module Lava.Eprover
( eprover
)
where
import Lava.Signal
import Lava.Netlist
import Lava.Generic
import Lava.Sequent
import Lava.Property
import Lava.Error
import Lava.LavaDir
import Lava.Verification
import Data.List
( intersperse
, nub
)
import System.IO
( openFile
, IOMode(..)
, hPutStrLn
, hClose
)
import Control.Exception
( try
)
import Lava.IOBuffering
( noBuffering
)
import Data.IORef
import System.Process (system)
import System.Exit (ExitCode(..))
eprover :: Checkable a => a -> IO ProofResult
eprover :: a -> IO ProofResult
eprover a :: a
a =
do IO ()
checkVerifyDir
IO ()
noBuffering
(props :: [Signal Bool]
props,_) <- a -> IO ([Signal Bool], Model -> [[String]])
forall a.
Checkable a =>
a -> IO ([Signal Bool], Model -> [[String]])
properties a
a
String -> IO () -> IO ProofResult
proveFile String
defsFile (String -> [Signal Bool] -> IO ()
writeDefinitions String
defsFile [Signal Bool]
props)
where
defsFile :: String
defsFile = String
verifyDir String -> String -> String
forall a. [a] -> [a] -> [a]
++ "/circuit.tptp"
writeDefinitions :: FilePath -> [Signal Bool] -> IO ()
writeDefinitions :: String -> [Signal Bool] -> IO ()
writeDefinitions file :: String
file props :: [Signal Bool]
props =
do Handle
han <- String -> IOMode -> IO Handle
openFile String
file IOMode
WriteMode
Handle -> String -> IO ()
hPutStrLn Handle
han "% Generated by Lava\n"
Handle -> String -> IO ()
hPutStrLn Handle
han "% definitions:\n"
IORef Int
ref <- Int -> IO (IORef Int)
forall a. a -> IO (IORef a)
newIORef (2 :: Int)
let clause :: String -> [String] -> IO ()
clause kind :: String
kind xs :: [String]
xs =
Handle -> String -> IO ()
hPutStrLn Handle
han (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ [String] -> String
unlines ([String] -> String) -> [String] -> String
forall a b. (a -> b) -> a -> b
$
[ "input_clause(name," String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
kind String -> String -> String
forall a. [a] -> [a] -> [a]
++ ",["
, [String] -> String
forall (t :: * -> *) a. Foldable t => t [a] -> [a]
concat (String -> [String] -> [String]
forall a. a -> [a] -> [a]
intersperse ", " [String]
xs)
, "])."
]
new :: IO String
new =
do Int
n <- IORef Int -> IO Int
forall a. IORef a -> IO a
readIORef IORef Int
ref
let n' :: Int
n' = Int
nInt -> Int -> Int
forall a. Num a => a -> a -> a
+1
Int
n' Int -> IO () -> IO ()
forall a b. a -> b -> b
`seq` IORef Int -> Int -> IO ()
forall a. IORef a -> a -> IO ()
writeIORef IORef Int
ref Int
n'
String -> IO String
forall (m :: * -> *) a. Monad m => a -> m a
return ("*" String -> String -> String
forall a. [a] -> [a] -> [a]
++ Int -> String
forall a. Show a => a -> String
show Int
n')
define :: String -> S String -> IO ()
define v :: String
v s :: S String
s =
do String -> String -> IO ()
definition String
v (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$
case S String
s of
Bool True -> Int -> String
int 1
Bool False -> Int -> String
int 0
VarBool s :: String
s -> String -> String -> String -> String
op2 "mod" String
s (Int -> String
int 2)
Inv x :: String
x -> String -> String -> String
op1 "inv" String
x
And xs :: [String]
xs -> String -> String -> [String] -> String
opl (Int -> String
int 1) "and" [String]
xs
Or xs :: [String]
xs -> String -> String -> [String] -> String
opl (Int -> String
int 0) "or" [String]
xs
Xor xs :: [String]
xs -> [String] -> String
xor [String]
xs
Int n :: Int
n -> Int -> String
int Int
n
Neg x :: String
x -> String -> String -> String
op1 "neg" String
x
Div x :: String
x y :: String
y -> String -> String -> String -> String
op2 "div" String
x String
y
Mod x :: String
x y :: String
y -> String -> String -> String -> String
op2 "mod" String
x String
y
Plus xs :: [String]
xs -> String -> String -> [String] -> String
opl (Int -> String
int 0) "add" [String]
xs
Times xs :: [String]
xs -> String -> String -> [String] -> String
opl (Int -> String
int 1) "mul" [String]
xs
Gte x :: String
x y :: String
y -> String -> String -> String -> String
op2 "gte" String
x String
y
If x :: String
x y :: String
y z :: String
z -> String -> String -> String -> String -> String
op3 "if" String
x String
y String
z
VarInt s :: String
s -> String
s
Equal [] -> Int -> String
int 1
Equal (x :: String
x:xs :: [String]
xs) -> String -> String -> [String] -> String
opl (Int -> String
int 1) "and" [String -> String -> String -> String
op2 "eq" String
x String
y | String
y <- [String]
xs]
DelayBool x :: String
x y :: String
y -> Error -> String
forall a. Error -> a
wrong Error
Lava.Error.DelayEval
DelayInt x :: String
x y :: String
y -> Error -> String
forall a. Error -> a
wrong Error
Lava.Error.DelayEval
where
definition :: String -> String -> IO ()
definition v :: String
v s :: String
s =
String -> [String] -> IO ()
clause "axiom" [ "++equal(" String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
v String -> String -> String
forall a. [a] -> [a] -> [a]
++ ":" String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
s String -> String -> String
forall a. [a] -> [a] -> [a]
++ "," String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
v String -> String -> String
forall a. [a] -> [a] -> [a]
++ ")" ]
op1 :: String -> String -> String
op1 f :: String
f x :: String
x = String
f String -> String -> String
forall a. [a] -> [a] -> [a]
++ "(" String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
x String -> String -> String
forall a. [a] -> [a] -> [a]
++ ")"
op2 :: String -> String -> String -> String
op2 f :: String
f x :: String
x y :: String
y = String
f String -> String -> String
forall a. [a] -> [a] -> [a]
++ "(" String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
x String -> String -> String
forall a. [a] -> [a] -> [a]
++ "," String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
y String -> String -> String
forall a. [a] -> [a] -> [a]
++ ")"
op3 :: String -> String -> String -> String -> String
op3 f :: String
f x :: String
x y :: String
y z :: String
z = String
f String -> String -> String
forall a. [a] -> [a] -> [a]
++ "(" String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
x String -> String -> String
forall a. [a] -> [a] -> [a]
++ "," String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
y String -> String -> String
forall a. [a] -> [a] -> [a]
++ "," String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
z String -> String -> String
forall a. [a] -> [a] -> [a]
++ ")"
opl :: String -> String -> [String] -> String
opl z :: String
z f :: String
f [] = String
z
opl z :: String
z f :: String
f [x :: String
x] = String
x
opl z :: String
z f :: String
f (x :: String
x:xs :: [String]
xs) = String -> String -> String -> String
op2 String
f String
x (String -> String -> [String] -> String
opl String
z String
f [String]
xs)
int :: Int -> String
int n :: Int
n = String -> String -> [String] -> String
opl "cZero" "add" (Int -> String -> [String]
forall a. Int -> a -> [a]
replicate Int
n "cOne")
xor :: [String] -> String
xor [] = Int -> String
int 0
xor [x :: String
x] = String
x
xor [x :: String
x,y :: String
y] = String -> String -> String -> String
op2 "xor" String
x String
y
xor (x :: String
x:xs :: [String]
xs) = String -> String -> String -> String
op2 "or" (String -> String -> String -> String
op2 "and" String
x (String -> String -> String
op1 "inv" (String -> String -> [String] -> String
opl (Int -> String
int 0) "or" [String]
xs)))
(String -> String -> String -> String
op2 "and" (String -> String -> String
op1 "inv" String
x) ([String] -> String
xor [String]
xs))
Struct String
outvs <- IO String
-> (String -> S String -> IO ())
-> Struct Symbol
-> IO (Struct String)
forall (f :: * -> *) v.
Sequent f =>
IO v -> (v -> S v -> IO ()) -> f Symbol -> IO (f v)
netlistIO IO String
new String -> S String -> IO ()
define ([Signal Bool] -> Struct Symbol
forall a. Generic a => a -> Struct Symbol
struct [Signal Bool]
props)
Handle -> String -> IO ()
hPutStrLn Handle
han "% conjecture:\n"
String -> [String] -> IO ()
clause "conjecture" [ "--truth(" String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
v String -> String -> String
forall a. [a] -> [a] -> [a]
++ ")" | String
v <- Struct String -> [String]
forall a. Struct a -> [a]
flatten Struct String
outvs ]
Handle -> IO ()
hClose Handle
han
IO ExitCode -> IO (Either IOError ExitCode)
forall e a. Exception e => IO a -> IO (Either e a)
try (do String -> IO String
readFile String
theoryFile
String -> IO ExitCode
system ("cat " String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
theoryFile String -> String -> String
forall a. [a] -> [a] -> [a]
++ " >> " String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
file))
:: IO (Either IOError ExitCode)
() -> IO ()
forall (m :: * -> *) a. Monad m => a -> m a
return ()
where
theoryFile :: String
theoryFile = "theory.tptp"
proveFile :: FilePath -> IO () -> IO ProofResult
proveFile :: String -> IO () -> IO ProofResult
proveFile file :: String
file before :: IO ()
before =
do String -> IO ()
putStr "Eprover: "
IO ()
before
String -> IO ()
putStr "... "
String
lavadir <- IO String
getLavaDir
ExitCode
x <- String -> IO ExitCode
system ( String
lavadir
String -> String -> String
forall a. [a] -> [a] -> [a]
++ "/Scripts/eprover.wrapper "
String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
file
String -> String -> String
forall a. [a] -> [a] -> [a]
++ " -showTime"
)
let res :: ProofResult
res = case ExitCode
x of
ExitSuccess -> ProofResult
Valid
ExitFailure 1 -> ProofResult
Indeterminate
ExitFailure _ -> ProofResult
Falsifiable
String -> IO ()
putStrLn (ProofResult -> String
forall a. Show a => a -> String
show ProofResult
res String -> String -> String
forall a. [a] -> [a] -> [a]
++ ".")
ProofResult -> IO ProofResult
forall (m :: * -> *) a. Monad m => a -> m a
return ProofResult
res