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README.md

Speculate

Speculate Build Status Speculate on Hackage Speculate on Stackage LTS Speculate on Stackage Nightly

Speculate logo

Speculate automatically discovers laws about Haskell functions. Give Speculate a bunch of Haskell functions and it will discover laws like:

  • equations, such as id x == x;
  • inequalities, such as 0 <= x * x;
  • conditional equations, such as x <= 0 ==> x + abs x == 0.

Speculate is similar to, and inspired by, QuickSpec.

Installing Speculate

To install the latest Speculate version from Hackage, just:

$ cabal update
$ cabal install speculate

Pre-requisites are cmdargs, express and leancheck. They should be automatically resolved and installed by Cabal.

Using Speculate

Speculate is used as a library: import it, then call the function speculate with relevant arguments. The following program Speculates about the functions (+) and abs:

import Test.Speculate

main :: IO ()
main = speculate args
  { constants =
      [ showConstant (0::Int)
      , showConstant (1::Int)
      , constant "+"   ((+)  :: Int -> Int -> Int)
      , constant "abs" (abs  :: Int -> Int)
      ]
  }

when run, it prints the following:

_ :: Int  (holes: Int)
0 :: Int
1 :: Int
(+) :: Int -> Int -> Int
abs :: Int -> Int

    abs (abs x) == abs x
          x + 0 == x
          x + y == y + x
    (x + y) + z == x + (y + z)
abs (x + abs x) == x + abs x
  abs x + abs x == abs (x + x)
abs (1 + abs x) == 1 + abs x

x <= abs x
0 <= abs x
x <= x + 1

Now, if we add <= and < as background constants on args

  , constants =
      [ showConstant (0::Int)
      , showConstant (1::Int)
      , constant "+"   ((+)  :: Int -> Int -> Int)
      , constant "abs" (abs  :: Int -> Int)
      , background
      , constant "<="  ((<=) :: Int -> Int -> Bool)
      , constant "<"   ((<)  :: Int -> Int -> Bool)
      ]

then run again, we get the following as well:

    y <= x ==> abs (x + abs y) == x + abs y
    x <= 0 ==>       x + abs x == 0
abs x <= y ==>     abs (x + y) == x + y
abs y <= x ==>     abs (x + y) == x + y

For more examples, see the eg folder.

Similarities and Differences to QuickSpec

Speculate is inspired by QuickSpec. Like QuickSpec, Speculate uses testing to speculate equational laws about given Haskell functions. There are some differences:

  • Speculate tests enumeratively using LeanCheck, QuickSpec tests randomly using QuickCheck;
  • Speculate is able to report inequalities directly;
  • QuickSpec allows polymorphism, Speculate does not;
  • For most examples, Speculate runs slower than QuickSpec 2 but faster than QuickSpec 1.

More documentation

For more examples, see the eg and bench folders.

Speculate has been subject to a paper, see the Speculate Paper on Haskell Symposium 2017. Speculate is also subject to a chapter in a PhD Thesis (2017).

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