{-# OPTIONS -fallow-undecidable-instances #-}

{- |

Module : $Header$

Description : Instance of class Logic for propositional logic

Copyright : (c) Dominik Luecke, Uni Bremen 2007

License : similar to LGPL, see HetCATS/LICENSE.txt or LIZENZ.txt

Maintainer : luecke@tzi.de

Stability : experimental

Portability : portable

Definition of abstract syntax for propositional logic

Ref.

-}

module Propositional.AS_BASIC_Propositional where

import Common.Id

import Common.DocUtils

import Data.Typeable

import Common.ATerm.Conversion

-- DrIFT command

{-! global: UpPos !-}

data Formula = Negation Formula Range

-- pos: not

| Conjunction [Formula] Range

-- pos: "/\"s

| Disjunction [Formula] Range

-- pos: "\/"s

| Implication Formula Formula Bool Range

-- pos: "=>"

| Equivalence Formula Formula Bool Range

-- pos: "<=>"

| True_atom Range

-- pos: "True"

| False_atom Range

-- pos: "False

| Predication Common.Id.Id

-- pos: Propositional Identifiers

deriving (Show, Eq, Ord)

instance Pretty Formula

instance Typeable Formula

instance ShATermConvertible Formula

-- True is always true -P

is_True_atom :: Formula -> Bool

is_True_atom (True_atom _) = True

is_True_atom _ = False

-- and False if always false

is_False_atom :: Formula -> Bool

is_False_atom (False_atom _) = False

is_False_atom _ = False