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=b04f517e7b0deb57c270604befb9690b5e20b54d;hb=03bae43bc16f1f8dc98cfe2dab15264bc129beb1;hpb=a6c01f0671ccbed18f9938799f7b50eeb5bc4c50
diff --git a/topics/week7_introducing_monads.mdwn b/topics/week7_introducing_monads.mdwn
index b04f517e..adcf0cc2 100644
--- a/topics/week7_introducing_monads.mdwn
+++ b/topics/week7_introducing_monads.mdwn
@@ -84,7 +84,7 @@ For instance, the following are Kleisli arrows:
In the first, `P` has become `int` and `Q` has become `bool`. (The boxed type Q is bool).
Note that the left-hand schema `P` is permitted to itself be a boxed type. That is, where
-if `α list` is our box type, we can write the second arrow as
+if `α list` is our box type, we can write the second type as:
int -> int list
@@ -107,11 +107,11 @@ Here are the types of our crucial functions, together with our pronunciation, an
<=< or mcomp : (Q -> R) -> (P -> Q) -> (P -> R)
->=> or mpmoc (flip mcomp): (P -> Q) -> (Q -> R) -> (P -> R)
+>=> (flip mcomp, should we call it mpmoc?): (P -> Q) -> (Q -> R) -> (P -> R)
>>= or mbind : (Q) -> (Q -> R) -> (R)
-=<< or mdnib (flip mbind) (Q) -> (Q -> R) -> (R)
+=<< (flip mbind, should we call it mdnib?) (Q -> R) -> (Q) -> (R)
join: P -> P
@@ -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 â f) = (map g) â (map f)
+
+ Essentially these say that `map` is a homomorphism from `(α -> β, â, id)` to (α -> β, â', id'), where `â'` and `id'` are `â` 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