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      • Term
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• Pseudo-term-fty

Pseudo-term-kind

Return the kind of a pseudo-term input (a keyword symbol).

Signature

(pseudo-term-kind x) → kind

Arguments

x — Guard (pseudo-termp x).

Returns

kind — Type (symbolp kind).

Definitions and Theorems

Function: pseudo-term-kind$inline

(defun pseudo-term-kind$inline (x)
  (declare (xargs :guard (pseudo-termp x)))
  (let ((__function__ 'pseudo-term-kind))
    (declare (ignorable __function__))
    (b* ((x (pseudo-term-fix x))
         ((when (atom x)) (if x :var :null))
         (fn (car x))
         ((when (eq fn 'quote)) :quote)
         ((when (consp fn)) :lambda))
      :fncall)))

Theorem: symbolp-of-pseudo-term-kind

(defthm symbolp-of-pseudo-term-kind
  (b* ((kind (pseudo-term-kind$inline x)))
    (symbolp kind))
  :rule-classes :type-prescription)

Theorem: pseudo-term-kind-possibilities

(defthm pseudo-term-kind-possibilities
  (or (equal (pseudo-term-kind x) :null)
      (equal (pseudo-term-kind x) :var)
      (equal (pseudo-term-kind x) :quote)
      (equal (pseudo-term-kind x) :lambda)
      (equal (pseudo-term-kind x) :fncall))
  :rule-classes
  ((:forward-chaining :trigger-terms ((pseudo-term-kind x)))))

Theorem: pseudo-term-kind$inline-of-pseudo-term-fix-x

(defthm pseudo-term-kind$inline-of-pseudo-term-fix-x
  (equal (pseudo-term-kind$inline (pseudo-term-fix x))
         (pseudo-term-kind$inline x)))

Theorem: pseudo-term-kind$inline-pseudo-term-equiv-congruence-on-x

(defthm pseudo-term-kind$inline-pseudo-term-equiv-congruence-on-x
  (implies (pseudo-term-equiv x x-equiv)
           (equal (pseudo-term-kind$inline x)
                  (pseudo-term-kind$inline x-equiv)))
  :rule-classes :congruence)