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Here's the approach I use to simulate Typeclasses (from <a href="http://code.google.com/p/fsharp-typeclasses/" rel="nofollow noreferrer">http://code.google.com/p/fsharp-typeclasses/</a> ). In your case, for Arrows could be something like this: <pre class="lang-ml prettyprint-override"><code>let inline i2 (a:^a,b:^b ) = ((^a or ^b ) : (static member instance: ^a* ^b -> _) (a,b )) let inline i3 (a:^a,b:^b,c:^c) = ((^a or ^b or ^c) : (static member instance: ^a* ^b* ^c -> _) (a,b,c)) type T = T with static member inline instance (a:'a ) = fun x -> i2(a , Unchecked.defaultof<'r>) x :'r static member inline instance (a:'a, b:'b) = fun x -> i3(a, b, Unchecked.defaultof<'r>) x :'r type Return = Return with static member instance (_Monad:Return, _:option<'a>) = fun x -> Some x static member instance (_Monad:Return, _:list<'a> ) = fun x -> [x] static member instance (_Monad:Return, _: 'r -> 'a ) = fun x _ -> x let inline return' x = T.instance Return x type Bind = Bind with static member instance (_Monad:Bind, x:option<_>, _:option<'b>) = fun f -> Option.bind f x static member instance (_Monad:Bind, x:list<_> , _:list<'b> ) = fun f -> List.collect f x static member instance (_Monad:Bind, f:'r->'a, _:'r->'b) = fun k r -> k (f r) r let inline (>>=) x (f:_->'R) : 'R = T.instance (Bind, x) f let inline (>=>) f g x = f x >>= g type Kleisli<'a, 'm> = Kleisli of ('a -> 'm) let runKleisli (Kleisli f) = f type Id = Id with static member instance (_Category:Id, _: 'r -> 'r ) = fun () -> id static member inline instance (_Category:Id, _:Kleisli<'a,'b>) = fun () -> Kleisli return' let inline id'() = T.instance Id () type Comp = Comp with static member instance (_Category:Comp, f, _) = (<<) f static member inline instance (_Category:Comp, Kleisli f, _) = fun (Kleisli g) -> Kleisli (g >=> f) let inline (<<<) f g = T.instance (Comp, f) g let inline (>>>) g f = T.instance (Comp, f) g type Arr = Arr with static member instance (_Arrow:Arr, _: _ -> _) = fun (f:_->_) -> f static member inline instance (_Arrow:Arr, _:Kleisli<_,_>) = fun f -> Kleisli (return' <<< f) let inline arr f = T.instance Arr f type First = First with static member instance (_Arrow:First, f, _: 'a -> 'b) = fun () (x,y) -> (f x, y) static member inline instance (_Arrow:First, Kleisli f, _:Kleisli<_,_>) = fun () -> Kleisli (fun (b,d) -> f b >>= fun c -> return' (c,d)) let inline first f = T.instance (First, f) () let inline second f = let swap (x,y) = (y,x) in arr swap >>> first f >>> arr swap let inline ( *** ) f g = first f >>> second g let inline ( &&& ) f g = arr (fun b -> (b,b)) >>> f *** g </code></pre> Usage: <pre class="lang-ml prettyprint-override"><code>> let f = Kleisli (fun y -> [y;y*2;y*3]) <<< Kleisli ( fun x -> [ x + 3 ; x * 2 ] ) ;; val f : Kleisli<int,int list> = Kleisli <fun:f@4-14> > runKleisli f <| 5 ;; val it : int list = [8; 16; 24; 10; 20; 30] > (arr (fun y -> [y;y*2;y*3])) 3 ;; val it : int list = [3; 6; 9] > let (x:option<_>) = runKleisli (arr (fun y -> [y;y*2;y*3])) 2 ;; val x : int list option = Some [2; 4; 6] > ( (*) 100) *** ((+) 9) <| (5,10) ;; val it : int * int = (500, 19) > ( (*) 100) &&& ((+) 9) <| 5 ;; val it : int * int = (500, 14) > let x:List<_> = (runKleisli (id'())) 5 ;; val x : List<int> = [5] </code></pre> Note: use <code>id'()</code> instead of <code>id</code> Update: you need F# 3.0 to compile this code, otherwise <a href="http://code.google.com/p/fsharp-typeclasses/source/browse/Arrow.fs?r=a6389b6ea46ee96103d46bc71c1d7939f4aa9ff2" rel="nofollow noreferrer">here's the F# 2.0 version</a>. And <a href="http://nut-cracker.azurewebsites.net/typeclasses-for-fsharp/" rel="nofollow noreferrer">here's</a> a detailed explanation of this technique which is type-safe, extensible and as you can see works even with some Higher Kind Typeclasses.
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1. POHow would I translate a Haskell type class into F#?
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1. COOut of curiosity, what's F# 3.0 specific on this code?
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2. CO@GustavoGuerra Function i3 will not compile in F# 2.0 because of a parser bug. There is a workaround using operators, but the code become less readable.
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