orthotope: Multidimensional arrays inspired by APL

[ array, library ] [ Propose Tags ]

Multidimensional arrays inspired by APL. The library contains a wide variety of structurual operations on arrays, but not actual algorithms.

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Dependencies base (==4.14.*), deepseq, dlist, pretty, QuickCheck, vector [details]
License LicenseRef-Apache
Copyright 2018 Google Inc
Maintainer lennart@augustsson.net
Category array
Source repo head: git clone https://github.com/augustss/orthotope
Uploaded by LennartAugustsson at 2020-09-16T22:18:56Z
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  • Data
    • Array
      • Data.Array.Convert
      • Data.Array.Dynamic
      • Data.Array.DynamicG
      • Data.Array.DynamicS
      • Data.Array.DynamicU
      • Data.Array.Internal
        • Data.Array.Internal.Dynamic
        • Data.Array.Internal.DynamicG
        • Data.Array.Internal.DynamicS
        • Data.Array.Internal.DynamicU
        • Data.Array.Internal.Ranked
        • Data.Array.Internal.RankedG
        • Data.Array.Internal.RankedS
        • Data.Array.Internal.RankedU
        • Data.Array.Internal.Shape
        • Data.Array.Internal.Shaped
        • Data.Array.Internal.ShapedG
        • Data.Array.Internal.ShapedS
        • Data.Array.Internal.ShapedU
      • Data.Array.Ranked
      • Data.Array.RankedG
      • Data.Array.RankedS
      • Data.Array.RankedU
      • Data.Array.Shape
      • Data.Array.Shaped
      • Data.Array.ShapedG
      • Data.Array.ShapedS
      • Data.Array.ShapedU


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This is not an officially supported Google product.


This is a library for multi-dimensional arrays inspired by APL.

Multi-dimensional arrays

Each array has a number of elements of the same type, and a shape. The shape can be described by a list of integers that gives the size for each of the dimensions. E.g. the array shape [2,3] is a 2x3 matrix (2 rows, 3 columns), and the shape [] is a single value (a scalar). The number of dimensions is called the rank of the array.

The shape may or may not be part of the type, depending on which version of the API you use.

API variants

The API comes in many variants, depending on how strongly typed it is and what the underlying storage is.


  • Dynamic, the shape is not part of the type, but is checked at runtime. E.g., Array Float is an array of Float which can have any shape.

  • Ranked, the rank of the array is part of the type, but the actual sizes of the dimensions are checked at runtime. E.g., Array 2 Float is the type of 2-dimensional arrays (i.e., matrices) of Float.

  • Shaped, the shape of the array is part of the type and is checked statically. E.g., Array [2,3] Float is the type of 2x3 arrays of Float.

Converting between these types is cheap since they all share the same underlying trepresentation.


Each of the type variants has several storage variants, indicated by a suffix of the module names.

  • G The generic array type where you can provide your own storage.

  • S Uses Data.Vector.Storable for storage.

  • U Uses Data.Vector.Unboxed for storage.

  • (empty suffix) Uses Data.Vector for storage.

Conversion between different storage types requires copying the data, so it is not a cheap operation.


The library API is mostly structural operations, i.e., operations that treat the elements in a uniform way. For more algorithmic operations, e.g., matrix multiplication, we suggest using a different library, like hmatrix.

Examples using Dynamic

Some preliminaries:

> import Data.Array.Dynamic
> import Text.PrettyPrint.HughesPJClass
> pp = putStrLn . prettyShow

An easy way to create an array from a list is to use fromList; the first argument is the shape of the array.

> m = fromList [2,3] [1..6]
> m
fromList [2,3] [1,2,3,4,5,6]
> shapeL m
> size m

Arrays can be pretty printed. They are shown in the APL way: The innermost dimension on a line, the next dimension vertically, the next dimension vertically with an empty line in betwee, and so on.

> pp m
1 2 3
4 5 6

We can have an arbitrary number of dimensions.

> s = fromList [] [42]
> v = fromList [3] [7,8,9]
> a = fromList [2,3,4] [1..24]
> pp s
> pp v
7 8 9
> pp a
 1  2  3  4
 5  6  7  8
 9 10 11 12

13 14 15 16
17 18 19 20
21 22 23 24