{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, DeriveDataTypeable

, FlexibleInstances, UndecidableInstances, OverlappingInstances

, ExistentialQuantification, GeneralizedNewtypeDeriving #-}

{- |

Module : ./Logic/Morphism.hs

Description : interface (type class) for logic projections (morphisms) in Hets

Copyright : (c) Till Mossakowski, Uni Bremen 2002-2004

License : GPLv2 or higher, see LICENSE.txt

Maintainer : till@informatik.uni-bremen.de

Stability : provisional

Portability : non-portable (via Logic)

Interface (type class) for logic projections (morphisms) in Hets

Provides data structures for institution morphisms.

These are just collections of

functions between (some of) the types of logics.

-}

{- References: see Logic.hs

Todo:

morphism modifications / representation maps

-}

module Logic.Morphism where

import Logic.Logic

import Logic.Comorphism

import Data.Data

import qualified Data.Set as Set

import ATerm.Lib

import Common.DocUtils

import Common.AS_Annotation

import Common.Id

import Common.Json

import Common.ToXml

class (Language cid,

Logic lid1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 sign_symbol1 symbol1 proof_tree1,

Logic lid2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 sign_symbol2 symbol2 proof_tree2) =>

Morphism cid

lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 sign_symbol1 symbol1 proof_tree1

lid2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 sign_symbol2 symbol2 proof_tree2

| cid -> lid1, cid -> lid2

, lid1 -> sublogics1 basic_spec1 sentence1 symb_items1

symb_map_items1 sign1 morphism1 sign_symbol1 symbol1 proof_tree1

, lid2 -> sublogics2 basic_spec2 sentence2 symb_items2

symb_map_items2 sign2 morphism2 sign_symbol2 symbol2 proof_tree2

where

{- source and target logic and sublogic

the source sublogic is the maximal one for which the comorphism works

the target sublogic is the resulting one -}

morSourceLogic :: cid -> lid1

morSourceSublogic :: cid -> sublogics1

morTargetLogic :: cid -> lid2

morTargetSublogic :: cid -> sublogics2

-- finer information of target sublogics corresponding to source sublogics

morMapSublogicSign :: cid -> sublogics1 -> sublogics2

-- information about the source sublogics corresponding to target sublogics

morMapSublogicSen :: cid -> sublogics2 -> sublogics1

{- the translation functions are partial

because the target may be a sublanguage

map_basic_spec :: cid -> basic_spec1 -> Maybe basic_spec2

we do not cover theoroidal morphisms,

since there are no relevant examples and they do not compose nicely

no mapping of theories, since signatures and sentences are mapped

contravariantly -}

morMap_sign :: cid -> sign1 -> Maybe sign2

morMap_morphism :: cid -> morphism1 -> Maybe morphism2

morMap_sentence :: cid -> sign1 -> sentence2 -> Maybe sentence1

{- also covers semi-morphisms ??

with no sentence translation

- but these are spans! -}

morMap_sign_symbol :: cid -> sign_symbol1 -> Set.Set sign_symbol2

-- morConstituents not needed, because composition only via lax triangles

-- | identity morphisms

data IdMorphism lid sublogics =

IdMorphism lid sublogics deriving (Typeable, Show)

instance Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism sign_symbol symbol proof_tree =>

Language (IdMorphism lid sublogics) where

language_name (IdMorphism lid sub) = "id_" ++ language_name lid

++ case sublogicName sub of

[] -> ""

h -> '.' : h

instance Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism sign_symbol symbol proof_tree =>

Morphism (IdMorphism lid sublogics)

lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism sign_symbol symbol proof_tree

lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism sign_symbol symbol proof_tree

where

morSourceLogic (IdMorphism lid _sub) = lid

morTargetLogic (IdMorphism lid _sub) = lid

morSourceSublogic (IdMorphism _lid sub) = sub

morTargetSublogic (IdMorphism _lid sub) = sub

-- changed to identities!

morMapSublogicSign _ x = x

morMapSublogicSen _ x = x

morMap_sign _ = Just

morMap_morphism _ = Just

morMap_sentence _ _ = Just

morMap_sign_symbol _ = Set.singleton

-- composition not needed, use lax triangles instead

-- | comorphisms inducing morphisms

class Comorphism cid

lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 sign_symbol1 symbol1 proof_tree1

lid2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 sign_symbol2 symbol2 proof_tree2 =>

InducingComorphism cid

lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 sign_symbol1 symbol1 proof_tree1

lid2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 sign_symbol2 symbol2 proof_tree2

where

indMorMap_sign :: cid -> sign2 -> Maybe sign1

indMorMap_morphism :: cid -> morphism2 -> Maybe morphism1

epsilon :: cid -> sign2 -> Maybe morphism2

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

-- Morphisms as spans of comorphisms

{- if the morphism is (psi, alpha, beta) : I -> J

it is replaced with the following span

SignI id -> SignI psi -> SignJ

SenI alpha <- psi;SenJ id -> psi;SenJ

ModI beta -> psi^op;ModJ id <- psi^op;ModJ -}

{- 1. introduce a new logic for the domain of the span

this logic will have

the name (SpanDomain cid) where cid is the name of the morphism

sublogics - pairs (s1, s2) with s1 being a sublogic of I and s2

being a sublogic of J; the lattice is the product lattice of the two

existing lattices

basic_spec will be () - the unit type, because we mix signatures

with sentences in specifications

sentence - sentences of J, wrapped

symb_items - ()

symb_map_items - ()

sign - signatures of I

morphism - morphisms of I

sign_symbol - sign_symbols of I

symbol - symbols of I

proof_tree - proof_tree of J -}

data SpanDomain cid = SpanDomain cid deriving (Eq, Show)

data SublogicsPair a b = SublogicsPair a b deriving (Eq, Ord, Show, Typeable)

instance Language cid => Language (SpanDomain cid) where

language_name (SpanDomain cid) = "SpanDomain" ++ language_name cid

{- the category of signatures is exactly the category of signatures of

the sublogic on which the morphism is defined, but with another name -}

instance (Morphism cid

lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 sign_symbol1 symbol1 proof_tree1

lid2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 sign_symbol2 symbol2 proof_tree2

, Pretty sign_symbol1)

=> Syntax (SpanDomain cid) () sign_symbol1 () ()

-- default is ok

newtype S2 s = S2 { sentence2 :: s }

deriving (Eq, Ord, Show, Typeable, Data, ShATermConvertible, Pretty

, GetRange, ToJson, ToXml)

instance (Morphism cid

lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 sign_symbol1 symbol1 proof_tree1

lid2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 sign_symbol2 symbol2 proof_tree2

, Category sign1 morphism1, Ord sign_symbol1, GetRange sign_symbol1)

=> Sentences (SpanDomain cid) (S2 sentence2) sign1 morphism1

sign_symbol1 where

{- one has to take care about signature and morphisms

and translate them to targetLogic

we get a Maybe sign/morphism -}

map_sen (SpanDomain cid) mor1 (S2 sen) =

case morMap_morphism cid mor1 of

Just mor2 -> fmap S2 $

map_sen (morTargetLogic cid) mor2 sen

Nothing -> statFail (SpanDomain cid) "map_sen"

simplify_sen (SpanDomain cid) sigma (S2 sen) =

case morMap_sign cid sigma of

Just sigma2 -> S2 $

simplify_sen (morTargetLogic cid) sigma2 sen

Nothing -> error "simplify_sen"

print_named (SpanDomain cid) = print_named (morTargetLogic cid)

. mapNamed sentence2

sym_of (SpanDomain cid) = sym_of (morSourceLogic cid)

symmap_of (SpanDomain cid) = symmap_of (morSourceLogic cid)

sym_name (SpanDomain cid) = sym_name (morSourceLogic cid)

instance (Morphism cid

lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 sign_symbol1 symbol1 proof_tree1

lid2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 sign_symbol2 symbol2 proof_tree2

, Ord symbol1, GetRange symbol1, Pretty symbol1, Typeable symbol1)

=> StaticAnalysis (SpanDomain cid) () (S2 sentence2) () ()

sign1 morphism1 sign_symbol1 symbol1 where

ensures_amalgamability l _ = statFail l "ensures_amalgamability"

symbol_to_raw (SpanDomain cid) = symbol_to_raw (morSourceLogic cid)

id_to_raw (SpanDomain cid) = id_to_raw (morSourceLogic cid)

matches (SpanDomain cid) = matches (morSourceLogic cid)

empty_signature (SpanDomain cid) = empty_signature (morSourceLogic cid)

signature_union (SpanDomain cid) = signature_union (morSourceLogic cid)

final_union (SpanDomain cid) = final_union (morSourceLogic cid)

morphism_union (SpanDomain cid) = morphism_union (morSourceLogic cid)

is_subsig (SpanDomain cid) = is_subsig (morSourceLogic cid)

subsig_inclusion (SpanDomain cid) = subsig_inclusion (morSourceLogic cid)

generated_sign (SpanDomain cid) = generated_sign (morSourceLogic cid)

cogenerated_sign (SpanDomain cid) = cogenerated_sign (morSourceLogic cid)

is_transportable (SpanDomain cid) = is_transportable (morSourceLogic cid)

is_injective (SpanDomain cid) = is_injective (morSourceLogic cid)

instance (SemiLatticeWithTop sublogics1, SemiLatticeWithTop sublogics2)

=> SemiLatticeWithTop (SublogicsPair sublogics1 sublogics2) where

top = SublogicsPair top top

lub (SublogicsPair x1 y1) (SublogicsPair x2 y2) =

SublogicsPair (lub x1 x2) (lub y1 y2)

instance (SemiLatticeWithTop sublogics1, MinSublogic sublogics2 sentence2)

=> MinSublogic (SublogicsPair sublogics1 sublogics2) (S2 sentence2) where

minSublogic (S2 sen2) = SublogicsPair top (minSublogic sen2)

{- just a dummy implementation, it should be the sublogic of sen2 in J

paired with its image through morMapSublogicSen? -}

instance (MinSublogic sublogics1 alpha, SemiLatticeWithTop sublogics2)

=> MinSublogic (SublogicsPair sublogics1 sublogics2) alpha where

minSublogic x = SublogicsPair (minSublogic x) top

{- also should have instances of MinSublogic class for Sublogics-pair

and morphism1, sign_symbol1, sign1 this is why the wrapping is needed -}

{- instance SemiLatticeWithTop sublogics => MinSublogic sublogics () where

minSublogic _ = top -}

instance (MinSublogic sublogics1 alpha, SemiLatticeWithTop sublogics2)

=> ProjectSublogic (SublogicsPair sublogics1 sublogics2) alpha where

projectSublogic _ x = x

-- it should be used for (), morphism1, sign_symbol1, sign1

instance (MinSublogic sublogics1 sign1, SemiLatticeWithTop sublogics2)

=> ProjectSublogicM (SublogicsPair sublogics1 sublogics2) sign1 where

projectSublogicM _ = Just

instance (ShATermConvertible a, ShATermConvertible b)

=> ShATermConvertible (SublogicsPair a b) where

toShATermAux att0 (SublogicsPair a b) = do

(att1, a') <- toShATerm' att0 a

(att2, b') <- toShATerm' att1 b

return $ addATerm (ShAAppl "SublogicsPair" [a', b'] []) att2

fromShATermAux ix att0 = case getShATerm ix att0 of

ShAAppl "SublogicsPair" [a, b] _ ->

case fromShATerm' a att0 of { (att1, a') ->

case fromShATerm' b att1 of { (att2, b') ->

(att2, SublogicsPair a' b') }}

u -> fromShATermError "SublogicsPair" u

instance (SublogicName sublogics1, SublogicName sublogics2)

=> SublogicName (SublogicsPair sublogics1 sublogics2) where

sublogicName (SublogicsPair sub1 sub2) =

let s1 = sublogicName sub1

s2 = sublogicName sub2

in if null s1 then s2 else if null s2 then s1 else

s1 ++ "|" ++ s2

instance ( MinSublogic sublogics1 ()

, Morphism cid

lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 sign_symbol1 symbol1 proof_tree1

lid2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 sign_symbol2 symbol2 proof_tree2

, Ord proof_tree2, Show proof_tree2)

=> Logic (SpanDomain cid) (SublogicsPair sublogics1 sublogics2) ()

(S2 sentence2) () () sign1 morphism1 sign_symbol1 symbol1 proof_tree2

where

stability (SpanDomain _) = Experimental

data_logic (SpanDomain _) = Nothing

top_sublogic (SpanDomain cid) = SublogicsPair

(top_sublogic $ morSourceLogic cid) $ top_sublogic $ morTargetLogic cid

all_sublogics (SpanDomain cid) =

[ SublogicsPair x y

| x <- all_sublogics (morSourceLogic cid)

, y <- all_sublogics (morTargetLogic cid) ]

-- project_sublogic_epsilon - default implementation for now

provers _ = []

cons_checkers _ = []

conservativityCheck _ = []

empty_proof_tree (SpanDomain cid) = empty_proof_tree (morTargetLogic cid)

-- * Morphisms

-- | Existential type for morphisms

data AnyMorphism = forall cid lid1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1 proof_tree1

lid2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2 proof_tree2 .

Morphism cid

lid1 sublogics1 basic_spec1 sentence1

symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1 proof_tree1

lid2 sublogics2 basic_spec2 sentence2

symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2 proof_tree2 =>

Morphism cid

{-

instance Eq AnyMorphism where

Morphism cid1 == Morphism cid2 =

constituents cid1 == constituents cid2

-- need to be refined, using morphism translations !!!

-}

instance Show AnyMorphism where

show (Morphism cid) = language_name cid

++ " : " ++ language_name (morSourceLogic cid)

++ " -> " ++ language_name (morTargetLogic cid)