I'm in the throws of trying to get multi-dimensional arrays working.
The theory behind this was developed by Barry Jay.
Basically, there's map:
(T ^ N) ^ M -> T ^ (N * M)
taking an array of arrays to a matrix. Example on values:
( (1,2), (3,4), (5,6) ) . 1 . 1 --> 4 (zero origin remember)
The second:
( 1, 2, 3, 4, 5, 6 ) . (1,1) --> 4
The underlying representation of both is the same: a linear array
of 6 integers. The index calculation is the same in both cases too:
1 * 2 + 1 = 3
However, the two data structures are utterly different: the data functor
here is ARRAY. The core rule for maps is:
MAP f (ARRAY T) --> ARRAY ( f T)
i.e. the map of f over an array is an array of f of each T. For the array
of arrays this means f applies to the inner array. For the matrix,
it means f applies to all the elements. In other words:
MAP f (matrix) = MAP (MAP f) (ARRAY . ARRAY)
The importance here is that an operator representing
the "reshaping" isomorphism determines where the map
maps its function argument.
--
john skaller
skal...@users.sourceforge.net
http://felix-lang.org
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