maybe we don't need projections?

Currently my unfinished parser can't handle projections, or bra's or a bunch of other stuff. Yeah, I will get to it eventually. But today a quick example showing maybe we don't need projections?

Consider this list:

the |list> => |number: 137> + |furniture: chair> + |animal: frog> + |furniture: table> + |number: 5573>

The idea was we could filter this down to numbers using: |_pself><number: *| and furniture using |_pself><furniture: *|
But, maybe we don't need that. Let me show you. First define these operators:

number-filter |*> #=> |>
furniture-filter |*> #=> |>
animal-filter |*> #=> |>
animal-number-filter |*> #=> |>

number-filter |number: *> #=> |_self>
animal-number-filter |number: *> #=> |_self>

furniture-filter |furniture: *> #=> |_self>

animal-filter |animal: *> #=> |_self>
animal-number-filter |animal: *> #=> |_self>

Now, put them to use:

sa: number-filter the |list>
|number: 137> + |number: 5573>

sa: furniture-filter the |list>
|furniture: chair> + |furniture: table>

sa: animal-filter the |list>
|animal: frog>

sa: animal-number-filter the |list>
|number: 137> + |animal: frog> + |number: 5573>

I don't yet have a use for this, but I'm pretty sure it will be useful eventually.

Update: if we did have projections, this is how we would define our filters:

number-filter |*> #=> |_pself><number: *||_self>
furniture-filter |*> #=> |_pself><furniture: *||_self>
animal-filter |*> #=> |_pself><animal: *||_self>
animal-number-filter |*> #=> |_pself><animal: *||_self> + |_pself><number: *||_self>

Update: Just an extra thing that would be fun:

-- define our operator:
sa: how-many-numbers-in |*> #=> how-many number-filter |_self>

-- try it out:
sa: how-many-numbers-in the |list>
2|number: 1> + 3|number: 0>

Which is not the answer you might expect! The reason is that our operator is linear. Let me expand that to show more clearly what I mean:

how-many-numbers-in the |list>
== how-many-numbers-in (|number: 137> + |furniture: chair> + |animal: frog> + |furniture: table> + |number: 5573>)
== how-many-numbers-in |number: 137> + how-many-numbers-in |furniture: chair> + how-many-numbers-in |animal: frog> + how-many-numbers-in |furniture: table> + how-many-numbers-in |number: 5573>
== |number: 1> + |number: 0> + |number: 0> + |number: 0> + |number: 1>
== 2|number: 1> + 3|number: 0>

Now, for it to work the way you might expect, then we need learn-sp rules. And then something like:

sa: how-many-numbers-in (*) #=> how-many number-filter |_self>
sa: how-many-numbers-in the |list>

Which should give the desired result of |number: 2>