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• Function-header

Function-header-fix

Fixing function for function-header structures.

Signature

(function-header-fix x) → new-x

Arguments

x — Guard (function-headerp x).

Returns

new-x — Type (function-headerp new-x).

Definitions and Theorems

Function: function-header-fix$inline

(defun function-header-fix$inline (x)
 (declare (xargs :guard (function-headerp x)))
 (let ((__function__ 'function-header-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b* ((name (identifier-fix (cdr (std::da-nth 0 x))))
        (inputs (typed-variable-list-fix (cdr (std::da-nth 1 x))))
        (outputs (typed-variable-list-fix (cdr (std::da-nth 2 x)))))
     (list (cons 'name name)
           (cons 'inputs inputs)
           (cons 'outputs outputs)))
   :exec x)))

Theorem: function-headerp-of-function-header-fix

(defthm function-headerp-of-function-header-fix
  (b* ((new-x (function-header-fix$inline x)))
    (function-headerp new-x))
  :rule-classes :rewrite)

Theorem: function-header-fix-when-function-headerp

(defthm function-header-fix-when-function-headerp
  (implies (function-headerp x)
           (equal (function-header-fix x) x)))

Function: function-header-equiv$inline

(defun function-header-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (function-headerp acl2::x)
                              (function-headerp acl2::y))))
  (equal (function-header-fix acl2::x)
         (function-header-fix acl2::y)))

Theorem: function-header-equiv-is-an-equivalence

(defthm function-header-equiv-is-an-equivalence
  (and (booleanp (function-header-equiv x y))
       (function-header-equiv x x)
       (implies (function-header-equiv x y)
                (function-header-equiv y x))
       (implies (and (function-header-equiv x y)
                     (function-header-equiv y z))
                (function-header-equiv x z)))
  :rule-classes (:equivalence))

Theorem: function-header-equiv-implies-equal-function-header-fix-1

(defthm function-header-equiv-implies-equal-function-header-fix-1
  (implies (function-header-equiv acl2::x x-equiv)
           (equal (function-header-fix acl2::x)
                  (function-header-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: function-header-fix-under-function-header-equiv

(defthm function-header-fix-under-function-header-equiv
  (function-header-equiv (function-header-fix acl2::x)
                         acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-function-header-fix-1-forward-to-function-header-equiv

(defthm
    equal-of-function-header-fix-1-forward-to-function-header-equiv
  (implies (equal (function-header-fix acl2::x)
                  acl2::y)
           (function-header-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-function-header-fix-2-forward-to-function-header-equiv

(defthm
    equal-of-function-header-fix-2-forward-to-function-header-equiv
  (implies (equal acl2::x (function-header-fix acl2::y))
           (function-header-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: function-header-equiv-of-function-header-fix-1-forward

(defthm function-header-equiv-of-function-header-fix-1-forward
  (implies (function-header-equiv (function-header-fix acl2::x)
                                  acl2::y)
           (function-header-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: function-header-equiv-of-function-header-fix-2-forward

(defthm function-header-equiv-of-function-header-fix-2-forward
  (implies
       (function-header-equiv acl2::x (function-header-fix acl2::y))
       (function-header-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)