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diff --git a/hints/assignment_7_hint_1.mdwn b/hints/assignment_7_hint_1.mdwn
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--- a/hints/assignment_7_hint_1.mdwn
+++ b/hints/assignment_7_hint_1.mdwn
@@ -1,15 +1,15 @@
-* Where Groenendijk, Stockhof and Veltman (GS&V) say "peg", that translates in our terminology into a new "reference cell" or "location" in a store.
+* Where Groenendijk, Stokhof and Veltman (GS&V) say "peg", that translates in our terminology into a new "reference cell" or "location" in a store.
* Where they represent pegs as natural numbers, that corresponds to our representing locations in a store by their indexes in the store.
-* Where they say "reference system," which they use the leter `r` for, that corresponds to what we've been calling "assignments", and have been using the letter `g` for.
+* Where they say "reference system," which they use the letter `r` for, that corresponds to what we've been calling "assignments", and have been using the letter `g` for.
-* Where they say `r[x/n]`, that's our `g{x:=n}`.
+* Where they say `r[x/n]`, that's our `g{x:=n}`, which we could represent in OCaml as `fun var -> if var = 'x' then n else g var`. (Earlier we represented assignments as lists of pairs, here we're representing them as functions. Either can work.)
-* Their function `g`, which assigns objects from the domain to pegs, corresponds to our store function, which assigns entities to indexes.
+* Their function `g`, which assigns entities from the domain to pegs, corresponds to a store with several indexes. To avoid confusion, I'll use `r` for assignments, like they do, and avoid using `g` altogether. Instead I'll use `h` for stores. (We can't use `s` because GS&V use that for something else, which they call "information states.")
-* At several places they talk about some things being *real extensions* of other things. This confused me at first, because they don't ever define a notion of "real extension." (They do define what they mean by "an extension.") At one point in the paper, it emerges that what they mean is what I'd call a *proper extension*: an extension which isn't identical to the original.
+* At several places they talk about some things being *real extensions* of other things. This confused me at first, because they don't ever define a notion of "real extension." (They do define what they mean by "extensions.") Eventually, it emerges that what they mean is what I'd call a *proper extension*: an extension which isn't identical to the original.
-* [More hints](/hints/assignment_7_hint_2).
+* Is that enough? If not, here are some [more hints](/hints/assignment_7_hint_2). But try to get as far as you can on your own.