• 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
        • Mmp-trees
        • Semaphore
        • Database
          • Databasep
          • Database-fix
          • Database-equiv
        • Cryptography
        • Rlp
        • Transactions
        • Hex-prefix
        • Basics
        • Addresses
      • Yul
      • 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

• Database

Databasep

Recognizer for database.

Signature

(databasep x) → *

Definitions and Theorems

Function: databasep

(defun databasep (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (consp (car x))
         (byte-list32p (caar x))
         (byte-listp (cdar x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (consp (cadr x))
                  (acl2::fast-<< (caar x) (caadr x))
                  (databasep (cdr x)))))))

Theorem: booleanp-of-databasep

(defthm booleanp-of-databasep
  (booleanp (databasep x)))

Theorem: mapp-when-databasep

(defthm mapp-when-databasep
  (implies (databasep x) (omap::mapp x))
  :rule-classes (:rewrite :forward-chaining))

Theorem: databasep-of-tail

(defthm databasep-of-tail
  (implies (databasep x)
           (databasep (omap::tail x))))

Theorem: byte-list32p-of-head-key-when-databasep

(defthm byte-list32p-of-head-key-when-databasep
  (implies (and (databasep x)
                (not (omap::emptyp x)))
           (byte-list32p (mv-nth 0 (omap::head x)))))

Theorem: byte-listp-of-head-val-when-databasep

(defthm byte-listp-of-head-val-when-databasep
  (implies (and (databasep x)
                (not (omap::emptyp x)))
           (byte-listp (mv-nth 1 (omap::head x)))))

Theorem: databasep-of-update

(defthm databasep-of-update
  (implies (and (databasep x)
                (byte-list32p k)
                (byte-listp v))
           (databasep (omap::update k v x))))

Theorem: databasep-of-update*

(defthm databasep-of-update*
  (implies (and (databasep x) (databasep y))
           (databasep (omap::update* x y))))

Theorem: databasep-of-delete

(defthm databasep-of-delete
  (implies (databasep x)
           (databasep (omap::delete k x))))

Theorem: databasep-of-delete*

(defthm databasep-of-delete*
  (implies (databasep x)
           (databasep (omap::delete* k x))))

Theorem: byte-list32p-when-assoc-databasep-binds-free-x

(defthm byte-list32p-when-assoc-databasep-binds-free-x
  (implies (and (omap::assoc k x) (databasep x))
           (byte-list32p k)))

Theorem: byte-list32p-of-car-of-assoc-databasep

(defthm byte-list32p-of-car-of-assoc-databasep
  (implies (and (databasep x) (omap::assoc k x))
           (byte-list32p (car (omap::assoc k x)))))

Theorem: byte-listp-of-cdr-of-assoc-databasep

(defthm byte-listp-of-cdr-of-assoc-databasep
  (implies (and (databasep x) (omap::assoc k x))
           (byte-listp (cdr (omap::assoc k x)))))

Theorem: byte-listp-of-lookup-when-databasep

(defthm byte-listp-of-lookup-when-databasep
  (implies (and (databasep x) (omap::assoc k x))
           (byte-listp (omap::lookup k x))))