X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=manipulating_trees_with_monads.mdwn;h=3a30561b515bf38abf84786bdb5eea579cdef165;hp=dcba312629435861a915ee767767cd9dad97b58d;hb=a01acebb0b88c52af2fd61859c31cd20e1e2396a;hpb=3ed8e56bf33b1c0cfa09b672abf26e9c397ea0f1 diff --git a/manipulating_trees_with_monads.mdwn b/manipulating_trees_with_monads.mdwn index dcba3126..3a30561b 100644 --- a/manipulating_trees_with_monads.mdwn +++ b/manipulating_trees_with_monads.mdwn @@ -89,7 +89,7 @@ behavior of a reader monad. Let's make that explicit. In general, we're on a journey of making our treemap function more and more flexible. So the next step---combining the tree transformer with a reader monad---is to have the treemap function return a (monadized) -tree that is ready to accept any `int->int` function and produce the +tree that is ready to accept any `int -> int` function and produce the updated tree. @@ -105,8 +105,8 @@ updated tree. f 7 f 11 That is, we want to transform the ordinary tree `t1` (of type `int -tree`) into a reader object of type `(int->int)-> int tree`: something -that, when you apply it to an `int->int` function returns an `int +tree`) into a reader object of type `(int -> int) -> int tree`: something +that, when you apply it to an `int -> int` function returns an `int tree` in which each leaf `x` has been replaced with `(f x)`. With previous readers, we always knew which kind of environment to @@ -114,9 +114,9 @@ expect: either an assignment function (the original calculator simulation), a world (the intensionality monad), an integer (the Jacobson-inspired link monad), etc. In this situation, it will be enough for now to expect that our reader will expect a function of -type `int->int`. +type `int -> int`. - type 'a reader = (int->int) -> 'a;; (* mnemonic: e for environment *) + type 'a reader = (int -> int) -> 'a;; (* mnemonic: e for environment *) let reader_unit (x : 'a) : 'a reader = fun _ -> x;; let reader_bind (u: 'a reader) (f : 'a -> 'c reader) : 'c reader = fun e -> f (u e) e;; @@ -128,7 +128,7 @@ It's easy to figure out how to turn an `int` into an `int reader`: But what do we do when the integers are scattered over the leaves of a tree? A binary tree is not the kind of thing that we can apply a -function of type `int->int` to. +function of type `int -> int` to. let rec treemonadizer (f : 'a -> 'b reader) (t : 'a tree) : 'b tree reader = match t with @@ -150,7 +150,7 @@ monad through the leaves. Here, our environment is the doubling function (`fun i -> i + i`). If we apply the very same `int tree reader` (namely, `treemonadizer -int2int_reader t1`) to a different `int->int` function---say, the +int2int_reader t1`) to a different `int -> int` function---say, the squaring function, `fun i -> i * i`---we get an entirely different result: