• 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
        • Syntax-for-tools
        • Atc
        • Language
        • Representation
        • Transformation-tools
          • Simpadd0
          • Deftrans
          • Splitgso
          • Constant-propagation
          • Split-fn
          • Copy-fn
          • Specialize
          • Split-all-gso
          • Rename
          • Utilities
            • Free-vars
            • Call-graphs
              • Qualified-ident
              • Call-graph-transitive-closure
              • Qualified-ident-option
              • Call-graph-transitive-closure0
              • Call-graph-initdeclor-list
              • Call-graph-fundef
              • Call-graph-statassert
              • Call-graph-initdeclor
              • Call-graph-decl
              • Call-graph-const-expr
              • Call-graph-transunit
              • Call-graph-extdecl-list
              • Call-graph-extdecl
              • Call-graph-update
              • Qualify-ident
              • Exists-call-pathp
              • Call-graph-filepath-transunit-map
              • Uncertain-call-pathp
              • Recursivep
              • Direct-recursivep
              • Call-graph-transunit-ensemble
              • Call-graph
                • Call-graphp
                • Call-graph-fix
                • Call-graph-equiv
              • Qualified-ident-option-set
              • Direct-fun-refp
            • Fresh-ident-utility
            • Collect-idents
        • Insertion-sort
        • Pack
      • Bv
      • Imp-language
      • 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

• Call-graph

Call-graph-fix

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

Signature

(call-graph-fix x) → *

Arguments

x — Guard (call-graphp x).

Definitions and Theorems

Function: call-graph-fix

(defun call-graph-fix (x)
  (declare (xargs :guard (call-graphp x)))
  (mbe :logic (if (call-graphp x) x nil)
       :exec x))

Theorem: call-graphp-of-call-graph-fix

(defthm call-graphp-of-call-graph-fix
  (call-graphp (call-graph-fix x)))

Theorem: call-graph-fix-when-call-graphp

(defthm call-graph-fix-when-call-graphp
  (implies (call-graphp x)
           (equal (call-graph-fix x) x)))

Theorem: emptyp-call-graph-fix

(defthm emptyp-call-graph-fix
  (implies (or (omap::emptyp x)
               (not (call-graphp x)))
           (omap::emptyp (call-graph-fix x))))

Theorem: emptyp-of-call-graph-fix-to-not-call-graph-or-emptyp

(defthm emptyp-of-call-graph-fix-to-not-call-graph-or-emptyp
  (equal (omap::emptyp (call-graph-fix x))
         (or (not (call-graphp x))
             (omap::emptyp x))))

Function: call-graph-equiv$inline

(defun call-graph-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (call-graphp acl2::x)
                              (call-graphp acl2::y))))
  (equal (call-graph-fix acl2::x)
         (call-graph-fix acl2::y)))

Theorem: call-graph-equiv-is-an-equivalence

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

Theorem: call-graph-equiv-implies-equal-call-graph-fix-1

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

Theorem: call-graph-fix-under-call-graph-equiv

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

Theorem: equal-of-call-graph-fix-1-forward-to-call-graph-equiv

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

Theorem: equal-of-call-graph-fix-2-forward-to-call-graph-equiv

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

Theorem: call-graph-equiv-of-call-graph-fix-1-forward

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

Theorem: call-graph-equiv-of-call-graph-fix-2-forward

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