{- |

Module : $Header$

Description : Abstract syntax for propositional logic

Copyright : (c) Dominik Luecke, Uni Bremen 2007

License : GPLv2 or higher, see LICENSE.txt

Maintainer : luecke@informatik.uni-bremen.de

Stability : experimental

Portability : portable

Definition of abstract syntax for propositional logic

-}

{-

Ref.

http://en.wikipedia.org/wiki/Propositional_logic

-}

module Propositional.AS_BASIC_Propositional

( FORMULA (..) -- datatype for Propositional Formulas

, BASIC_ITEMS (..) -- Items of a Basic Spec

, BASIC_SPEC (..) -- Basic Spec

, SYMB_ITEMS (..) -- List of symbols

, SYMB (..) -- Symbols

, SYMB_MAP_ITEMS (..) -- Symbol map

, SYMB_OR_MAP (..) -- Symbol or symbol map

, PRED_ITEM (..) -- Predicates

, isPrimForm

) where

import Common.Id as Id

import Common.Doc

import Common.DocUtils

import Common.Keywords

import Common.AS_Annotation as AS_Anno

-- DrIFT command

{-! global: GetRange !-}

-- | predicates = propotions

data PRED_ITEM = Pred_item [Id.Token] Id.Range

deriving Show

newtype BASIC_SPEC = Basic_spec [AS_Anno.Annoted (BASIC_ITEMS)]

deriving Show

data BASIC_ITEMS =

Pred_decl PRED_ITEM

| Axiom_items [AS_Anno.Annoted (FORMULA)]

-- pos: dots

deriving Show

-- | Datatype for propositional formulas

data FORMULA =

False_atom Id.Range

-- pos: "False

| True_atom Id.Range

-- pos: "True"

| Predication Id.Token

-- pos: Propositional Identifiers

| Negation FORMULA Id.Range

-- pos: not

| Conjunction [FORMULA] Id.Range

-- pos: "/\"s

| Disjunction [FORMULA] Id.Range

-- pos: "\/"s

| Implication FORMULA FORMULA Id.Range

-- pos: "=>"

| Equivalence FORMULA FORMULA Id.Range

-- pos: "<=>"

deriving (Show, Eq, Ord)

data SYMB_ITEMS = Symb_items [SYMB] Id.Range

-- pos: SYMB_KIND, commas

deriving (Show, Eq)

newtype SYMB = Symb_id Id.Token

-- pos: colon

deriving (Show, Eq)

data SYMB_MAP_ITEMS = Symb_map_items [SYMB_OR_MAP] Id.Range

-- pos: SYMB_KIND, commas

deriving (Show, Eq)

data SYMB_OR_MAP = Symb SYMB

| Symb_map SYMB SYMB Id.Range

-- pos: "|->"

deriving (Show, Eq)

-- All about pretty printing

-- we chose the easy way here :)

instance Pretty FORMULA where

pretty = printFormula

instance Pretty BASIC_SPEC where

pretty = printBasicSpec

instance Pretty SYMB where

pretty = printSymbol

instance Pretty SYMB_ITEMS where

pretty = printSymbItems

instance Pretty SYMB_MAP_ITEMS where

pretty = printSymbMapItems

instance Pretty BASIC_ITEMS where

pretty = printBasicItems

instance Pretty SYMB_OR_MAP where

pretty = printSymbOrMap

instance Pretty PRED_ITEM where

pretty = printPredItem

isPrimForm :: FORMULA -> Bool

isPrimForm f = case f of

True_atom _ -> True

False_atom _ -> True

Predication _ -> True

Negation _ _ -> True

_ -> False

-- Pretty printing for formulas

printFormula :: FORMULA -> Doc

printFormula frm =

let ppf p f = (if p f then id else parens) $ printFormula f

isJunctForm f = case f of

Implication _ _ _ -> False

Equivalence _ _ _ -> False

_ -> True

in case frm of

False_atom _ -> text falseS

True_atom _ -> text trueS

Predication x -> pretty x

Negation f _ -> notDoc <+> ppf isPrimForm f

Conjunction xs _ -> sepByArbitrary andDoc $ map (ppf isPrimForm) xs

Disjunction xs _ -> sepByArbitrary orDoc $ map (ppf isPrimForm) xs

Implication x y _ -> ppf isJunctForm x <+> implies <+> ppf isJunctForm y

Equivalence x y _ -> ppf isJunctForm x <+> equiv <+> ppf isJunctForm y

sepByArbitrary :: Doc -> [Doc] -> Doc

sepByArbitrary d = fsep . prepPunctuate (d <> space)

printPredItem :: PRED_ITEM -> Doc

printPredItem (Pred_item xs _) = fsep $ map pretty xs

printBasicSpec :: BASIC_SPEC -> Doc

printBasicSpec (Basic_spec xs) = vcat $ map pretty xs

printBasicItems :: BASIC_ITEMS -> Doc

printBasicItems (Axiom_items xs) = vcat $ map pretty xs

printBasicItems (Pred_decl x) = pretty x

printSymbol :: SYMB -> Doc

printSymbol (Symb_id sym) = pretty sym

printSymbItems :: SYMB_ITEMS -> Doc

printSymbItems (Symb_items xs _) = fsep $ map pretty xs

printSymbOrMap :: SYMB_OR_MAP -> Doc

printSymbOrMap (Symb sym) = pretty sym

printSymbOrMap (Symb_map source dest _) =

pretty source <+> mapsto <+> pretty dest

printSymbMapItems :: SYMB_MAP_ITEMS -> Doc

printSymbMapItems (Symb_map_items xs _) = fsep $ map pretty xs