X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=topics%2Fweek2_encodings.mdwn;h=85d4d77b3b8d77f7e68124f6913afa227cb2923d;hp=290cd5d82f85bda88464c44990dd154b5e75dbb3;hb=c70ea8653fd391ba094c8a64419f3532af2076ce;hpb=07ebc9292a8db8b98707232d2d01717293f473e9
diff --git a/topics/week2_encodings.mdwn b/topics/week2_encodings.mdwn
index 290cd5d8..85d4d77b 100644
--- a/topics/week2_encodings.mdwn
+++ b/topics/week2_encodings.mdwn
@@ -397,6 +397,8 @@ In fact, there's a way of looking at this that makes it look incredibly natural.
\x. f (g x)
+For example, the operation that maps a number `n` to n2+1 is the composition of the successor function and the squaring function (first we square, then we take the successor).
+
The composition of a function `f` with itself, namely:
\x. f (f x)
@@ -415,13 +417,13 @@ we are proposing to encode it as:
And indeed this is the Church encoding of the numbers:
-0 ≡ \f z. I z ; or \f z. f0 z
-1 ≡ \f z. f z ; or \f z. f1 z
-2 ≡ \f z. f (f z) ; or \f z. f2 z
-3 ≡ \f z. f (f (f z)) ; or \f z. f3 z
+0 ≡ \f z. z ; <~~> \f z. I z, or \f z. f0 z
+1 ≡ \f z. f z ; or \f z. f1 z
+2 ≡ \f z. f (f z) ; or \f z. f2 z
+3 ≡ \f z. f (f (f z)) ; or \f z. f3 z
...
-The encoding for `0` is equivalent to `\f z. z`, which we've also proposed as the encoding for `[]` and for `false`. Don't read too much into this.
+The encoding for `0` is what we also proposed as the encoding for `[]` and for `false`. Don't read too much into this.
Given the above, can you figure out how to define the `succ` function? We already worked through the definition of `cons`, and this is just a simplification of that, so you should be able to do it. We'll make it a homework.