Vocabulary/zcapco

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x Z: y

Terminate Fold

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

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Terminates Fold, in whole or part.

_2 Z: 0   NB. no-op
_2 Z: 1   NB. force termination of overrunning Fold

The phrases (x Z: 1) and (_3 Z: n) are the only ways to terminate F. and F: .

But the primitive Z: can prematurely terminate any Fold, or skip the production of wasted data in any given iteration of Fold.

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Common Uses

1. Halt Unlimited Fold (F. or F:) after COUNT calls of Fold operand u or raise limit error.

   v=: __&$: :(4 : 0)  
   NB. ^^^ Fold’s v-operand is always dyadic. But we want effectively monadic here
echo COUNT
_2 Z: -.*COUNT=:COUNT-1 
_3 Z: 5      NB. prevent runaway
y+1 return.  NB. sample recurrence relation for Fold; ignores x
)

   ]F:v 10 [ COUNT=:3
3
2
1
11 12
   
   ]F:v 10 [ COUNT=:666
666
665
664
663
662
|fold limit
|       ]F:v 10[COUNT=:666

2. Increase computational efficiency by aborting a wasteful computation.

Similar code to #1 except:

• the x-argument of Z: should be an integer in the list: (_3 _2 _1 0 1).
• the y-argument of Z: should be a boolean condition detecting a wasteful application of u and/or v.

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More Information

The result of (x Z: y) is always $0 (an empty list).

• If y is 0, no action is performed.
• If y is 1, the action depends on x as shown in the table below.

 

Executed phrase	Effect
_3 Z: n	If the Fold has already started execution of v at least n times, abort the fold with a fold limit error. Otherwise continue. Useful to ensure that an unlimited fold (viz. F. or F:) does not run forever.
_2 Z: 1	Execution of the enclosing Fold terminates immediately, with the result being the result after the last execution of u. If nothing has been added to the overall result, a domain error is raised.
_1 Z: 1	Execution of the current iteration terminates immediately. The next iteration begins with the next new value as x. The value of y in the next iteration is the result of the most recent execution of v that ran to completion. Nothing is added to the overall result for the current iteration.
0 Z: 1	Execution of the enclosing Fold continues, but the result of the current execution of u is ignored. For Fold Multiple, nothing is added to the overall result. For Fold Single, the overall result is left unchanged from the previous iteration.
1 Z: 1	Execution of the enclosing Fold continues but stops after the next completion of u.