Type-variable assignment

Consider an attempt to define a generic array type consisting of both vectors and bool vectors:

(et-defalias MyNaiveArray [E]
  (or Vector<E>
      BoolVector))

(et-expand-aliases (et MyNaiveArray<Number>))
;; -> Vector<Number> | BoolVector

However, BoolVector is clearly not an array of numbers. The solution is to attach a variable assignment to the BoolVector case:

(et-defalias MyArray [E]
  (or Vector<E>
      BoolVector{E:=:Boolean}))

(et-expand-aliases (et MyArray<Number>))
;; -> Vector<Number>
(et-expand-aliases (et MyArray<Boolean>))
;; -> Vector<Boolean> | BoolVector
(et-expand-aliases (et MyArray<Any>))
;; -> Vector<Any>

As shown, :=: only succeeds when the type variable matches exactly (it is an invariant assignment). Alternatively, :>: (covariant assignment) succeeds when the type variable contains its assignment, and the less common :<: (contravariant assignment) succeeds when the type variable is contained within its assignment.

Since the read-only version of an alias is designed to turn the alias from invariant to covariant, it will automatically convert all invariant assignments to covariant ones.

&MyArray<E> := &Vector<E> | BoolVector{E:>:Boolean} ; auto-generated

(et-expand-aliases (et &MyArray<Number>))
;; -> &Vector<Number>
(et-expand-aliases (et &MyArray<Boolean>))
;; -> &Vector<Boolean> | BoolVector
(et-expand-aliases (et &MyArray<Any>))
;; -> &Vector<Any> | BoolVector

Variable assignments can also be used to detect the appropriate type for a type variable:

(et-defun my-array-get ([T] array: &MyArray<T>) T
  ...)

(my-array-get (:type &Vector<Number>))
;; >> Number
(my-array-get (:type BoolVector))
;; >> Boolean
(my-array-get (:type &Vector<Number>|BoolVector))
;; >> Number | Boolean