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.
Speculate has been subject to a paper, see the
Speculate Paper on Haskell Symposium 2017.