The Universe of Discourse

Fri, 31 Jan 2014

Twingler, a generic data structure munger

(Like everything else in this section, these are notes for a project that was never completed.)


These incomplete notes from 1997-2001 are grappling with the problem of transforming data structures in a language like Perl, Python, Java, Javascript, or even Haskell. A typical problem is to take an input of this type:

    [Chi, Ill],
    [NY, NY],
    [Alb, NY],
    [Spr, Ill],
    [Tr, NJ],
    [Ev, Ill],

and to transform it to an output of this type:

  { Ill => [Chi, Ev, Spr],
    NY  => [Alb, NY],
    NJ  => [Tr],

One frequently writes code of this sort, and it should be possible to specify the transformation with some sort of high-level declarative syntax that is easier to read and write than the following gibberish:

   my $out;
   for my $pair (@$in) {
       push @{$out->{$pair->[0]}}, $pair->[1];
   for my $k (keys %$out) {
       @{$out->{$k}} = sort @{$out->{$k}};

This is especially horrible in Perl, but it is bad in any language. Here it is in a hypothetical language with a much less crusty syntax:

 for pair (in.items) :
 for list (out.values) :

You still can't see what it really going on without executing the code in your head. It is hard for a beginner to write, and hard to anyone to understand.

Original undated notes from around 1997–1998

Consider this data structure DS1:

    [Chi, Ill],
    [NY, NY],
    [Alb, NY],
    [Spr, Ill],                DS1
    [Tr, NJ],
    [Ev, Ill],

This could be transformed several ways:

    Chi => Ill,
    NY => NY, 
    Alb => NY,
    Spr => Ill,                DS2
    Tr => NJ,
    Ev => Ill,

  { Ill => [Chi, Spr, Ev],
    NY  => [NY, Alb],        DS3
    NJ  => Tr,
  { Ill => 3,
    NY  => 2,
    NJ  => 1,

  [ Chi, Ill, NY, NY, Alb, NY, Spr, Ill, Tr, NJ, Ev, Ill]    DS4

Basic idea: Transform original structure of nesting depth N into an N-dimensional table. If Nth nest is a hash, index table ranks by hash keys; if an array, index by numbers. So for example, DS1 becomes

        1        2
    1   Chi Ill
    2   NY  NY
    3   Alb NY
    4   Spr Ill
    5   Tr  NJ
    6   Ev  Ill

Or maybe hashes should be handled a little differently? The original basic idea was more about DS2 and transformed it into

            Ill        NY        NJ
    Chi     X
    NY              X
    Alb             X
    Spr     X
    Tr                      X
    Ev      X

Maybe the rule is: For hashes, use a boolean table indexed by keys and values; for arrays, use a string table index by integers.

Notation idea: Assign names to the dimensions of the table, say X and Y. Then denote transformations by:

    [([X, Y])]        (DS1)
    {(X => Y)}        (DS2)
    {X => [Y]}        (DS3)
    [(X, Y)]        (DS4)

The (...) are supposed to incdicate a chaining of elements within the larger structure. But maybe this isn't right.

At the bottom: How do we say whether

    X=>Y, X=>Z

turns into

    [ X => Y, X => Z ]                (chaining)

or [ X => [Y, Z] ] (accumulation)


      A B C
    D . . .
    E . .
    F .   .

<...> means ITERATE over the thing inside and make a list of the results. It's basically `map'.

Note that:

    <X,Y>     |=   (D,A,D,B,D,C,E,A,E,B,F,A,F,C)
    <X,[<Y>]> |=   (D,[A,B,C],E,[A,B],F,[A,C])

Brackets and braces just mean brackets and braces. Variables at the same level of nesting imply a loop over the cartesian join. Variables subnested imply a nested loop. So:

    <X,Y> means

    for x in X
      for y in Y
        push @result, (x,y) if present(x,y);


    <X,<Y>> means
    for x in X
      for y in Y
        push @yresult, (y) if present(x,y);
      push @result, @yresult 

Hmmm. Maybe there's a better syntax for this.

Well, with this plan:

    DS1: [ <[X,Y]> ]
    DS2: { <X=>Y>  }
    DS3: { <X => [<Y>]> }
    DS4: [ <X, Y> ]

It seems pretty flexible. You could just as easily write

    { <X => max(<Y>) }

and you'd get

    { D => C, E => B, F => C }

If there's a `count' function, you can get

    { D => 3, E => 2, F => 2 }

or maybe we'll just overload scalar' to meancount'.

Question: How to invert this process? That's important so that you can ask it to convert one data structure to another. Also, then you could write something like

    [ <city, state> ]  |= { <state => [<city>] > }

and omit the X's and Y's.

Real example: From proddir. Given


For example:

    A / AAA / red     / pink   / Aaa
    B / BBB / yellow  / tawny  / Bbb
    A / AAA / green   / nude   / Aaa
    B / BBB / blue    / violet / Bbb
    C / CCC / black   / nude   / Ccc

Turn this into

    { A => [ AAA, [ [red, pink], [green, nude] ], Aaa],
      B => [ BBB, [ [yellow, tawny], [blue, violet] ], Bbb],
      C => [ CCC, [ [black, nude] ], CCC]

    { < ID => [
                 [ <[shade, palette]> ]

Something interesting happened here. Suppose we have

    [ [A, B]
      [A, B]

And we ask for <A, B>. Do we get (A, B, A, B), or just (A, B)? Does it remove duplicate items for us or not? We might want either.

In the example above, why didn't we get

    { A => [ AAA, [ [red, pink], [green, nude] ], Aaa],
      A => [ AAA, [ [red, pink], [green, nude] ], Aaa],
      B => [ BBB, [ [yellow, tawny], [blue, violet] ], Bbb],
      B => [ BBB, [ [yellow, tawny], [blue, violet] ], Bbb],
      C => [ CCC, [ [black, nude] ], CCC]

If the outer iteration was supposed to be over all id-name-desc triples? Maybe we need

    <...>                all triples
    <!...!>                unique triples only

Then you could say

    <X>  |= <!X!>

to indicate that you want to uniq a list.

But maybe the old notation already allowed this:

    <X> |= keys %{< X => 1 >}

It's still unclear how to write the example above, which has unique key-triples. But it's in a hash, so it gets uniqed on ID anyway; maybe that's all we need.


Rather than defining some bizarre metalanguage to describe the transformation, it might be easier all around if the user just enters a sample input, a sample desired output, and lets the twingler figure out what to do. Certainly the parser and internal representation will be simpler.

For example:

    [ [ A, B ],
      [ C, B ],
      [ D, E ] ]
    { B => [A, C],
      E => [D],

should be enough for it to figure out that the code is:

    for my $a1 (@$input) {
      my ($e1, $e2) = @$a1;
      push @{$output{$e2}}, $e1;

Advantage: After generating the code, it can run it on the sample input to make sure that the output is correct; otherwise it has a bug.

Input grammar:

    %token ELEMENT
    expr: array | hash ;
    array: '[' csl ']' ;
    csl: ELEMENT | ELEMENT ',' csl | /* empty */ ;
    hash: '{' cspl '}' ;
    cspl: pair | pair ',' cspl | /* empty */ ;
    pair: ELEMENT '=>' ELEMENT;

Simple enough. Note that (...) lines are not allowed. They are only useful at the top level. A later version can allow them. It can replace the outer (...) with [...] or {...] as appropirate when it sees the first top-level separator. (If there is a => at the top level, it is a hash, otherwise an array.)

Idea for code generation: Generate pseudocode first. Then translate to Perl. Then you can insert a peephole optimizer later. For example

    foreachkey k (somehash) {
      push somearray, $somehash{k}

could be optimized to

    somearray = values somehash;

add into hash: as key, add into value, replace value add into array: at end only

How do we analyze something like:

    [ [ A, B ],
      [ C, B ],
      [ D, E ] ]
    { B => [A, C],
      E => [D],

Idea: Analyze structure of input. Analyze structure of output and figure out an expression to deposit each kind of output item. Iterate over input items. Collect all input items into variables. Deposit items into output in appropriate places.

For an input array, tag the items with index numbers. See where the indices go in the output. Try to discern a pattern. The above example:

    Try #1:
    A: 1
    B: 2
    C: 1
    B: 2  -- consistent with B above
    D: 1
    E: 2

    Output:  2 => [1, 1]
             2 => [1]

OK—2s are keys, 1s are array elements.

A different try fails:

    A: 1
    B: 1
    C: 2
    B: 2 -- inconsistent, give up on this.

Now consider:

    [ [ A, B ],
      [ C, B ],
      [ D, E ] ]
    { A => B,
      C => B,
      D => E,

A,C,D get 1; B,E get 2. this works again. 1s are keys, 2s are values.

I need a way of describing an element of a nested data structure as a simple descriptor so that I can figure out the mappings between descriptors. For arrays and nested arrays, it's pretty easy: Use the sequence of numeric indices. What about hashes? Just K/V? Or does V need to be qualified with the key perhaps?

Example above:

    IN:        A:11  B:12 22 C:21 D:31 E:32
    OUT:    A:K   B:V     C:K  D:K  E:V

Now try to find a mapping from the top set of labels to the bottom. x1 => K, x2 => V works.

Problem with this:

    [ [ A, B ],
      [ B, C ],
    { A => B,
      B => C,

is unresolvable. Still, maybe this works well enough in most common cases.

Let's consider:

    [[ A , AAA , red     , pink   , Aaa], 
     [ B , BBB , yellow  , tawny  , Bbb],
     [ A , AAA , green   , nude   , Aaa],
     [ B , BBB , blue    , violet , Bbb],
     [ C , CCC , black   , nude   , Ccc],
    { A => [ AAA, [ [red, pink], [green, nude] ], Aaa],
      B => [ BBB, [ [yellow, tawny], [blue, violet] ], Bbb],
      C => [ CCC, [ [black, nude] ], CCC]

    A:        00,20 => K
    AAA:        01,21 => V0
    red:        02    => V100
    pink:        03    => V101
    Aaa:    04    => V2
    B:      10,30 => K
    C:      40    => K


Conclusion: x0 => K; x1 => V0; x2 => V100; x3 => V101; x4 => V2

How to reverse?

Simpler reverse example:

    { A => [ B, C ],
      E => [ D ],
    [ [ A, B ],
      [ A, C ],
      [ E, D ],

    A: K        => 00, 10
    B: V0   => 01
    C: V1   => 11
    D: V0   => 21
    E: K    => 20

Conclusion: K => x0; V => x1 This isn't enough information. Really, V => k1, where k is whatever the key was!

What if V items have the associated key too?

    A: K        => 00, 10
    B: V{A}0=> 01
    C: V{A}1=> 11
    D: V{E}0=> 21
    E: K    => 20

Now there's enough information to realize that B amd C stay with the A, if we're smart enough to figure out how to use it.


Sent to Nyk Cowham


Sent to Timur Shtatland


Here's a great example. The output from HTML::LinkExtor is a list like

    ([img, src, URL1, losrc, URL2],
     [a, href, URL3],

we want to transform this into

    (URL1 => undef, 
     URL2 => undef, 
     URL3 => undef, 

[Other articles in category /notes] permanent link

Sun, 19 Jan 2014

Notes on a system for abbreviating SQL queries

(This post inaugurates a new section on my blog, for incomplete notes. It often happens that I have some idea, usually for software, and I write up a bunch of miscellaneous notes about it, and then never work on it. I'll use this section to post some of those notes, mainly just because I think they might be interesting, but also in the faint hope that someone might get interested and do something with it.)

Why are simple SQL queries so verbose?

For example:

    UPDATE batches b
      join products p using (product_id)
      join clients c using (client_id)
    SET b.scheduled_date = NOW()
    WHERE b.scheduled_date > NOW()
      and b.batch_processor = 'batchco'
      and c.login_name = 'mjd' ;

(This is 208 characters.)

I guess about two-thirds of this is unavoidable, but those join-using clauses ought to be omittable, or inferrable, or abbreviatable, or something.

b.batch_processor should be abbreviated to at least batch_processsor, since that's the only field in those three tables with that name. In fact it could probably be inferred from b_p. Similarly c.login_name -> login_name -> log or l_n.

   update batches set sch_d = NOW()
   where sch_d > NOW()
   and bp = 'batchco'
   and cl.ln = 'mjd'

(Only 94 characters.)

cl.ln is inferrable: Only two tables begin with cl. None of the field names in the client_transaction_view table look like ln. So cl.ln unambiguously means client.login_name.

Then the question arises of how to join the batches to the clients. This is the only really interesting part of this project, and the basic rule is that it shouldn't do anything really clever. There is a graph, which the program can figure out from looking at the foreign key constraints. And the graph should clearly have a short path from batches through products to clients.

bp might be globally ambiguous, but it can be disambiguated by assuming it's in one of the three tables involved.

If something is truly ambiguous, we can issue an intelligent request for clarification:

"bp" is ambiguous. Did you mean:
  1. batches.batch_processor
  2. batches.bun_predictor
  0. None of the above
which? _


  1. Debreviate table names
  2. Figure out required joins and join fields
  3. Debreviate field names

Can 1 and 2 really be separated? They can in the example above, but maybe not in general.

I think separating 3 and putting it at the end is a good idea: don't try to use field name abbreviations to disambiguate and debreviate table names. Only go the other way. But this means that we can't debreviate cl, since it might be client_transaction_view.

What if something like cl were left as ambiguous after stage 1, and disambiguated only in stage 3? Then information would be unavailable to the join resolution, which is the part that I really want to work.

About abbreviations

Abbreviations for batch_processor:


There is a tradeoff here: the more different kinds of abbreviations you accept, the more likely there are to be ambiguities.

About table inference

There could also be a preferences file that lists precedences for tables and fields: if it lists clients, then anything that could debreviate to clients or to client_transaction_view automatically debreviates to clients. The first iteration could just be a list of table names.

About join inference

Short join paths are preferred to long join paths.

If it takes a long time to generate the join graph, cache it. Build it automatically on the first run, and then rebuild it on request later on.

More examples

(this section blank)

Implementation notes

Maybe convert the input to a SQL::Abstract first, then walk the resulting structure, first debreviating names, then inserting joins, then debreviating the rest of the names. Then you can output the text version of the result if you want to.

Note that this requires that the input be valid SQL. Your original idea for the abbreviated SQL began with

   update set batches.sch_d = NOW()

rather than

   update batches set sch_d = NOW()

but the original version would probably be ruled out by this implementation. In this case that is not a big deal, but this choice of implementation might rule out more desirable abbreviations in the future.

Correcting dumb mistakes in the SQL language design might be in Quirky's purview. For example, suppose you do

     select * from table where (something)

Application notes

RJBS said he would be reluctant to use the abbreviated version of a query in a program. I agree: it would be very foolish to do so, because adding a table or a field might change the meaning of an abbreviated SQL query that was written into a program ten years ago and has worked ever since. This project was never intended to abbreviate queries in program source code.

Quirky is mainly intended for one-off queries. I picture it going into an improved replacement for the MySQL command-line client. It might also find use in throwaway programs. I also picture a command-line utility that reads your abbreviated query and prints the debreviated version for inserting into your program.

Miscellaneous notes

(In the original document this section was blank. I have added here some notes I made in pen on a printout of the foregoing, on an unknown date.)

Maybe also abbreviate update => u, where => w, and => &. This cuts the abbreviated query from 94 to 75 characters.

Since debreviation is easier [than join inference] do it first!

Another idea: "id" always means the main table's primary key field.

[Other articles in category /notes] permanent link