+ fun (lifted_predicate : entity reader -> bool reader) ->
+ fun r -> exists (fun (obj : entity) -> lifted_predicate (unit_reader obj) r)
+
+ That would be the meaning of \[[∃]], which we'd use like this:
+
+ <pre><code>\[[∃]] \[[Q]]
+ </code></pre>
+
+ or this:
+
+ <pre><code>\[[∃]] ( \[[lambda x]] \[[Qx]] )
+ </code></pre>
+
+ 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 (unit_reader obj) r)
+ in fun bool_reader -> lifted_exists (shift 'x' bool_reader)
+
+ which we can simplify as:
+
+ 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 (unit_reader 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' (unit_reader obj) r)
+
+ fun bool_reader ->
+ let shifted'' r obj =
+ let new_value = (unit_reader 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]]<sub>reader</sub> ( \[[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>