-- needs ghc -fglasgow-exts -package data

{- HetCATS/LogicRepr.hs

$Id$

Till Mossakowski, Christian Maeder

Provides data structures logic representations.

Logic representations are just collections of

functions between (some of) the types of logics.

References: see Logic.hs

Todo:

Weak amalgamability, also for reprs

repr maps

reprs out of sublogic relationships

-}

module LogicRepr where

import Logic

import FiniteSet

import Maybe(catMaybes)

-- Simple logic representations (possibly also morphisms via adjointness)

data (Logic lid1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1,

Logic lid2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2) =>

LogicRepr lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1

lid2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2

=

LogicRepr {repr_name :: String,

source :: lid1, source_sublogic :: sublogics1,

target :: lid2, target_sublogic :: sublogics2,

-- the translation functions are partial

-- because the target may be a sublanguage

-- map_basic_spec :: basic_spec1 -> Maybe basic_spec2,

map_sign :: sign1 -> Maybe (sign2,[sentence2]),

projection:: Maybe (-- the right adjoint functor Psi

sign2 -> sign1, morphism2 -> morphism1,

-- the counit

sign2 -> morphism2,

-- basic_spec2 -> basic_spec1,

-- corresponding symbol translation

symbol2 -> Maybe symbol1),

map_morphism :: morphism1 -> Maybe morphism2,

map_sentence :: sign1 -> sentence1 -> Maybe sentence2,

-- also covers semi-representations

-- with no sentence translation

map_symbol :: symbol1 -> Set symbol2

-- codings may be more complex

}

instance (Logic lid1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1,

Logic lid2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2) =>

Eq (LogicRepr lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1

lid2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2)

where

r1==r2 = repr_name r1 == repr_name r2 &&

language_name (source r1) == language_name (source r2) &&

language_name (target r1) == language_name (target r2) &&

coerce (source r1) (source r2) (source_sublogic r1) ==

Just (source_sublogic r2) &&

coerce (target r1) (target r2) (target_sublogic r1) ==

Just (target_sublogic r2)

id_repr ::

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol =>

lid ->

LogicRepr lid sublogics basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol

lid sublogics basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol

id_repr lid =

LogicRepr {repr_name = "id_"++language_name lid,

source = lid, source_sublogic = top,

target = lid, target_sublogic = top,

map_sign = \sigma -> Just(sigma,[]),

projection= Just (-- the right adjoint functor Psi

id, id,

-- the counit

ide lid,

-- corresponding symbol translation

Just),

map_morphism = Just,

map_sentence = \sigma -> Just,

map_symbol = single

}

-- composition of logic representations (diagrammatic order)

comp_repr ::

(Logic lid1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1,

Logic lid2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2,

Logic lid3 sublogics3

basic_spec3 sentence3 symb_items3 symb_map_items3

sign3 morphism3 symbol3 raw_symbol3

) =>

LogicRepr lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1

lid2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2

-> LogicRepr lid2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2

lid3 sublogics3 basic_spec3 sentence3 symb_items3 symb_map_items3

sign3 morphism3 symbol3 raw_symbol3

-> Maybe (

LogicRepr lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1

lid3 sublogics3 basic_spec3 sentence3 symb_items3 symb_map_items3

sign3 morphism3 symbol3 raw_symbol3 )

comp_repr r1 r2 = if target_sublogic r1 <= source_sublogic r2 then

Just(LogicRepr{

repr_name = repr_name r1++";"++repr_name r2,

source = source r1, target = target r2,

source_sublogic = source_sublogic r1,

target_sublogic = target_sublogic r2,

map_sentence =

\si1 se1 ->

do (si2,_) <- map_sign r1 si1

se2 <- map_sentence r1 si1 se1

map_sentence r2 si2 se2 ,

map_sign =

\si1 ->

do (si2, se2s) <- map_sign r1 si1

(si3, se3s) <- map_sign r2 si2

return (si3, se3s ++ catMaybes

(map (map_sentence r2 si2) se2s)) ,

projection = undefined ,

map_morphism = \ m1 -> map_morphism r1 m1 >>= map_morphism r2 ,

map_symbol = \ s1 -> unions

(map (map_symbol r2) (toList (map_symbol r1 s1)))

}) else Nothing