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      • Term
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        • Pseudo-termp
          • Pseudo-term-fty
            • Pseudo-term-lambda
              • Pseudo-term-lambda->formals
              • Pseudo-term-call->fn
              • Pseudo-term-call->args
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• Pseudo-term-fty

Pseudo-term-lambda

Constructor for a lambda call (:lambda) pseudo-term.

Signature

(pseudo-term-lambda formals body args) → term

Arguments

formals — Guard (symbol-listp formals).

body — Guard (pseudo-termp body).

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

Returns

term — Type (pseudo-termp term).

Definitions and Theorems

Function: pseudo-term-lambda

(defun pseudo-term-lambda (formals body args)
  (declare (xargs :guard (and (symbol-listp formals)
                              (pseudo-termp body)
                              (pseudo-term-listp args))))
  (declare (xargs :guard (equal (len args) (len formals))))
  (let ((__function__ 'pseudo-term-lambda))
    (declare (ignorable __function__))
    (mbe :logic (cons (pseudo-lambda formals body)
                      (take (len formals)
                            (pseudo-term-list-fix args)))
         :exec (cons (list 'lambda formals body)
                     args))))

Theorem: pseudo-termp-of-pseudo-term-lambda

(defthm pseudo-termp-of-pseudo-term-lambda
  (b* ((term (pseudo-term-lambda formals body args)))
    (pseudo-termp term))
  :rule-classes :rewrite)

Theorem: kind-of-pseudo-term-lambda

(defthm kind-of-pseudo-term-lambda
  (equal (pseudo-term-kind (pseudo-term-lambda formals body args))
         :lambda))

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

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

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

(defthm pseudo-term-call->args-of-pseudo-term-lambda
 (equal
     (pseudo-term-call->args (pseudo-term-lambda formals body args))
     (take (len formals)
           (pseudo-term-list-fix args))))

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

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

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

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

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

(defthm base-ev-of-pseudo-term-lambda
  (equal (base-ev (pseudo-term-lambda formals body args)
                  a)
         (base-ev body
                  (pairlis$ formals (base-ev-list args a)))))

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

(defthm base-ev-when-pseudo-term-lambda
 (implies
  (equal (pseudo-term-kind x) :lambda)
  (equal (base-ev x a)
         (base-ev (pseudo-term-lambda->body x)
                  (pairlis$ (pseudo-term-lambda->formals x)
                            (base-ev-list (pseudo-term-call->args x)
                                          a))))))

Theorem: pseudo-term-lambda-of-accessors

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

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

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

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

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

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

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

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

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

Subtopics

Pseudo-term-lambda->formals

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

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-lambda->body

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

Pseudo-term-lambda->fn

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

Pseudo-term-lambda->args

Alias for pseudo-term-call->args.