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      • Term
        • Lambda
        • Pseudo-termp
          • Pseudo-term-fty
            • Pseudo-term-lambda
            • Pseudo-term-call
            • Pseudo-term-fncall
            • Pseudo-lambda
              • Pseudo-lambda-fix
              • Pseudo-lambda->formals
              • Pseudo-lambda->body
              • Pseudo-lambda-p
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• Pseudo-term-fty

Pseudo-lambda

Type of, and constructor for, a lambda function, used in the FTY support for pseudo-terms.

Signature

(pseudo-lambda formals body) → lambda

Arguments

formals — Guard (symbol-listp formals).

body — Guard (pseudo-termp body).

Returns

lambda — Type (pseudo-lambda-p lambda).

Definitions and Theorems

Function: pseudo-lambda

(defun pseudo-lambda (formals body)
  (declare (xargs :guard (and (symbol-listp formals)
                              (pseudo-termp body))))
  (let ((__function__ 'pseudo-lambda))
    (declare (ignorable __function__))
    (mbe :logic (list 'lambda
                      (replace-non-symbols-with-nil formals)
                      (pseudo-term-fix body))
         :exec (list 'lambda formals body))))

Theorem: pseudo-lambda-p-of-pseudo-lambda

(defthm pseudo-lambda-p-of-pseudo-lambda
 (b* ((lambda (pseudo-lambda formals body)))
   (pseudo-lambda-p lambda))
 :rule-classes
 (:rewrite
     (:type-prescription :typed-term (pseudo-lambda formals body))))

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

(defthm pseudo-lambda->formals-of-pseudo-lambda
  (equal (pseudo-lambda->formals (pseudo-lambda formals body))
         (replace-non-symbols-with-nil formals)))

Theorem: pseudo-lambda->body-of-pseudo-lambda

(defthm pseudo-lambda->body-of-pseudo-lambda
  (equal (pseudo-lambda->body (pseudo-lambda body body))
         (pseudo-term-fix body)))

Theorem: pseudo-lambda-of-accessors

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

Theorem: pseudo-lambda-of-pseudo-term-fix-body

(defthm pseudo-lambda-of-pseudo-term-fix-body
  (equal (pseudo-lambda formals (pseudo-term-fix body))
         (pseudo-lambda formals body)))

Theorem: pseudo-lambda-pseudo-term-equiv-congruence-on-body

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

Subtopics

Pseudo-lambda-fix

Pseudo-lambda->formals

Pseudo-lambda->body

Pseudo-lambda-p