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

{- |

Module : $Header$

Copyright : (c) Till Mossakowski, and Uni Bremen 2002-2006

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

Maintainer : till@tzi.de

Stability : provisional

Portability : non-portable (various -fglasgow-exts extensions)

Provides data structures for logics (with symbols). Logics are

a type class with an /identity/ type (usually interpreted

by a singleton set) which serves to treat logics as

data. All the functions in the type class take the

identity as first argument in order to determine the logic.

For logic (co)morphisms see "Logic.Comorphism"

This module uses multiparameter type classes

(<http://haskell.org/ghc/docs/latest/html/users_guide/type-extensions.html#multi-param-type-classes>)

with functional dependencies (<http://haskell.org/hawiki/FunDeps>)

for defining an interface for the notion of logic. Multiparameter type

classes are needed because a logic consists of a collection of types,

together with operations on these. Functional dependencies

are needed because no operation will involve all types of

the multiparameter type class; hence we need a method to derive

the missing types. We chose an easy way: for each logic, we

introduce a new singleton type that constitutes the identity

of the logic. All other types of the multiparameter type class

depend on this 'identy constituting' type, and all operations take

the 'identity constituting' type as first arguments. The value

of the argument of the 'identity constituting' type is irrelevant

(note that there is only one value of such a type anyway).

References:

J. A. Goguen and R. M. Burstall

Institutions: Abstract Model Theory for Specification and

Programming

JACM 39, p. 95--146, 1992

(general notion of logic - model theory only)

J. Meseguer

General Logics

Logic Colloquium 87, p. 275--329, North Holland, 1989

(general notion of logic - also proof theory;

notion of logic representation, called map there)

T. Mossakowski:

Specification in an arbitrary institution with symbols

14th WADT 1999, LNCS 1827, p. 252--270

(treatment of symbols and raw symbols, see also CASL semantics)

T. Mossakowski, B. Klin:

Institution Independent Static Analysis for CASL

15h WADT 2001, LNCS 2267, p. 221-237, 2002.

(what is needed for static anaylsis)

S. Autexier and T. Mossakowski

Integrating HOLCASL into the Development Graph Manager MAYA

FroCoS 2002, to appear

(interface to provers)

Todo:

ATerm, XML

Weak amalgamability

Metavars

raw symbols are now symbols, symbols are now signature symbols

provide both signature symbol set and symbol set of a signature

introduce coercion safer functions (separately for each type)

-}

module Logic.Logic where

import Common.Id

import Common.GlobalAnnotations

import qualified Common.Lib.Set as Set

import qualified Common.Lib.Map as Map

import Common.Lib.Graph as Tree

import Common.AnnoState

import Common.Result

import Common.AS_Annotation

import Common.Doc

import Common.DocUtils

import Logic.Prover -- for one half of class Sentences

import Common.DynamicUtils

import Common.ATerm.Lib -- (ShATermConvertible)

import ATC.DefaultMorphism()

import Common.Amalgamate -- passed to ensures_amalgamability

import Common.Taxonomy

import Taxonomy.MMiSSOntology (MMiSSOntology)

-- | Stability of logic implementations

data Stability = Stable | Testing | Unstable | Experimental

deriving (Eq, Show)

-- | shortcut for class constraints

class (Show a, Pretty a, Typeable a, ShATermConvertible a)

=> PrintTypeConv a

-- | shortcut for class constraints with equality

class (Eq a, PrintTypeConv a) => EqPrintTypeConv a

instance (Show a, Pretty a, Typeable a,

ShATermConvertible a) => PrintTypeConv a

instance (Eq a, PrintTypeConv a) => EqPrintTypeConv a

type EndoMap a = Map.Map a a

-- languages, define like "data CASL = CASL deriving Show"

class Show lid => Language lid where

language_name :: lid -> String

language_name i = show i

description :: lid -> String

-- default implementation

description _ = "No description available"

-- Categories are given by a quotient,

-- i.e. we need equality

-- Should we allow arbitrary composition graphs and build paths?

class (Language lid, Eq sign, Eq morphism)

=> Category lid sign morphism | lid -> sign morphism where

ide :: lid -> sign -> morphism

comp :: lid -> morphism -> morphism -> Result morphism

-- diagrammatic order

dom, cod :: lid -> morphism -> sign

legal_obj :: lid -> sign -> Bool

legal_mor :: lid -> morphism -> Bool

-- abstract syntax, parsing and printing

class (Language lid, PrintTypeConv basic_spec,

EqPrintTypeConv symb_items,

EqPrintTypeConv symb_map_items)

=> Syntax lid basic_spec symb_items symb_map_items

| lid -> basic_spec symb_items symb_map_items

where

-- parsing

parse_basic_spec :: lid -> Maybe(AParser st basic_spec)

parse_symb_items :: lid -> Maybe(AParser st symb_items)

parse_symb_map_items :: lid -> Maybe(AParser st symb_map_items)

-- default implementations

parse_basic_spec _ = Nothing

parse_symb_items _ = Nothing

parse_symb_map_items _ = Nothing

-- sentences (plus prover stuff and "symbol" with "Ord" for efficient lookup)

class (Category lid sign morphism, Ord sentence,

Ord symbol,

PrintTypeConv sign, PrintTypeConv morphism,

PrintTypeConv sentence, PrintTypeConv symbol,

Eq proof_tree, Show proof_tree, ShATermConvertible proof_tree,

Ord proof_tree, Typeable proof_tree)

=> Sentences lid sentence proof_tree sign morphism symbol

| lid -> sentence proof_tree sign morphism symbol

where

-- sentence translation

map_sen :: lid -> morphism -> sentence -> Result sentence

map_sen l _ _ = statErr l "map_sen"

-- simplification of sentences (leave out qualifications)

simplify_sen :: lid -> sign -> sentence -> sentence

simplify_sen _ _ = id -- default implementation

-- parsing of sentences

parse_sentence :: lid -> Maybe (AParser st sentence)

parse_sentence _ = Nothing

-- print a sentence with comments

print_named :: lid -> Named sentence -> Doc

print_named _ = printAnnoted (addBullet . pretty) . fromLabelledSen

sym_of :: lid -> sign -> Set.Set symbol

symmap_of :: lid -> morphism -> EndoMap symbol

sym_name :: lid -> symbol -> Id

provers :: lid -> [Prover sign sentence proof_tree]

provers _ = []

cons_checkers :: lid -> [ConsChecker sign sentence morphism proof_tree]

cons_checkers _ = []

conservativityCheck :: lid -> (sign, [Named sentence]) ->

morphism -> [Named sentence] -> Result (Maybe Bool)

conservativityCheck l _ _ _ = statErr l "conservativityCheck"

-- | a dummy function to allow type checking *.inline.hs files

inlineAxioms :: StaticAnalysis lid

basic_spec sentence proof_tree symb_items symb_map_items

sign morphism symbol raw_symbol => lid -> String -> [Named sentence]

inlineAxioms _ _ = error "inlineAxioms"

-- static analysis

statErr :: (Language lid, Monad m) => lid -> String -> m a

statErr lid str = fail ("Logic." ++ str ++ " nyi for: " ++ language_name lid)

class ( Syntax lid basic_spec symb_items symb_map_items

, Sentences lid sentence proof_tree sign morphism symbol

, Ord raw_symbol, Pretty raw_symbol, Typeable raw_symbol)

=> StaticAnalysis lid

basic_spec sentence proof_tree symb_items symb_map_items

sign morphism symbol raw_symbol

| lid -> basic_spec sentence proof_tree symb_items symb_map_items

sign morphism symbol raw_symbol

where

-- static analysis of basic specifications and symbol maps

basic_analysis :: lid ->

Maybe((basic_spec, -- abstract syntax tree

sign, -- efficient table for env signature

GlobalAnnos) -> -- global annotations

Result (basic_spec,sign,sign,[Named sentence]))

-- the resulting bspec has analyzed axioms in it

-- sign's: sigma_local, sigma_complete, i.e.

-- the second output sign united with the input sign

-- should yield the first output sign

-- the second output sign is the accumulated sign

-- default implementation

basic_analysis _ = Nothing

-- Shouldn't the following deliver Maybes???

sign_to_basic_spec :: lid -> sign -> [Named sentence] -> basic_spec

stat_symb_map_items ::

lid -> [symb_map_items] -> Result (EndoMap raw_symbol)

stat_symb_map_items _ _ = fail "Logic.stat_symb_map_items"

stat_symb_items :: lid -> [symb_items] -> Result [raw_symbol]

stat_symb_items l _ = statErr l "stat_symb_items"

-- amalgamation

weaklyAmalgamableCocone :: lid -> Tree.Gr sign morphism

-> Result (sign, Map.Map Int morphism)

weaklyAmalgamableCocone l _ = statErr l "weaklyAmalgamableCocone"

-- architectural sharing analysis

ensures_amalgamability :: lid ->

([CASLAmalgOpt], -- the program options

Tree.Gr sign morphism, -- the diagram to be analyzed

[(Int, morphism)], -- the sink

Tree.Gr String String) -- the descriptions of nodes and edges

-> Result Amalgamates

ensures_amalgamability l _ = statErr l "ensures_amalgamability"

-- symbols and symbol maps

symbol_to_raw :: lid -> symbol -> raw_symbol

id_to_raw :: lid -> Id -> raw_symbol

matches :: lid -> symbol -> raw_symbol -> Bool

-- operations on signatures and morphisms

empty_signature :: lid -> sign

signature_union :: lid -> sign -> sign -> Result sign

signature_union l _ _ = statErr l "signature_union"

morphism_union :: lid -> morphism -> morphism -> Result morphism

morphism_union l _ _ = statErr l "morphism_union"

final_union :: lid -> sign -> sign -> Result sign

final_union l _ _ = statErr l "final_union"

is_transportable :: lid -> morphism -> Bool

is_transportable l _ =

error ("Logic.is_transportable nyi for logic"++language_name l)

-- see CASL reference manual, III.4.1.2

is_subsig :: lid -> sign -> sign -> Bool

inclusion :: lid -> sign -> sign -> Result morphism

inclusion l _ _ = statErr l "inclusion"

generated_sign, cogenerated_sign ::

lid -> Set.Set symbol -> sign -> Result morphism

generated_sign l _ _ = statErr l "generated_sign"

cogenerated_sign l _ _ = statErr l "cogenerated_sign"

induced_from_morphism ::

lid -> EndoMap raw_symbol -> sign -> Result morphism

induced_from_morphism l _ _ = statErr l "induced_from_morphism"

induced_from_to_morphism ::

lid -> EndoMap raw_symbol -> sign -> sign -> Result morphism

induced_from_to_morphism l _ _ _ =

statErr l "induced_from_to_morphism"

-- generate taxonomy from theory

theory_to_taxonomy :: lid

-> TaxoGraphKind

-> MMiSSOntology

-> sign -> [Named sentence]

-> Result MMiSSOntology

theory_to_taxonomy l _ _ _ _ = statErr l "theory_to_taxonomy"

-- sublogics

class (Eq l, Show l) => SemiLatticeWithTop l where

join :: l -> l -> l

top :: l

instance SemiLatticeWithTop () where

join _ _ = ()

top = ()

isSubElem :: SemiLatticeWithTop l => l -> l -> Bool

isSubElem a b = join a b == b

class MinSublogic sublogic item where

minSublogic :: item -> sublogic

-- a default instance for no sublogics

instance MinSublogic () a where

minSublogic _ = ()

{-

instance SemiLatticeWithTop s => MinSublogic s a where

minSublogic _ = top

-}

class MinSublogic sublogic item => ProjectSublogic sublogic item where

projectSublogic :: sublogic -> item -> item

-- a default instance for no sublogics

instance ProjectSublogic () b where

projectSublogic _ = id

{-

instance MinSublogic a b => ProjectSublogic a b where

projectSublogic _ = id

-}

class MinSublogic sublogic item => ProjectSublogicM sublogic item where

projectSublogicM :: sublogic -> item -> Maybe item

-- a default instance for no sublogics

instance ProjectSublogicM () b where

projectSublogicM _ = Just

{-

instance (SemiLatticeWithTop a, MinSublogic a b) => ProjectSublogicM a b where

projectSublogicM l i = if isSubElem (minSublogic i) l

then Just i else Nothing

-}

class Sublogics l where

sublogic_names :: l -> [String]

instance Sublogics () where

sublogic_names () = [""]

-- logics

class (StaticAnalysis lid

basic_spec sentence proof_tree symb_items symb_map_items

sign morphism symbol raw_symbol,

SemiLatticeWithTop sublogics,

MinSublogic sublogics sentence,

ProjectSublogic sublogics basic_spec,

ProjectSublogicM sublogics symb_items,

ProjectSublogicM sublogics symb_map_items,

ProjectSublogic sublogics sign,

ProjectSublogic sublogics morphism,

ProjectSublogicM sublogics symbol,

Typeable sublogics,

ShATermConvertible sublogics,

Sublogics sublogics)

=> Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree

| lid -> sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree

where

-- stability of the implementation

stability :: lid -> Stability

-- default

stability _ = Experimental

-- for a process logic, return its data logic

data_logic :: lid -> Maybe AnyLogic

data_logic _ = Nothing

top_sublogic :: lid -> sublogics

top_sublogic _ = top

all_sublogics :: lid -> [sublogics]

all_sublogics li = [top_sublogic li]

proj_sublogic_epsilon :: lid -> sublogics -> sign -> morphism

proj_sublogic_epsilon li _ s = ide li s

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

-- Derived functions

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

empty_theory :: StaticAnalysis lid

basic_spec sentence proof_tree symb_items symb_map_items

sign morphism symbol raw_symbol =>

lid -> Theory sign sentence proof_tree

empty_theory lid = Theory (empty_signature lid) Map.empty

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

-- Existential type covering any logic

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

data AnyLogic = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

Logic lid

instance Show AnyLogic where

show (Logic lid) = language_name lid

instance Eq AnyLogic where

Logic lid1 == Logic lid2 = language_name lid1 == language_name lid2

tyconAnyLogic :: TyCon

tyconAnyLogic = mkTyCon "Logic.Logic.AnyLogic"

instance Typeable AnyLogic where

typeOf _ = mkTyConApp tyconAnyLogic []

{- class hierarchy:

Language

__________/

Category

| /

Sentences Syntax

\ /

StaticAnalysis (no sublogics)

\

\

Logic

-}