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.

Crash Course

Install pre-requisites:

$ cabal install cmdargs
$ cabal install leancheck

Clone and enter the repository:

$ git clone https://github.com/rudymatela/speculate
$ cd speculate

There are some examples in the eg folter. For example eg/plus-abs.hs:

$ cat eg/plus-abs.hs
...
...

Compile and run with:

$ ghc -isrc eg/plus-abs.hs
$ ./eg/plus-abs
...

Installing Speculate

Pre-requisites are cmdargs and leancheck. You can install them with:

$ cabal install cmdargs
$ cabal install leancheck

No cabal package has been made yet. For now, clone the repository with:

$ git clone https://github.com/rudymatela/speculate

and compile programs that use it with:

$ ghc -ipath/to/speculate/src program.hs

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.