fast-combinatorics

This is a library for fast combinatorics using ATS. As such, make sure a C compiler is installed. It may not work on windows, so if you run into bugs building this please open an issue.

Currently it is a work-in-progress, being somewhat constrained by the fact that I have yet to figure out how to share arbitrary-precision types between ATS and Haskell.

Benchmarks

Computation	Version (ATS/Haskell)	Time
12!	ATS	9.301 ns
12!	Haskell	27.84 ns
13 `choose` 4	ATS	12.28 ns
13 `choose` 4	Haskell	28.38 ns
isPrime 2017	ATS	118.9 ns
isPrime 2017	Haskell	497.3 ns
3 ^ 7	ATS	9.050 ns
3 ^ 7	Haskell	37.02 ns

Building

The Haskell library comes with the C bundled, however you may wish to build from source if you are hacking on the library. To that end, you can install stack, patscc, and pats-filter and build with

 $ ./shake.hs

You will also likely want to install GHC as well as cabal.

Documentation

Using the ATS library

One of the nice things about a Haskell wrapper is that some of Haskell's tooling/libraries may be used. You may want to try the REPL:

 $ cabal new-repl

Using the Haskell library

You may wish to read the ATS source code for an indication of what sorts of things ATS allows us to prove things about our programs, particularly proofs of termination.

There are also a few caveats: note that all results and arguments must be of the Int type. This unfortunate constraint will hopefully be fixed in the future, but right now it limits the usefulness of the library.