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Expression-struct-component

Expression-struct-component->struct

Get the struct field from a expression-struct-component.

Signature
(expression-struct-component->struct x) → struct
Arguments: x — Guard (expressionp x).
Returns: struct — Type (expressionp struct).

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

Definitions and Theorems

Function: expression-struct-component->struct$inline

(defun expression-struct-component->struct$inline (x)
  (declare (xargs :guard (expressionp x)))
  (declare (xargs :guard (equal (expression-kind x)
                                :struct-component)))
  (let ((__function__ 'expression-struct-component->struct))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (expression-kind x)
                             :struct-component)
                      x)))
           (expression-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: expressionp-of-expression-struct-component->struct

(defthm expressionp-of-expression-struct-component->struct
  (b* ((struct (expression-struct-component->struct$inline x)))
    (expressionp struct))
  :rule-classes :rewrite)

Theorem: expression-struct-component->struct$inline-of-expression-fix-x

(defthm
     expression-struct-component->struct$inline-of-expression-fix-x
 (equal
     (expression-struct-component->struct$inline (expression-fix x))
     (expression-struct-component->struct$inline x)))

Theorem: expression-struct-component->struct$inline-expression-equiv-congruence-on-x

(defthm
 expression-struct-component->struct$inline-expression-equiv-congruence-on-x
 (implies
      (expression-equiv x x-equiv)
      (equal (expression-struct-component->struct$inline x)
             (expression-struct-component->struct$inline x-equiv)))
 :rule-classes :congruence)

Theorem: expression-struct-component->struct-when-wrong-kind

(defthm expression-struct-component->struct-when-wrong-kind
  (implies (not (equal (expression-kind x)
                       :struct-component))
           (equal (expression-struct-component->struct x)
                  (expression-fix nil))))