• 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 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}, 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 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 "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.

• Is that enough? If not, here are some more hints. But try to get as far as you can on your own.