in (truth_value', r, h))
in bind_set u (fun one_dpm -> unit_set (bind_dpm one_dpm eliminate_non_Qxs))
- The first three seven lines here just perfom the operation we described: return a `bool dpm` computation that only yields `true` whether its input `(r, h)` associates variable `x` with the right sort of entity. The last line performs the `bind_set` operation. This works by taking each `dpm` in the set and returning a `unit_set` of a filtered `dpm`. The definition of `bind_set` takes care of collecting together all of the `unit_set`s that result for each different set element we started with.
+ The first seven lines here just perfom the operation we described: return a `bool dpm` computation that only yields `true` when its input `(r, h)` associates variable `x` with the right sort of entity. The last line performs the `bind_set` operation. This works by taking each `dpm` in the set and returning a `unit_set` of a filtered `dpm`. The definition of `bind_set` takes care of collecting together all of the `unit_set`s that result for each different set element we started with.
We can call the `(fun one_dpm -> ...)` part \[[Qx]] and then updating `u` with \[[Qx]] will be:
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)
- Doing things this way will discard `bool dpm`s that start out wrapping `false`, and will pass through other `bool dpm`s that start out wrapping `true` but which our current filter transforms to a wrapped `false`. You might instead aim for consistency, and always pass through wrapped `false`s, whether they started out that way or are only now being generated; or instead always discard such, and only pass through wrapped `true`s. But what we have here will work fine too.
+ 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`.
+
+ Doing things this way will discard `bool dpm`s from the set that started out wrapping `false`, and will pass through other `bool dpm`s that start out wrapping `true` but which our current filter transforms to a wrapped `false`. You might instead aim for consistency, and always pass through wrapped `false`s, whether they started out that way or are only now being generated; or instead always discard such, and only pass through wrapped `true`s. But what we have here will work fine too.
If we let that be \[[Q]], then \[[Q]] \[[x]] would be:
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)
- which is:
+ 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 ->
+ 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 ->
+ 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`).
+ 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 returning any wrapped `false`s).
* Reviewing: now we've determined how to define \[[Q]] and \[[x]] such that \[[Qx]] can be the result of applying the function \[[Q]] to the `entity dpm` \[[x]]. And \[[Qx]] in turn is now a function that takes a `bool dpm` as input and returns a `bool dpm set` as output. We compose this with a `bool dpm set` we already have on hand: