• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
    • Theories
    • Rule-classes
    • Proof-builder
    • Recursion-and-induction
    • Hons-and-memoization
    • Events
    • Parallelism
    • History
    • Programming
    • Operational-semantics
    • Real
    • Start-here
    • Debugging
    • Miscellaneous
      • Term
        • Lambda
        • Pseudo-termp
          • Pseudo-term-fty
            • Pseudo-term-lambda
            • Pseudo-term-call
            • Pseudo-term-fncall
              • Pseudo-term-call->fn
              • Pseudo-term-call->args
              • Pseudo-term-fncall->fn
              • Pseudo-term-fncall->args
            • Pseudo-lambda
            • Pseudo-term-var
            • Pseudo-term-quote
            • Pseudo-term-kind
            • Pseudo-term-null
            • Pseudo-fnsym
            • Pseudo-term-case
            • Pseudo-term-count
            • Def-ev-pseudo-term-fty-support
            • Def-ev-pseudo-term-congruence
            • Pseudo-term-fix
            • Pseudo-var
            • Pseudo-term-list-fix
            • Pseudo-fn
          • Std/typed-lists/pseudo-term-listp
        • Term-order
        • Pseudo-term-listp
        • Guard-holders
        • Termp
        • Termify
        • L<
        • Kwote
        • Kwote-lst
      • Ld
      • Hints
      • Type-set
      • Ordinals
      • Clause
      • ACL2-customization
      • With-prover-step-limit
      • Set-prover-step-limit
      • With-prover-time-limit
      • Local-incompatibility
      • Set-case-split-limitations
      • Subversive-recursions
      • Specious-simplification
      • Defsum
      • Gcl
      • Oracle-timelimit
      • Thm
      • Defopener
      • Case-split-limitations
      • Set-gc-strategy
      • Default-defun-mode
      • Top-level
      • Reader
      • Ttags-seen
      • Adviser
      • Ttree
      • Abort-soft
      • Defsums
      • Gc$
      • With-timeout
      • Coi-debug::fail
      • Expander
      • Gc-strategy
      • Coi-debug::assert
      • Sin-cos
      • Def::doc
      • Syntax
      • Subversive-inductions
    • Output-controls
    • Macros
    • Interfacing-tools
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Pseudo-term-fty

Pseudo-term-fncall

Constructor for function call (:fncall) pseudo-terms.

Signature

(pseudo-term-fncall fn args) → term

Arguments

fn — Guard (pseudo-fnsym-p fn).

args — Guard (pseudo-term-listp args).

Returns

term — Type (pseudo-termp term).

Definitions and Theorems

Function: pseudo-term-fncall

(defun pseudo-term-fncall (fn args)
  (declare (xargs :guard (and (pseudo-fnsym-p fn)
                              (pseudo-term-listp args))))
  (let ((__function__ 'pseudo-term-fncall))
    (declare (ignorable __function__))
    (cons (pseudo-fnsym-fix fn)
          (pseudo-term-list-fix args))))

Theorem: pseudo-termp-of-pseudo-term-fncall

(defthm pseudo-termp-of-pseudo-term-fncall
  (b* ((term (pseudo-term-fncall fn args)))
    (pseudo-termp term))
  :rule-classes :rewrite)

Theorem: kind-of-pseudo-term-fncall

(defthm kind-of-pseudo-term-fncall
  (equal (pseudo-term-kind (pseudo-term-fncall fn args))
         :fncall))

Theorem: pseudo-term-call->args-of-pseudo-term-fncall

(defthm pseudo-term-call->args-of-pseudo-term-fncall
  (equal (pseudo-term-call->args (pseudo-term-fncall fn args))
         (pseudo-term-list-fix args)))

Theorem: pseudo-term-fncall->fn-of-pseudo-term-fncall

(defthm pseudo-term-fncall->fn-of-pseudo-term-fncall
  (equal (pseudo-term-fncall->fn (pseudo-term-fncall fn args))
         (pseudo-fnsym-fix fn)))

Theorem: base-ev-of-pseudo-term-fncall

(defthm base-ev-of-pseudo-term-fncall
  (equal (base-ev (pseudo-term-fncall fn args) a)
         (base-ev (cons (pseudo-fnsym-fix fn) args)
                  a)))

Theorem: base-ev-when-pseudo-term-fncall

(defthm base-ev-when-pseudo-term-fncall
  (implies (and (equal (pseudo-term-kind x) :fncall)
                (equal new-x
                       (cons (pseudo-term-fncall->fn x)
                             (pseudo-term-call->args x)))
                (syntaxp (not (equal new-x x))))
           (equal (base-ev x a)
                  (base-ev new-x a))))

Theorem: pseudo-term-fncall-of-accessors

(defthm pseudo-term-fncall-of-accessors
  (implies (equal (pseudo-term-kind x) :fncall)
           (equal (pseudo-term-fncall (pseudo-term-fncall->fn x)
                                      (pseudo-term-call->args x))
                  (pseudo-term-fix x))))

Theorem: pseudo-term-fncall-of-pseudo-fnsym-fix-fn

(defthm pseudo-term-fncall-of-pseudo-fnsym-fix-fn
  (equal (pseudo-term-fncall (pseudo-fnsym-fix fn)
                             args)
         (pseudo-term-fncall fn args)))

Theorem: pseudo-term-fncall-pseudo-fnsym-equiv-congruence-on-fn

(defthm pseudo-term-fncall-pseudo-fnsym-equiv-congruence-on-fn
  (implies (pseudo-fnsym-equiv fn fn-equiv)
           (equal (pseudo-term-fncall fn args)
                  (pseudo-term-fncall fn-equiv args)))
  :rule-classes :congruence)

Theorem: pseudo-term-fncall-of-pseudo-term-list-fix-args

(defthm pseudo-term-fncall-of-pseudo-term-list-fix-args
  (equal (pseudo-term-fncall fn (pseudo-term-list-fix args))
         (pseudo-term-fncall fn args)))

Theorem: pseudo-term-fncall-pseudo-term-list-equiv-congruence-on-args

(defthm pseudo-term-fncall-pseudo-term-list-equiv-congruence-on-args
  (implies (pseudo-term-list-equiv args args-equiv)
           (equal (pseudo-term-fncall fn args)
                  (pseudo-term-fncall fn args-equiv)))
  :rule-classes :congruence)

Subtopics

Pseudo-term-call->fn

Accessor for the function of a function call or lambda call pseduo-term.

Pseudo-term-call->args

Accessor for the arguments of a lambda or function call pseudo-term.

Pseudo-term-fncall->fn

Access the function symbol of a function call pseudo-term.

Pseudo-term-fncall->args

Alias for pseudo-term-call->args.