{- |

Module : $Header$

Description : interface to Reduce CAS

Copyright : (c) Dominik Dietrich, DFKI Bremen, 2010

License : GPLv2 or higher

Maintainer : Dominik.Dietrich@dfki.de

Stability : provisional

Portability : portable

Interface for Reduce CAS system.

-}

module CSL.Reduce_Interface where

import Common.AS_Annotation

import Common.Id

import Data.Time (midnight)

import Logic.Prover

import CSL.AS_BASIC_CSL

import CSL.Parse_AS_Basic

import CSL.Lemma_Export

import System.IO

import System.Process

type Session = (Handle, Handle)

-- | returns the name of the reduce prover

reduceS :: String

reduceS = "Reduce"

{- | returns a basic proof status for conjecture with name n

where [EXPRESSION] represents the proof tree. -}

openReduceProofStatus :: String -> [EXPRESSION] -> ProofStatus [EXPRESSION]

openReduceProofStatus n = openProofStatus n reduceS

closedReduceProofStatus :: Ord pt => String -- ^ name of the goal

-> pt -> ProofStatus pt

closedReduceProofStatus goalname proof_tree =

ProofStatus

{ goalName = goalname

, goalStatus = Proved True

, usedAxioms = []

, usedProver = reduceS

, proofTree = proof_tree

, usedTime = midnight

, tacticScript = TacticScript "" }

{-

For Quantifier Elimination:

off nat;

load redlog;

rlset reals;

rlqe(exp...);

-}

-- | connects to the CAS, prepares the streams and sets initial options

connectCAS :: String -> IO (Handle, Handle, Handle, ProcessHandle)

connectCAS reducecmd = do

putStrLn "succeeded"

(inp, out, err, pid) <- runInteractiveCommand $ reducecmd ++ " -w"

hSetBuffering out NoBuffering

hSetBuffering inp LineBuffering

hPutStrLn inp "off nat;"

hPutStrLn inp "load redlog;"

hPutStrLn inp "rlset reals;"

hGetLine out

hGetLine out

hGetLine out

hGetLine out

hGetLine out

hGetLine out

hGetLine out

putStrLn "done"

return (inp, out, err, pid)

-- | closes the connection to the CAS

disconnectCAS :: (Handle, Handle) -> IO ()

disconnectCAS (inp, _) = do

hPutStrLn inp "quit;"

putStrLn "CAS disconnected"

return ()

{- | reads characters from the specified output until the next result is

complete, indicated by $ when using the maxima mode off nat; -}

getNextResultOutput :: Handle -> IO String

getNextResultOutput out = do

b <- hIsEOF out

if b then return "" else do

c <- hGetChar out

if c == '$' then return [] else do

r <- getNextResultOutput out

return (c : r)

exportExps :: [EXPRESSION] -> String

exportExps [] = ""

exportExps (e1 : e2 : e3) = exportExp e1 ++ "," ++ exportExps (e2 : e3)

exportExps (e1 : []) = exportExp e1

-- | those operators declared as infix in Reduce

infixOps :: [String]

infixOps = ["+", "-", "/", "**", "^", "=", "*", "and", "impl", "or"]

-- | exports an expression to Reduce format

exportExp :: EXPRESSION -> String

exportExp (Var token) = tokStr token

exportExp (Op s _ [e1, e2] _) =

if elem s infixOps

then "(" ++ exportExp e1 ++ s ++ exportExp e2 ++ ")"

else s ++ "(" ++ exportExp e1 ++ "," ++ exportExp e2 ++ ")"

exportExp (Op s _ exps _) = s ++ if (length exps == 0) then "" else "("

++ exportExps exps ++

if (length exps == 0) then ")" else ""

exportExp (List exps _) = "{" ++ exportExps exps ++ "}"

exportExp (Int i _) = show i

exportExp (Double d _) = show d

-- | exports command to Reduce Format

exportReduce :: Named CMD -> String

exportReduce namedcmd = case sentence namedcmd of

Cmd "simplify" exps -> exportExp $ head exps

Cmd "ask" exps -> exportExp $ head exps

Cmd cmd exps -> cmd ++ "(" ++ exportExps exps ++ ")"

_ -> error "exportReduce: not implemented for this case" -- TODO: implement

procCmd :: (Handle, Handle) -> Named CMD

-> IO (ProofStatus [EXPRESSION], [(Named CMD, ProofStatus [EXPRESSION])])

procCmd (inp, out) cmd = case cmdstring of

"simplify" -> cassimplify (inp, out) cmd

"ask" -> casask (inp, out) cmd

"divide" -> casremainder (inp, out) cmd

"rlqe" -> casqelim (inp, out) cmd

"factorize" -> casfactorExp (inp, out) cmd

"int" -> casint (inp, out) cmd

"solve" -> cassolve (inp, out) cmd

_ -> error "Command not supported"

where Cmd cmdstring _ = sentence cmd

-- | removes the newlines 4: from the beginning of the string

skipReduceLineNr :: String -> String

skipReduceLineNr s = dropWhile (`elem` " \n") $ tail

$ dropWhile (/= ':') s

-- | sends the given string to the CAS, reads the result and tries to parse it.

procString :: (Handle, Handle) -> String -> String -> IO (ProofStatus [EXPRESSION])

procString (inp, out) axname s = do

putStrLn $ "Send CAS cmd " ++ s

hPutStrLn inp s

res <- getNextResultOutput out

putStrLn $ "Result is " ++ res

putStrLn $ "Parsing of --" ++ skipReduceLineNr res ++ "-- yields "

++ show (parseResult (skipReduceLineNr res))

case (parseResult (skipReduceLineNr res)) of

Just e -> return $ closedReduceProofStatus axname [e]

Nothing -> return $ openReduceProofStatus axname []

-- | factors a given expression over the reals

casfactorExp :: (Handle, Handle) -> Named CMD -> IO ((ProofStatus [EXPRESSION]),[(Named CMD, ProofStatus [EXPRESSION])])

casfactorExp (inp, out) cmd =

do

proofstatus <- procString (inp, out) (senAttr cmd) $ exportReduce cmd ++ ";"

return (proofstatus,[exportLemmaFactor cmd proofstatus])

-- | solves a single equation over the reals

cassolve :: (Handle, Handle) -> Named CMD -> IO (ProofStatus [EXPRESSION],[(Named CMD, ProofStatus [EXPRESSION])])

cassolve (inp, out) cmd =

do

proofstatus <- procString (inp, out) (senAttr cmd) $ exportReduce cmd ++ ";"

return (proofstatus,[])

-- | simplifies a given expression over the reals

cassimplify :: (Handle, Handle) -> Named CMD -> IO ((ProofStatus [EXPRESSION]),[(Named CMD, ProofStatus [EXPRESSION])])

cassimplify (inp, out) cmd = do

proofstatus <- procString (inp, out) (senAttr cmd) $ exportReduce cmd ++ ";"

return (proofstatus,[exportLemmaSimplify cmd proofstatus])

-- | asks value of a given expression

casask :: (Handle, Handle) -> Named CMD -> IO ((ProofStatus [EXPRESSION]),[(Named CMD, ProofStatus [EXPRESSION])])

casask (inp, out) cmd = do

proofstatus <- procString (inp, out) (senAttr cmd) $ exportReduce cmd ++ ";"

return (proofstatus,[exportLemmaAsk cmd proofstatus])

-- | computes the remainder of a division

casremainder :: (Handle, Handle) -> Named CMD -> IO ((ProofStatus [EXPRESSION]),[(Named CMD, ProofStatus [EXPRESSION])])

casremainder (inp, out) cmd =

do

proofstatus <- procString (inp, out) (senAttr cmd) $ exportReduce (makeNamed (senAttr cmd) (Cmd "divide" args)) ++ ";"

return (proofstatus,[exportLemmaRemainder cmd proofstatus])

where Cmd _ args = sentence cmd

-- | integrates the given expression

casint :: (Handle, Handle) -> Named CMD -> IO ((ProofStatus [EXPRESSION]),[(Named CMD, ProofStatus [EXPRESSION])])

casint (inp, out) cmd =

do

proofstatus <- procString (inp, out) (senAttr cmd) $ exportReduce cmd ++ ";"

return (proofstatus,[exportLemmaInt cmd proofstatus])

-- | performs quantifier elimination of a given expression

casqelim :: (Handle, Handle) -> Named CMD -> IO ((ProofStatus [EXPRESSION]),[(Named CMD, ProofStatus [EXPRESSION])])

casqelim (inp, out) cmd =

do

proofstatus <- procString (inp, out) (senAttr cmd) $ exportReduce cmd ++ ";"

return (proofstatus,[exportLemmaQelim cmd proofstatus])

exportLemmaQelim :: Named CMD -> ProofStatus [EXPRESSION] -> (Named CMD, ProofStatus [EXPRESSION])

exportLemmaQelim namedcmd ps =

((makeNamed lemmaname lemma), closedReduceProofStatus lemmaname [(Op "Proof" [] [] nullRange)])

where Cmd _ exps = sentence namedcmd

lemma = Cmd "=" [head exps, head (proofTree ps)]

lemmaname = (ganame namedcmd)

-- | declares an operator, such that it can used infix/prefix in CAS

casDeclareOperators :: (Handle, Handle) -> [EXPRESSION] -> IO ()

casDeclareOperators (inp, out) varlist = do

hPutStrLn inp $ "operator " ++ exportExps varlist ++ ";"

hGetLine out

return ()

-- | declares an equation x := exp

casDeclareEquation :: (Handle, Handle) -> CMD -> IO ()

casDeclareEquation (inp, out) (Cmd s exps) =

if s == ":=" then

do

putStrLn $ (exportExp (exps !! 0)) ++ ":=" ++ (exportExp (exps !! 1))

hPutStrLn inp $ (exportExp (exps !! 0)) ++ ":=" ++ (exportExp (exps !! 1)) ++ ";"

res <- getNextResultOutput out

putStrLn $ "Declaration Result: " ++ res

return ()

else error "Expression is not an equation"

casDeclareEquation _ _ =

error "casDeclareEquation: not implemented for this case" -- TODO: implement

-- | generates the lemma for cmd with result ProofStatus

exportLemmaFactor :: Named CMD -> ProofStatus [EXPRESSION] -> (Named CMD, ProofStatus [EXPRESSION])

exportLemmaFactor namedcmd ps =

((makeNamed lemmaname lemma), closedReduceProofStatus lemmaname [(Op "Proof" [] [] nullRange)])

where Cmd _ exps = sentence namedcmd

lemma = Cmd "=" [head exps, head (proofTree ps)]

lemmaname = (ganame namedcmd)

exportLemmaSolve :: Named CMD -> ProofStatus [EXPRESSION] -> (Named CMD, ProofStatus [EXPRESSION])

exportLemmaSolve namedcmd ps =

((makeNamed lemmaname lemma), closedReduceProofStatus lemmaname [(Op "Proof" [] [] nullRange)])

where Cmd _ exps = sentence namedcmd

lemma = Cmd "=" [head exps, head (proofTree ps)]

lemmaname = (ganame namedcmd)

exportLemmaSimplify :: Named CMD -> ProofStatus [EXPRESSION] -> (Named CMD, ProofStatus [EXPRESSION])

exportLemmaSimplify namedcmd ps =

((makeNamed lemmaname lemma), closedReduceProofStatus lemmaname [(Op "Proof" [] [] nullRange)])

where Cmd _ exps = sentence namedcmd

lemma = Cmd "=" [head exps, head (proofTree ps)]

lemmaname = (ganame namedcmd)

exportLemmaAsk :: Named CMD -> ProofStatus [EXPRESSION] -> (Named CMD, ProofStatus [EXPRESSION])

exportLemmaAsk namedcmd ps =

((makeNamed lemmaname lemma), closedReduceProofStatus lemmaname [(Op "Proof" [] [] nullRange)])

where Cmd _ exps = sentence namedcmd

lemma = Cmd "=" [head exps, head (proofTree ps)]

lemmaname = (ganame namedcmd)

exportLemmaRemainder :: Named CMD -> ProofStatus [EXPRESSION] -> (Named CMD, ProofStatus [EXPRESSION])

exportLemmaRemainder namedcmd ps =

((makeNamed lemmaname lemma), closedReduceProofStatus lemmaname [(Op "Proof" [] [] nullRange)])

where Cmd _ exps = sentence namedcmd

lemma = Cmd "=" [head exps, head (proofTree ps)]

lemmaname = (ganame namedcmd)

exportLemmaInt :: Named CMD -> ProofStatus [EXPRESSION] -> (Named CMD, ProofStatus [EXPRESSION])

exportLemmaInt namedcmd ps =

((makeNamed lemmaname lemma), closedReduceProofStatus lemmaname [(Op "Proof" [] [] nullRange)])

where Cmd _ exps = sentence namedcmd

lemma = Cmd "=" [head exps, head (proofTree ps)]

lemmaname = (ganame namedcmd)