From: Jim Pryor
Date: Wed, 1 Dec 2010 06:38:10 +0000 (-0500)
Subject: lists-monad tweaks
X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=5e8eadce75352b7c2ec2ad78c8c92b89bd6ee778
lists-monad tweaks
Signed-off-by: Jim Pryor
---
diff --git a/list_monad_as_continuation_monad.mdwn b/list_monad_as_continuation_monad.mdwn
index b4158b16..8d442ae0 100644
--- a/list_monad_as_continuation_monad.mdwn
+++ b/list_monad_as_continuation_monad.mdwn
@@ -10,7 +10,7 @@ Rethinking the list monad
To construct a monad, the key element is to settle on a type
constructor, and the monad more or less naturally follows from that.
We'll remind you of some examples of how monads follow from the type
-constructor in a moment. This will involve some review of familair
+constructor in a moment. This will involve some review of familiar
material, but it's worth doing for two reasons: it will set up a
pattern for the new discussion further below, and it will tie together
some previously unconnected elements of the course (more specifically,
@@ -114,7 +114,7 @@ result to applying the function to the elements of the list:
List.map (fun i -> [i;i+1]) [1;2] ~~> [[1; 2]; [2; 3]]
-and List.concat takes a list of lists and erases the embdded list
+and List.concat takes a list of lists and erases the embedded list
boundaries:
List.concat [[1; 2]; [2; 3]] ~~> [1; 2; 2; 3]
@@ -138,7 +138,7 @@ have a collection of lists, one for each of the `'a`'s. One
possibility is that we could gather them all up in a list, so that
`bind' [1;2] (fun i -> [i;i]) ~~> [[1;1];[2;2]]`. But that restricts
the object returned by the second argument of `bind` to always be of
-type `'b list list`. We can elimiate that restriction by flattening
+type `'b list list`. We can eliminate that restriction by flattening
the list of lists into a single list: this is
just List.concat applied to the output of List.map. So there is some logic to the
choice of unit and bind for the list monad.
@@ -146,12 +146,12 @@ choice of unit and bind for the list monad.
Yet we can still desire to go deeper, and see if the appropriate bind
behavior emerges from the types, as it did for the previously
considered monads. But we can't do that if we leave the list type as
-a primitive Ocaml type. However, we know several ways of implementing
+a primitive OCaml type. However, we know several ways of implementing
lists using just functions. In what follows, we're going to use type
3 lists, the right fold implementation (though it's important and
intriguing to wonder how things would change if we used some other
-strategy for implementating lists). These were the lists that made
-lists look like Church numerals with extra bits embdded in them:
+strategy for implementing lists). These were the lists that made
+lists look like Church numerals with extra bits embedded in them:
empty list: fun f z -> z
list with one element: fun f z -> f 1 z
@@ -174,7 +174,7 @@ types should be ourselves):
We can see what the consistent, general principle types are at the end, so we
can stop. These types should remind you of the simply-typed lambda calculus
types for Church numerals (`(o -> o) -> o -> o`) with one extra type
-thrown in, the type of the element a the head of the list
+thrown in, the type of the element at the head of the list
(in this case, an int).
So here's our type constructor for our hand-rolled lists:
@@ -182,7 +182,7 @@ So here's our type constructor for our hand-rolled lists:
type 'b list' = (int -> 'b -> 'b) -> 'b -> 'b
Generalizing to lists that contain any kind of element (not just
-ints), we have
+`int`s), we have
type ('a, 'b) list' = ('a -> 'b -> 'b) -> 'b -> 'b
@@ -206,9 +206,9 @@ Unpacking the types gives:
(f : 'a -> ('c -> 'd -> 'd) -> 'd -> 'd)
: ('c -> 'd -> 'd) -> 'd -> 'd = ...
-Perhaps a bit intimiating.
+Perhaps a bit intimidating.
But it's a rookie mistake to quail before complicated types. You should
-be no more intimiated by complex types than by a linguistic tree with
+be no more intimidated by complex types than by a linguistic tree with
deeply embedded branches: complex structure created by repeated
application of simple rules.