{- |

Module : $Header$

Copyright : (c) Pascal Schmidt, Christian Maeder, and Uni Bremen 2002-2005

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

Maintainer : maeder@tzi.de

Stability : experimental

Portability : portable

This module provides the sublogic functions (as required by Logic.hs) for

HasCASL. The functions allow to compute the minimal sublogics needed by a

given element, to check whether an item is part of a given sublogic, and --

not yet -- to project an element into a given sublogic.

-}

module HasCASL.Sublogic ( -- * datatypes

HasCASL_Sublogics(..),

HasCASL_Formulas(..),

-- * functions for LatticeWithTop instance

top,

sublogics_max,

sublogics_min,

-- * functions for Logic instance

-- * sublogic to string converstion

sublogics_name,

-- * list of all sublogics

sublogics_all,

-- * checks if element is in given sublogic

in_basicSpec,

in_sentence,

in_symbItems,

in_symbMapItems,

in_env,

in_morphism,

in_symbol,

-- * computes the sublogic of a given element

sl_basicSpec,

sl_sentence,

sl_symbItems,

sl_symbMapItems,

sl_env,

sl_morphism,

sl_symbol,

) where

import qualified Common.Lib.Map as Map

import qualified Common.Lib.Set as Set

import Common.AS_Annotation

import Common.Id

import HasCASL.As

import HasCASL.AsUtils

import HasCASL.Le

import HasCASL.Builtin

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

-- | Datatypes for HasCASL sublogics

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

data HasCASL_Formulas = Atomic -- atomic logic

| Horn -- positive conditional logic

| GHorn -- generalized positive conditional logic

| FOL -- first-order logic

| HOL -- higher-order logic

deriving (Show,Ord,Eq)

data HasCASL_Sublogics = HasCASL_SL

{ has_sub :: Bool, -- subsorting

has_part :: Bool, -- partiality

has_eq :: Bool, -- equality

has_pred :: Bool, -- predicates

has_ho :: Bool, -- higher order

has_type_classes :: Bool,

has_polymorphism :: Bool,

has_type_constructors :: Bool,

which_logic::HasCASL_Formulas

} deriving (Show,Ord,Eq)

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

-- Special sublogics elements

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

-- top element

--

top :: HasCASL_Sublogics

top = (HasCASL_SL True True True True True True True True HOL)

-- bottom element

--

bottom :: HasCASL_Sublogics

bottom = (HasCASL_SL False False False False False False False False Atomic)

-- the following are used to add a needed feature to a given

-- sublogic via sublogics_max, i.e. (sublogics_max given needs_part)

-- will force partiality in addition to what features given already

-- has included

-- minimal sublogic with subsorting

--

need_sub :: HasCASL_Sublogics

need_sub = bottom { has_sub = True }

-- minimal sublogic with partiality

--

need_part :: HasCASL_Sublogics

need_part = bottom { has_part = True }

-- minimal sublogic with equality

--

need_eq :: HasCASL_Sublogics

need_eq = bottom { has_eq = True }

-- minimal sublogic with predicates

--

need_pred :: HasCASL_Sublogics

need_pred = bottom { has_pred = True }

-- minimal sublogic with higher order

--

need_ho :: HasCASL_Sublogics

need_ho = bottom { has_ho = True }

-- minimal sublogic with type classes

--

need_type_classes :: HasCASL_Sublogics

need_type_classes = bottom { has_type_classes = True }

-- minimal sublogic with polymorhism

--

need_polymorphism :: HasCASL_Sublogics

need_polymorphism = bottom { has_polymorphism = True }

-- minimal sublogic with type constructors

--

need_type_constructors :: HasCASL_Sublogics

need_type_constructors = bottom { has_type_constructors = True }

need_horn :: HasCASL_Sublogics

need_horn = bottom { which_logic = Horn }

need_ghorn :: HasCASL_Sublogics

need_ghorn = bottom { which_logic = GHorn }

need_fol :: HasCASL_Sublogics

need_fol = bottom { which_logic = FOL }

need_hol :: HasCASL_Sublogics

need_hol = bottom { which_logic = HOL }

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

-- Functions to generate a list of all sublogics for HasCASL

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

sublogics_all :: [HasCASL_Sublogics]

sublogics_all = [HasCASL_SL {has_sub = sub,

has_part = part,

has_eq = eq,

has_pred = pre,

has_ho = ho,

has_type_classes = tyCl,

has_polymorphism = poly,

has_type_constructors = tyCon,

which_logic = logic}

| sub <- [False,True],

part <- [False,True],

eq <- [False,True],

pre <- [False,True],

ho <- [False,True],

tyCl <- [False,True],

poly <- [False,True],

tyCon <- [False,True],

logic <- [Atomic, Horn, GHorn, FOL, HOL] ]

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

-- Conversion functions (to String)

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

-- "formulas_name :: has_pred -> has_ho -> which_logic -> String"

formulas_name :: Bool -> Bool -> HasCASL_Formulas -> String

formulas_name True True HOL = "HOL"

formulas_name True False HOL = "HOL" -- ?!

formulas_name False True HOL = "HOL"

formulas_name False False HOL = "HOL" -- ?!

formulas_name True True FOL = "HOL" -- ?!

formulas_name True False FOL = "FOL"

formulas_name False True FOL = "HO-FOAlg" -- ?!

formulas_name False False FOL = "FOAlg"

formulas_name True True GHorn = "HO-GHorn"

formulas_name True False GHorn = "GHorn"

formulas_name False True GHorn = "HO-GCond"

formulas_name False False GHorn = "GCond"

formulas_name True True Horn = "HO-Horn"

formulas_name True False Horn = "Horn"

formulas_name False True Horn = "HO-Cond"

formulas_name False False Horn = "Cond"

formulas_name True True Atomic = "HO-Atom"

formulas_name True False Atomic = "Atom"

formulas_name False True Atomic = "HO-Eq"

formulas_name False False Atomic = "Eq"

sublogics_name :: HasCASL_Sublogics -> [String]

sublogics_name x = [

( if (has_sub x) then "Sub" else "")

++ ( if (has_part x) then "P" else "")

++ ( if (has_type_classes x) then "TyCl" else "")

++ ( if (has_polymorphism x) then "Poly" else "")

++ ( if (has_type_constructors x) then "TyCons" else "")

++ ( formulas_name (has_pred x) (has_ho x) (which_logic x) )

++ ( if (has_eq x) then "=" else "")]

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

-- min/join and max/meet functions

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

formulas_max :: HasCASL_Formulas -> HasCASL_Formulas -> HasCASL_Formulas

formulas_max x y = if (x<y) then y else x

formulas_min :: HasCASL_Formulas -> HasCASL_Formulas -> HasCASL_Formulas

formulas_min x y = if (x<y) then x else y

sublogics_max :: HasCASL_Sublogics -> HasCASL_Sublogics -> HasCASL_Sublogics

sublogics_max a b = HasCASL_SL

(has_sub a || has_sub b)

(has_part a || has_part b)

(has_eq a || has_eq b)

(has_pred a || has_pred b)

(has_ho a || has_ho b)

(has_type_classes a || has_type_classes b)

(has_polymorphism a || has_polymorphism b)

(has_type_constructors a || has_type_constructors b)

(formulas_max (which_logic a) (which_logic b))

sublogics_min :: HasCASL_Sublogics -> HasCASL_Sublogics -> HasCASL_Sublogics

sublogics_min a b = HasCASL_SL

(has_sub a && has_sub b)

(has_part a && has_part b)

(has_eq a && has_eq b)

(has_pred a && has_pred b)

(has_ho a && has_ho b)

(has_type_classes a && has_type_classes b)

(has_polymorphism a && has_polymorphism b)

(has_type_constructors a && has_type_constructors b)

(formulas_min (which_logic a) (which_logic b))

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

-- Helper functions

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

-- compute sublogics from a list of sublogics

--

comp_list :: [HasCASL_Sublogics] -> HasCASL_Sublogics

comp_list l = foldl sublogics_max bottom l

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

-- Functions to analyse formulae

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

{- ---------------------------------------------------------------------------

These functions are based on Till Mossakowski's paper "Sublanguages of

CASL", which is CoFI Note L-7. The functions implement an adaption of

the reduced grammar given there for formulae in a specific expression

logic by, checking whether a formula would match the productions from the

grammar. Which function checks for which nonterminal from the paper is

given as a comment before each function.

They are adapted for HasCASL, especially HasCASLs abstract syntax (As.hs)

--------------------------------------------------------------------------- -}

-- Atomic Logic (subsection 3.4 of the paper)

-- FORMULA, P-ATOM

--

is_atomic_t :: Term -> Bool

is_atomic_t (QuantifiedTerm q _ t _) = (is_atomic_q q) && (is_atomic_t t)

is_atomic_t (ApplTerm (QualOp Fun (InstOpId i _ _) t _) (TupleTerm ts _) _) =

-- P-Conjunction and ExEq

(((i == andId)

&& (and $ map is_atomic_t ts))

|| (i == exEq))

&& (t == logType)

&& (not (null ts))

is_atomic_t (QualOp Fun (InstOpId i _ _) t _) =

(i == trueId)

&& (t == logType)

--is_atomic_t (Predication _ _ _) = True

is_atomic_t (ApplTerm (QualOp Fun (InstOpId i _ _) t _) _ _) =

(i == defId)

&& (t == logType)

is_atomic_t _ = False

-- QUANTIFIER

--

is_atomic_q :: Quantifier -> Bool

is_atomic_q (Universal) = True

is_atomic_q _ = False

-- Positive Conditional Logic (subsection 3.2 in the paper)

-- FORMULA

--

is_horn_t :: Term -> Bool

is_horn_t (QuantifiedTerm q _ f _) =

(is_atomic_q q)

&& (is_horn_t f)

is_horn_t (ApplTerm (QualOp Fun (InstOpId i _ _) t _) (TupleTerm f _) _) =

(i == implId)

&& (t == logType)

&& (is_horn_p_conj (head f))

&& (is_horn_a (last f))

is_horn_t _ = False

-- P-CONJUNCTION

--

is_horn_p_conj :: Term -> Bool

is_horn_p_conj (ApplTerm (QualOp Fun (InstOpId i _ _) t _) (TupleTerm ts _) _) =

(i == andId)

&& (t == logType)

&& (not (null ts))

&& (and $ map is_horn_a ts)

is_horn_p_conj _ = False

-- ATOM

--

is_horn_a :: Term -> Bool

is_horn_a (QualOp Fun (InstOpId i _ _) t _) =

(i == trueId)

&& (t == logType)

-- is_horn_a (Predication _ _ _) = True

is_horn_a (ApplTerm (QualOp Fun (InstOpId i _ _) t _) _ _) =

((i == defId)

|| (i == exEq)

|| (i == eqId))

&& (t == logType)

--is_horn_a (Membership _ _ _) = True

is_horn_a _ = False

-- P-ATOM

--

is_horn_p_a :: Term -> Bool

is_horn_p_a (QualOp Fun (InstOpId i _ _) t _) =

(i == trueId)

&& (t == logType)

-- is_horn_p_a (Predication _ _ _) = True

is_horn_p_a (ApplTerm (QualOp Fun (InstOpId i _ _) t _) _ _) =

((i == defId)

|| (i == exEq))

&& (t == logType)

-- is_horn_p_a (Membership _ _ _) = True

is_horn_p_a _ = False

-- Generalized Positive Conditional Logic (subsection 3.3 of the paper)

-- FORMULA, ATOM

--

is_ghorn_t :: Term -> Bool

is_ghorn_t (QuantifiedTerm q _ t _) = (is_atomic_q q) && (is_ghorn_t t)

is_ghorn_t (ApplTerm (QualOp Fun (InstOpId i _ _) t _) (TupleTerm f _) _) =

(t == logType)

&& (((i == andId) && (not (null f)) && ((is_ghorn_c_conj f) || (is_ghorn_f_conj f)))

||

((i == implId) && (is_ghorn_prem (head f)) && (is_ghorn_conc (last f)))

||

((i == eqvId) && (is_ghorn_prem (head f)) && (is_ghorn_prem (last f))))

is_ghorn_t (QualOp Fun (InstOpId i _ _) t _) =

(i == trueId)

&& (t == logType)

-- is_ghorn_t (Predication _ _ _) = True

is_ghorn_t (ApplTerm (QualOp Fun (InstOpId i _ _) t _) _ _) =

((i == defId)

|| (i == exEq)

|| (i == eqId))

&& (t == logType)

-- is_ghorn_t (Membership _ _ _) = True

is_ghorn_t _ = False

-- C-CONJUNCTION

--

is_ghorn_c_conj :: [Term] -> Bool

is_ghorn_c_conj t = (not(null t)) && (and ((map is_ghorn_conc) t))

-- F-CONJUNCTION

--

is_ghorn_f_conj :: [Term] -> Bool

is_ghorn_f_conj t = (not(null t)) && (and ((map is_ghorn_t) t))

-- P-CONJUNCTION

--

is_ghorn_p_conj :: [Term] -> Bool

is_ghorn_p_conj t = (not(null t)) && (and (map is_ghorn_prem t))

-- PREMISE

--

is_ghorn_prem :: Term -> Bool

is_ghorn_prem (ApplTerm (QualOp Fun (InstOpId i _ _) t _) (TupleTerm ts _) _) =

(i == andId)

&& (t == logType)

&& (not (null ts))

&& (is_ghorn_p_conj ts)

is_ghorn_prem x = is_horn_p_a x

-- CONCLUSION

--

is_ghorn_conc :: Term -> Bool

is_ghorn_conc (ApplTerm (QualOp Fun (InstOpId i _ _) t _) (TupleTerm ts _) _) =

(i == andId)

&& (t == logType)

&& (not (null ts))

&& (is_ghorn_c_conj ts)

is_ghorn_conc x = is_horn_a x

is_fol_t :: Term -> Bool

is_fol_t (LambdaTerm _ _ _ _) = False

is_fol_t (CaseTerm _ _ _) = False

is_fol_t (LetTerm _ _ _ _) = False

is_fol_t _ = True

{- FOL:

no lambda/let/case,

no higher types (i.e. all types are basic, tuples, or tuple -> basic)

-}

-- compute logic of a formula by checking all logics in turn

--

get_logic :: Term -> HasCASL_Sublogics

get_logic t = if (is_atomic_t t) then bottom else

if (is_horn_t t) then need_horn else

if (is_ghorn_t t) then need_ghorn else

if (is_fol_t t) then need_fol else

need_hol

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

-- Functions to compute minimal sublogic for a given element; these work

-- by recursing into all subelements

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

sl_basicSpec :: BasicSpec -> HasCASL_Sublogics

sl_basicSpec (BasicSpec l) = comp_list $ map sl_basicItem

$ map item l

sl_basicItem :: BasicItem -> HasCASL_Sublogics

sl_basicItem (SigItems l) = sl_sigItems l

sl_basicItem (ProgItems l _) = comp_list $ map sl_progEq

$ map item l

sl_basicItem (ClassItems _ l _) = sublogics_max need_type_classes

(comp_list $ map sl_classItem

$ map item l)

sl_basicItem (GenVarItems l _) = comp_list $ map sl_genVarDecl l

sl_basicItem (FreeDatatype l _) = comp_list $ map sl_datatypeDecl

$ map item l

sl_basicItem (GenItems l _) = (comp_list $ map sl_sigItems

$ map item l)

sl_basicItem (AxiomItems l m _) = sublogics_max

(comp_list $ map sl_genVarDecl l)

(comp_list $ map sl_term

$ map item m)

sl_basicItem (Internal l _) = comp_list $ map sl_basicItem

$ map item l

sl_sigItems :: SigItems -> HasCASL_Sublogics

sl_sigItems (TypeItems i l _) = sublogics_max (sl_instance i)

(comp_list $ map sl_typeItem

$ map item l)

sl_sigItems (OpItems b l _) = sublogics_max (sl_opBrand b)

(comp_list $ map sl_opItem

$ map item l)

sl_opBrand :: OpBrand -> HasCASL_Sublogics

sl_opBrand (Pred) = need_pred

sl_opBrand _ = bottom

sl_instance :: Instance -> HasCASL_Sublogics

sl_instance (Instance) = need_type_classes

sl_instance _ = bottom

sl_classItem :: ClassItem -> HasCASL_Sublogics

sl_classItem (ClassItem c l _) = sublogics_max (sl_classDecl c)

(comp_list $ map sl_basicItem

$ map item l)

sl_classDecl :: ClassDecl -> HasCASL_Sublogics

sl_classDecl (ClassDecl _ _ _) = need_type_classes

sl_Rawkind :: RawKind -> HasCASL_Sublogics

sl_Rawkind (ClassKind _) = bottom

sl_Rawkind (FunKind _ _ _ _) = need_hol

sl_kind :: Kind -> HasCASL_Sublogics

sl_kind (ClassKind i) = if i == universeId then bottom else need_type_classes

sl_kind (FunKind _ k1 k2 _) = comp_list [need_hol, (sl_kind k1), (sl_kind k2)]

sl_typeItem :: TypeItem -> HasCASL_Sublogics

sl_typeItem (TypeDecl l k _) = sublogics_max (sl_kind k)

(comp_list $ map sl_typePattern l)

sl_typeItem (SubtypeDecl l _ _) = sublogics_max need_sub

(comp_list $ map sl_typePattern l)

sl_typeItem (IsoDecl l _) = sublogics_max need_sub

(comp_list $ map sl_typePattern l)

sl_typeItem (SubtypeDefn tp _ t term _) =

comp_list [need_sub,

(sl_typePattern tp),

(sl_type t),

(sl_term (item term))]

sl_typeItem (AliasType tp (Just k) ts _) = comp_list [(sl_kind k), (sl_typePattern tp),

(sl_typeScheme ts)]

sl_typeItem (AliasType tp Nothing ts _) = sublogics_max (sl_typePattern tp)

(sl_typeScheme ts)

sl_typeItem (Datatype dDecl) = sl_datatypeDecl dDecl

sl_typePattern :: TypePattern -> HasCASL_Sublogics

sl_typePattern (TypePattern _ l _) = comp_list $ map sl_typeArg l

-- non-empty args --> type constructor!

sl_typePattern (MixfixTypePattern l) = comp_list $ map sl_typePattern l

sl_typePattern (BracketTypePattern _ l _) = comp_list $ map sl_typePattern l

sl_typePattern (TypePatternArg _ _) = need_polymorphism

sl_typePattern _ = bottom

sl_type :: Type -> HasCASL_Sublogics

sl_type = sl_BasicFun

sl_Basictype :: Type -> HasCASL_Sublogics

sl_Basictype ty = case ty of

TypeName _ k v -> sublogics_max

(if v /= 0 then need_polymorphism else bottom) $ sl_Rawkind k

KindedType t k _ -> sublogics_max (sl_Basictype t) $ sl_kind k

ExpandedType _ t -> sl_Basictype t

BracketType Parens [t] _ -> sl_Basictype t

_ -> case getTypeAppl ty of

(TypeName ide _ _, [_, _]) | isArrow ide ->

sublogics_max need_ho $ sl_BasicFun ty

(TypeName ide _ _, [arg]) | ide == lazyTypeId ->

sublogics_max need_hol $ sl_Basictype arg

(_, args) -> comp_list $ need_type_constructors :

map sl_Basictype args

sl_BasicProd :: Type -> HasCASL_Sublogics

sl_BasicProd ty = case getTypeAppl ty of

(TypeName ide _ _, tyArgs@(_:_:_)) | ide == productId (length tyArgs)

-> comp_list $ map sl_Basictype tyArgs

_ -> sl_Basictype ty

sl_BasicFun :: Type -> HasCASL_Sublogics

sl_BasicFun ty = case getTypeAppl ty of

(TypeName ide _ _, [arg, res]) | isArrow ide ->

comp_list [if isPartialArrow ide then need_part else bottom,

sl_BasicProd arg, sl_Basictype res]

_ -> sl_Basictype ty

-- FOL i.e. no higher types (i.e. all types are basic, tuples, or tuple -> basic)

sl_typeScheme :: TypeScheme -> HasCASL_Sublogics

sl_typeScheme (TypeScheme l t _) =

comp_list $ sl_type t : map sl_typeArg l

sl_opItem :: OpItem -> HasCASL_Sublogics

sl_opItem (OpDecl l t m _) =

comp_list [(comp_list $ map sl_opId l),

(sl_typeScheme t),

(comp_list $ map sl_opAttr m)]

sl_opItem (OpDefn i v ts p t _) =

comp_list [(sl_opId i),

(comp_list $ map sl_varDecl (concat v)),

(sl_typeScheme ts),

(sl_partiality p),

(sl_term t)]

sl_partiality :: Partiality -> HasCASL_Sublogics

sl_partiality (Partial) = need_part

sl_partiality _ = bottom

sl_opAttr :: OpAttr -> HasCASL_Sublogics

sl_opAttr (UnitOpAttr t _) = sl_term t

sl_opAttr _ = need_eq

sl_datatypeDecl :: DatatypeDecl -> HasCASL_Sublogics

sl_datatypeDecl (DatatypeDecl t k l c _) =

let sl = comp_list [(sl_typePattern t),

(sl_kind k),

(comp_list $ map sl_alternative

$ map item l)]

in

if (null c) then sl

else sublogics_max need_type_classes sl

sl_alternative :: Alternative -> HasCASL_Sublogics

sl_alternative (Constructor _ l p _) = sublogics_max (sl_partiality p)

(comp_list $ map sl_component

(concat l))

sl_alternative (Subtype l _) = sublogics_max need_sub

(comp_list $ map sl_type l)

sl_component :: Component -> HasCASL_Sublogics

sl_component (Selector _ p t _ _) =

sublogics_max (sl_partiality p) (sl_type t)

sl_component (NoSelector t) = sl_type t

sl_term :: Term -> HasCASL_Sublogics

sl_term t = sublogics_max (get_logic t) (sl_t t)

sl_t :: Term -> HasCASL_Sublogics

sl_t (QualVar vd) = sl_varDecl vd

sl_t (QualOp b i t _) =

comp_list [(sl_opBrand b),

(sl_instOpId i),

(sl_typeScheme t)]

--sl_t (ResolvedMixTerm _ l _) = comp_list $ map sl_t l

sl_t (ApplTerm t1 t2 _) = sublogics_max (sl_t t1) (sl_t t2)

sl_t (TupleTerm l _) = comp_list $ map sl_t l

sl_t (TypedTerm t _ ty _) = sublogics_max (sl_t t) (sl_type ty)

sl_t (QuantifiedTerm _ l t _) = sublogics_max (sl_t t)

(comp_list $ map sl_genVarDecl l)

sl_t (LambdaTerm l p t _) =

comp_list [(comp_list $ map sl_pattern l),

(sl_partiality p),

(sl_t t)]

sl_t (CaseTerm t l _) = sublogics_max (sl_t t)

(comp_list $ map sl_progEq l)

sl_t (LetTerm _ l t _) = sublogics_max (sl_t t)

(comp_list $ map sl_progEq l)

sl_t (MixTypeTerm _ t _) = sl_type t

sl_t (MixfixTerm l) = comp_list $ map sl_t l

sl_t (BracketTerm _ l _) = comp_list $ map sl_t l

sl_t (AsPattern vd p2 _) = sublogics_max (sl_varDecl vd) (sl_pattern p2)

sl_t _ = bottom

sl_pattern :: Pattern -> HasCASL_Sublogics

sl_pattern = sl_t

sl_progEq :: ProgEq -> HasCASL_Sublogics

sl_progEq (ProgEq p t _) = sublogics_max (sl_pattern p) (sl_t t)

sl_varDecl :: VarDecl -> HasCASL_Sublogics

sl_varDecl (VarDecl _ t _ _) = sl_type t

sl_varKind :: VarKind -> HasCASL_Sublogics

sl_varKind vk = case vk of

VarKind k -> sl_kind k

Downset t -> sublogics_max need_sub $ sl_type t

_ -> bottom

sl_typeArg :: TypeArg -> HasCASL_Sublogics

sl_typeArg (TypeArg _ _ k _ _ _ _) =

sublogics_max need_polymorphism (sl_varKind k)

sl_genVarDecl :: GenVarDecl -> HasCASL_Sublogics

sl_genVarDecl (GenVarDecl v) = sl_varDecl v

sl_genVarDecl (GenTypeVarDecl v) = sl_typeArg v

sl_opId :: OpId -> HasCASL_Sublogics

sl_opId (OpId _ l _) = comp_list $ map sl_typeArg l

sl_instOpId :: InstOpId -> HasCASL_Sublogics

sl_instOpId (InstOpId i l _) =

if ((i == exEq) || (i == eqId))

then sublogics_max need_eq (comp_list $ map sl_type l)

else comp_list $ map sl_type l

sl_symbItems :: SymbItems -> HasCASL_Sublogics

sl_symbItems (SymbItems k l _ _) = sublogics_max (sl_symbKind k)

(comp_list $ map sl_symb l)

sl_symbMapItems :: SymbMapItems -> HasCASL_Sublogics

sl_symbMapItems (SymbMapItems k l _ _) = sublogics_max (sl_symbKind k)

(comp_list $ map sl_symbOrMap l)

sl_symbKind :: SymbKind -> HasCASL_Sublogics

sl_symbKind (SK_pred) = need_pred

sl_symbKind (SK_class) = need_type_classes

sl_symbKind _ = bottom

sl_symb :: Symb -> HasCASL_Sublogics

sl_symb (Symb _ Nothing _) = bottom

sl_symb (Symb _ (Just l) _) = sl_symbType l

sl_symbType :: SymbType -> HasCASL_Sublogics

sl_symbType (SymbType t) = sl_typeScheme t

sl_symbOrMap :: SymbOrMap -> HasCASL_Sublogics

sl_symbOrMap (SymbOrMap s Nothing _) = sl_symb s

sl_symbOrMap (SymbOrMap s (Just t) _) =

sublogics_max (sl_symb s) (sl_symb t)

-- the maps have no influence since all sorts,ops,preds in them

-- must also appear in the signatures, so any features needed by

-- them will be included by just checking the signatures

--

sl_env :: Env -> HasCASL_Sublogics

sl_env e =

let classes = if Map.null $ classMap e

then bottom else need_type_classes

types = comp_list $ map sl_typeInfo (Map.elems (typeMap e))

ops = comp_list $ map sl_opInfos (Map.elems (assumps e))

in comp_list [classes, types, ops]

sl_typeInfo :: TypeInfo -> HasCASL_Sublogics

sl_typeInfo t = let s = sl_typeDefn (typeDefn t) in

if Set.null $ superTypes t then s else

sublogics_max need_sub s

sl_typeDefn :: TypeDefn -> HasCASL_Sublogics

sl_typeDefn (DatatypeDefn de) = sl_dataEntry de

sl_typeDefn (AliasTypeDefn t) = sl_typeScheme t

sl_typeDefn _ = bottom

sl_dataEntry :: DataEntry -> HasCASL_Sublogics

sl_dataEntry (DataEntry _ _ _ l _ m) =

sublogics_max (comp_list $ map sl_typeArg l)

(comp_list $ map sl_altDefn m)

sl_opInfos :: OpInfos -> HasCASL_Sublogics

sl_opInfos o = comp_list $ map sl_opInfo (opInfos o)

sl_opInfo :: OpInfo -> HasCASL_Sublogics

sl_opInfo o = comp_list [(sl_typeScheme (opType o)),

(comp_list $ map sl_opAttr (opAttrs o)),

(sl_opDefn (opDefn o))]

sl_opDefn :: OpDefn -> HasCASL_Sublogics

sl_opDefn (NoOpDefn b) = sl_opBrand b

sl_opDefn (SelectData l _) = comp_list $ map sl_constrInfo l

sl_opDefn (Definition b t) =

sublogics_max (sl_opBrand b) (sl_term t)

sl_opDefn _ = bottom

sl_constrInfo :: ConstrInfo -> HasCASL_Sublogics

sl_constrInfo c = sl_typeScheme (constrType c)

sl_sentence :: Sentence -> HasCASL_Sublogics

sl_sentence (Formula t) = sl_term t

sl_sentence (ProgEqSen _ ts pq) =

sublogics_max (sl_typeScheme ts) (sl_progEq pq)

sl_sentence (DatatypeSen l) = comp_list $ map sl_dataEntry l

sl_altDefn :: AltDefn -> HasCASL_Sublogics

sl_altDefn (Construct _ l p m) =

comp_list [(comp_list $ map sl_type l),

(sl_partiality p),

(comp_list $ map sl_selector $ concat m)]

sl_selector :: Selector -> HasCASL_Sublogics

sl_selector (Select _ t p) = sublogics_max (sl_type t)

(sl_partiality p)

sl_morphism :: Morphism -> HasCASL_Sublogics

sl_morphism m = sublogics_max (sl_env $ msource m) (sl_env $ mtarget m)

sl_symbol :: Symbol -> HasCASL_Sublogics

sl_symbol (Symbol _ t e) =

sublogics_max (sl_symbolType t) (sl_env e)

sl_symbolType :: SymbolType a -> HasCASL_Sublogics

sl_symbolType (OpAsItemType t) = sl_typeScheme t

sl_symbolType (ClassAsItemType _) = need_type_classes

sl_symbolType _ = bottom

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

-- comparison functions

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

-- negated implication

--

nimpl :: Bool -> Bool -> Bool

nimpl True _ = True

nimpl False False = True

nimpl False True = False

-- check if a "new" sublogic is contained in/equal to a given

-- sublogic

--

sl_in :: HasCASL_Sublogics -> HasCASL_Sublogics -> Bool

sl_in given new = (nimpl (has_sub given) (has_sub new)) &&

(nimpl (has_part given) (has_part new)) &&

(nimpl (has_eq given) (has_eq new)) &&

(nimpl (has_pred given) (has_pred new)) &&

(nimpl (has_polymorphism given)

(has_polymorphism new)) &&

(nimpl (has_ho given) (has_ho new)) &&

(nimpl (has_type_classes given)

(has_type_classes new)) &&

(nimpl (has_type_constructors given)

(has_type_constructors new)) &&

((which_logic given) >= (which_logic new))

in_x :: HasCASL_Sublogics -> a -> (a -> HasCASL_Sublogics) -> Bool

in_x l x f = sl_in l (f x)

in_basicSpec :: HasCASL_Sublogics -> BasicSpec -> Bool

in_basicSpec l x = in_x l x sl_basicSpec

in_sentence :: HasCASL_Sublogics -> Sentence -> Bool

in_sentence l x = in_x l x sl_sentence

in_symbItems :: HasCASL_Sublogics -> SymbItems -> Bool

in_symbItems l x = in_x l x sl_symbItems

in_symbMapItems :: HasCASL_Sublogics -> SymbMapItems -> Bool

in_symbMapItems l x = in_x l x sl_symbMapItems

in_env :: HasCASL_Sublogics -> Env -> Bool

in_env l x = in_x l x sl_env

in_morphism :: HasCASL_Sublogics -> Morphism -> Bool

in_morphism l x = in_x l x sl_morphism

in_symbol :: HasCASL_Sublogics -> Symbol -> Bool

in_symbol l x = in_x l x sl_symbol