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diff --git a/hints/assignment_7_hint_3.mdwn b/hints/assignment_7_hint_3.mdwn
index 1cd62133..3fec7e2d 100644
--- a/hints/assignment_7_hint_3.mdwn
+++ b/hints/assignment_7_hint_3.mdwn
@@ -5,21 +5,25 @@
 
 *	They say the denotation of a variable is the object which the store `g` assigns to the index that the assignment function `r` assigns to the variable. In other words, if the variable is `'x'`, its denotation wrt `(r, g, w)` is `g[r['x']]`.
 
-We're going to keep all of that, except dropping the worlds. And instead of talking about "\[[expression]] in discourse possibility `(r, g, w)`," we'll just talk about "\[[expression]]" and let that be a monadic object, implemented in part by a function that takes `(r, g)` as an argument.
+We're going to keep all of that, except dropping the worlds. And instead of talking about
 
-More specifically, "\[[expression]]" will be a set of 'a discourse possibility monads, where 'a is the appropriate type for "expression," and the discourse possibility monads are themselves state monads where `(r, g)` is the state that gets updated. Those are implemented as functions from `(r, g)` to `(a, r', g')`, where `a` is a value of type `'a`, and `r', g'` are possibly altered assignment functions and stores.
+>	\[[expression]] in possibility `(r, g, w)`
+
+we'll just talk about \[[expression]] and let that be a monadic object, implemented in part by a function that takes `(r, g)` as an argument.
+
+More specifically, \[[expression]] will be a set of `'a discourse_possibility` monads, where `'a` is the appropriate type for *expression*, and the discourse possibility monads are themselves state monads where `(r, g)` is the state that gets updated. Those are implemented as functions from `(r, g)` to `(a, r', g')`, where `a` is a value of type `'a`, and `r', g'` are possibly altered assignment functions and stores.
 
 *	In def 2.7, GS&V talk about an operation that takes an existing set of discourse possibilities, and extends each member in the set by allocating a new location in the store, and assigning a variable `'x'` to that location, which holds some object `d` from the domain. It will be useful to have a shorthand way of referring to this operation:
 
-		let newpeg_and_bind (variable : char) (d : entity) =
+		let newpeg_and_bind (bound_variable : char) (d : entity) =
 			fun ((r, g) : assignment * store) ->
 				let newindex = List.length g
 				(* first we store d at index newindex in g, which is at the very end *)
 				(* the following line achieves that in a simple but very inefficient way *)
 				in let g' = List.append g [d]
 				(* next we assign 'x' to location newindex *)
-				in let r' = fun variable' ->
-					if variable' = variable then newindex else r variable'
+				in let r' = fun v ->
+					if v = bound_variable then newindex else r v
 				(* the reason for returning a triple with () in first position will emerge *)
 				in ((), r',g')