• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • C
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
      • Semantics
      • Abstract-syntax
        • Aexp
          • Aexp-case
          • Aexp-fix
          • Aexpp
          • Aexp-count
          • Aexp-equiv
          • Aexp-mul
          • Aexp-add
          • Aexp-var
          • Aexp-const
          • Aexp-kind
        • Bexp
        • Comm
        • Comm-list
        • Command-fixtypes
      • Interpreter
    • Sidekick
    • Leftist-trees
    • Java
    • Taspi
    • Bitcoin
    • Riscv
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
    • Where-do-i-place-my-book
    • Axe
    • Bigmems
    • Builtins
    • Execloader
    • Aleo
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Aexp

Aexp-count

Measure for recurring over aexp structures.

Signature

(aexp-count x) → count

Arguments

x — Guard (aexpp x).

Returns

count — Type (natp count).

Definitions and Theorems

Function: aexp-count

(defun aexp-count (x)
  (declare (xargs :guard (aexpp x)))
  (let ((__function__ 'aexp-count))
    (declare (ignorable __function__))
    (case (aexp-kind x)
      (:const 1)
      (:var 1)
      (:add (+ 3 (aexp-count (aexp-add->left x))
               (aexp-count (aexp-add->right x))))
      (:mul (+ 3 (aexp-count (aexp-mul->left x))
               (aexp-count (aexp-mul->right x)))))))

Theorem: natp-of-aexp-count

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

Theorem: aexp-count-of-aexp-fix-x

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

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

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

Theorem: aexp-count-of-aexp-add

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

Theorem: aexp-count-of-aexp-add->left

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

Theorem: aexp-count-of-aexp-add->right

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

Theorem: aexp-count-of-aexp-mul

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

Theorem: aexp-count-of-aexp-mul->left

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

Theorem: aexp-count-of-aexp-mul->right

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