{-# 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 : non-portable (imports Logic.Logic)

Instance of class Logic for the propositional logic

Also the instances for Syntax and Category.

-}

{-

Ref.

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

Till Mossakowski, Joseph Goguen, Razvan Diaconescu, Andrzej Tarlecki.

What is a Logic?.

In Jean-Yves Beziau (Ed.), Logica Universalis, pp. 113-@133. Birkhäuser.

2005.

-}

module Propositional.Logic_Propositional

(module Propositional.Logic_Propositional

, Sign

, Morphism

) where

import Logic.Logic

import Propositional.Sign as Sign

import Propositional.Morphism as Morphism

import qualified Propositional.AS_BASIC_Propositional as AS_BASIC

import qualified Propositional.ATC_Propositional()

import qualified Propositional.Symbol as Symbol

import qualified Propositional.Parse_AS_Basic as Parse_AS

import qualified Propositional.Analysis as Analysis

import qualified Propositional.InverseAnalysis as IAna

import qualified Propositional.Sublogic as Sublogic

import qualified Common.Id as Id()

-- | Lid for propositional logic

data Propositional = Propositional deriving Show --lid

instance Language Propositional where

description _ =

"Propositional Logic\n\

\for more information please refer to\n\

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

-- | Instance of Category for propositional logic

instance Category Propositional Sign.Sign Morphism.Morphism where

-- Identity morhpism

ide Propositional = Morphism.idMor

-- Returns the domain of a morphism

dom Propositional = Morphism.source

-- Returns the codomain of a morphism

cod Propositional = Morphism.target

-- all sets are legal objects

legal_obj Propositional s = Sign.isLegalSignature s

-- tests if the morphism is ok

legal_mor Propositional f = Morphism.isLegalMorphism f

-- composition of morphisms

comp Propositional f g = Morphism.composeMor f g

-- | Instance of Sentences for propositional logic

instance Sentences Propositional AS_BASIC.FORMULA ()

Sign.Sign Morphism.Morphism Symbol.Symbol where

-- returns the set of symbols

sym_of Propositional = Symbol.symOf

-- returns the symbol map

symmap_of Propositional = Symbol.getSymbolMap

-- returns the name of a symbol

sym_name Propositional = Symbol.getSymbolName

-- default entry

empty_proof_tree Propositional = error "Not yet implemented"

-- translation of sentences along signature morphism

map_sen Propositional = Morphism.mapSentence

-- there is nothing to leave out

simplify_sen Propositional _ form = form

-- | Syntax of Propositional logic

instance Syntax Propositional AS_BASIC.BASIC_SPEC

AS_BASIC.SYMB_ITEMS AS_BASIC.SYMB_MAP_ITEMS where

parse_basic_spec Propositional = Just Parse_AS.basicSpec

parse_symb_items _ = Nothing

parse_symb_map_items _ = Nothing

-- | Instance of Logic for propositional logc

instance Logic Propositional

Sublogic.PropSL -- Sublogics

AS_BASIC.BASIC_SPEC -- basic_spec

AS_BASIC.FORMULA -- sentence

AS_BASIC.SYMB_ITEMS -- symb_items

AS_BASIC.SYMB_MAP_ITEMS -- symb_map_items

Sign.Sign -- sign

Morphism.Morphism -- morphism

Symbol.Symbol -- symbol

() -- raw_symbol

() -- proof_tree

where

stability Propositional = Experimental

-- | Static Analysis for propositional logic

instance StaticAnalysis Propositional

AS_BASIC.BASIC_SPEC -- basic_spec

AS_BASIC.FORMULA -- sentence

() -- proof_tree

AS_BASIC.SYMB_ITEMS -- symb_items

AS_BASIC.SYMB_MAP_ITEMS -- symb_map_items

Sign.Sign -- sign

Morphism.Morphism -- morphism

Symbol.Symbol -- symbol

() -- raw_symbol

where

basic_analysis Propositional = Just $

Analysis.basicPropositionalAnalysis

empty_signature Propositional = Sign.emptySig

inclusion Propositional = Morphism.inclusionMap

signature_union Propositional = Sign.sigUnion

is_subsig Propositional = Sign.isSubSigOf

signature_difference Propositional = Sign.diffOfSigs

sign_to_basic_spec Propositional = IAna.signToBasicSpec

-- Default implementations since we are having no raw_symbols

symbol_to_raw Propositional _ = ()

id_to_raw Propositional _ = ()

matches Propositional _ _ = False

-- | Sublogics

instance SemiLatticeWithTop Sublogic.PropSL where

join = Sublogic.sublogics_max

top = Sublogic.top

instance MinSublogic Sublogic.PropSL AS_BASIC.BASIC_SPEC where

minSublogic it = Sublogic.sl_basic_spec Sublogic.bottom it

instance MinSublogic Sublogic.PropSL Sign.Sign where

minSublogic si = Sublogic.sl_sig Sublogic.bottom si

instance Sublogics Sublogic.PropSL where

sublogic_names = Sublogic.sublogics_name

instance MinSublogic Sublogic.PropSL AS_BASIC.FORMULA where

minSublogic frm = Sublogic.sl_form Sublogic.bottom frm

instance MinSublogic Sublogic.PropSL Symbol.Symbol where

minSublogic sym = Sublogic.sl_sym Sublogic.bottom sym

instance MinSublogic Sublogic.PropSL AS_BASIC.SYMB_ITEMS where

minSublogic symit = Sublogic.sl_symit Sublogic.bottom symit

instance MinSublogic Sublogic.PropSL Morphism.Morphism where

minSublogic symor = Sublogic.sl_mor Sublogic.bottom symor

instance MinSublogic Sublogic.PropSL AS_BASIC.SYMB_MAP_ITEMS where

minSublogic sm = Sublogic.sl_symmap Sublogic.bottom sm

instance ProjectSublogicM Sublogic.PropSL Symbol.Symbol

instance ProjectSublogic Sublogic.PropSL Sign.Sign

instance ProjectSublogic Sublogic.PropSL Morphism.Morphism

instance ProjectSublogicM Sublogic.PropSL AS_BASIC.SYMB_MAP_ITEMS

instance ProjectSublogicM Sublogic.PropSL AS_BASIC.SYMB_ITEMS

instance ProjectSublogic Sublogic.PropSL AS_BASIC.BASIC_SPEC

instance ProjectSublogic Sublogic.PropSL AS_BASIC.FORMULA