X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=list_monad_as_continuation_monad.mdwn;h=7a57ea7b73c5a9565f7644311ef8737f88200d4f;hp=0edec2552c4f1b0fa6bf6238dd9864b9cfc0fc56;hb=d9bf1d89baaef4a0ceeb5c84db4d2a7172aaf400;hpb=c51397c5a41cbf75e37382905b212868e427b16b diff --git a/list_monad_as_continuation_monad.mdwn b/list_monad_as_continuation_monad.mdwn index 0edec255..7a57ea7b 100644 --- a/list_monad_as_continuation_monad.mdwn +++ b/list_monad_as_continuation_monad.mdwn @@ -88,7 +88,7 @@ need to posit a store `s` that we can apply `u` to. Once we do so, however, we won't have an `'a`; we'll have a pair whose first element is an `'a`. So we have to unpack the pair: - ... let (a, s') = u s in ... (f a) ... + ... let (a, s') = u s in ... f a ... Abstracting over the `s` and adjusting the types gives the result: @@ -222,7 +222,7 @@ fold that function over its type `'a` members, and that's where we can get at th ... u (fun (a : 'a) (b : 'b) -> ... f a ... ) ... -In order for `u` to have the kind of argument it needs, the `fun a b -> ... f a ...` has to have type `'a -> 'b -> 'b`; so the `... f a ...` has to evaluate to a result of type `'b`. The easiest way to do this is to collapse (or "unify") the types `'b` and `'d`, with the result that `f a` will have type `('c -> 'b -> 'b) -> 'b -> 'b`. Let's postulate an argument `k` of type `('c -> 'b -> 'b)` and supply it to `(f a)`: +In order for `u` to have the kind of argument it needs, the `fun a b -> ... f a ...` has to have type `'a -> 'b -> 'b`; so the `... f a ...` has to evaluate to a result of type `'b`. The easiest way to do this is to collapse (or "unify") the types `'b` and `'d`, with the result that `f a` will have type `('c -> 'b -> 'b) -> 'b -> 'b`. Let's postulate an argument `k` of type `('c -> 'b -> 'b)` and supply it to `f a`: ... u (fun (a : 'a) (b : 'b) -> ... f a k ... ) ... @@ -276,7 +276,7 @@ So if, for example, we let `k` be `+` and `z` be `0`, then the computation would right-fold + and 2+4+2+4+8+0 over [2] = 2+(2+4+(2+4+8+(0))) ==> right-fold + and 2+2+4+2+4+8+0 over [] = 2+(2+4+(2+4+8+(0))) -which indeed is the result of right-folding + and 0 over `[2; 2; 4; 2; 4; 8]`. If you trace through how this works, you should be able to persuade yourself that our formula: +which indeed is the result of right-folding `+` and `0` over `[2; 2; 4; 2; 4; 8]`. If you trace through how this works, you should be able to persuade yourself that our formula: fun k z -> u (fun a b -> f a k b) z