This project really is a source of questions for me.
I already learned about polymorphic recursion and I understand why it is a special case and therefore F# needs full type annotations.
For regular functions I might need some fiddeling but usually get it right. Now I'm trying to adapt a (working) basic toSeq to a more specialized finger tree, but can't.
My feeling is that the use of the computation expression has something to do with it. This is the condensed working version:
module ThisWorks =
module Node =
type Node<'a> =
| Node2 of 'a * 'a
| Node3 of 'a * 'a * 'a
let toList = function
| Node2(a, b) -> [a; b]
| Node3(a, b, c) -> [a; b; c]
module Digit =
type Digit<'a> =
| One of 'a
| Two of 'a * 'a
| Three of 'a * 'a * 'a
| Four of 'a * 'a * 'a * 'a
let toList = function
| One a -> [a]
| Two(a, b) -> [a; b]
| Three(a, b, c) -> [a; b; c]
| Four(a, b, c, d) -> [a; b; c; d]
module FingerTree =
open Node
open Digit
type FingerTree<'a> =
| Empty
| Single of 'a
| Deep of Digit<'a> * Lazy<FingerTree<Node<'a>>> * Digit<'a>
let rec toSeq<'a> (tree:FingerTree<'a>) : seq<'a> = seq {
match tree with
| Single single ->
yield single
| Deep(prefix, Lazy deeper, suffix) ->
yield! prefix |> Digit.toList
yield! deeper |> toSeq |> Seq.collect Node.toList
yield! suffix |> Digit.toList
| Empty -> ()
}
The one I don't manage to get to compile is this:
module ThisDoesnt =
module Monoids =
type IMonoid<'m> =
abstract Zero:'m
abstract Plus:'m -> 'm
type IMeasured<'m when 'm :> IMonoid<'m>> =
abstract Measure:'m
type Size(value) =
new() = Size 0
member __.Value = value
interface IMonoid<Size> with
member __.Zero = Size()
member __.Plus rhs = Size(value + rhs.Value)
type Value<'a> =
| Value of 'a
interface IMeasured<Size> with
member __.Measure = Size 1
open Monoids
module Node =
type Node<'m, 'a when 'm :> IMonoid<'m>> =
| Node2 of 'm * 'a * 'a
| Node3 of 'm * 'a * 'a * 'a
let toList = function
| Node2(_, a, b) -> [a; b]
| Node3(_, a, b, c) -> [a; b; c]
module Digit =
type Digit<'m, 'a when 'm :> IMonoid<'m>> =
| One of 'a
| Two of 'a * 'a
| Three of 'a * 'a * 'a
| Four of 'a * 'a * 'a * 'a
let toList = function
| One a -> [a]
| Two(a, b) -> [a; b]
| Three(a, b, c) -> [a; b; c]
| Four(a, b, c, d) -> [a; b; c; d]
module FingerTree =
open Node
open Digit
type FingerTree<'m, 'a when 'm :> IMonoid<'m>> =
| Empty
| Single of 'a
| Deep of 'm * Digit<'m, 'a> * Lazy<FingerTree<'m, Node<'m, 'a>>> * Digit<'m, 'a>
let unpack (Value v) = v
let rec toSeq<'a> (tree:FingerTree<Size, Value<'a>>) : seq<'a> = seq {
match tree with
| Single(Value single) ->
yield single
| Deep(_, prefix, Lazy deeper, suffix) ->
yield! prefix |> Digit.toList |> List.map unpack
#if ITERATE
for (Value deep) in toSeq deeper do
^^^^^
yield deep
#else
yield! deeper |> toSeq |> Seq.collect (Node.toList >> List.map unpack)
^^^^^
#endif
yield! suffix |> Digit.toList |> List.map unpack
| Empty -> ()
}
The error message I get says
Error Type mismatch. Expecting a
FingerTree<Size,Node<Size,Value<'a>>> -> 'b
but given a
FingerTree<Size,Value<'c>> -> seq<'c>
The type 'Node<Size,Value<'a>>' does not match the type 'Value<'b>'
and the squiggles underline the recursive call of toSeq.
I know that the “deeper” type is encapsulated in a Node and in the working code I just unpack it afterwards. But here the compiler trips already before I get the chance to unpack. Trying a for (Value deep) in toSeq deeper do yield deep has the same problem.
I already have a way out, namely to use the Not true, trying that yields a very similar error message.toSeq of the “base” Tree and Seq.map unpack afterwards.
I'm curious what makes this code break and how it could be fixed.
