Merge branch 'pryor'

[lambda.git] / week1.mdwn

diff --git a/week1.mdwn b/week1.mdwn
index e49724d..5c880fb 100644 (file)
--- a/week1.mdwn
+++ b/week1.mdwn
@@ -191,27 +191,27 @@ When M and N are such that there's some P that M reduces to by zero or more step
 
        M <~~> N
 
-This is what plays the role of equality in the lambda calculus. Hankin uses the symbol `=` for this. So too do Hindley and Seldin.
+This is what plays the role of equality in the lambda calculus. Hankin uses the symbol `=` for this. So too do Hindley and Seldin. Personally, I keep confusing that with the relation to be described next, so let's use this notation instead. Note that `M <~~> N` doesn't mean that each of `M` and `N` are reducible to each other; that only holds when `M` and `N` are the same expression. (Or, with our convention of only saying "reducible" for one or more reduction steps, it never holds.)
 
-In the metatheory, it's also sometimes useful to talk about formulas that are syntactically equivalent *before any reductions take place*. Hankin uses the symbol &equiv; for this. So too do Hindley and Seldin. We'll use that too, and will avoid using `=` when discussing metatheory for the lambda calculus. Instead we'll use `<~~>` as we said above. When we want to introduce a stipulative definition, we'll write it out longhand, as in:
+In the metatheory, it's also sometimes useful to talk about formulas that are syntactically equivalent *before any reductions take place*. Hankin uses the symbol <code>&equiv;</code> for this. So too do Hindley and Seldin. We'll use that too, and will avoid using `=` when discussing metatheory for the lambda calculus. Instead we'll use `<~~>` as we said above. When we want to introduce a stipulative definition, we'll write it out longhand, as in:
 
 >      T is defined to be `(M N)`.
 
 We'll regard the following two expressions:
 
-       (\x x y)
+       (\x (x y))
 
-       (\z z y)
+       (\z (z y))
 
 as syntactically equivalent, since they only involve a typographic change of a bound variable. Read Hankin section 2.3 for discussion of different attitudes one can take about this.
 
 Note that neither of those expressions are identical to:
 
-       (\x x w)
+       (\x (x w))
 
 because here it's a free variable that's been changed. Nor are they identical to:
 
-       (\y y y)
+       (\y (y y))
 
 because here the second occurrence of `y` is no longer free.