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README
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
Prerequisites 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](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](eg) and [bench](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).