• 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-lambda->formals
              • Pseudo-term-call->fn
              • Pseudo-term-call->args
              • Pseudo-term-lambda->body
              • Pseudo-term-lambda->fn
              • Pseudo-term-lambda->args
            • Pseudo-term-call
            • Pseudo-term-fncall
            • 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-lambda

Pseudo-term-lambda->formals

Accessor for the lambda formals of a lambda call pseudo-term.

Signature

(pseudo-term-lambda->formals x) → formals

Arguments

x — Guard (pseudo-termp x).

Returns

formals — Type (symbol-listp formals).

Definitions and Theorems

Function: pseudo-term-lambda->formals

(defun pseudo-term-lambda->formals (x)
  (declare (xargs :guard (pseudo-termp x)))
  (declare (xargs :guard (eq (pseudo-term-kind x) :lambda)))
  (let ((__function__ 'pseudo-term-lambda->formals))
    (declare (ignorable __function__))
    (mbe :logic (and (eq (pseudo-term-kind x) :lambda)
                     (replace-non-symbols-with-nil (cadr (car x))))
         :exec (cadr (car x)))))

Theorem: symbol-listp-of-pseudo-term-lambda->formals

(defthm symbol-listp-of-pseudo-term-lambda->formals
  (b* ((formals (pseudo-term-lambda->formals x)))
    (symbol-listp formals))
  :rule-classes (:rewrite :type-prescription))

Theorem: len-of-pseudo-term-lambda->formals

(defthm len-of-pseudo-term-lambda->formals
  (implies (equal (pseudo-term-kind x) :lambda)
           (equal (len (pseudo-term-lambda->formals x))
                  (len (pseudo-term-call->args x)))))

Theorem: pseudo-lambda->formals-of-pseudo-term-lambda->fn

(defthm pseudo-lambda->formals-of-pseudo-term-lambda->fn
  (equal (pseudo-lambda->formals (pseudo-term-lambda->fn x))
         (pseudo-term-lambda->formals x)))

Theorem: pseudo-term-lambda->formals-of-pseudo-term-fix-x

(defthm pseudo-term-lambda->formals-of-pseudo-term-fix-x
  (equal (pseudo-term-lambda->formals (pseudo-term-fix x))
         (pseudo-term-lambda->formals x)))

Theorem: pseudo-term-lambda->formals-pseudo-term-equiv-congruence-on-x

(defthm
      pseudo-term-lambda->formals-pseudo-term-equiv-congruence-on-x
  (implies (pseudo-term-equiv x x-equiv)
           (equal (pseudo-term-lambda->formals x)
                  (pseudo-term-lambda->formals x-equiv)))
  :rule-classes :congruence)