*	How shall we handle \[[∃x]]? As we said, GS&V really tell us how to interpret \[[∃xPx]], but what they say about this breaks naturally into two pieces, such that we can represent the update of our starting set `u` with \[[∃xPx]] as:

	<pre><code>u >>=<sub>set</sub> \[[&exist;x]] >>=<sub>set</sub> \[[Px]]
	</code></pre>

	What does \[[&exist;x]] need to be here? Here's what they say, on the top of p. 13:

	>	Suppose an information state `s` is updated with the sentence &exist;xPx. Possibilities in `s` in which no entity has the property P will be eliminated.

	We can defer that to a later step, where we do `... >>= \[[Px]]`.
 
	>	The referent system of the remaining possibilities will be extended with a new peg, which is associated with `x`. And for each old possibility `i` in `s`, there will be just as many extensions `i[x/d]` in the new state `s'` and there are entities `d` which in the possible world of `i` have the property P.

	Deferring the "property P" part, this corresponds to:

	<pre><code>u updated with \[[&exist;x]] &equiv;
		let extend_one = fun one_dpm ->
			fun truth_value ->
				if truth_value = false
				then empty_set
				else List.map (fun d -> new_peg_and_assign 'x' d) domain
		in bind_set u extend_one
	</code></pre>

	where `new_peg_and_assign` is the operation we defined in [hint 3](/hints/assignment_7_hint_3):

		let new_peg_and_assign (var_to_bind : char) (d : entity) =
			fun ((r, h) : assignment * store) ->
				(* first we calculate an unused index *)
				let newindex = List.length h
				(* next we store d at h[newindex], which is at the very end of h *)
				(* the following line achieves that in a simple but inefficient way *)
				in let h' = List.append h [d]
				(* next we assign 'x' to location newindex *)
				in let r' = fun v ->
					if v = var_to_bind then newindex else r v
				(* the reason for returning true as an initial element should now be apparent *)
				in (true, r',h')
	
	What's going on in this representation of `u` updated with \[[&exist;x]]? For each `bool dpm` in `u` that wraps a `true`, we collect `dpm`s that are the result of extending their input `(r, h)` by allocating a new peg for entity `d`, for each `d` in our whole domain of entities, and binding the variable `x` to the index of that peg. For `bool dpm`s in `u` that wrap `false`, we just discard them. We could if we wanted instead return `unit_set (unit_dpm false)`.

	A later step can then filter out all the `dpm`s according to which the 
entity `d` we did that with doesn't have property P.

	So if we just call the function `extend_one` defined above \[[&exist;x]], then `u` updated with \[[&exist;x]] updated with \[[Px]] is just:

	<pre><code>u >>= \[[&exist;x]] >>= \[[Px]]
	</code></pre>

	or, being explicit about which "bind" operation we're representing here with `>>=`, that is:

	<pre><code>bind_set (bind_set u \[[&exist;x]]) \[[Px]]
	</code></pre>

*	Can you figure out how to handle \[[not &phi;]] on your own? If not, here are some [more hints](/hints/assignment_7_hint_6).