X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=towards_monads.mdwn;h=acdfbb3304a0627ab2f33a743c68811c544f2489;hp=3671d2730cf38bb5639032ce7a25920787ff53d8;hb=4227828f80f4c9c05f10bfc14435747c31fbb934;hpb=34c70399625b1a258682e542622d3c26d3b3795a diff --git a/towards_monads.mdwn b/towards_monads.mdwn index 3671d273..acdfbb33 100644 --- a/towards_monads.mdwn +++ b/towards_monads.mdwn @@ -48,13 +48,13 @@ the output of the safe-division function as input for further division operations. So we have to jack up the types of the inputs:
-let div' (x:int option) (y:int option) = - match y with +let div' (u:int option) (v:int option) = + match v with None -> None | Some 0 -> None - | Some n -> (match x with + | Some y -> (match u with None -> None - | Some m -> Some (m / n));; + | Some x -> Some (x / y));; (* val div' : int option -> int option -> int option =@@ -74,12 +74,12 @@ I prefer to line up the `match` alternatives by using OCaml's built-in tuple type: -let div' (x:int option) (y:int option) = - match (x, y) with +let div' (u:int option) (v:int option) = + match (u, v) with (None, _) -> None | (_, None) -> None | (_, Some 0) -> None - | (Some m, Some n) -> Some (m / n);; + | (Some x, Some y) -> Some (x / y);;So far so good. But what if we want to combine division with @@ -88,11 +88,11 @@ aware of the possibility that one of their arguments will trigger a presupposition failure:-let add' (x:int option) (y:int option) = - match (x, y) with +let add' (u:int option) (v:int option) = + match (u, v) with (None, _) -> None | (_, None) -> None - | (Some m, Some n) -> Some (m + n);; + | (Some x, Some y) -> Some (x + y);; (* val add' : int option -> int option -> int option =@@ -112,16 +112,16 @@ Haskell, etc., is to define a `bind` operator (the name `bind` is not well chosen to resonate with linguists, but what can you do). To continue our mnemonic association, we'll put a `'` after the name "bind" as well. -let bind' (x: int option) (f: int -> (int option)) = - match x with +let bind' (u: int option) (f: int -> (int option)) = + match u with None -> None - | Some n -> f n;; + | Some x -> f x;; -let add' (x: int option) (y: int option) = - bind' x (fun x -> bind' y (fun y -> Some (x + y)));; +let add' (u: int option) (v: int option) = + bind' u (fun x -> bind' v (fun y -> Some (x + y)));; -let div' (x: int option) (y: int option) = - bind' x (fun x -> bind' y (fun y -> if (0 = y) then None else Some (x / y)));; +let div' (u: int option) (v: int option) = + bind' u (fun x -> bind' v (fun y -> if (0 = y) then None else Some (x / y)));; (* # div' (div' (Some 12) (Some 2)) (Some 4);;