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

-- the Generic Model Parser Abstract Syntax

-- Copyright 2007, Lutz Schroeder and Georgel Calin

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

module GMPAS where

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

-- Abstract Syntax

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

-- Datatype for the clauses ---------------------------------------------------

data Clause = Cl [Literal]

deriving Show

data Literal = PLit Int

| NLit Int

deriving Show

-- Datatypes for the modal index ----------------------------------------------

data ModalK = ModalK () -- K modal logic index

deriving (Eq, Ord)

data ModalKD = ModalKD () -- KD modal logic index

deriving (Eq, Ord)

data GML = GML Integer -- Graded modal logic index

deriving (Eq, Ord)

data CL = CL Integer -- Coalition modal logic index

deriving (Eq, Ord)

data Kars = Kars [Char] -- Generic modal logic index

deriving (Eq, Ord)

-- Formula Datatype -----------------------------------------------------------

data Otype = Square | Angle -- type of the Modal Operator

deriving (Eq, Ord)

data Junctor = And | Or | If | Fi | Iff

deriving (Eq, Ord)

data Mop a = Mop a Otype -- Modal Operator: index & type

deriving (Eq, Ord)

data Formula a = F -- datatype for the formulae

| T

| Neg (Formula a)

| Junctor (Formula a) Junctor (Formula a)

| Mapp (Mop a) (Formula a) -- modal appl constr

| Var Char Integer -- variables

deriving (Eq, Ord)

-- Truth Value & Modal Atom type ----------------------------------------------

data MATV a = MATV (Formula a, Bool)

deriving (Eq, Ord)

data RoClause a = Implies ([Formula a],[Formula a])

deriving (Eq, Ord)

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

-- Show Instances 4 Abstract Syntax

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

instance Show a => Show (Mop a) where

show m = case m of

Mop x Square -> "[" ++ show x ++ "]"

Mop x Angle -> "<" ++ show x ++ ">"

instance Show Junctor where

show j = case j of

And -> "/\\"

Or -> "\\/"

If -> "->"

Fi -> "<-"

Iff -> "<->"

instance Show a => Show (Formula a) where

show f = case f of

F -> "F"

T -> "T"

Neg x -> "~" ++ show x

Junctor x j y -> "(" ++ show x ++ " " ++ show j ++ " " ++ show y ++ ")"

Mapp m x -> show m ++ " " ++ show x

Var x i -> show ([x] ++ show i)

instance Show Kars where

show (Kars l) = show l

instance Show CL where

show (CL s) = let (d,p)=divMod s 2 in

if (d == 0) then show p

else show (CL d) ++ show p

instance Show ModalK where

show (ModalK ()) = ""

instance Show ModalKD where

show (ModalKD ()) = ""

instance Show a => Show (MATV a) where

show (MATV (x,y)) = "(" ++ show x ++ "," ++ show y ++ ")"