Sublogic.hs revision 1dfd1687e9ee6a45e2cb5268a701ead79c1c1f79
21155e63bac193abc764d791360132392eb79c4dcmaeder{- |
21155e63bac193abc764d791360132392eb79c4dcmaederModule : $Header$
21155e63bac193abc764d791360132392eb79c4dcmaederDescription : sublogic analysis for CASL
21155e63bac193abc764d791360132392eb79c4dcmaederCopyright : (c) Pascal Schmidt, C. Maeder, and Uni Bremen 2002-2006
21155e63bac193abc764d791360132392eb79c4dcmaederLicense : GPLv2 or higher, see LICENSE.txt
21155e63bac193abc764d791360132392eb79c4dcmaeder
21155e63bac193abc764d791360132392eb79c4dcmaederMaintainer : Christian.Maeder@dfki.de
21155e63bac193abc764d791360132392eb79c4dcmaederStability : experimental
21155e63bac193abc764d791360132392eb79c4dcmaederPortability : portable
21155e63bac193abc764d791360132392eb79c4dcmaeder
21155e63bac193abc764d791360132392eb79c4dcmaederSublogic analysis for CASL
21155e63bac193abc764d791360132392eb79c4dcmaeder
21155e63bac193abc764d791360132392eb79c4dcmaederThis module provides the sublogic functions (as required by Logic.hs)
21155e63bac193abc764d791360132392eb79c4dcmaeder for CASL. The functions allow to compute the minimal sublogics needed
21155e63bac193abc764d791360132392eb79c4dcmaeder by a given element, to check whether an item is part of a given
21155e63bac193abc764d791360132392eb79c4dcmaeder sublogic, and to project an element into a given sublogic.
21155e63bac193abc764d791360132392eb79c4dcmaeder-}
21155e63bac193abc764d791360132392eb79c4dcmaeder
21155e63bac193abc764d791360132392eb79c4dcmaedermodule CASL.Sublogic
21155e63bac193abc764d791360132392eb79c4dcmaeder ( -- * types
21155e63bac193abc764d791360132392eb79c4dcmaeder CASL_Sublogics
21155e63bac193abc764d791360132392eb79c4dcmaeder , CASL_SL (..)
21155e63bac193abc764d791360132392eb79c4dcmaeder , CASL_Formulas (..)
21155e63bac193abc764d791360132392eb79c4dcmaeder , SubsortingFeatures (..)
55282ad62e8b6758abec43734ebde0015ac14b89Eugen Kuksa , SortGenerationFeatures (..)
21155e63bac193abc764d791360132392eb79c4dcmaeder -- * class
21155e63bac193abc764d791360132392eb79c4dcmaeder , Lattice (..)
21155e63bac193abc764d791360132392eb79c4dcmaeder -- * predicates on CASL_SL
21155e63bac193abc764d791360132392eb79c4dcmaeder , has_sub
21155e63bac193abc764d791360132392eb79c4dcmaeder , has_cons
21155e63bac193abc764d791360132392eb79c4dcmaeder -- * functions for SemiLatticeWithTop instance
21155e63bac193abc764d791360132392eb79c4dcmaeder , mkTop
21155e63bac193abc764d791360132392eb79c4dcmaeder , top
, caslTop
, cFol
, sublogics_max
, comp_list
-- * functions for the creation of minimal sublogics
, bottom
, mkBot
, emptyMapConsFeature
, need_sub
, need_pred
, need_horn
, need_fol
, updExtFeature
-- * functions for Logic instance sublogic to string conversion
, sublogics_name
, parseSL
, parseBool
-- ** list of all sublogics
, sublogics_all
, sDims
-- * computes the sublogic of a given element
, sl_sig_items
, sl_basic_spec
, sl_opkind
, sl_op_type
, sl_op_item
, sl_pred_item
, sl_sentence
, sl_term
, sl_symb_items
, sl_symb_map_items
, sl_sign
, sl_morphism
, sl_symbol
-- * projects an element into a given sublogic
, pr_basic_spec
, pr_symb_items
, pr_symb_map_items
, pr_sign
, pr_morphism
, pr_epsilon
, pr_symbol
) where
import Data.List
import Data.Maybe
import qualified Data.Map as Map
import qualified Data.Set as Set
import qualified Common.Lib.MapSet as MapSet
import qualified Common.Lib.Rel as Rel
import Common.Id
import Common.AS_Annotation
import Common.Lattice
import Control.Monad
import CASL.AS_Basic_CASL
import CASL.Sign
import CASL.Morphism
import CASL.Fold
{- ----------------------------------------------------------------------------
datatypes for CASL sublogics
---------------------------------------------------------------------------- -}
data CASL_Formulas = Atomic -- ^ atomic logic
| Horn -- ^ positive conditional logic
| GHorn -- ^ generalized positive conditional logic
| FOL -- ^ first-order logic
| SOL -- ^ second-order logic
deriving (Show, Eq, Ord)
data SubsortingFeatures = NoSub
| LocFilSub
| Sub
deriving (Show, Eq, Ord)
data SortGenerationFeatures =
NoSortGen
| SortGen { emptyMapping :: Bool
-- ^ Mapping of indexed sorts is empty
, onlyInjConstrs :: Bool
-- ^ only constructors that are subsort injections
} deriving (Show, Eq, Ord)
joinSortGenFeature :: (Bool -> Bool -> Bool)
-> SortGenerationFeatures -> SortGenerationFeatures
-> SortGenerationFeatures
joinSortGenFeature f x y =
case x of
NoSortGen -> y
SortGen em_x ojc_x -> case y of
NoSortGen -> x
SortGen em_y ojc_y -> SortGen (f em_x em_y) (f ojc_x ojc_y)
data CASL_SL a = CASL_SL
{ sub_features :: SubsortingFeatures, -- ^ subsorting
has_part :: Bool, -- ^ partiality
cons_features :: SortGenerationFeatures, -- ^ sort generation constraints
has_eq :: Bool, -- ^ equality
has_pred :: Bool, -- ^ predicates
which_logic :: CASL_Formulas, -- ^ first order sublogics
has_empty_sorts :: Bool, -- ^ may sorts be empty
ext_features :: a -- ^ features of extension
} deriving (Show, Eq, Ord)
updExtFeature :: (a -> a) -> CASL_SL a -> CASL_SL a
updExtFeature f s = s { ext_features = f $ ext_features s }
type CASL_Sublogics = CASL_SL ()
{- -----------------------
old selector functions
----------------------- -}
has_sub :: CASL_SL a -> Bool
has_sub sl = case sub_features sl of
NoSub -> False
_ -> True
has_cons :: CASL_SL a -> Bool
has_cons sl = case cons_features sl of
NoSortGen -> False
_ -> True
{- ---------------------------------------------------------------------------
Special sublogics elements
--------------------------------------------------------------------------- -}
-- top element
mkTop :: a -> CASL_SL a
mkTop = CASL_SL Sub True (SortGen False False) True True SOL True
top :: Lattice a => CASL_SL a
top = mkTop ctop
caslTop :: Lattice a => CASL_SL a
caslTop = top
{ has_empty_sorts = False
, which_logic = FOL
}
cFol :: Lattice a => CASL_SL a
cFol = caslTop
{ sub_features = NoSub -- no subsorting
, has_part = False -- no partiality
}
mkBot :: a -> CASL_SL a
mkBot = CASL_SL NoSub False NoSortGen False False Atomic False
-- bottom element
bottom :: Lattice a => CASL_SL a
bottom = mkBot bot
need_empty_sorts :: Lattice a => CASL_SL a
need_empty_sorts = bottom { has_empty_sorts = True }
{- 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 sublogics with subsorting
need_sub :: Lattice a => CASL_SL a
need_sub = need_horn { sub_features = Sub }
need_sul :: Lattice a => CASL_SL a
need_sul = need_horn { sub_features = LocFilSub }
-- minimal sublogic with partiality
need_part :: Lattice a => CASL_SL a
need_part = bottom { has_part = True }
emptyMapConsFeature :: SortGenerationFeatures
emptyMapConsFeature = SortGen
{ emptyMapping = True
, onlyInjConstrs = False }
-- minimal sublogics with sort generation constraints
need_cons :: Lattice a => CASL_SL a
need_cons = bottom
{ cons_features = SortGen { emptyMapping = False
, onlyInjConstrs = False} }
need_e_cons :: Lattice a => CASL_SL a
need_e_cons = bottom
{ cons_features = emptyMapConsFeature }
need_s_cons :: Lattice a => CASL_SL a
need_s_cons = bottom
{ cons_features = SortGen { emptyMapping = False
, onlyInjConstrs = True} }
need_se_cons :: Lattice a => CASL_SL a
need_se_cons = bottom
{ cons_features = SortGen { emptyMapping = True
, onlyInjConstrs = True} }
-- minimal sublogic with equality
need_eq :: Lattice a => CASL_SL a
need_eq = bottom { has_eq = True }
-- minimal sublogic with predicates
need_pred :: Lattice a => CASL_SL a
need_pred = bottom { has_pred = True }
need_horn :: Lattice a => CASL_SL a
need_horn = bottom { which_logic = Horn }
need_fol :: Lattice a => CASL_SL a
need_fol = bottom { which_logic = FOL }
{- ---------------------------------------------------------------------------
Functions to generate a list of all sublogics for CASL
--------------------------------------------------------------------------- -}
{- all elements
create a list of all CASL sublogics by generating all possible
feature combinations and then filtering illegal ones out -}
sublogics_all :: Lattice a => [a] -> [CASL_SL a]
sublogics_all l = bottom : map mkBot l ++ concat (sDims [])
++ let subPAtom = (sublogics_max need_part need_pred) { sub_features = Sub } in
[ sublogics_max need_fol need_eq
, comp_list [subPAtom, need_horn, need_eq]
, subPAtom
, sublogics_max subPAtom need_cons
, cFol, caslTop, top]
sDims :: Lattice a => [[a]] -> [[CASL_SL a]]
sDims l = let
t = True
b = bottom
bools = [True, False]
in
map (map mkBot) l ++
[ [ b { sub_features = s_f } | s_f <- [LocFilSub, Sub]]
, [b { has_part = t } ]
, [b { cons_features = c_f } | c_f <- [ SortGen m s | m <- bools, s <- bools]]
, [b { has_eq = t } ]
, [b { has_pred = t } ]
, [b { has_empty_sorts = t } ]
, [b { which_logic = fo } | fo <- reverse [SOL, FOL, GHorn, Horn]]]
{- ----------------------------------------------------------------------------
Conversion functions (to String)
---------------------------------------------------------------------------- -}
formulas_name :: Bool -> CASL_Formulas -> String
formulas_name b f = let Just s = lookup (b, f) nameList in s
nameList :: [((Bool, CASL_Formulas), String)]
nameList =
[ ((True, SOL), "SOL")
, ((False, SOL), "SOAlg")
, ((True, FOL), "FOL")
, ((False, FOL), "FOAlg")
, ((True, GHorn), "GHorn")
, ((False, GHorn), "GCond")
, ((True, Horn), "Horn")
, ((False, Horn), "Cond")
, ((True, Atomic), "Atom")
, ((False, Atomic), "Eq")]
sublogics_name :: (a -> String) -> CASL_SL a -> String
sublogics_name f x = f (ext_features x)
++ (case sub_features x of
NoSub -> ""
LocFilSub -> "Sul"
Sub -> "Sub")
++ (if has_part x then "P" else "")
++ (if has_cons x
then (if onlyInjConstrs (cons_features x)
then "s" else "") ++
(if emptyMapping (cons_features x)
then "e" else "") ++ "C"
else "")
++ formulas_name (has_pred x) (which_logic x)
++ (if has_eq x then "=" else "")
++ if has_empty_sorts x then "E" else ""
parseBool :: String -> String -> (Bool, String)
parseBool p s = case stripPrefix p s of
Just r -> (True, r)
Nothing -> (False, s)
parseSL :: (String -> Maybe (a, String)) -> String -> Maybe (CASL_SL a)
parseSL f s0 = do
(a, s1) <- f s0
(sub, s2) <- case stripPrefix "Su" s1 of
Just r -> case r of
c : t -> case c of
'l' -> Just (LocFilSub, t)
'b' -> Just (Sub, t)
_ -> Nothing
"" -> Nothing
Nothing -> Just (NoSub, s1)
let (pa, s3) = parseBool "P" s2
(c, s4) = parseCons s3
((pr, l), s5) <- parseForm s4
let (eq, s6) = parseBool "=" s5
(es, s7) = parseBool "E" s6
unless (null s7) Nothing
return (mkBot a)
{ sub_features = sub
, has_part = pa
, cons_features = c
, has_pred = pr
, which_logic = l
, has_eq = eq
, has_empty_sorts = es }
parseForm :: String -> Maybe ((Bool, CASL_Formulas), String)
parseForm s = foldr (\ (q, p) m -> case m of
Just _ -> m
Nothing -> case stripPrefix p s of
Just r -> Just (q, r)
Nothing -> m) Nothing nameList
parseCons :: String -> (SortGenerationFeatures, String)
parseCons s = case stripPrefix "seC" s of
Just r -> (SortGen True True, r)
Nothing -> case stripPrefix "sC" s of
Just r -> (SortGen False True, r)
Nothing -> case stripPrefix "eC" s of
Just r -> (SortGen True False, r)
Nothing -> case stripPrefix "C" s of
Just r | not $ isPrefixOf "ond" r -> (SortGen False False, r)
_ -> (NoSortGen, s)
{- ----------------------------------------------------------------------------
join or max functions
---------------------------------------------------------------------------- -}
sublogics_join :: (Bool -> Bool -> Bool)
-> (SubsortingFeatures -> SubsortingFeatures
-> SubsortingFeatures)
-> (SortGenerationFeatures -> SortGenerationFeatures
-> SortGenerationFeatures)
-> (CASL_Formulas -> CASL_Formulas -> CASL_Formulas)
-> (a -> a -> a)
-> CASL_SL a -> CASL_SL a -> CASL_SL a
sublogics_join jB jS jC jF jE a b = CASL_SL
{ sub_features = jS (sub_features a) (sub_features b)
, ext_features = jE (ext_features a) (ext_features b)
, has_part = jB (has_part a) $ has_part b
, cons_features = jC (cons_features a) (cons_features b)
, has_eq = jB (has_eq a) $ has_eq b
, has_pred = jB (has_pred a) $ has_pred b
, has_empty_sorts = jB (has_empty_sorts a) $ has_empty_sorts b
, which_logic = jF (which_logic a) (which_logic b)
}
sublogics_max :: Lattice a => CASL_SL a -> CASL_SL a
-> CASL_SL a
sublogics_max = sublogics_join max max (joinSortGenFeature min) max cjoin
{- ----------------------------------------------------------------------------
Helper functions
---------------------------------------------------------------------------- -}
-- compute sublogics from a list of sublogics
comp_list :: Lattice a => [CASL_SL a] -> CASL_SL a
comp_list = foldl sublogics_max bottom
{- map a function returning Maybe over a list of arguments
. a list of Pos is maintained by removing an element if the
function f returns Nothing on the corresponding element of
the argument list
. leftover elements in the Pos list after the argument
list is exhausted are appended at the end with Nothing
as a substitute for f's result -}
mapMaybePos :: [Pos] -> (a -> Maybe b) -> [a] -> [(Maybe b, Pos)]
mapMaybePos [] _ _ = []
mapMaybePos (p1 : pl) f [] = (Nothing, p1) : mapMaybePos pl f []
mapMaybePos (p1 : pl) f (h : t) = let res = f h in
(if isJust res then ((res, p1) :) else id) $ mapMaybePos pl f t
{- map with partial function f on Maybe type
will remove elements from given Pos list for elements of [a]
where f returns Nothing
given number of elements from the beginning of Range are always
kept -}
mapPos :: Int -> Range -> (a -> Maybe b) -> [a] -> ([b], Range)
mapPos c (Range p) f l = let
(res, pos) = unzip $ mapMaybePos (drop c p) f l
in
(catMaybes res, Range (take c p ++ pos))
{- ----------------------------------------------------------------------------
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.
--------------------------------------------------------------------------- -}
sl_form_level :: (f -> CASL_Formulas)
-> (Bool, Bool) -> FORMULA f -> CASL_Formulas
sl_form_level ff (isCompound, leftImp) phi =
case phi of
Quantification q _ f _ ->
let ql = sl_form_level ff (isCompound, leftImp) f
in if is_atomic_q q then ql else max FOL ql
Junction j l _ -> maximum $ case j of
Con -> map (sl_form_level ff (True, leftImp)) l
Dis -> FOL : map (sl_form_level ff (False, False)) l
Relation l1 c l2 _ -> maximum $ sl_form_level ff (True, True) l1
: case c of
Equivalence -> [ sl_form_level ff (True, True) l2
, if leftImp then FOL else GHorn ]
_ -> [ sl_form_level ff (True, False) l2
, if leftImp then FOL else
if isCompound then GHorn else Horn ]
Negation f _ -> max FOL $ sl_form_level ff (False, False) f
Atom b _ -> if b then Atomic else FOL
Equation _ e _ _
| e == Existl -> Atomic
| leftImp -> FOL
| otherwise -> Horn
QuantOp {} -> SOL -- it can't get worse
QuantPred {} -> SOL
ExtFORMULA f -> ff f
_ -> Atomic
-- QUANTIFIER
is_atomic_q :: QUANTIFIER -> Bool
is_atomic_q Universal = True
is_atomic_q _ = False
-- compute logic of a formula by checking all logics in turn
get_logic :: Lattice a => (f -> CASL_SL a)
-> FORMULA f -> CASL_SL a
get_logic ff f = bottom
{ which_logic = sl_form_level (which_logic . ff) (False, False) f }
-- for the formula inside a subsort-defn
get_logic_sd :: Lattice a => (f -> CASL_SL a)
-> FORMULA f -> CASL_SL a
get_logic_sd ff f = bottom
{ which_logic =
max Horn $ sl_form_level (which_logic . ff) (False, False) f }
{- ----------------------------------------------------------------------------
Functions to compute minimal sublogic for a given element, these work
by recursing into all subelements
---------------------------------------------------------------------------- -}
sl_basic_spec :: Lattice a => (b -> CASL_SL a)
-> (s -> CASL_SL a)
-> (f -> CASL_SL a)
-> BASIC_SPEC b s f -> CASL_SL a
sl_basic_spec bf sf ff (Basic_spec l) =
comp_list $ map (sl_basic_items bf sf ff . item) l
sl_basic_items :: Lattice a => (b -> CASL_SL a)
-> (s -> CASL_SL a)
-> (f -> CASL_SL a)
-> BASIC_ITEMS b s f -> CASL_SL a
sl_basic_items bf sf ff bi = case bi of
Sig_items i -> sl_sig_items sf ff i
Free_datatype sk l _ -> needsEmptySorts sk
$ comp_list $ map (sl_datatype_decl . item) l
Sort_gen l _ -> sublogics_max need_se_cons
$ comp_list $ map (sl_sig_items sf ff . item) l
Var_items l _ -> comp_list $ map sl_var_decl l
Local_var_axioms d l _ -> comp_list
$ map sl_var_decl d ++ map (sl_formula ff . item) l
Axiom_items l _ -> comp_list $ map (sl_formula ff . item) l
Ext_BASIC_ITEMS b -> bf b
needsEmptySorts :: Lattice a => SortsKind -> CASL_SL a -> CASL_SL a
needsEmptySorts sk = case sk of
NonEmptySorts -> id
PossiblyEmptySorts -> sublogics_max need_empty_sorts
sl_sig_items :: Lattice a => (s -> CASL_SL a)
-> (f -> CASL_SL a)
-> SIG_ITEMS s f -> CASL_SL a
sl_sig_items sf ff si = case si of
Sort_items sk l _ -> needsEmptySorts sk
$ comp_list $ map (sl_sort_item ff . item) l
Op_items l _ -> comp_list $ map (sl_op_item ff . item) l
Pred_items l _ -> comp_list $ map (sl_pred_item ff . item) l
Datatype_items sk l _ -> needsEmptySorts sk
$ comp_list $ map (sl_datatype_decl . item) l
Ext_SIG_ITEMS s -> sf s
{- Subsort_defn needs to compute the expression logic needed seperately
because the expressiveness allowed in the formula may be different
from more general formulae in the same expression logic -}
sl_sort_item :: Lattice a => (f -> CASL_SL a)
-> SORT_ITEM f -> CASL_SL a
sl_sort_item ff si = case si of
Subsort_decl {} -> need_sul
Subsort_defn _ _ _ f _ -> sublogics_max
(get_logic_sd ff $ item f)
(sublogics_max need_sul
(sl_formula ff $ item f))
Iso_decl _ _ -> need_sul
_ -> bottom
sl_op_item :: Lattice a => (f -> CASL_SL a)
-> OP_ITEM f -> CASL_SL a
sl_op_item ff oi = case oi of
Op_decl _ t l _ -> sublogics_max (sl_op_type t)
(comp_list $ map (sl_op_attr ff) l)
Op_defn _ h t _ -> sublogics_max (sl_op_head h)
(sl_term ff $ item t)
sl_op_attr :: Lattice a => (f -> CASL_SL a)
-> OP_ATTR f -> CASL_SL a
sl_op_attr ff oa = case oa of
Unit_op_attr t -> sl_term ff t
_ -> need_eq
sl_op_type :: Lattice a => OP_TYPE -> CASL_SL a
sl_op_type ot = case ot of
Op_type Partial _ _ _ -> need_part
_ -> bottom
sl_op_head :: Lattice a => OP_HEAD -> CASL_SL a
sl_op_head oh = case oh of
Op_head Partial _ _ _ -> need_part
_ -> bottom
sl_pred_item :: Lattice a => (f -> CASL_SL a)
-> PRED_ITEM f -> CASL_SL a
sl_pred_item ff i = case i of
Pred_decl {} -> need_pred
Pred_defn _ _ f _ -> sublogics_max need_pred (sl_formula ff $ item f)
sl_datatype_decl :: Lattice a => DATATYPE_DECL -> CASL_SL a
sl_datatype_decl (Datatype_decl _ l _) =
comp_list $ map (sl_alternative . item) l
sl_alternative :: Lattice a => ALTERNATIVE -> CASL_SL a
sl_alternative a = case a of
Alt_construct Total _ l _ -> comp_list $ map sl_components l
Alt_construct Partial _ _ _ -> need_part
Subsorts _ _ -> need_sul
sl_components :: Lattice a => COMPONENTS -> CASL_SL a
sl_components c = case c of
Cons_select Partial _ _ _ -> need_part
_ -> bottom
sl_var_decl :: Lattice a => VAR_DECL -> CASL_SL a
sl_var_decl _ = bottom
{- without subsorts casts are trivial and would not even require
need_part, but testing sortOfTerm is not save for formulas in basic specs
that are only parsed (and resolved) but not enriched with sorts -}
slRecord :: Lattice a => (f -> CASL_SL a) -> Record f (CASL_SL a) (CASL_SL a)
slRecord ff = (constRecord ff comp_list bottom)
{ foldPredication = \ _ _ l _ -> comp_list $ need_pred : l
, foldEquation = \ _ t _ u _ -> comp_list [need_eq, t, u]
, foldSort_gen_ax = \ _ constraints _ ->
case recover_Sort_gen_ax constraints of
(_, ops, m) -> case (m, filter (\ o -> case o of
Op_name _ -> True
Qual_op_name n _ _ ->
not (isInjName n)) ops) of
([], []) -> need_se_cons
([], _) -> need_e_cons
(_, []) -> need_s_cons
_ -> need_cons
, foldQuantPred = \ _ _ _ f -> sublogics_max need_pred f
, foldCast = \ _ t _ _ -> sublogics_max need_part t
}
sl_term :: Lattice a => (f -> CASL_SL a) -> TERM f -> CASL_SL a
sl_term = foldTerm . slRecord
sl_formula :: Lattice a => (f -> CASL_SL a)
-> FORMULA f -> CASL_SL a
sl_formula ff f = sublogics_max (get_logic ff f) (sl_form ff f)
sl_form :: Lattice a => (f -> CASL_SL a)
-> FORMULA f -> CASL_SL a
sl_form = foldFormula . slRecord
sl_symb_items :: Lattice a => SYMB_ITEMS -> CASL_SL a
sl_symb_items (Symb_items k l _) = sublogics_max (sl_symb_kind k)
(comp_list $ map sl_symb l)
sl_symb_kind :: Lattice a => SYMB_KIND -> CASL_SL a
sl_symb_kind pk = case pk of
Preds_kind -> need_pred
_ -> bottom
sl_symb :: Lattice a => SYMB -> CASL_SL a
sl_symb s = case s of
Symb_id _ -> bottom
Qual_id _ t _ -> sl_type t
sl_type :: Lattice a => TYPE -> CASL_SL a
sl_type ty = case ty of
O_type t -> sl_op_type t
P_type _ -> need_pred
_ -> bottom
sl_symb_map_items :: Lattice a => SYMB_MAP_ITEMS -> CASL_SL a
sl_symb_map_items (Symb_map_items k l _) = sublogics_max (sl_symb_kind k)
(comp_list $ map sl_symb_or_map l)
sl_symb_or_map :: Lattice a => SYMB_OR_MAP -> CASL_SL a
sl_symb_or_map syms = case syms of
Symb s -> sl_symb s
Symb_map s 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_sign :: Lattice a => (e -> CASL_SL a) -> Sign f e -> CASL_SL a
sl_sign f s =
let rel = sortRel s
subs | Rel.noPairs rel = bottom
| Rel.locallyFiltered rel = need_sul
| otherwise = need_sub
esorts = if Set.null $ emptySortSet s then bottom
else need_empty_sorts
preds = if MapSet.null $ predMap s then bottom else need_pred
partial = if any isPartial $ Set.toList
$ MapSet.elems $ opMap s then need_part else bottom
in comp_list [subs, esorts, preds, partial, f $ extendedInfo s]
sl_sentence :: Lattice a => (f -> CASL_SL a) -> FORMULA f -> CASL_SL a
sl_sentence = sl_formula
sl_morphism :: Lattice a => (e -> CASL_SL a) -> Morphism f e m -> CASL_SL a
sl_morphism f m = sublogics_max (sl_sign f $ msource m) (sl_sign f $ mtarget m)
sl_symbol :: Lattice a => Symbol -> CASL_SL a
sl_symbol (Symbol _ t) = sl_symbtype t
sl_symbtype :: Lattice a => SymbType -> CASL_SL a
sl_symbtype st = case st of
OpAsItemType t -> sl_optype t
PredAsItemType _ -> need_pred
_ -> bottom
sl_optype :: Lattice a => OpType -> CASL_SL a
sl_optype = sl_opkind . opKind
sl_opkind :: Lattice a => OpKind -> CASL_SL a
sl_opkind fk = case fk of
Partial -> need_part
_ -> bottom
{- ----------------------------------------------------------------------------
projection functions
---------------------------------------------------------------------------- -}
sl_in :: Lattice a => CASL_SL a -> CASL_SL a -> Bool
sl_in given new = sublogics_max given new == given
in_x :: Lattice a => CASL_SL a -> b -> (b -> CASL_SL a) -> Bool
in_x l x f = sl_in l (f x)
-- process Annoted type like simple type, simply keep all annos
pr_annoted :: CASL_SL s -> (CASL_SL s -> a -> Maybe a)
-> Annoted a -> Maybe (Annoted a)
pr_annoted sl f a =
fmap (`replaceAnnoted` a) $ f sl (item a)
{- project annoted type, by-producing a [SORT]
used for projecting datatypes: sometimes it is necessary to
introduce a SORT_DEFN for a datatype that was erased
completely, for example by only having partial constructors
and partiality forbidden in the desired sublogic - the sort
name may however still be needed for formulas because it can
appear there like in (forall x,y:Datatype . x=x), a formula
that does not use partiality (does not use any constructor
or selector) -}
pr_annoted_dt :: CASL_SL s
-> (CASL_SL s -> a -> (Maybe a, [SORT]))
-> Annoted a -> (Maybe (Annoted a), [SORT])
pr_annoted_dt sl f a =
let (res, lst) = f sl (item a)
in (fmap (`replaceAnnoted` a) res
, lst)
-- keep an element if its computed sublogic is in the given sublogic
pr_check :: Lattice a => CASL_SL a -> (b -> CASL_SL a)
-> b -> Maybe b
pr_check l f e = if in_x l e f then Just e else Nothing
checkRecord :: CASL_SL a -> (CASL_SL a -> f -> Maybe (FORMULA f))
-> Record f (FORMULA f) (TERM f)
checkRecord l ff = (mapRecord id)
{ foldExtFORMULA = \ o _ -> case o of
ExtFORMULA f -> fromMaybe (error "checkRecord") $ ff l f
_ -> error "checkRecord.foldExtFORMULA" }
toCheck :: Lattice a => CASL_SL a
-> (CASL_SL a -> f -> Maybe (FORMULA f))
-> f -> CASL_SL a
toCheck l ff = maybe top (const l) . ff l
pr_formula :: Lattice a => (CASL_SL a -> f -> Maybe (FORMULA f))
-> CASL_SL a -> FORMULA f -> Maybe (FORMULA f)
pr_formula ff l =
fmap (foldFormula $ checkRecord l ff)
. pr_check l (sl_formula $ toCheck l ff)
pr_term :: Lattice a => (CASL_SL a -> f -> Maybe (FORMULA f))
-> CASL_SL a -> TERM f -> Maybe (TERM f)
pr_term ff l =
fmap (foldTerm $ checkRecord l ff)
. pr_check l (sl_term $ toCheck l ff)
-- make full Annoted Sig_items out of a SORT list
pr_make_sorts :: [SORT] -> Annoted (BASIC_ITEMS b s f)
pr_make_sorts s =
Annoted (Sig_items (Sort_items NonEmptySorts
[Annoted (Sort_decl s nullRange) nullRange [] []]
nullRange))
nullRange [] []
{- when processing BASIC_SPEC, add a Sort_decl in front for sorts
defined by DATATYPE_DECLs that had to be removed completely,
otherwise formulas might be broken by the missing sorts, thus
breaking the projection -}
pr_basic_spec :: Lattice a =>
(CASL_SL a -> b -> (Maybe (BASIC_ITEMS b s f), [SORT]))
-> (CASL_SL a -> s -> (Maybe (SIG_ITEMS s f), [SORT]))
-> (CASL_SL a -> f -> Maybe (FORMULA f))
-> CASL_SL a -> BASIC_SPEC b s f -> BASIC_SPEC b s f
pr_basic_spec fb fs ff l (Basic_spec s) =
let
res = map (pr_annoted_dt l $ pr_basic_items fb fs ff) s
items = mapMaybe fst res
toAdd = concatMap snd res
ret = if null toAdd then
items
else
pr_make_sorts toAdd : items
in
Basic_spec ret
{- returns a non-empty list of [SORT] if datatypes had to be removed
completely -}
pr_basic_items :: Lattice a =>
(CASL_SL a -> b -> (Maybe (BASIC_ITEMS b s f), [SORT]))
-> (CASL_SL a -> s -> (Maybe (SIG_ITEMS s f), [SORT]))
-> (CASL_SL a -> f -> Maybe (FORMULA f))
-> CASL_SL a -> BASIC_ITEMS b s f
-> (Maybe (BASIC_ITEMS b s f), [SORT])
pr_basic_items fb fs ff l bi = case bi of
Sig_items s ->
let
(res, lst) = pr_sig_items fs ff l s
in
if isNothing res then
(Nothing, lst)
else
(Just (Sig_items (fromJust res)), lst)
Free_datatype sk d p ->
let
(res, pos) = mapPos 2 p (pr_annoted l pr_datatype_decl) d
lst = pr_lost_dt l (map item d)
in
if null res then
(Nothing, lst)
else
(Just (Free_datatype sk res pos), lst)
Sort_gen s p ->
if has_cons l then
let
tmp = map (pr_annoted_dt l $ pr_sig_items fs ff) s
res = mapMaybe fst tmp
lst = concatMap snd tmp
in
if null res then
(Nothing, lst)
else
(Just (Sort_gen res p), lst)
else
(Nothing, [])
Var_items v p -> (Just (Var_items v p), [])
Local_var_axioms v f p ->
let
(res, pos) = mapPos (length v) p
(pr_annoted l $ pr_formula ff) f
in
if null res then
(Nothing, [])
else
(Just (Local_var_axioms v res pos), [])
Axiom_items f p ->
let
(res, pos) = mapPos 0 p (pr_annoted l $ pr_formula ff) f
in
if null res then
(Nothing, [])
else
(Just (Axiom_items res pos), [])
Ext_BASIC_ITEMS b -> fb l b
pr_datatype_decl :: CASL_SL a -> DATATYPE_DECL -> Maybe DATATYPE_DECL
pr_datatype_decl l (Datatype_decl s a p) =
let
(res, pos) = mapPos 1 p (pr_annoted l pr_alternative) a
in
if null res then
Nothing
else
Just (Datatype_decl s res pos)
pr_alternative :: CASL_SL a -> ALTERNATIVE -> Maybe ALTERNATIVE
pr_alternative l alt = case alt of
Alt_construct Total n c p ->
let
(res, pos) = mapPos 1 p (pr_components l) c
in
if null res then
Nothing
else
Just (Alt_construct Total n res pos)
Alt_construct Partial _ _ _ ->
if has_part l then
Just alt
else
Nothing
Subsorts s p ->
if has_sub l then
Just (Subsorts s p)
else
Nothing
pr_components :: CASL_SL a -> COMPONENTS -> Maybe COMPONENTS
pr_components l sel = case sel of
Cons_select Partial _ _ _ ->
if has_part l then
Just sel
else
Nothing
_ -> Just sel
{- takes a list of datatype declarations and checks whether a
whole declaration is invalid in the given sublogic - if this
is the case, the sort that would be declared by the type is
added to a list of SORT that is emitted -}
pr_lost_dt :: CASL_SL a -> [DATATYPE_DECL] -> [SORT]
pr_lost_dt sl = concatMap (\ dt@(Datatype_decl s _ _) ->
case pr_datatype_decl sl dt of
Nothing -> [s]
_ -> [])
pr_symbol :: Lattice a => CASL_SL a -> Symbol -> Maybe Symbol
pr_symbol l = pr_check l sl_symbol
{- returns a non-empty list of [SORT] if datatypes had to be removed
completely -}
pr_sig_items :: Lattice a =>
(CASL_SL a -> s -> (Maybe (SIG_ITEMS s f), [SORT]))
-> (CASL_SL a -> f -> Maybe (FORMULA f))
-> CASL_SL a -> SIG_ITEMS s f -> (Maybe (SIG_ITEMS s f), [SORT])
pr_sig_items sf ff l si = case si of
Sort_items sk s p ->
let
(res, pos) = mapPos 1 p (pr_annoted l pr_sort_item) s
in
if null res then
(Nothing, [])
else
(Just (Sort_items sk res pos), [])
Op_items o p ->
let
(res, pos) = mapPos 1 p (pr_annoted l $ pr_op_item ff) o
in
if null res then
(Nothing, [])
else
(Just (Op_items res pos), [])
Pred_items i p ->
if has_pred l then
(Just (Pred_items i p), [])
else
(Nothing, [])
Datatype_items sk d p ->
let
(res, pos) = mapPos 1 p (pr_annoted l pr_datatype_decl) d
lst = pr_lost_dt l (map item d)
in
if null res then
(Nothing, lst)
else
(Just (Datatype_items sk res pos), lst)
Ext_SIG_ITEMS s -> sf l s
pr_op_item :: Lattice a => (CASL_SL a -> f -> Maybe (FORMULA f))
-> CASL_SL a -> OP_ITEM f -> Maybe (OP_ITEM f)
pr_op_item ff l oi = case oi of
Op_defn o h f r -> do
g <- pr_annoted l (pr_term ff) f
return $ Op_defn o h g r
_ -> Just oi
{- subsort declarations and definitions are reduced to simple
sort declarations if the sublogic disallows subsorting to
avoid loosing sorts in the projection -}
pr_sort_item :: CASL_SL a -> SORT_ITEM f -> Maybe (SORT_ITEM f)
pr_sort_item _ (Sort_decl s p) = Just (Sort_decl s p)
pr_sort_item l (Subsort_decl sl s p) =
if has_sub l then
Just (Subsort_decl sl s p)
else
Just (Sort_decl (s : sl) nullRange)
pr_sort_item l (Subsort_defn s1 v s2 f p) =
if has_sub l then
Just (Subsort_defn s1 v s2 f p)
else
Just (Sort_decl [s1] nullRange)
pr_sort_item _ (Iso_decl s p) = Just (Iso_decl s p)
pr_symb_items :: Lattice a => CASL_SL a -> SYMB_ITEMS
-> Maybe SYMB_ITEMS
pr_symb_items l (Symb_items k s p) =
if in_x l k sl_symb_kind then
let
(res, pos) = mapPos 1 p (pr_symb l) s
in
if null res then
Nothing
else
Just (Symb_items k res pos)
else
Nothing
pr_symb_map_items :: Lattice a => CASL_SL a -> SYMB_MAP_ITEMS
-> Maybe SYMB_MAP_ITEMS
pr_symb_map_items l (Symb_map_items k s p) =
if in_x l k sl_symb_kind then
let
(res, pos) = mapPos 1 p (pr_symb_or_map l) s
in
if null res then
Nothing
else
Just (Symb_map_items k res pos)
else
Nothing
pr_symb_or_map :: Lattice a => CASL_SL a -> SYMB_OR_MAP
-> Maybe SYMB_OR_MAP
pr_symb_or_map l (Symb s) =
let
res = pr_symb l s
in
if isNothing res then
Nothing
else
Just (Symb (fromJust res))
pr_symb_or_map l (Symb_map s t p) =
let
a = pr_symb l s
b = pr_symb l t
in
if isJust a && isJust b then
Just (Symb_map s t p)
else
Nothing
pr_symb :: Lattice a => CASL_SL a -> SYMB -> Maybe SYMB
pr_symb _ (Symb_id i) = Just (Symb_id i)
pr_symb l (Qual_id i t p) =
if in_x l t sl_type then
Just (Qual_id i t p)
else
Nothing
pr_sign :: CASL_SL a -> Sign f e -> Sign f e
pr_sign _sl s = s -- do something here
pr_morphism :: Lattice a => CASL_SL a -> Morphism f e m
-> Morphism f e m
pr_morphism l m =
m { msource = pr_sign l $ msource m
, mtarget = pr_sign l $ mtarget m
, op_map = pr_op_map l $ op_map m
, pred_map = pr_pred_map l $ pred_map m }
{- predicates only rely on the has_pred feature, so the map
can be kept or removed as a whole -}
pr_pred_map :: CASL_SL a -> Pred_map -> Pred_map
pr_pred_map l x = if has_pred l then x else Map.empty
pr_op_map :: Lattice a => CASL_SL a -> Op_map -> Op_map
pr_op_map = Map.filterWithKey . pr_op_map_entry
pr_op_map_entry :: Lattice a => CASL_SL a -> (Id, OpType) -> (Id, OpKind)
-> Bool
pr_op_map_entry l (_, t) (_, b) =
has_part l || in_x l t sl_optype && b == Partial
{- compute a morphism that consists of the original signature
and the projected signature -}
pr_epsilon :: m -> CASL_SL a -> Sign f e -> Morphism f e m
pr_epsilon extEm l s = embedMorphism extEm s $ pr_sign l s