6 ms·

Is an array language a language where you only have arrays? That honestly sounds a bit odd.

by slver 5y ago

mjaniczek 5y ago
You could consider Pandas / numpy an array language, even though it's really a library for Python. The exposed API is IMHO what's important.
- Wezl 5y ago
  I agree, but you have to take extensibility into account. You either have an extensible language and extend it[0], you make it an array language to the core, or you just have a few slightly convenient functions (not a language). (I don't have enough experience to judge which category Pandas / numpy are in) [0]: https://github.com/phantomics/april https://github.com/phantomics/april
klibertp 5y ago
No, an array language is one in which all the built-in operations are applicable to arrays. Take addition as an example: 4 + 4 8 In array languages the same operator can be used for arrays; or equivalently you can say that the example above sums two arrays of length 1. In J, you can do this and expect it to work: 4 4 4 + 2 2 2 6 6 6 This is true for all the built-ins, and many user defined operations (as long as you don't fiddle with so called rank of the verb you're defining). Numpy is close to that, but there's still a distinction between arrays and scalars, while in array langauges that distinction is often blurred: 4 + 1 2 3 5 6 7 Edit: in J, you can have atoms, or scalars, but you need to box them: (3;4;5) ┌─┬─┬─┐ │3│4│5│ └─┴─┴─┘ but then you can't do anything with them until you unbox them again: (3;4;5) + 3 |domain error | (3;4;5) +3 (+&4) each (3;4;5) ┌─┬─┬─┐ │7│8│9│ └─┴─┴─┘ (Examples straight from J REPL)
- slver 5y ago
  It seems almost as if it'd be more useful to not explicitly expose operators as applicable to arrays, but implement SIMD optimization for operator expressions in .map(function) and something like .binaryMap(right, function) ex. [1, 2, 3].binaryMap([10, 10, 10], (a, b) => a * b) // Produces [10, 20, 30] This would be easier to optimize when compiled because the expressions can be simplified and mapped to the right SIMD instructions.
  - klibertp 5y ago
    Unfortunately, I have no idea about the implementation and what optimizations are done in J or APL for which operations :( I know that there are hardcoded "fast path" expressions (particular combinations of operations) which have much better performance than more general expressions doing the same thing, so it might be that the optimization happens at that level. OTOH, your example is very verbose when compared to J's version: 1 2 3 * 10 10 20 30 Plus, in J it generalizes to higher dimensional arrays: i. 3 3 0 1 2 3 4 5 6 7 8 (1 + i. 3 3) * 10 10 20 30 40 50 60 70 80 90
    - slver 5y ago
      My example is verbose in order to clearly communicate the principle. I can trivially shorten it to [1, 2, 3].map(a => a * 10) if I wanted to literally carry out that task alone. [[0, 1, 2], [3, 4, 5], [6, 7, 8]].flatMap(a => a * 10)
      - klibertp 5y ago
        I think this is pseudo-code? `flatMap` and `=>` for lambdas look like Scala, but there are no array literals using `[]` there. Assuming you mean Scala-like semantics, your second example wouldn't work at all: scala> Array(Array(1,2), Array(4,5)).flatMap(a => a * 10) ^ error: value * is not a member of Array[Int] You would need to write it like this: scala> Array(Array(1,2), Array(4,5)).flatMap(a => a.map(x => x * 10)) But then you'd get a flattened array of ints, not array of arrays of ints: res6: Array[Int] = Array(10, 20, 40, 50) So to get the same result as (i. 2 2) * 10 You'd need to write: scala> Array(Array(1,2), Array(4,5)).map(a => a.map(x => x * 10)) res7: Array[Array[Int]] = Array(Array(10, 20), Array(40, 50)) ...which is more verbose, no? :) EDIT: obviously, I mean "map in map" part, not the Array initialization! The problem with list comprehensions and `map`, `filter` and friends is that they work very well for flat lists, or lists of lists in some specific circumstances (ie. when you can use `flatMap`). 2D arrays in the general case, and arrays with higher dimensions are really hard to work with using these primitives, unless you have some clever overloads, like what Clojure does. I think Haskell also has a solution for this, but I don't know it enough to comment further, unfortunately :)
mlochbaum 5y ago
That's the case in APL and J. K uses nested lists to represent arrays, and has non-lists (atoms). But the convention is that an n-times nested list is considered an n-dimensional array so even an atom is an array, with 0 dimensions. There's a page on the various approaches to arrays in the APL family at https://aplwiki.com/wiki/Array_model https://aplwiki.com/wiki/Array_model .
rklmno 5y ago
Mostly yes. Numbers (and character) are implemented as arrays with 0 dimensions. Text would be an array of characters with 1 dimension (the number of characters), and generally speaking the dimension of an array is a one dimensional list of non-negative integers. Many array languages also include an array type which is approximately the same as a C pointer to an array, with a bit of jargon thrown in to distinguish a reference to an array from the array itself. Something like an SQL table in an array language would be implemented as a list of columns (rather than as a list of rows) and a corresponding list of column labels. This has some interesting benefits. That said, functions in array language are typically not arrays (though they presumably would have a textual representation). So... not everything is an array.
- rscho 5y ago
  From the J docs: https://www.jsoftware.com/help/dictionary/dx005.htm https://www.jsoftware.com/help/dictionary/dx005.htm nub=: (i.@# = i.~) # ] 5!:2 <'nub' +-------------------+-+-+ |+--------+-+------+|#|]| ||+--+-+-+|=|+--+-+|| | | |||i.|@|#|| ||i.|~||| | | ||+--+-+-+| |+--+-+|| | | |+--------+-+------+| | | +-------------------+-+-+ ... so J functions have an array representation, at least.
  - rklmno 5y ago
    Yes, each J function has several array representations.

Is an array language a language where you only have arrays? That honestly sounds a bit odd.

by slver 5y ago

Is an array language a language where you only have arrays? That honestly sounds a bit odd.

You could consider Pandas / numpy an array language, even though it's really a library for Python. The exposed API is IMHO what's important.

Wezl 5y ago
I agree, but you have to take extensibility into account. You either have an extensible language and extend it[0], you make it an array language to the core, or you just have a few slightly convenient functions (not a language). (I don't have enough experience to judge which category Pandas / numpy are in) [0]: https://github.com/phantomics/april https://github.com/phantomics/april

klibertp 5y ago

No, an array language is one in which all the built-in operations are applicable to arrays. Take addition as an example: 4 + 4 8 In array languages the same operator can be used for arrays; or equivalently you can say that the example above sums two arrays of length 1. In J, you can do this and expect it to work: 4 4 4 + 2 2 2 6 6 6 This is true for all the built-ins, and many user defined operations (as long as you don't fiddle with so called rank of the verb you're defining). Numpy is close to that, but there's still a distinction between arrays and scalars, while in array langauges that distinction is often blurred: 4 + 1 2 3 5 6 7 Edit: in J, you can have atoms, or scalars, but you need to box them: (3;4;5) ┌─┬─┬─┐ │3│4│5│ └─┴─┴─┘ but then you can't do anything with them until you unbox them again: (3;4;5) + 3 |domain error | (3;4;5) +3 (+&4) each (3;4;5) ┌─┬─┬─┐ │7│8│9│ └─┴─┴─┘ (Examples straight from J REPL)

slver 5y ago
It seems almost as if it'd be more useful to not explicitly expose operators as applicable to arrays, but implement SIMD optimization for operator expressions in .map(function) and something like .binaryMap(right, function) ex. [1, 2, 3].binaryMap([10, 10, 10], (a, b) => a * b) // Produces [10, 20, 30] This would be easier to optimize when compiled because the expressions can be simplified and mapped to the right SIMD instructions.
- klibertp 5y ago
  Unfortunately, I have no idea about the implementation and what optimizations are done in J or APL for which operations :( I know that there are hardcoded "fast path" expressions (particular combinations of operations) which have much better performance than more general expressions doing the same thing, so it might be that the optimization happens at that level. OTOH, your example is very verbose when compared to J's version: 1 2 3 * 10 10 20 30 Plus, in J it generalizes to higher dimensional arrays: i. 3 3 0 1 2 3 4 5 6 7 8 (1 + i. 3 3) * 10 10 20 30 40 50 60 70 80 90
  - slver 5y ago
    My example is verbose in order to clearly communicate the principle. I can trivially shorten it to [1, 2, 3].map(a => a * 10) if I wanted to literally carry out that task alone. [[0, 1, 2], [3, 4, 5], [6, 7, 8]].flatMap(a => a * 10)
    - klibertp 5y ago
      I think this is pseudo-code? `flatMap` and `=>` for lambdas look like Scala, but there are no array literals using `[]` there. Assuming you mean Scala-like semantics, your second example wouldn't work at all: scala> Array(Array(1,2), Array(4,5)).flatMap(a => a * 10) ^ error: value * is not a member of Array[Int] You would need to write it like this: scala> Array(Array(1,2), Array(4,5)).flatMap(a => a.map(x => x * 10)) But then you'd get a flattened array of ints, not array of arrays of ints: res6: Array[Int] = Array(10, 20, 40, 50) So to get the same result as (i. 2 2) * 10 You'd need to write: scala> Array(Array(1,2), Array(4,5)).map(a => a.map(x => x * 10)) res7: Array[Array[Int]] = Array(Array(10, 20), Array(40, 50)) ...which is more verbose, no? :) EDIT: obviously, I mean "map in map" part, not the Array initialization! The problem with list comprehensions and `map`, `filter` and friends is that they work very well for flat lists, or lists of lists in some specific circumstances (ie. when you can use `flatMap`). 2D arrays in the general case, and arrays with higher dimensions are really hard to work with using these primitives, unless you have some clever overloads, like what Clojure does. I think Haskell also has a solution for this, but I don't know it enough to comment further, unfortunately :)

mlochbaum 5y ago

That's the case in APL and J. K uses nested lists to represent arrays, and has non-lists (atoms). But the convention is that an n-times nested list is considered an n-dimensional array so even an atom is an array, with 0 dimensions. There's a page on the various approaches to arrays in the APL family at https://aplwiki.com/wiki/Array_model https://aplwiki.com/wiki/Array_model .

rklmno 5y ago

Mostly yes. Numbers (and character) are implemented as arrays with 0 dimensions. Text would be an array of characters with 1 dimension (the number of characters), and generally speaking the dimension of an array is a one dimensional list of non-negative integers. Many array languages also include an array type which is approximately the same as a C pointer to an array, with a bit of jargon thrown in to distinguish a reference to an array from the array itself. Something like an SQL table in an array language would be implemented as a list of columns (rather than as a list of rows) and a corresponding list of column labels. This has some interesting benefits. That said, functions in array language are typically not arrays (though they presumably would have a textual representation). So... not everything is an array.

rscho 5y ago
From the J docs: https://www.jsoftware.com/help/dictionary/dx005.htm https://www.jsoftware.com/help/dictionary/dx005.htm nub=: (i.@# = i.~) # ] 5!:2 <'nub' +-------------------+-+-+ |+--------+-+------+|#|]| ||+--+-+-+|=|+--+-+|| | | |||i.|@|#|| ||i.|~||| | | ||+--+-+-+| |+--+-+|| | | |+--------+-+------+| | | +-------------------+-+-+ ... so J functions have an array representation, at least.
- rklmno 5y ago
  Yes, each J function has several array representations.