Speculate

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 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	QuickSpec
testing	enumerative (LeanCheck)	random (QuickCheck)
equational laws	yes (after completion)	yes (as discovered)
inequational laws	yes	no
conditional laws	yes	restricted to a set of predicates
polymorphism	no	yes
performance	slower	faster

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.