set builder in BKO

OK. It seems to me that it would be useful to have the equivalent of set-builder/list comprehensions in BKO. Currently not even close to implemented in the parser, but never mind.

The thing is, a lot of things you think you need a set-builder for, you can actually do directly.

Let's consider some data:

$ grep "^president-era" early-us-presidents.sw
president-era |Washington> => |year: 1789> + |year: 1790> + |year: 1791> + |year: 1792> + |year: 1793> + |year: 1794> + |year: 1795> + |year: 1796> + |year: 1797>
president-era |Adams> => |year: 1797> + |year: 1798> + |year: 1799> + |year: 1800> + |year: 1801>
president-era |Jefferson> => |year: 1801> + |year: 1802> + |year: 1803> + |year: 1804> + |year: 1805> + |year: 1806> + |year: 1807> + |year: 1808> + |year: 1809>
president-era |Madison> => |year: 1809> + |year: 1810> + |year: 1811> + |year: 1812> + |year: 1813> + |year: 1814> + |year: 1815> + |year: 1816> + |year: 1817>
president-era |Monroe> => |year: 1817> + |year: 1818> + |year: 1819> + |year: 1820> + |year: 1821> + |year: 1822> + |year: 1823> + |year: 1824> + |year: 1825>
president-era |Q Adams> => |year: 1825> + |year: 1826> + |year: 1827> + |year: 1828> + |year: 1829>

Now we can ask: "Who was the president in 1825?"

-- initially you might try something like this:
|x> in "" |early US Presidents: _list> such that <year: 1825|president-era|x> > 0.5

-- but using inverse we can do it directly:
inverse-president-era |year: 1825>

Indeed, let's do it:

sa: load early-us-presidents.sw
sa: create inverse
sa: inverse-president-era |year: 1825>
|Monroe> + |Q Adams> 

Now, let's consider some more data:

$ grep "^president-number" early-us-presidents.sw
president-number |Washington> => |number: 1>
president-number |Adams> => |number: 2>
president-number |Jefferson> => |number: 3>
president-number |Madison> => |number: 4>
president-number |Monroe> => |number: 5>
president-number |Q Adams> => |number: 6>

And now we might ask: "What was the party of the third president?"

-- again, you might ask it in set-builder form:
party |x> for |x> in "" |early US Presidents: _list> such that president-number|x> == |number: 3>

-- but once again, it is cleaner and easier to do it directly:
sa: inverse-president-number |number: 3>
|Jefferson>

sa: party inverse-president-number |number: 3>
|party: Democratic-Republican> 

Anyway, the general proposed form for set-builder in BKO is something like this:
KET in SUPERPOSITION such that TRUTH-STATEMENT
and
OP-SEQUENCE KET for KET in SUPERPOSITION such that TRUTH-STATEMENT
And I'm not 100% sure on using "such that". Also considering "st", "such-that", and "where".

And I guess that is about it.
OK. How about some notes first:
1) notice how easy it is to grep sw files to extract what you are interested in. This is the big win from having no multi-line constructs in BKO. Heh, and also the reason why \r and \n are not allowed inside bras and kets.
2) Note how the direct version always mentions "inverse-OP" (here "inverse-president-era" and "inverse-president-number"). This is probably to be expected because it is replacing a set builder, and set builders are in some sense an inverse. I need to explain this clearer sometime.
3) the BKO set-builder notation is much closer to standard SQL and SPARQL than the direct method.

Update: Let's try and expand note (2).
Consider:
{x in R | f(x) = y }
this is the same as the inverse function:
x = f^-1(y)

Likewise, in BKO:
|x> in "" |number: _list> such that foo |x> == |y>
this is the same as the inverse direct version:
inverse-foo |y>

Here, let me show a quick example in the console:

sa: foo |a1> => |y>
sa: foo |a2> => |y>
sa: foo |a3> => |y>
sa: foo |a4> => |y>
sa: foo |a5> => |fish>
sa: foo |a6> => |soup>
sa: foo |a7> => |fish>
sa: create inverse

sa: inverse-foo |y>
|a1> + |a2> + |a3> + |a4>

sa: inverse-foo |fish>
|a5> + |a7>

sa: inverse-foo |soup>
|a6>

Update: in note (1) above I noted how easy it is to grep sw files. Well, it just occurred to me that it is easy to find supported operators in a sw file.
eg:

$ sed 's/|.*$//g' early-us-presidents.sw | sort | uniq

----------------------------------------

dissolved
founded
full-name
party
president-era
president-number
supported-ops

$ sed 's/|.*$//g' improved-imdb.sw | sort | uniq

----------------------------------------
actors
movies
supported-ops

$ sed 's/|.*$//g' imdb-ratings.sw | sort | uniq
imdb-rating
imdb-rating-self
imdb-votes
imdb-votes-self

Cool and useful!