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• Abstract-syntax-operations

Direct-supertype

Return the direct supertype of a type, if any.

Signature

(direct-supertype type tops) → super?

Arguments

type — Guard (typep type).

tops — Guard (toplevel-listp tops).

Returns

super? — Type (maybe-typep super?).

Only a type defined as a subtype has a direct supertype, namely the one referenced in the subtype definition. All the other types do not.

Definitions and Theorems

Function: direct-supertype

(defun direct-supertype (type tops)
  (declare (xargs :guard (and (typep type)
                              (toplevel-listp tops))))
  (let ((__function__ 'direct-supertype))
    (declare (ignorable __function__))
    (type-case
         type :boolean nil :character nil :string
         nil :integer nil :set nil :sequence
         nil :map nil :option nil :defined
         (b* ((typedef (get-type-definition type.name tops))
              ((when (not typedef)) nil)
              (definer (type-definition->body typedef))
              ((when (not definer)) nil))
           (type-definer-case
                definer
                :product nil
                :sum nil
                :subset (type-subset->supertype definer.get))))))

Theorem: maybe-typep-of-direct-supertype

(defthm maybe-typep-of-direct-supertype
  (b* ((super? (direct-supertype type tops)))
    (maybe-typep super?))
  :rule-classes :rewrite)

Theorem: defined-type-when-direct-supertype

(defthm defined-type-when-direct-supertype
  (implies (direct-supertype type tops)
           (type-case type :defined))
  :rule-classes :forward-chaining)

Theorem: direct-supertype-of-type-fix-type

(defthm direct-supertype-of-type-fix-type
  (equal (direct-supertype (type-fix type) tops)
         (direct-supertype type tops)))

Theorem: direct-supertype-type-equiv-congruence-on-type

(defthm direct-supertype-type-equiv-congruence-on-type
  (implies (type-equiv type type-equiv)
           (equal (direct-supertype type tops)
                  (direct-supertype type-equiv tops)))
  :rule-classes :congruence)

Theorem: direct-supertype-of-toplevel-list-fix-tops

(defthm direct-supertype-of-toplevel-list-fix-tops
  (equal (direct-supertype type (toplevel-list-fix tops))
         (direct-supertype type tops)))

Theorem: direct-supertype-toplevel-list-equiv-congruence-on-tops

(defthm direct-supertype-toplevel-list-equiv-congruence-on-tops
  (implies (toplevel-list-equiv tops tops-equiv)
           (equal (direct-supertype type tops)
                  (direct-supertype type tops-equiv)))
  :rule-classes :congruence)