X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=topics%2Fweek7_introducing_monads.mdwn;h=adcf0cc2d42333ff35f1311dca7d215d2aa95cb9;hp=b3ab5aa94c1842248ed8f30ab2a483ebf245cd54;hb=03bae43bc16f1f8dc98cfe2dab15264bc129beb1;hpb=99b3142a496512789b209f717ba1d00603672965 diff --git a/topics/week7_introducing_monads.mdwn b/topics/week7_introducing_monads.mdwn index b3ab5aa9..adcf0cc2 100644 --- a/topics/week7_introducing_monads.mdwn +++ b/topics/week7_introducing_monads.mdwn @@ -127,7 +127,11 @@ certain useful guarantees. if there is a `map` function defined for that box type with the type given above. This has to obey the following Map Laws: - TODO LAWS + map (id : α -> α) = (id : α -> α) + map (g ○ f) = (map g) ○ (map f) + + Essentially these say that `map` is a homomorphism from `(α -> β, ○, id)` to (α -> β, ○', id'), where `○'` and `id'` are `○` and `id` restricted to arguments of type _. + * ***MapNable*** (in Haskelese, "Applicatives") A Mappable box type is *MapNable* if there are in addition `map2`, `mid`, and `mapply`. (Given either