b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu{-# OPTIONS -fallow-undecidable-instances #-}

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu{- |

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert SavuModule : $Header$

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert SavuDescription : central interface (type class) for logics in Hets

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert SavuCopyright : (c) Till Mossakowski, and Uni Bremen 2002-2006

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert SavuLicense : similar to LGPL, see HetCATS/LICENSE.txt or LIZENZ.txt

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert SavuMaintainer : till@informatik.uni-bremen.de

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert SavuStability : provisional

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert SavuPortability : non-portable (various -fglasgow-exts extensions)

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert SavuCentral interface (type class) for logics in Hets

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert SavuProvides data structures for logics (with symbols). Logics are

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu a type class with an /identity type/ (usually interpreted

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu by a singleton set) which serves to treat logics as

239330cd665aac95fcf9cf95449594c96667cbc2Robert Savu data. All the functions in the type class take the

69b1e90bbb27ce2dd365628c07c0f03a3ae97b26Robert Savu identity as first argument in order to determine the logic.

ad2e68e571352b6759441733df697e075ceed341Robert Savu

0a03acf9fa28e6ff00f4d7c9c6acbae64cf09c56Ewaryst Schulz For logic (co)morphisms see "Logic.Comorphism"

0a03acf9fa28e6ff00f4d7c9c6acbae64cf09c56Ewaryst Schulz

239330cd665aac95fcf9cf95449594c96667cbc2Robert Savu This module uses multiparameter type classes with functional dependencies

239330cd665aac95fcf9cf95449594c96667cbc2Robert Savu (<http://www.haskell.org/haskellwiki/Functional_dependencies>)

37dd4c99dbe470cce3fe0d89a011186f080e8910Robert Savu for defining an interface for the notion of logic. Multiparameter type

37dd4c99dbe470cce3fe0d89a011186f080e8910Robert Savu classes are needed because a logic consists of a collection of types,

37dd4c99dbe470cce3fe0d89a011186f080e8910Robert Savu together with operations on these. Functional dependencies

37dd4c99dbe470cce3fe0d89a011186f080e8910Robert Savu are needed because no operation will involve all types of

0a03acf9fa28e6ff00f4d7c9c6acbae64cf09c56Ewaryst Schulz the multiparameter type class; hence we need a method to derive

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu the missing types. We chose an easy way: for each logic, we

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu introduce a new singleton type that is the name, or constitutes the identity

0a03acf9fa28e6ff00f4d7c9c6acbae64cf09c56Ewaryst Schulz of the logic. All other types of the multiparameter type class

ad306df140215d8fb88d14bbb7d685011e0f770bRobert Savu depend on this /identity constituting/ type, and all operations take

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu the 'identity constituting' type as first arguments. The value

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu of the argument of the /identity constituting/ type is irrelevant

0a03acf9fa28e6ff00f4d7c9c6acbae64cf09c56Ewaryst Schulz (note that there is only one value of such a type anyway).

ad2e68e571352b6759441733df697e075ceed341Robert Savu

ad2e68e571352b6759441733df697e075ceed341Robert Savu Note that we tend to use @lid@ both for the /identity type/

239330cd665aac95fcf9cf95449594c96667cbc2Robert Savu of a logic, as well as for its unique inhabitant, i.e. @lid :: lid@.

ad2e68e571352b6759441733df697e075ceed341Robert Savu

ad2e68e571352b6759441733df697e075ceed341Robert Savu The other types involved in the definition of logic are as follows:

ad2e68e571352b6759441733df697e075ceed341Robert Savu

ad2e68e571352b6759441733df697e075ceed341Robert Savu * sign: signatures, that is, contexts, or non-logical vocabularies,

ad2e68e571352b6759441733df697e075ceed341Robert Savu typically consisting of a set of declared sorts, predicates,

ad2e68e571352b6759441733df697e075ceed341Robert Savu function symbols, propositional letters etc., together with their

239330cd665aac95fcf9cf95449594c96667cbc2Robert Savu typing.

239330cd665aac95fcf9cf95449594c96667cbc2Robert Savu

239330cd665aac95fcf9cf95449594c96667cbc2Robert Savu * sentence: logical formulas.

239330cd665aac95fcf9cf95449594c96667cbc2Robert Savu

ad2e68e571352b6759441733df697e075ceed341Robert Savu * basic_spec: abstract syntax of basic specifications. The latter are

ad2e68e571352b6759441733df697e075ceed341Robert Savu human-readable presentations of a signature together with some sentences.

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu * symbol: symbols that may occur in a signature, fully qualified

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu with their types

ad306df140215d8fb88d14bbb7d685011e0f770bRobert Savu

ad306df140215d8fb88d14bbb7d685011e0f770bRobert Savu * raw_symbol: symbols that may occur in a signature, possibly not

ad2e68e571352b6759441733df697e075ceed341Robert Savu or partially qualified

ad2e68e571352b6759441733df697e075ceed341Robert Savu

0a03acf9fa28e6ff00f4d7c9c6acbae64cf09c56Ewaryst Schulz * morphism: maps between signatures (typically preserving the structure).

ad2e68e571352b6759441733df697e075ceed341Robert Savu

ad2e68e571352b6759441733df697e075ceed341Robert Savu * symb_items: abstract syntax of symbol lists, used for declaring some

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu symbols of a signature as hidden.

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu

ad306df140215d8fb88d14bbb7d685011e0f770bRobert Savu * symb_map_items: abstract syntax of symbol maps, i.e. human-readable

ad306df140215d8fb88d14bbb7d685011e0f770bRobert Savu presentations of signature morphisms.

239330cd665aac95fcf9cf95449594c96667cbc2Robert Savu

ec95eebae395ed8858ba5b51d992d6b4c50cec86Robert Savu * sublogics: sublogics of the given logic. This type might be a

ec95eebae395ed8858ba5b51d992d6b4c50cec86Robert Savu record of Boolean flags, indicating whether some feature is

ec95eebae395ed8858ba5b51d992d6b4c50cec86Robert Savu present in the sublogi of not.

ec95eebae395ed8858ba5b51d992d6b4c50cec86Robert Savu

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu * proof_tree: proof trees.

239330cd665aac95fcf9cf95449594c96667cbc2Robert Savu

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu References:

239330cd665aac95fcf9cf95449594c96667cbc2Robert Savu

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu J. A. Goguen and R. M. Burstall

ec95eebae395ed8858ba5b51d992d6b4c50cec86Robert Savu Institutions: Abstract Model Theory for Specification and

ad2e68e571352b6759441733df697e075ceed341Robert Savu Programming

0a03acf9fa28e6ff00f4d7c9c6acbae64cf09c56Ewaryst Schulz JACM 39, p. 95-146, 1992

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu (general notion of logic - model theory only)

239330cd665aac95fcf9cf95449594c96667cbc2Robert Savu

239330cd665aac95fcf9cf95449594c96667cbc2Robert Savu J. Meseguer

ad2e68e571352b6759441733df697e075ceed341Robert Savu General Logics

ad2e68e571352b6759441733df697e075ceed341Robert Savu Logic Colloquium 87, p. 275-329, North Holland, 1989

e09066e7b76cea97557974b825bb057455b24ab0Robert Savu (general notion of logic - also proof theory;

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu notion of logic representation, called map there)

0a03acf9fa28e6ff00f4d7c9c6acbae64cf09c56Ewaryst Schulz

ad2e68e571352b6759441733df697e075ceed341Robert Savu T. Mossakowski:

b3df7e69d4d6066fdfae0a8a2f3b4a161eaaf540Robert Savu Specification in an arbitrary institution with symbols

ad306df140215d8fb88d14bbb7d685011e0f770bRobert Savu 14th WADT 1999, LNCS 1827, p. 252-270

ad306df140215d8fb88d14bbb7d685011e0f770bRobert Savu (treatment of symbols and raw symbols, see also CASL semantics

ad2e68e571352b6759441733df697e075ceed341Robert Savu in the CASL reference manual)

ad2e68e571352b6759441733df697e075ceed341Robert Savu

ad2e68e571352b6759441733df697e075ceed341Robert Savu T. Mossakowski, B. Klin:

ad2e68e571352b6759441733df697e075ceed341Robert Savu Institution Independent Static Analysis for CASL

a9c461443a740732a62d58c1c465b88cba3c606bRobert Savu 15h WADT 2001, LNCS 2267, p. 221-237, 2002.

0a03acf9fa28e6ff00f4d7c9c6acbae64cf09c56Ewaryst Schulz (what is needed for static anaylsis)

0a03acf9fa28e6ff00f4d7c9c6acbae64cf09c56Ewaryst Schulz

0a03acf9fa28e6ff00f4d7c9c6acbae64cf09c56Ewaryst Schulz S. Autexier and T. Mossakowski

239330cd665aac95fcf9cf95449594c96667cbc2Robert Savu Integrating HOLCASL into the Development Graph Manager MAYA

FroCoS 2002, LNCS 2309, p. 2-17, 2002.

(interface to provers)

CoFI (ed.): CASL Reference Manual, LNCS 2960, Springer Verlag, 2004.

(static semantics of CASL structured and architectural specifications)

T. Mossakowski

Heterogeneous specification and the heterogeneous tool set

Habilitation thesis, University of Bremen, 2005

(the general picture of heterogeneous specification)

-}

module Logic.Logic where

import Logic.Prover (Prover, ConsChecker, Theory(..))

import Taxonomy.MMiSSOntology (MMiSSOntology)

import ATC.DefaultMorphism ()

import Common.AS_Annotation

import Common.ATerm.Lib (ShATermConvertible)

import Common.Amalgamate

import Common.AnnoState

import Common.Consistency

import Common.DefaultMorphism

import Common.Doc

import Common.DocUtils

import Common.ExtSign

import Common.GlobalAnnotations

import Common.Id

import Common.Lib.Graph

import Common.LibName

import Common.Result

import Common.Taxonomy

import qualified Data.Set as Set

import qualified Data.Map as Map

import Data.Typeable

-- | 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

-- | maps from a to a

type EndoMap a = Map.Map a a

{- | the name of a logic.

Define instances 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 as usual: objects, morphisms, identities,

domain, codomain and composition. The type id is the name, or

the identity of the category. It is an argument to all functions

of the type class, serving disambiguation among instances

(via the functional dependency lid -> object morphism).

The types for objects and morphisms may be restricted to

subtypes, using legal_obj and legal_mor. For example, for the

category of sets and injective maps, legal_mor would check

injectivity. Since Eq is a subclass of Category, it is also

possible to impose a quotient on the types for objects and morphisms.

-}

class (Eq object, Eq morphism)

=> Category object morphism | morphism -> object where

-- | identity morphisms

ide :: object -> morphism

-- | composition, in diagrammatic order

comp :: morphism -> morphism -> Result morphism

-- | domain and codomain of morphisms

dom, cod :: morphism -> object

-- | the inverse of a morphism

inverse :: morphism -> Result morphism

inverse _ = fail "Logic.Logic.Category.inverse not implemented"

-- | test if the signature morphism an inclusion

isInclusion :: morphism -> Bool

isInclusion _ = False -- in general no inclusion

-- | is a value of type morphism denoting a legal morphism?

legal_mor :: morphism -> Bool

instance Eq sign => Category sign (DefaultMorphism sign) where

dom = domOfDefaultMorphism

cod = codOfDefaultMorphism

ide = ideOfDefaultMorphism

isInclusion = isInclusionDefaultMorphism

comp = compOfDefaultMorphism

legal_mor = legalDefaultMorphism (const True)

{- | Abstract syntax, parsing and printing.

There are three types for abstract syntax:

basic_spec is for basic specifications (see CASL RefMan p. 5ff.),

symb_items is for symbol lists (see CASL RefMan p. 35ff.),

symb_map_items is for symbol maps (see CASL RefMan p. 35ff.).

-}

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

-- | parser for basic specifications

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

-- | parser for symbol lists

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

-- | parser for symbol maps

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, provers and symbols.

Provers capture the entailment relation between sets of sentences

and sentences. They may return proof trees witnessing proofs.

Signatures are equipped with underlying sets of symbols

(such that the category of signatures becomes a concrete category),

see CASL RefMan p. 191ff.

-}

class (Language lid, Category sign morphism, Ord sentence,

Ord symbol, -- for efficient lookup

PrintTypeConv sign, PrintTypeConv morphism,

PrintTypeConv sentence, PrintTypeConv symbol)

=> Sentences lid sentence sign morphism symbol

| lid -> sentence sign morphism symbol

where

----------------------- sentences ---------------------------

-- | check whether a sentence belongs to a signature

is_of_sign :: lid -> sentence -> signature -> Bool

is_of_sign l _ _ = error $ statErrMsg l "is_of_sign"

-- | sentence translation along a signature morphism

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_sign :: lid -> sign -> Doc

print_sign _ = pretty

-- | print a sentence with comments

print_named :: lid -> Named sentence -> Doc

print_named _ = printAnnoted (addBullet . pretty) . fromLabelledSen

----------------------- symbols ---------------------------

-- | set of symbols for a signature

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

sym_of _ _ = Set.empty

-- | symbol map for a signature morphism

symmap_of :: lid -> morphism -> EndoMap symbol

symmap_of _ _ = Map.empty

-- | symbols have a name, see CASL RefMan p. 192

sym_name :: lid -> symbol -> Id

sym_name l _ = error $ statErrMsg l "sym_name"

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

inlineAxioms :: StaticAnalysis lid

basic_spec sentence symb_items symb_map_items

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

inlineAxioms _ _ = error "inlineAxioms"

-- | fail function for static analysis

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

statErr lid = fail . statErrMsg lid

-- | error message for static analysis

statErrMsg :: (Language lid) => lid -> String -> String

statErrMsg lid str = "Logic." ++ str ++ " nyi for: " ++ language_name lid

{- static analysis

This type class provides the data needed for an institution with symbols,

as explained in the structured specification semantics in the CASL

reference manual, chapter III.4.

The static analysis computes signatures from basic specifications,

and signature morphisms from symbol lists and symbol maps. The latter

needs an intermediate stage, so-called raw symbols, which are possibly

unqualified symbols. Normal symbols are always fully qualified.

In the CASL reference manual, our symbols are called "signature symbols",

and our raw symbols are called "symbols". (Terminology should be adapted.)

-}

class ( Syntax lid basic_spec symb_items symb_map_items

, Sentences lid sentence sign morphism symbol

, Ord raw_symbol, Pretty raw_symbol, Typeable raw_symbol)

=> StaticAnalysis lid

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol

| lid -> basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol

where

----------------------- static analysis ---------------------------

{- | static analysis of basic specifications and symbol maps.

The resulting bspec has analyzed axioms in it.

The resulting sign is an extension of the input sign

plus newly declared or redeclared symbols.

See CASL RefMan p. 138 ff. -}

basic_analysis :: lid ->

Maybe((basic_spec, -- abstract syntax tree

sign, -- input signature, for the local

-- environment, carrying the previously

-- declared symbols

GlobalAnnos) -> -- global annotations

Result (basic_spec, ExtSign sign symbol

, [Named sentence]))

-- default implementation

basic_analysis _ = Nothing

-- | static analysis of symbol maps, see CASL RefMan p. 222f.

stat_symb_map_items ::

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

stat_symb_map_items l _ = statErr l "stat_symb_map_items"

-- | static analysis of symbol lists, see CASL RefMan p. 221f.

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

stat_symb_items l _ = statErr l "stat_symb_items"

------------------------- amalgamation ---------------------------

{- | Computation of colimits of signature diagram.

Indeed, it suffices to compute a coconce that is weakly amalgamable

see Till Mossakowski,

Heterogeneous specification and the heterogeneous tool set

p. 25ff. -}

-- | architectural sharing analysis, see CASL RefMan p. 247ff.

ensures_amalgamability :: lid ->

([CASLAmalgOpt], -- the program options

Gr sign (Int,morphism), -- the diagram to be analyzed

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

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

-> Result Amalgamates

ensures_amalgamability l _ = warning Amalgamates

("amalgamability test not implemented for logic " ++ show l)

nullRange

-- | signature colimits

signature_colimit :: lid -> Gr sign (Int, morphism)

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

signature_colimit l _ = statErr l "signature_colimit"

{- | rename and qualify the symbols considering incoming morphisms,

code out overloading and

create sentences for the overloading relation -}

qualify :: lid -> SIMPLE_ID -> LIB_ID -> [morphism] -> sign

-> Result (morphism, [Named sentence])

qualify l _ _ _ = statErr l "qualify"

-------------------- symbols and raw symbols ---------------------

{- | Construe a symbol, like f:->t, as a raw symbol.

This is a one-sided inverse to the function SymSySigSym

in the CASL RefMan p. 192. -}

symbol_to_raw :: lid -> symbol -> raw_symbol

symbol_to_raw l _ = error $ statErrMsg l "symbol_to_raw"

{- | Construe an identifier, like f, as a raw symbol.

See CASL RefMan p. 192, function IDAsSym -}

id_to_raw :: lid -> Id -> raw_symbol

id_to_raw l _ = error $ statErrMsg l "id_to_raw"

{- | Check wether a symbol matches a raw symbol, for

example, f:s->t matches f. See CASL RefMan p. 192 -}

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

matches l _ _ = error $ statErrMsg l "matches"

--------------- operations on signatures and morphisms -----------

-- | the empty (initial) signature, see CASL RefMan p. 193

empty_signature :: lid -> sign

-- | union of signatures, see CASL RefMan p. 193

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

signature_union l _ _ = statErr l "signature_union"

-- | intersection of signatures

intersection :: lid -> sign -> sign -> Result sign

intersection l _ _ = statErr l "intersection"

-- | final union of signatures, see CASL RefMan p. 194

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

final_union l _ _ = statErr l "final_union"

-- | union of signature morphims, see CASL RefMan p. 196

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

morphism_union l _ _ = statErr l "morphism_union"

{- | construct the inclusion morphisms between subsignatures,

see CASL RefMan p. 194 -}

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

inclusion l _ _ = statErr l "inclusion"

{- | the signature (co)generated by a set of symbols in another

signature is the smallest (largest) signature containing

(excluding) the set of symbols. Needed for revealing and

hiding, see CASL RefMan p. 197ff. -}

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"

{- | Induce a signature morphism from a source signature and

a raw symbol map. Needed for translation (SP with SM).

See CASL RefMan p. 198 -}

induced_from_morphism ::

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

induced_from_morphism l _ _ = statErr l "induced_from_morphism"

{- | Induce a signature morphism between two signatures by a

raw symbol map. Needed for instantiation and views.

See CASL RefMan p. 198f. -}

induced_from_to_morphism ::

lid -> EndoMap raw_symbol -> ExtSign sign symbol

-> ExtSign sign symbol -> Result morphism

induced_from_to_morphism l _ _ _ =

statErr l "induced_from_to_morphism"

{- | Check whether a signature morphism is transportable.

See CASL RefMan p. 304f. -}

is_transportable :: lid -> morphism -> Bool

is_transportable _ _ = False -- safe default

{- | Check whether the underlying symbol map of a signature morphism

is injective -}

is_injective :: lid -> morphism -> Bool

is_injective _ _ = False -- safe default

------------------- generate taxonomy from theory ----------------

-- | generate an ontological taxonomy, if this makes sense

theory_to_taxonomy :: lid

-> TaxoGraphKind

-> MMiSSOntology

-> sign -> [Named sentence]

-> Result MMiSSOntology

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

-- | subsignatures, see CASL RefMan p. 194

is_subsig :: StaticAnalysis lid

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol => lid -> sign -> sign -> Bool

is_subsig lid s = maybe False (const True) . maybeResult . inclusion lid s

{- | semi lattices with top (needed for sublogics). Note that `Ord` is

only used for efficiency and is not related to the /partial/ order given

by the lattice. Only `Eq` is used to define `isSubElem` -}

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

join :: l -> l -> l

top :: l

instance SemiLatticeWithTop () where

join _ _ = ()

top = ()

-- | less or equal for semi lattices

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

isSubElem a b = join a b == b

-- | class providing the minimal sublogic of an item

class MinSublogic sublogic item where

minSublogic :: item -> sublogic

-- | a default instance for no sublogics

instance MinSublogic () a where

minSublogic _ = ()

-- | class providing also the projection of an item to a sublogic

class MinSublogic sublogic item => ProjectSublogic sublogic item where

projectSublogic :: sublogic -> item -> item

-- | a default instance for no sublogics

instance ProjectSublogic () b where

projectSublogic _ = id

-- | like ProjectSublogic, but providing a partial projection

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

-- | class for providing a list of sublogic names

class Sublogics l where

sublogic_names :: l -> [String]

instance Sublogics () where

sublogic_names () = [""]

{- Type class logic. The central type class of Hets, providing the

interface for logics. This type class is instantiated for many logics,

and it is used for the logic independent parts of Hets.

It hence provides an sbatraction barrier between logic specific and

logic indepdendent code.

This type class extends the class StaticAnalysis by a sublogic mechanism.

Sublogics are important since they avoid the need to provide an own

instance of the class logic for each sublogic. Instead, the sublogic

can use the datastructures and operations of the main logic, and

functions are provided to test whether a given item lies within the

sublogic. Also, projection functions from a super-logic to a sublogic

are provided.

-}

class (StaticAnalysis lid

basic_spec sentence 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,

Eq proof_tree, Show proof_tree, ShATermConvertible proof_tree,

Ord proof_tree, Typeable proof_tree)

=> 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

-- | the top sublogic, corresponding to the whole logic

top_sublogic :: lid -> sublogics

top_sublogic _ = top

-- | list all the sublogics of the current logic

all_sublogics :: lid -> [sublogics]

all_sublogics li = [top_sublogic li]

{- | provide the embedding of a projected signature into the

original signature -}

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

proj_sublogic_epsilon _ _ s = ide s

----------------------- provers ---------------------------

-- | several provers can be provided. See module "Logic.Prover"

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

provers _ = [] -- default implementation

-- | consistency checkers

cons_checkers :: lid

-> [ConsChecker sign sentence

sublogics morphism proof_tree]

cons_checkers _ = [] -- default implementation

-- | conservativity checkers

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

morphism -> [Named sentence]

-> Result (Maybe (ConsistencyStatus,[sentence]))

conservativityCheck l _ _ _ = statErr l "conservativityCheck"

-- | the empty proof tree

empty_proof_tree :: lid -> proof_tree

empty_proof_tree l = error $ statErrMsg l "empty_proof_tree"

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

-- Derived functions

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

-- | the empty theory

empty_theory :: StaticAnalysis lid

basic_spec sentence 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

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

-- | the disjoint union of all logics

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

deriving Typeable

instance Show AnyLogic where

show (Logic lid) = language_name lid

instance Eq AnyLogic where

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

{- class hierarchy:

Language

__________/

Category

| /

Sentences Syntax

\ /

StaticAnalysis (no sublogics)

\

\

Logic

-}