fix previous overwrite

[lambda.git] / topics / week2_lambda_intro.mdwn

diff --git a/topics/week2_lambda_intro.mdwn b/topics/week2_lambda_intro.mdwn
index 091e123..4b09175 100644 (file)
--- a/topics/week2_lambda_intro.mdwn
+++ b/topics/week2_lambda_intro.mdwn
@@ -228,7 +228,12 @@ abbreviates:
 
     ((\x (\y (x y))) x)
 
 
     ((\x (\y (x y))) x)
 

-We didn't have to insert any parentheses around the inner body of `\y. (x y)` because they were already there.
+The outermost parentheses were added because we have an application. `(\x. \y.
+...)` became `(\x (\y. ...))` because of the rule for dots. We didn't have to
+insert any parentheses around the inner body of `\y. (x y)` because they were
+already there. That is, in expressions of the form `\y. (...)`, the dot abbreviates
+nothing. It's harmless to write such a dot, though, and it can be conceptually
+helpful especially in light of the next convention...

 
 
 **Merging lambdas** An expression of the form `(\x (\y M))`, or equivalently, `(\x. \y. M)`, can be abbreviated as:
 
 
 **Merging lambdas** An expression of the form `(\x (\y M))`, or equivalently, `(\x. \y. M)`, can be abbreviated as:


@@ -312,7 +317,7 @@ are distinct lambda expressions:
 
     (\z z)
 
 
     (\z z)
 

-yet when applied to any argument M, all of these will always return M. So they
+yet when applied to any argument `M`, all of these will always return `M`. So they

 have the same extension. It's also true, though you may not yet be in a
 position to see, that no other function can differentiate between them when
 they're supplied as an argument to it. However, these expressions are all
 have the same extension. It's also true, though you may not yet be in a
 position to see, that no other function can differentiate between them when
 they're supplied as an argument to it. However, these expressions are all


@@ -432,7 +437,7 @@ expressions to assign values to variables.  For instance,
     let x match 2
     in (x, x) 
 
     let x match 2
     in (x, x) 
 

-evaluates to the ordered pair (2, 2).  It may be helpful to think of
+evaluates to the ordered pair `(2, 2)`.  It may be helpful to think of

 a redex in the lambda calculus as a particular sort of `let`
 construction.
 
 a redex in the lambda calculus as a particular sort of `let`
 construction.