+ If we wanted to compose \[[∃]] with \[[lambda x]], we'd get:
+
+ let shift var_to_bind clause =
+ fun entity_reader r ->
+ let new_value = entity_reader r
+ in let r' = fun var -> if var = var_to_bind then new_value else r var
+ in clause r'
+ in let lifted_exists =
+ fun lifted_predicate ->
+ fun r -> exists (fun obj -> lifted_predicate (reader_unit obj) r)
+ in fun bool_reader -> lifted_exists (shift 'x' bool_reader)
+
+ which we can simplify to:
+
+ <!--
+ let shifted clause =
+ fun entity_reader r ->
+ let new_value = entity_reader r
+ in let r' = fun var -> if var = 'x' then new_value else r var
+ in clause r'
+ in let lifted_exists =
+ fun lifted_predicate ->
+ fun r -> exists (fun obj -> lifted_predicate (reader_unit obj) r)
+ in fun bool_reader -> lifted_exists (shifted bool_reader)
+
+ fun bool_reader ->
+ let shifted' =
+ fun entity_reader r ->
+ let new_value = entity_reader r
+ in let r' = fun var -> if var = 'x' then new_value else r var
+ in bool_reader r'
+ in fun r -> exists (fun obj -> shifted' (reader_unit obj) r)
+
+ fun bool_reader ->
+ let shifted'' r obj =
+ let new_value = (reader_unit obj) r
+ in let r' = fun var -> if var = 'x' then new_value else r var
+ in bool_reader r'
+ in fun r -> exists (fun obj -> shifted'' r obj)
+
+ fun bool_reader ->
+ let shifted'' r obj =
+ let new_value = obj
+ in let r' = fun var -> if var = 'x' then new_value else r var
+ in bool_reader r'
+ in fun r -> exists (shifted'' r)
+ -->
+
+ fun bool_reader ->
+ let shifted r new_value =
+ let r' = fun var -> if var = 'x' then new_value else r var
+ in bool_reader r'
+ in fun r -> exists (shifted r)
+
+ This gives us a value for \[[∃x]], which we use like this:
+
+ <pre><code>\[[∃x]] ( \[[Qx]] )
+ </code></pre>
+
+ Contrast the way we use \[[∃x]] in GS&V's system. Here we don't have a function that takes \[[Qx]] as an argument. Instead we have a operation that gets bound in a discourse chain:
+
+ <pre><code>u >>= \[[∃x]] >>= \[[Qx]]
+ </code></pre>
+
+ The crucial difference in GS&V's system is that the distinctive effect of the \[[∃x]]---to allocate new pegs in the store and associate variable `x` with the objects stored there---doesn't last only while interpreting some clauses supplied as arguments to \[[∃x]]. Instead, it persists through the discourse, possibly affecting the interpretation of claims outside the logical scope of the quantifier. This is how we'll able to interpret claims like:
+
+ > If ∃x (man x and ∃y y is wife of x) then (x kisses y).
+
+ See the discussion on pp. 24-5 of GS&V.
+
+
+* Can you figure out how to handle \[[not φ]] and the other connectives? If not, here are some [more hints](/hints/assignment_7_hint_6). But try to get as far as you can on your own.
+