Function types

• Function types are quite different from Typed Racket
  • anything can implement the IFn interface
  • In core.typed the Function type is more a special type than the type for lambdas

Common things that are IFns:

- clojure.lang.Function
- c.l.Keyword
  - [Any -> Any]
- (c.l.PersistentHashMap k v)
  - (All [x] 
      (Fn [Any -> (U nil v)]
          [Any x -> (U x v)]))
- (c.l.PersistentHashSet v)
  - (All [x]
      (Fn [Any -> (U nil v)]))
- c.l.Symbol
  - [Any -> Any]
- (Value :a)
  - (All [x] 
      [Any -> x :filters {:then (is {:a x} 0)}])
- (Value sym)
  - (All [x] [Any -> (U nil v)])

The IFn class might be parameterised by a Function type. The immediate problem is intersections allows us to have more than one function type.

eg. What function type is this?

(I (Value :a)
   (All [x] 
     [Any -> x :filters {:then (is {:a x} 0)}])

Even (Value :a) inherits two function types:

• that for c.l.Keyword
• that for (Value :a)

(Value :a) <: (IFn x) infers x to be:

(I [Any -> Any]
   (All [x] 
     [Any -> x :filters {:then (is {:a x} 0)}])

The second member of the intersection is more specific, thus can be simplified to:

(All [x] 
  [Any -> x :filters {:then (is {:a x} 0)}])

Does this work in general? As long as there is a subtyping relationship between the possible Function types, we can infer the most useful one.