming-language
      • Prime-fields
      • Java
      • C
      • Syntheto
      • Number-theory
      • Cryptography
      • Lists-light
      • File-io-light
      • Json
      • Built-ins
      • Solidity
      • Axe
      • Std-extensions
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Execloader
    • Axe
  • Testing-utilities
  • Math

• Database

Database-fix

(database-fix x) is a usual ACL2::fty omap fixing function.

Signature

(database-fix x) → *

Arguments

x — Guard (databasep x).

Definitions and Theorems

Function: database-fix

(defun database-fix (x)
       (declare (xargs :guard (databasep x)))
       (mbe :logic (if (databasep x) x nil)
            :exec x))

Theorem: databasep-of-database-fix

(defthm databasep-of-database-fix
        (databasep (database-fix x)))

Theorem: database-fix-when-databasep

(defthm database-fix-when-databasep
        (implies (databasep x)
                 (equal (database-fix x) x)))

Theorem: empty-database-fix

(defthm empty-database-fix
        (implies (or (omap::empty x) (not (databasep x)))
                 (omap::empty (database-fix x))))

Theorem: empty-of-database-fix-to-not-database-or-empty

(defthm empty-of-database-fix-to-not-database-or-empty
        (equal (omap::empty (database-fix x))
               (or (not (databasep x))
                   (omap::empty x))))

Function: database-equiv$inline

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

Theorem: database-equiv-is-an-equivalence

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

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

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

Theorem: database-fix-under-database-equiv

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

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

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

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

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

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

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

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

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