-- needs ghc -fglasgow-exts

{- HetCATS/Grothendieck.hs

$Id$

Till Mossakowski

The Grothendieck logic is defined to be the

heterogeneous logic over the logic graph.

This will be the logic over which the data

structures and algorithms for specification in-the-large

are built.

References:

R. Diaconescu:

Grothendieck institutions

J. applied categorical structures 10, 2002, p. 383-402.

T. Mossakowski:

Heterogeneous development graphs and heterogeneous borrowing

Fossacs 2002, LNCS 2303, p. 326-341

T. Mossakowski: Foundations of heterogeneous specification

Submitted

T. Mossakowski:

Relating CASL with Other Specification Languages:

the Institution Level

Theoretical Computer Science 286, 2002, p. 367-475

Todo:

-}

module Grothendieck where

import Logic

import LogicRepr

import PrettyPrint

import Pretty

import PPUtils (fsep_latex, comma_latex)

data G_basic_spec = forall id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol .

Logic id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol =>

G_basic_spec id basic_spec

instance Show G_basic_spec where

show (G_basic_spec _ s) = show s

instance PrettyPrint G_basic_spec where

printText0 ga (G_basic_spec _ s) = printText0 ga s

printLatex0 ga (G_basic_spec _ s) = printLatex0 ga s

instance Eq G_basic_spec where

(G_basic_spec i1 s1) == (G_basic_spec i2 s2) =

coerce i1 i2 s1 == Just s2

data G_sentence = forall id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol .

Logic id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol =>

G_sentence id sentence

instance Show G_sentence where

show (G_sentence _ s) = show s

data G_l_sentence_list = forall id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol .

Logic id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol =>

G_l_sentence id [(String,sentence)]

data G_sign = forall id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol .

Logic id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol =>

G_sign id sign

instance Show G_sign where

show (G_sign _ s) = show s

data G_sign_list = forall id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol .

Logic id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol =>

G_sign_list id [sign]

data G_symbol = forall id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol .

Logic id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol =>

G_symbol id symbol

instance Show G_symbol where

show (G_symbol _ s) = show s

instance Eq G_symbol where

(G_symbol i1 s1) == (G_symbol i2 s2) =

coerce i1 i2 s1 == Just s2

data G_symb_items_list = forall id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol .

Logic id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol =>

G_symb_items_list id [symb_items]

instance Show G_symb_items_list where

show (G_symb_items_list _ l) = show l

instance PrettyPrint G_symb_items_list where

printText0 ga (G_symb_items_list _ l) =

fsep $ punctuate comma $ map (printText0 ga) l

printLatex0 ga (G_symb_items_list _ l) =

fsep_latex $ punctuate comma_latex $ map (printLatex0 ga) l

instance Eq G_symb_items_list where

(G_symb_items_list i1 s1) == (G_symb_items_list i2 s2) =

coerce i1 i2 s1 == Just s2

data G_symb_map_items_list = forall id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol .

Logic id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol =>

G_symb_map_items_list id [symb_map_items]

instance Show G_symb_map_items_list where

show (G_symb_map_items_list _ l) = show l

instance PrettyPrint G_symb_map_items_list where

printText0 ga (G_symb_map_items_list _ l) =

fsep $ punctuate comma $ map (printText0 ga) l

printLatex0 ga (G_symb_map_items_list _ l) =

fsep_latex $ punctuate comma_latex $ map (printLatex0 ga) l

instance Eq G_symb_map_items_list where

(G_symb_map_items_list i1 s1) == (G_symb_map_items_list i2 s2) =

coerce i1 i2 s1 == Just s2

data G_diagram = forall id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol .

Logic id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol =>

G_diagram id (Diagram sign morphism)

data G_sublogics = forall id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol .

Logic id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol =>

G_sublogics id sublogics

data G_morphism = forall id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol .

Logic id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol =>

G_morphism id morphism

g_ide (G_sign id sigma) = G_morphism id (ide id sigma)

-- Existential types for logics and representations

data AnyLogic = forall id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol .

Logic id sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol =>

Logic id

data AnyRepresentation = forall id1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1

id2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2 .

(Logic id1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1,

Logic id2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2) =>

Repr(LogicRepr id1 sublogics1 basic_spec1 sentence1

symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1

id2 sublogics2 basic_spec2 sentence2

symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2)

type LogicGraph = ([AnyLogic],[AnyRepresentation])

{- This does not work due to needed ordering:

instance Functor Set where

fmap = mapSet

instance Monad Set where

return = unitSet

m >>= k = unionManySets (setToList (fmap k m))

-}

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

-- The Grothendieck signature category

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

comp_repr :: AnyRepresentation -> AnyRepresentation -> Maybe AnyRepresentation

comp_repr (Repr (r1 :: {-Logic id1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1,

Logic id2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2) => -}

LogicRepr id1 sublogics1 basic_spec1 sentence1

symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1

id2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2))

(Repr (r2 :: {-Logic id3 sublogics3

basic_spec3 sentence3 symb_items3 symb_map_items3

sign3 morphism3 symbol3 raw_symbol3,

Logic id4 sublogics4

basic_spec4 sentence4 symb_items4 symb_map_items4

sign4 morphism4 symbol4 raw_symbol4) => -}

LogicRepr id3 sublogics3 basic_spec3 sentence3

symb_items3 symb_map_items3

sign3 morphism3 symbol3 raw_symbol3

id4 sublogics4 basic_spec4 sentence4 symb_items4 symb_map_items4

sign4 morphism4 symbol4 raw_symbol4)) =

case coerce (target r1) (source r2) r2 :: Maybe(

LogicRepr id2 sublogics2 basic_spec2 sentence2

symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2

id4 sublogics4 basic_spec4 sentence4 symb_items4 symb_map_items4

sign4 morphism4 symbol4 raw_symbol4)

of

Nothing -> Nothing

Just r3 -> case LogicRepr.comp_repr r1 r3 of

Nothing -> Nothing

Just r4 -> Just (Repr r4)

data GMorphism = forall id1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1

id2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2 .

(Logic id1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1,

Logic id2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2) =>

GMorphism id1 id2

(LogicRepr id1 sublogics1 basic_spec1 sentence1

symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1

id2 sublogics2 basic_spec2 sentence2

symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2)

morphism2