From: jim
Date: Sun, 22 Feb 2015 21:39:30 +0000 (-0500)
Subject: tweaks
X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=7d5f235b46a5fb4ac8d6aaeffa65d0244522bdd0;ds=sidebyside
tweaks
---
diff --git a/topics/week4_fixed_point_combinators.mdwn b/topics/week4_fixed_point_combinators.mdwn
index ca9ab649..41a52737 100644
--- a/topics/week4_fixed_point_combinators.mdwn
+++ b/topics/week4_fixed_point_combinators.mdwn
@@ -297,7 +297,7 @@ which beta-reduces to:
Î¦[...LENGTH...]
-where that whole formula is convertible with the term LENGTH itself. In other words, the term `Î¦[...LENGTH...]` contains (a term that convertible with) itself --- despite being only finitely long. (If it had to contain a term *syntactically identical to* itself, this could not be achieved.)
+where that whole formula is convertible with the term `LENGTH` itself. In other words, the term `Î¦[...LENGTH...]` contains (a term that convertible with) itself --- despite being only finitely long. (If it had to contain a term *syntactically identical to* itself, this could not be achieved.)
The key to achieving all this is finding a fixed point for `h`. The strategy we will present will turn out to be a general way of
finding a fixed point for any lambda term.
@@ -314,7 +314,7 @@ work, but examining the way in which it fails will lead to a solution.
h h <~~> \xs. (empty? xs) 0 (succ (h (tail xs)))
-The problem is that in the subexpression `h (tail list)`, we've
+The problem is that in the subexpression `h (tail xs)`, we've
applied `h` to a list, but `h` expects as its first argument the
length function.
@@ -329,7 +329,7 @@ to discuss generalizations of this strategy.)
Shifting to `H` is the key creative step. Instead of applying `u` to a list, as happened
when we self-applied `h`, `H` applies its argument `u` first to *itself*: `u u`.
-After `u` gets an argument, the *result* is ready to apply to a list, so we've solved the problem noted above with `h (tail list)`.
+After `u` gets an argument, the *result* is ready to apply to a list, so we've solved the problem noted above with `h (tail xs)`.
We're not done yet, of course; we don't yet know what argument `u` to give
to `H` that will behave in the desired way.
@@ -573,7 +573,7 @@ returns itself (a copy of `sink`); if the argument is boolean false
sink true true false <~~> I
sink true true true false <~~> I
-Evidently, then, `sink true <~~> sink`. So we want `sink` to be the fixed point
+To get this behavior, we want `sink` to be the fixed point
of `\sink. \b. b sink I`. That is, `sink â¡ Y (\sb.bsI)`:
1. sink false