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• Static-semantics

Check-type

Check if a type is statically well-formed.

Signature

(check-type type ctxt) → yes/no

Arguments

type — Guard (typep type).

ctxt — Guard (contextp ctxt).

Returns

yes/no — Type (booleanp yes/no).

The primitive types are always well-formed. The collection types and the option type are well-formed iff their argument types are. A defined type is well-formed iff it references a defined type in the existing top-level constructs, or one of the types being currently defined.

Definitions and Theorems

Function: check-type

(defun check-type (type ctxt)
 (declare (xargs :guard (and (typep type) (contextp ctxt))))
 (let ((__function__ 'check-type))
  (declare (ignorable __function__))
  (type-case
       type
       :boolean t
       :character t
       :string t
       :integer t
       :set (check-type type.element ctxt)
       :sequence (check-type type.element ctxt)
       :map (and (check-type type.domain ctxt)
                 (check-type type.range ctxt))
       :option (check-type type.base ctxt)
       :defined
       (bool-fix
            (or (get-type-definition type.name (context->tops ctxt))
                (member-equal type.name (context->types ctxt)))))))

Theorem: booleanp-of-check-type

(defthm booleanp-of-check-type
  (b* ((yes/no (check-type type ctxt)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: check-type-of-type-fix-type

(defthm check-type-of-type-fix-type
  (equal (check-type (type-fix type) ctxt)
         (check-type type ctxt)))

Theorem: check-type-type-equiv-congruence-on-type

(defthm check-type-type-equiv-congruence-on-type
  (implies (type-equiv type type-equiv)
           (equal (check-type type ctxt)
                  (check-type type-equiv ctxt)))
  :rule-classes :congruence)

Theorem: check-type-of-context-fix-ctxt

(defthm check-type-of-context-fix-ctxt
  (equal (check-type type (context-fix ctxt))
         (check-type type ctxt)))

Theorem: check-type-context-equiv-congruence-on-ctxt

(defthm check-type-context-equiv-congruence-on-ctxt
  (implies (context-equiv ctxt ctxt-equiv)
           (equal (check-type type ctxt)
                  (check-type type ctxt-equiv)))
  :rule-classes :congruence)