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Expr-funcall

Expr-funcall->fun

Get the fun field from a expr-funcall.

Signature
(expr-funcall->fun x) → fun
Arguments: x — Guard (exprp x).
Returns: fun — Type (exprp fun).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: expr-funcall->fun$inline

(defun expr-funcall->fun$inline (x)
  (declare (xargs :guard (exprp x)))
  (declare (xargs :guard (equal (expr-kind x) :funcall)))
  (let ((__function__ 'expr-funcall->fun))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (expr-kind x) :funcall) x)))
           (expr-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: exprp-of-expr-funcall->fun

(defthm exprp-of-expr-funcall->fun
  (b* ((fun (expr-funcall->fun$inline x)))
    (exprp fun))
  :rule-classes :rewrite)

Theorem: expr-funcall->fun$inline-of-expr-fix-x

(defthm expr-funcall->fun$inline-of-expr-fix-x
  (equal (expr-funcall->fun$inline (expr-fix x))
         (expr-funcall->fun$inline x)))

Theorem: expr-funcall->fun$inline-expr-equiv-congruence-on-x

(defthm expr-funcall->fun$inline-expr-equiv-congruence-on-x
  (implies (expr-equiv x x-equiv)
           (equal (expr-funcall->fun$inline x)
                  (expr-funcall->fun$inline x-equiv)))
  :rule-classes :congruence)

Theorem: expr-funcall->fun-when-wrong-kind

(defthm expr-funcall->fun-when-wrong-kind
  (implies (not (equal (expr-kind x) :funcall))
           (equal (expr-funcall->fun x)
                  (expr-fix nil))))