X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment5.mdwn;h=85ac9a180a6d29cba48e9200aa68d507cd476df5;hp=61096c4e7a2b34a344e02d6755fe1e53f8bd30b1;hb=ae46ef3c2cb5de4b994fc7df4a95055d03c6b867;hpb=17eb4f0a0146d06ef52c2532405f6805cbaef0ec

diff --git a/assignment5.mdwn b/assignment5.mdwn
index 61096c4e..85ac9a18 100644
--- a/assignment5.mdwn
+++ b/assignment5.mdwn
@@ -35,38 +35,38 @@ Types and OCaml
 
 2.	Throughout this problem, assume that we have
 
-		let rec omega x = omega x;;
+		let rec blackhole x = blackhole x;;
 
 	All of the following are well-typed.
 	Which ones terminate?  What are the generalizations?
 
-		omega;;
+		blackhole;;
 
-		omega ();;
+		blackhole ();;
 
-		fun () -> omega ();;
+		fun () -> blackhole ();;
 
-		(fun () -> omega ()) ();;
+		(fun () -> blackhole ()) ();;
 
-		if true then omega else omega;;
+		if true then blackhole else blackhole;;
 
-		if false then omega else omega;;
+		if false then blackhole else blackhole;;
 
-		if true then omega else omega ();;
+		if true then blackhole else blackhole ();;
 
-		if false then omega else omega ();;
+		if false then blackhole else blackhole ();;
 
-		if true then omega () else omega;;
+		if true then blackhole () else blackhole;;
 
-		if false then omega () else omega;;
+		if false then blackhole () else blackhole;;
 
-		if true then omega () else omega ();;
+		if true then blackhole () else blackhole ();;
 
-		if false then omega () else omega ();;
+		if false then blackhole () else blackhole ();;
 
-		let _ = omega in 2;;
+		let _ = blackhole in 2;;
 
-		let _ = omega () in 2;;
+		let _ = blackhole () in 2;;
 
 3.	This problem is to begin thinking about controlling order of evaluation.
 The following expression is an attempt to make explicit the
@@ -104,15 +104,15 @@ and that "bool" is any boolean.  Then we can try the following:
 
 	However,
 
-		let rec omega x = omega x in
-		if true then omega else omega ();;
+		let rec blackhole x = blackhole x in
+		if true then blackhole else blackhole ();;
 
 	terminates, but
 
-		let rec omega x = omega x in
+		let rec blackhole x = blackhole x in
 		let b = true in
-		let y = omega in
-		let n = omega () in
+		let y = blackhole in
+		let n = blackhole () in
 		match b with true -> y | false -> n;;
 
 	does not terminate.  Incidentally, `match bool with true -> yes |
@@ -123,32 +123,12 @@ and that "bool" is any boolean.  Then we can try the following:
 
 	[[Hint assignment 5 problem 3]]
 
-Baby monads
------------
-
-Read the lecture notes for week 6, then write a
-function `lift` that generalized the correspondence between + and
-`add`: that is, `lift` takes any two-place operation on integers
-and returns a version that takes arguments of type `int option`
-instead, returning a result of `int option`.  In other words,
-`lift` will have type
-
-	(int -> int -> int) -> (int option) -> (int option) -> (int option)
-
-so that `lift (+) (Some 3) (Some 4)` will evalute to `Some 7`.  
-Don't worry about why you need to put `+` inside of parentheses.
-You should make use of `bind` in your definition of `lift`:
-
-	let bind (x: int option) (f: int -> (int option)) =
-		match x with None -> None | Some n -> f n;;
-
-
 Booleans, Church numbers, and Church lists in OCaml
 ---------------------------------------------------
 
 (These questions adapted from web materials by Umut Acar. See <http://www.mpi-sws.org/~umut/>.)
 
-The idea is to get booleans, Church numbers, "Church" lists, and
+The idea is to get booleans, Church numbers, v3 lists, and
 binary trees working in OCaml.
 
 Recall from class System F, or the polymorphic λ-calculus.
@@ -215,3 +195,23 @@ leaves in an int tree.
 Write a function `inOrder` : τ tree → τ list that computes the in-order traversal of a binary tree. You
 may assume the above encoding of lists; define any auxiliary functions you need.
 
+Baby monads
+-----------
+
+Read the lecture notes for week 6, then write a
+function `lift'` that generalized the correspondence between + and
+`add'`: that is, `lift'` takes any two-place operation on integers
+and returns a version that takes arguments of type `int option`
+instead, returning a result of `int option`.  In other words,
+`lift'` will have type
+
+	(int -> int -> int) -> (int option) -> (int option) -> (int option)
+
+so that `lift' (+) (Some 3) (Some 4)` will evalute to `Some 7`.  
+Don't worry about why you need to put `+` inside of parentheses.
+You should make use of `bind'` in your definition of `lift'`:
+
+	let bind' (x: int option) (f: int -> (int option)) =
+		match x with None -> None | Some n -> f n;;
+
+