Vocabulary/squarelfco

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[:

Cap

Rank Infinity -- operates on [x and] y as a whole -- WHY IS THIS IMPORTANT?

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1. Raises valence error whenever executed as monad or dyad, whatever the argument(s).

2. In a tacit phrase ([: f g): caps the left branch of a fork.

This is a syntactic trick to employ a fork to implement: f(g(x)) -- the composition of the two functions: f and g.

The primitive: [: is not actually executed.

   13 : 'f(g(y))'
[: f g

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Common uses

1. To force an error when a tacitly defined verb only meant to be used monadically is accidentally employed dyadically, and vice-versa

Note the use of Monad-Dyad (:) to provide separate tacit definitions for monadic and dyadic uses of the verb.

   star=: *         NB. Any verb can be executed as monad or dyad
   star _99 99 0
_1 1 0
   3 star 5
15

   signum=: * : [:  NB. This verb will fail if executed dyadically
   signum _99 99 0
_1 1 0
   3 signum 5
|valence error: signum
|   3     signum 5

   times=: [: : *   NB. This verb will fail if executed monadically
   3 times 5
15
   times _99 99 0
|valence error: times
|       times _99 99 0

2. To implement f(g(y) as above.

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Related primitives

Compose (&), Appose (&:), At (@:), Atop (@), Hook ((u v)), Fork ((f g h))

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More Information

1. Except for its appearance in code, ([: g h) is exactly equivalent to g@:h .
2. If you use a synonym for the Cap verb ([:), the synonym must be defined before it is used to create a capped fork.

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Use These Combinations

Combinations using [: that have exceptionally good performance include those shown in Searching and Matching Items: Fast List Operations (FLOs), as well as the following:

What it does	Type; Precisions; Ranks	Syntax	Variants; Restrictions	Benefits; Bug Warnings
Applying f/ after g (f and g are any atomic verbs)		x f/@:g y x ([: f/ g) y		avoids recopying arguments
Extract multiple substrings into a list	Boolean list, byte list	x ;@:(<;.0) y	or [: ; <;.0	avoids boxing, avoids creating subarrays
Razed selections		x (;@{) y	also x ([: ; {) y
Concatenated results on intervals		;@:(<@u;.n) y x ;@:(<@u;.n) y	n e. _2 _1 1 2; also [: ; (<@u;.n); also <@:u	Bug Warning: This is computed as <@:u even if <@u is coded
Concatenated running totals on intervals (running total, but total is reset at start of each interval)		;@:(<@(f/\);.n) y x ;@:(<@(f/\);.n) y (f is any verb)	n e. _2 _1 1 2; also [: ; (f... also <@:(f/\); also <@:
Arrays of random numbers		x ?@$ y x([: ? $)y	?. in place of ? @: in place of @ # in place of $	does not create x $ y

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