• 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
        • Semantics
        • Abstract-syntax
          • Aexp
          • Bexp
            • Bexp-case
            • Bexp-fix
            • Bexpp
            • Bexp-count
            • Bexp-equiv
            • Bexp-less
            • Bexp-equal
            • Bexp-and
            • Bexp-const
            • Bexp-not
            • Bexp-kind
          • Comm
          • Comm-list
          • Command-fixtypes
        • Interpreter
      • Event-macros
      • Java
      • Bitcoin
      • Ethereum
      • 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

• Bexp

Bexp-count

Measure for recurring over bexp structures.

Signature

(bexp-count x) → count

Arguments

x — Guard (bexpp x).

Returns

count — Type (natp count).

Definitions and Theorems

Function: bexp-count

(defun bexp-count (x)
  (declare (xargs :guard (bexpp x)))
  (let ((__function__ 'bexp-count))
    (declare (ignorable __function__))
    (case (bexp-kind x)
      (:const 1)
      (:equal 1)
      (:less 1)
      (:not (+ 2 (bexp-count (bexp-not->arg x))))
      (:and (+ 3 (bexp-count (bexp-and->left x))
               (bexp-count (bexp-and->right x)))))))

Theorem: natp-of-bexp-count

(defthm natp-of-bexp-count
  (b* ((count (bexp-count x)))
    (natp count))
  :rule-classes :type-prescription)

Theorem: bexp-count-of-bexp-fix-x

(defthm bexp-count-of-bexp-fix-x
  (equal (bexp-count (bexp-fix x))
         (bexp-count x)))

Theorem: bexp-count-bexp-equiv-congruence-on-x

(defthm bexp-count-bexp-equiv-congruence-on-x
  (implies (bexp-equiv x x-equiv)
           (equal (bexp-count x)
                  (bexp-count x-equiv)))
  :rule-classes :congruence)

Theorem: bexp-count-of-bexp-not

(defthm bexp-count-of-bexp-not
  (implies t
           (< (+ (bexp-count arg))
              (bexp-count (bexp-not arg))))
  :rule-classes :linear)

Theorem: bexp-count-of-bexp-not->arg

(defthm bexp-count-of-bexp-not->arg
  (implies (equal (bexp-kind x) :not)
           (< (bexp-count (bexp-not->arg x))
              (bexp-count x)))
  :rule-classes :linear)

Theorem: bexp-count-of-bexp-and

(defthm bexp-count-of-bexp-and
  (implies t
           (< (+ (bexp-count left) (bexp-count right))
              (bexp-count (bexp-and left right))))
  :rule-classes :linear)

Theorem: bexp-count-of-bexp-and->left

(defthm bexp-count-of-bexp-and->left
  (implies (equal (bexp-kind x) :and)
           (< (bexp-count (bexp-and->left x))
              (bexp-count x)))
  :rule-classes :linear)

Theorem: bexp-count-of-bexp-and->right

(defthm bexp-count-of-bexp-and->right
  (implies (equal (bexp-kind x) :and)
           (< (bexp-count (bexp-and->right x))
              (bexp-count x)))
  :rule-classes :linear)