CODEWITHSUNDEEP
dependent-typehigher-rank-typesidris
András Kovács
András Kovács

Reputation: 30103

Doing rank-n quantification in Idris

I can only do rank-n types in Idris 0.9.12 in a rather clumsy way:

tupleId : ((a : Type) -> a -> a) -> (a, b) -> (a, b)
tupleId f (a, b) = (f _ a, f _ b)

I need the underscores wherever there's a type application, because Idris throws parse errors when I try to make the (nested) type arguments implicit:

tupleId : ({a : Type} -> a -> a) -> (a, b) -> (a, b) -- doesn't compile

A probably bigger issue is that I can't do class constraints in higher-rank types at all. I can't translate the following Haskell function to Idris:

appShow :: Show a => (forall a. Show a => a -> String) -> a -> String
appShow show x = show x

This also prevents me from using Idris functions as type synonyms for types such as Lens, which is Lens s t a b = forall f. Functor f => (a -> f b) -> s -> f t in Haskell.

Any way to remedy or circumvent the above issues?

Upvotes: 33

Views: 1806

Answers (1)

Edwin Brady
Edwin Brady

Reputation: 4586

I've just implemented this in master, allowing implicits in arbitrary scopes, and it'll be in the next hackage release. It's not well tested yet though! I have at least tried the following simple examples, and a few others:

appShow : Show a => ({b : _} -> Show b => b -> String) -> a -> String
appShow s x = s x

AppendType : Type
AppendType = {a, n, m : _} -> Vect n a -> Vect m a -> Vect (n + m) a

append : AppendType
append [] ys = ys
append (x :: xs) ys = x :: append xs ys

tupleId : ({a : _} -> a -> a) -> (a, b) -> (a, b)
tupleId f (a, b) = (f a, f b)

Proxy  : Type -> Type -> Type -> Type -> (Type -> Type) -> Type -> Type

Producer' : Type -> (Type -> Type) -> Type -> Type
Producer' a m t = {x', x : _} -> Proxy x' x () a m t

yield : Monad m => a -> Producer' a m ()

The main constraint at the minute is that you can't give values for implicit arguments directly, except at the top level. I'll do something about that eventually...

Upvotes: 23

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