X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=hints%2Fassignment_7_hint_4.mdwn;h=ae17ce1d551ee945796adb589e9b76f9185dcc44;hp=346d98b30bcd90c4d387d11f0460de7220ab4b49;hb=c0d0fef36aacfcb9e66c43b39281491f44757850;hpb=002bbc4734d89967f6941fcff5021b4d1c661f2b

diff --git a/hints/assignment_7_hint_4.mdwn b/hints/assignment_7_hint_4.mdwn
index 346d98b3..ae17ce1d 100644
--- a/hints/assignment_7_hint_4.mdwn
+++ b/hints/assignment_7_hint_4.mdwn
@@ -46,15 +46,16 @@
 
 	Finally, we realize that we're going to have a set of `bool dpm`s to start with, and we need to compose \[[Qx]] with them. We don't want any of the monadic values in the set that wrap `false` to become `true`; instead, we want to apply a filter that checks whether values that formerly wrapped `true` should still continue to do so.
 
-	This is most easily done like this:
+	This could be handled like this:
 
 		fun entity_dpm ->
-			fun truth_value ->
+			let eliminate_non_Qxs = fun truth_value ->
 				if truth_value = false
 				then empty_set
-				else unit_set (bind dpm entity_dpm (fun e -> unit_dpm (Q e)))
+				else unit_set (bind_dpm entity_dpm (fun e -> unit_dpm (Q e)))
+			in fun one_dpm -> (bind_dpm one_dpm eliminate_non_Qxs)
 
-	Applied to an entity_dpm, that yields a function that we can bind to a `bool dpm set` and that will transform the doubly-wrapped `bool` into a new `bool dpm set`.
+	Applied to an `entity_dpm`, that yields a function that we can bind to a `bool dpm set` and that will transform the doubly-wrapped `bool` into a new `bool dpm set`.
 
 	Doing things this way will discard `bool dpm`s from the set that started out wrapping `false`, and will pass through other `bool dpm`s that start out wrapping `true` but which our current filter transforms to a wrapped `false`. You might instead aim for consistency, and always pass through wrapped `false`s, whether they started out that way or are only now being generated; or instead always discard such, and only pass through wrapped `true`s. But what we have here will work fine too.
 
@@ -64,27 +65,29 @@
 			let obj = List.nth h (r 'x')
 			in (obj, r, h)
 		in let entity_dpm = getx
-		in fun truth_value ->
+		in let eliminate_non_Qxs = fun truth_value ->
 			if truth_value = false
 			then empty_set
 			else unit_set (bind_dpm entity_dpm (fun e -> unit_dpm (Q e)))
+		in fun one_dpm -> (bind_dpm one_dpm eliminate_non_Qxs)
 
 	or, simplifying:
 
 		let getx = fun (r, h) ->
 			let obj = List.nth h (r 'x')
 			in (obj, r, h)
-		in fun truth_value ->
+		in let eliminate_non_Qxs = fun truth_value ->
 			if truth_value
 			then unit_set (bind_dpm getx (fun e -> unit_dpm (Q e)))
 			else empty_set
+		in fun one_dpm -> (bind_dpm one_dpm eliminate_non_Qxs)
 
-	which is:
+	unpacking the definition of `bind_dpm`, that is:
 
 		let getx = fun (r, h) ->
 			let obj = List.nth h (r 'x')
 			in (obj, r, h)
-		in fun truth_value ->
+		in let eliminate_non_Qxs = fun truth_value ->
 			if truth_value
 			then unit_set (
 				fun (r, h) ->
@@ -92,10 +95,11 @@
 					in let u' = (fun e -> unit_dpm (Q e)) a
 					in u' (r', h')
 			) else empty_set
-		
+		in fun one_dpm -> (bind_dpm one_dpm eliminate_non_Qxs)
+
 	which is:
 
-		in fun truth_value ->
+		let eliminate_non_Qxs = fun truth_value ->
 			if truth_value
 			then unit_set (
 				fun (r, h) ->
@@ -104,18 +108,22 @@
 					in let u' = (fun e -> unit_dpm (Q e)) a
 					in u' (r', h')
 			) else empty_set
-		
+		in fun one_dpm -> (bind_dpm one_dpm eliminate_non_Qxs)
+
 	which is:
 
-		in fun truth_value ->
+		let eliminate_non_Qxs = fun truth_value ->
 			if truth_value
 			then unit_set (
 				fun (r, h) ->
 					let obj = List.nth h (r 'x')
 					in let u' = unit_dpm (Q obj)
-					in u' (r', h')
+					in u' (r, h)
 			) else empty_set
-		
+		in fun one_dpm -> (bind_dpm one_dpm eliminate_non_Qxs)
+
+	This is a function that takes a `bool dpm` as input and returns a `bool dpm set` as output.
+
 	This is a bit different than the \[[Qx]] we had before:
 
 		let eliminate_non_Qxs = (fun truth_value ->
@@ -125,9 +133,9 @@
 					then let obj = List.nth h (r 'x') in Q obj
 					else false
 				in (truth_value', r, h))
-		in (fun one_dpm -> unit_set (bind_dpm one_dpm eliminate_non_Qxs))
+		in fun one_dpm -> unit_set (bind_dpm one_dpm eliminate_non_Qxs)
 
-	because that one passed through every `bool dpm` that wrapped a `false`; whereas now we're discarding some of them. But these will work equally well. We can implement either behavior (or, as we said before, the behavior of never passing through a wrapped `false`).
+	because that one passed through every `bool dpm` that wrapped a `false`; whereas now we're discarding some of them. But these will work equally well. We can implement either behavior (or, as we said before, the behavior of never returning any wrapped `false`s).
 
 *	Reviewing: now we've determined how to define \[[Q]] and \[[x]] such that \[[Qx]] can be the result of applying the function \[[Q]] to the `entity dpm` \[[x]]. And \[[Qx]] in turn is now a function that takes a `bool dpm` as input and returns a `bool dpm set` as output. We compose this with a `bool dpm set` we already have on hand: