Finally, we realize that we're going to have a set of `bool dpm`s to start with, and we need to compose \[[Qx]] with them. We don't want any of the monadic values in the set that wrap `false` to become `true`; instead, we want to apply a filter that checks whether values that formerly wrapped `true` should still continue to do so.
- This is most easily done like this:
+ This could be handled like this:
fun entity_dpm ->
- fun truth_value ->
+ let eliminate_non_Qxs = fun truth_value ->
if truth_value = false
then empty_set
- else unit_set (bind dpm entity_dpm (fun e -> unit_dpm (Q e)))
+ else unit_set (bind_dpm entity_dpm (fun e -> unit_dpm (Q e)))
+ in fun one_dpm -> (bind_dpm one_dpm eliminate_non_Qxs)
Applied to an `entity_dpm`, that yields a function that we can bind to a `bool dpm set` and that will transform the doubly-wrapped `bool` into a new `bool dpm set`.
let obj = List.nth h (r 'x')
in (obj, r, h)
in let entity_dpm = getx
- in fun truth_value ->
+ in let eliminate_non_Qxs = fun truth_value ->
if truth_value = false
then empty_set
else unit_set (bind_dpm entity_dpm (fun e -> unit_dpm (Q e)))
+ in fun one_dpm -> (bind_dpm one_dpm eliminate_non_Qxs)
or, simplifying:
let getx = fun (r, h) ->
let obj = List.nth h (r 'x')
in (obj, r, h)
- in fun truth_value ->
+ in let eliminate_non_Qxs = fun truth_value ->
if truth_value
then unit_set (bind_dpm getx (fun e -> unit_dpm (Q e)))
else empty_set
+ in fun one_dpm -> (bind_dpm one_dpm eliminate_non_Qxs)
unpacking the definition of `bind_dpm`, that is:
let getx = fun (r, h) ->
let obj = List.nth h (r 'x')
in (obj, r, h)
- in fun truth_value ->
+ in let eliminate_non_Qxs = fun truth_value ->
if truth_value
then unit_set (
fun (r, h) ->
in let u' = (fun e -> unit_dpm (Q e)) a
in u' (r', h')
) else empty_set
-
+ in fun one_dpm -> (bind_dpm one_dpm eliminate_non_Qxs)
+
which is:
- in fun truth_value ->
+ fun truth_value ->
if truth_value
then unit_set (
- fun (r, h) ->
+ let eliminate_non_Qxs = fun (r, h) ->
let obj = List.nth h (r 'x')
let (a, r', h') = (obj, r, h)
in let u' = (fun e -> unit_dpm (Q e)) a
in u' (r', h')
) else empty_set
-
+ in fun one_dpm -> (bind_dpm one_dpm eliminate_non_Qxs)
+
which is:
- in fun truth_value ->
+ let eliminate_non_Qxs = fun truth_value ->
if truth_value
then unit_set (
fun (r, h) ->
let obj = List.nth h (r 'x')
in let u' = unit_dpm (Q obj)
- in u' (r', h')
+ in u' (r, h)
) else empty_set
-
+ in fun one_dpm -> (bind_dpm one_dpm eliminate_non_Qxs)
+
+ This is a function that takes a `bool dpm` as input and returns a `bool dpm set` as output.
+
This is a bit different than the \[[Qx]] we had before:
let eliminate_non_Qxs = (fun truth_value ->
then let obj = List.nth h (r 'x') in Q obj
else false
in (truth_value', r, h))
- in (fun one_dpm -> unit_set (bind_dpm one_dpm eliminate_non_Qxs))
+ in fun one_dpm -> unit_set (bind_dpm one_dpm eliminate_non_Qxs)
because that one passed through every `bool dpm` that wrapped a `false`; whereas now we're discarding some of them. But these will work equally well. We can implement either behavior (or, as we said before, the behavior of never passing through a wrapped `false`).