Poly-dimensionality

FISh supports the usual Hindley-Milner style of polymorphism. It also supports polymorphism in array sizes (unlike earlier Algol-like languages) and in the number of dimensions of an array. That is, FISh supports polydimensional programming. For example, the map function is defined to have type

                           map : (a -> b) -> [a] -> [b]

and so may act on a vector, matrix or higher-dimensional array. However, the existence of the simple imperative features means that this can be compiled into a sequence of nested for-loops corresponding to the number of dimensions of the array argument. Polydimensionality is a form of shape polymorphism.

Example

An example of this programming style is the generic difference equation solver. An application of this is the little program hotspot.fsh intended as a crude model of a warm plate in a cold environment. Here are the results when applied to a vector of length 4, and 3x4 matrix and a 2x3x4 array.

>-|> %run hotspot1;;
fill { 4 : float_shape }
with [
  5.752120,8.598921,8.598921,5.752120
]
>-|> %run hotspot2;;
fill { 3,4 : float_shape }
with [
  2.429224,3.253875,3.253875,2.429224,
  3.055436,4.238389,4.238389,3.055436,
  2.429224,3.253875,3.253875,2.429224
]
>-|> %run hotspot3;;
fill { 2,3,4 : float_shape }
with [
  1.546959,1.847372,1.847372,1.546959,
  1.797130,2.233605,2.233605,1.797130,
  1.546959,1.847372,1.847372,1.546959,
  1.546959,1.847372,1.847372,1.546959,
  1.797130,2.233605,2.233605,1.797130,
  1.546959,1.847372,1.847372,1.546959
]

hotspot3 should be visualised as 2 3x4 matrices, each with central entries of 2.23.

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