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.