cut to fit

[tangentstorm]

Similar to an old request of mine, I propose an extension to ;..

The request is for a new application of !.. Fit should apply to monads derived from the cut conjunction such that:

   u;._1!.n  ↔   u;._1 @: (n&,)
   u;._2!.n  ↔   u;._2 @: (,&n)
   u;. 1!.n  ↔   u;. 1 @: (n&,)
   u;. 2!.n  ↔   u;. 2 @: (,&n)

and when u =: < then the respective inverses are:

   [: }.@:; n&,&.>
   [: }:@:; ,&n&.>
      }.@:;
      }:@:;

I'm not sure what do to for inverses of other u, as u^:_1 is probably not what's wanted. (For example, the inverse of < is > but what we want here is ; instead.)

However, that is not a large obstacle, because I think that:

u&.>&.(<;.m!.n)

will mostly cover the ground. Given that, I believe the idiom should be given special consideration and be supported by special code.

The optimization would ideally apply for all u, but it should at least apply to all u which (cut503) already supports in ;@:(<@:u;.1) (viz my previous request). Special code which supports the idioms <@:u;.m and u&.>@:(<;.m) might also be considered for extension.

Motivations and disincentives for implementing this proposal are as detailed in the original Forum message:

Advantages:

• Concise.
• Solves a common problem.
  ** No worrying about losing the shard.
• Backwards compatible.
  ** Centralized, easily optimized. In particular, in <;._2 y,n the catenation (and attendant copying of y) need not be performed.
  ** Could easily provide for other optimizations which would support a large body of extant and likely future code. In particular, f&.>&.(<;._2!.n) could be optimized for well-behaved f (the initial definition of "well behaved" might be "doesn't change the type or shape of its argument"). For example:

dtb&.>&.(<;._2!.LF) NB. dtb from lines

though this is "poorly behaved" because it changes the shape of its argument.

• In the spirit of !.
• In the spirit of ^:_1

Drawbacks (in addition to those associated with every backwards-compatible change to the language):

• <;._2 sans fit couldn't have an inverse, or, if it did, it would be inconsistent with the definition of the inverse of fitted cut (cf. previous request).
• Every !. reduces the consistency of J; they should be used sparingly, if at all.

-- Dan Bron <2007-10-30T00:19:42Z>

[HenryHRich]

I like it