module GMPSAT where

import qualified Data.Set as Set

import GMPAS

import ModalLogic

-------------------------------------------------------------------------------

-- 1. Guess Pseudovaluation H for f -- genPV

-------------------------------------------------------------------------------

guessPV :: (Ord t) => Formula t -> [Set.Set (TVandMA t)]

guessPV f =

let l = genPV f

in filter (eval f) l

-- modify the set of truth values / generate the next truth values set --------

genTV :: (Ord t) => Set.Set (TVandMA t) -> Set.Set (TVandMA t)

genTV s =

let

(TVandMA (x,t),y) = Set.deleteFindMin s

in if (t == False)

then (Set.insert (TVandMA (x,True)) y)

else if (y == Set.empty)

then Set.empty

else let

aux = genTV(y)

in if (aux == Set.empty)

then Set.empty

else (Set.insert (TVandMA (x,False)) aux)

-- generate a list with all Pseudovaluations of a formula ---------------------

genPV :: (Eq t, Ord t) => Formula t -> [Set.Set (TVandMA t)]

genPV f =

let aux = setMA f

in if (aux == Set.empty)

then aux:[]

else let recMakeList s =

let nextset = genTV s

in if (nextset == Set.empty)

then []

else (nextset:(recMakeList nextset))

in (aux:(recMakeList aux))

-- Junctor evaluation ---------------------------------------------------------

jmap :: Junctor -> Bool -> Bool -> Bool

jmap j x y =

case j of

And -> and([x,y])

Or -> or([x,y])

If -> or([not(x),y])

Fi -> or([x,not(y)])

Iff -> and([or([not(x),y]),or([x,not(y)])])

-- Formula Evaluation with truth values provided by the TVandMA set -----------

eval :: (Eq a) => (Formula a) -> Set.Set (TVandMA a) -> Bool

eval f ts =

case f of

T -> True

F -> False

Neg f1 -> not(eval f1 ts)

Junctor f1 j f2 -> (jmap j (eval f1 ts) (eval f2 ts))

Mapp i f1 -> let findInS s ff =

if (s == Set.empty)

then False -- this could very well be True

else let (TVandMA (x,t),y) = Set.deleteFindMin s

in if (x == ff)

then t

else findInS y ff

in

findInS ts (Mapp i f1)

-- make (Truth Values, Modal Atoms) set from Formula f ------------------------

setMA :: (Ord t) => Formula t -> Set.Set (TVandMA t)

setMA f =

case f of

T -> Set.empty

F -> Set.empty

Neg f1 -> setMA f1

Junctor f1 _ f2 -> Set.union (setMA f1) (setMA f2)

Mapp i f1 -> Set.insert (TVandMA (Mapp i f1,False)) Set.empty

-------------------------------------------------------------------------------

-- 2. Choose a ctr. cl. Ro /= F over MA(H) s.t. H "entails" ~Ro -- roFromPV

-------------------------------------------------------------------------------

-- reverse the truth values of the set elements -------------------------------

revTV :: (Ord t, Eq t) => Set.Set (TVandMA t) -> Set.Set (TVandMA t)

revTV s = if (s == Set.empty)

then Set.empty

else let (TVandMA (x,t),aux) = Set.deleteFindMin s

in Set.insert (TVandMA (x,not(t))) (revTV aux)

-- return the list of sets of n choose k of the set s -------------------------

nck :: (Ord t) => Set.Set (TVandMA t) -> Int -> Int -> [Set.Set (TVandMA t)]

nck s n k =

case (n-k) of

0 -> [revTV s]

_ ->

case k of

0 -> [Set.empty]

_ -> let (TVandMA (x,t),aux) = Set.deleteFindMin s

in (map (Set.insert (TVandMA (x,not(t)))) (nck aux (n-1) (k-1)))

++ (nck aux (n-1) k)

-- generate all unpermuted sets of size <= n of the set s ---------------------

genAllSets :: (Ord t) => Set.Set (TVandMA t) -> Int -> [Set.Set (TVandMA t)]

genAllSets s n =

case n of

0 -> []

_ -> let size = Set.size s

in (nck s size n) ++ (genAllSets s (n-1))

-- generates all ro lists from a given pseudovaluation ------------------------

roFromPV :: (Ord t) => Set.Set (TVandMA t) -> [[TVandMA t]]

roFromPV s = let l = genAllSets s (Set.size s)

ll = genAllLists l

in if (null (head ll)) then ll

else filter (not.null) ll

-- return the list of lists -> permutations of a set --------------------------

perm :: (Ord t) => Set.Set t -> [[t]]

perm s =

if (Set.size s <= 1)

then [Set.toList s]

else let (x,aux1) = Set.deleteFindMin s

(y,aux2) = Set.deleteFindMin aux1

in map (x:) (perm aux1) ++ map (y:) (perm (Set.insert x aux2))

-- returns the input by transforming each set to list and permuting it --------

genAllLists :: (Ord t) => [Set.Set t] -> [[t]]

genAllLists l =

case l of

[] -> [[]]

_ -> (perm (head l)) ++ (genAllLists (tail l))

-------------------------------------------------------------------------------

-- 5. Recursively check that ~c(R,Ro) is satisfiable. -- checkSAT

-------------------------------------------------------------------------------

-- Substitutes the literals in a clause by the formulae under the modal atoms

-- and negates the resulted clause/formula

--negSubst :: Clause -> [TVandMA a] -> Formula a

negSubst c ro =

case c of

Cl [] ->

case ro of

[] -> T

_ -> error ("error @ GMPSAT.negSubst 1 "

++ show c ++ " " ++ show ro)

Cl (PLit _ : ll) ->

case ro of

TVandMA (Mapp _ ff,_):ml -> let g = negSubst (Cl ll) ml

in Junctor (Neg ff) And g

_ -> error ("error @ GMPSAT.negSubst 2 "

++ show c ++ " " ++ show ro)

Cl (NLit _ : ll) ->

case ro of

TVandMA (Mapp _ ff,_):ml -> let g = negSubst (Cl ll) ml

in Junctor ff And g

_ -> error ("error @ GMPSAT.negSubst 3 "

++ show c ++ " " ++ show ro)

-- evaluate formula -----------------------------------------------------------

evalPF :: (Ord a, ModalLogic a b) => Formula a -> Bool

evalPF f =

case f of

T -> True

F -> False

Neg g -> let e = evalPF g in not e

Junctor f1 j f2 -> let e1 = evalPF f1

e2 = evalPF f2

in jmap j e1 e2

_ -> error "error @ GMPSAT.evalPF: Embedded modal atoms not working yet."

{-

Mapp i ff -> let x = checksat (Mapp i ff)

g = Neg (Mapp i ff)

y = checksat g

in if x then x -- this has to be adapted

else y

-}

-------------------------------------------------------------------------------

-- TO BE DELETED. JUST FOR ORIENTATION ...

-- genPV -- generate all pseudovaluations of a formula

-- roFromPV -- generate all rho from a given pseudovaluation

-- matchRO -- match a rho against the rules of the logic

-- guessClause -- guess a clause from the premise of the rules

-- negSubst -- substitute underMA for literals and negate the result

-- genPV :: (Ord t) => Formula t -> [Data.Set.Set (TVandMA t)]

-- roFromPV :: (Ord t) => Data.Set.Set (TVandMA t) -> [[TVandMA t]]

-- matchRO :: (ModalLogic a b) => [TVandMA a] -> [b]

-- guessClause :: (ModalLogic a b) => b -> [Clause]

-- negSubst :: Clause -> [TVandMA a] -> Formula a

-------------------------------------------------------------------------------

--checksat :: (Ord a, ModalLogic a b) => Formula a -> Bool

checksat f = any(\h->all(\ro->all(\mr->any(\cl->evalPF(negSubst cl ro))(guessClause mr))(matchRO ro))(roFromPV h))(genPV f)