{-# LANGUAGE DeriveDataTypeable #-}

{- |

Module : ./CASL/AS_Basic_CASL.der.hs

Description : Abstract syntax of CASL basic specifications

Copyright : (c) Klaus Luettich, Christian Maeder, Uni Bremen 2002-2006

License : GPLv2 or higher, see LICENSE.txt

Maintainer : Christian.Maeder@dfki.de

Stability : provisional

Portability : portable

Abstract Syntax of CASL Basic_specs, Symb_items and Symb_map_items.

Follows Sect. II:2.2 of the CASL Reference Manual.

-}

module CASL.AS_Basic_CASL where

import Common.Id

import Common.AS_Annotation

import Data.Data

import Data.Function

import Data.List

import qualified Data.Set as Set

-- DrIFT command

{-! global: GetRange !-}

data BASIC_SPEC b s f = Basic_spec [Annoted (BASIC_ITEMS b s f)]

deriving (Show, Typeable, Data)

data BASIC_ITEMS b s f = Sig_items (SIG_ITEMS s f)

{- the Annotation following the keyword is dropped

but preceding the keyword is now an Annotation allowed -}

| Free_datatype SortsKind [Annoted DATATYPE_DECL] Range

-- pos: free, type, semi colons

| Sort_gen [Annoted (SIG_ITEMS s f)] Range

-- pos: generated, opt. braces

| Var_items [VAR_DECL] Range

-- pos: var, semi colons

| Local_var_axioms [VAR_DECL] [Annoted (FORMULA f)] Range

-- pos: forall, semi colons, dots

| Axiom_items [Annoted (FORMULA f)] Range

-- pos: dots

| Ext_BASIC_ITEMS b

deriving (Show, Typeable, Data)

data SortsKind = NonEmptySorts | PossiblyEmptySorts deriving (Show, Typeable, Data)

data SIG_ITEMS s f = Sort_items SortsKind [Annoted (SORT_ITEM f)] Range

-- pos: sort, semi colons

| Op_items [Annoted (OP_ITEM f)] Range

-- pos: op, semi colons

| Pred_items [Annoted (PRED_ITEM f)] Range

-- pos: pred, semi colons

| Datatype_items SortsKind [Annoted DATATYPE_DECL] Range

-- type, semi colons

| Ext_SIG_ITEMS s

deriving (Show, Typeable, Data)

data SORT_ITEM f = Sort_decl [SORT] Range

-- pos: commas

| Subsort_decl [SORT] SORT Range

-- pos: commas, <

| Subsort_defn SORT VAR SORT (Annoted (FORMULA f)) Range

{- pos: "=", "{", ":", ".", "}"

the left anno list stored in Annoted Formula is

parsed after the equal sign -}

| Iso_decl [SORT] Range

-- pos: "="s

deriving (Show, Typeable, Data)

data OP_ITEM f = Op_decl [OP_NAME] OP_TYPE [OP_ATTR f] Range

-- pos: commas, colon, OP_ATTR sep. by commas

| Op_defn OP_NAME OP_HEAD (Annoted (TERM f)) Range

-- pos: "="

deriving (Show, Typeable, Data)

data OpKind = Total | Partial deriving (Show, Eq, Ord, Typeable, Data)

data OP_TYPE = Op_type OpKind [SORT] SORT Range

-- pos: "*"s, "->" ; if null [SORT] then Range = [] or pos: "?"

deriving (Show, Eq, Ord, Typeable, Data)

args_OP_TYPE :: OP_TYPE -> [SORT]

args_OP_TYPE (Op_type _ args _ _) = args

res_OP_TYPE :: OP_TYPE -> SORT

res_OP_TYPE (Op_type _ _ res _) = res

data OP_HEAD = Op_head OpKind [VAR_DECL] (Maybe SORT) Range

-- pos: "(", semicolons, ")", colon

deriving (Show, Eq, Ord, Typeable, Data)

data OP_ATTR f = Assoc_op_attr | Comm_op_attr | Idem_op_attr

| Unit_op_attr (TERM f)

deriving (Show, Eq, Ord, Typeable, Data)

data PRED_ITEM f = Pred_decl [PRED_NAME] PRED_TYPE Range

-- pos: commas, colon

| Pred_defn PRED_NAME PRED_HEAD (Annoted (FORMULA f)) Range

-- pos: "<=>"

deriving (Show, Typeable, Data)

data PRED_TYPE = Pred_type [SORT] Range

-- pos: if null [SORT] then "(",")" else "*"s

deriving (Show, Eq, Ord, Typeable, Data)

data PRED_HEAD = Pred_head [VAR_DECL] Range

-- pos: "(",semi colons , ")"

deriving (Show, Typeable, Data)

data DATATYPE_DECL = Datatype_decl SORT [Annoted ALTERNATIVE] Range

-- pos: "::=", "|"s

deriving (Show, Typeable, Data)

data ALTERNATIVE = Alt_construct OpKind OP_NAME [COMPONENTS] Range

-- pos: "(", semi colons, ")" optional "?"

| Subsorts [SORT] Range

-- pos: sort, commas

deriving (Show, Typeable, Data)

data COMPONENTS = Cons_select OpKind [OP_NAME] SORT Range

-- pos: commas, colon or ":?"

| Sort SORT

deriving (Show, Typeable, Data)

data VAR_DECL = Var_decl [VAR] SORT Range

-- pos: commas, colon

deriving (Show, Eq, Ord, Typeable, Data)

varDeclRange :: VAR_DECL -> [Pos]

varDeclRange (Var_decl vs s _) = case vs of

[] -> []

v : _ -> joinRanges [tokenRange v, idRange s]

{- Position definition for FORMULA:

Information on parens are also encoded in Range. If there

are more Pos than necessary there is a pair of Pos enclosing the

other Pos informations which encode the brackets of every kind

-}

data Junctor = Con | Dis deriving (Show, Eq, Ord, Typeable, Data)

dualJunctor :: Junctor -> Junctor

dualJunctor Con = Dis

dualJunctor Dis = Con

data Relation = Implication | RevImpl | Equivalence

deriving (Show, Eq, Ord, Typeable, Data)

data Equality = Strong | Existl deriving (Show, Eq, Ord, Typeable, Data)

data FORMULA f = Quantification QUANTIFIER [VAR_DECL] (FORMULA f) Range

-- pos: QUANTIFIER, semi colons, dot

| Junction Junctor [FORMULA f] Range

-- pos: "/\"s or "\/"s

| Relation (FORMULA f) Relation (FORMULA f) Range

{- pos: "<=>", "=>" or "if"

Note: The first formula is the premise also for "if"!

Explicitly: During parsing, "f2 if f1" is saved as

"Relation f1 RevImpl f2 _" -}

| Negation (FORMULA f) Range

-- pos: not

| Atom Bool Range

-- pos: true or false

| Predication PRED_SYMB [TERM f] Range

-- pos: opt. "(",commas,")"

| Definedness (TERM f) Range

-- pos: def

| Equation (TERM f) Equality (TERM f) Range

-- pos: =e= or =

| Membership (TERM f) SORT Range

-- pos: in

| Mixfix_formula (TERM f)

{- Mixfix_ Term/Token/(..)/[..]/{..}

a formula left original for mixfix analysis -}

| Unparsed_formula String Range

-- pos: first Char in String

| Sort_gen_ax [Constraint] Bool -- flag: belongs to a free type?

| QuantOp OP_NAME OP_TYPE (FORMULA f) -- second order quantifiers

| QuantPred PRED_NAME PRED_TYPE (FORMULA f)

| ExtFORMULA f

-- needed for CASL extensions

deriving (Show, Eq, Ord, Typeable, Data)

mkSort_gen_ax :: [Constraint] -> Bool -> FORMULA f

mkSort_gen_ax = Sort_gen_ax . sortConstraints

is_True_atom :: FORMULA f -> Bool

is_True_atom f = case f of

Atom b _ -> b

_ -> False

is_False_atom :: FORMULA f -> Bool

is_False_atom f = case f of

Atom b _ -> not b

_ -> False

boolForm :: Bool -> FORMULA f

boolForm b = Atom b nullRange

trueForm :: FORMULA f

trueForm = boolForm True

falseForm :: FORMULA f

falseForm = boolForm False

{- In the CASL institution, sort generation constraints have an

additional signature morphism component (Sect. III:2.1.3, p.134 of the

CASL Reference Manual). The extra signature morphism component is

needed because the naive translation of sort generation constraints

along signature morphisms may violate the satisfaction condition,

namely when sorts are identified by the translation, with the effect

that new terms can be formed. We avoid this extra component here and

instead use natural numbers to decorate sorts, in this way retaining

their identity w.r.t. the original signature. The newSort in a

Constraint is implicitly decorated with its index in the list of

Constraints. The opSymbs component collects all the operation symbols

with newSort (with that index!) as a result sort. The argument sorts

of an operation symbol are decorated explicitly via a list [Int] of

integers. The origSort in a Constraint is the original sort

corresponding to the index. A negative index indicates a sort outside

the constraint (i.e. a "parameter sort"). Note that this representation of

sort generation constraints is efficiently tailored towards both the use in

the proof calculus (Chap. IV:2, p. 282 of the CASL Reference Manual)

and the coding into second order logic (p. 429 of Theoret. Comp. Sci. 286).

-}

data Constraint = Constraint { newSort :: SORT,

opSymbs :: [(OP_SYMB, [Int])],

origSort :: SORT }

deriving (Show, Typeable, Data)

instance Ord Constraint where

compare (Constraint s1 cs1 _) (Constraint s2 cs2 _) =

compare (s1, map fst cs1) (s2, map fst cs2)

instance Eq Constraint where

a == b = compare a b == EQ

sortConstraints :: [Constraint] -> [Constraint]

sortConstraints cs = let

nCs = sort cs

iS = map(\ c -> let

Just j = findIndex ((origSort c ==) . origSort) nCs in j) cs

updInd i = if i < 0 then i else iS !! i

in

map (\ (Constraint s os o) ->

Constraint s (sortBy (on compare fst)

$ map (\ (c, is) -> (c, map updInd is)) os) o) nCs

-- | no duplicate sorts, i.e. injective sort map?

isInjectiveList :: Ord a => [a] -> Bool

isInjectiveList l = Set.size (Set.fromList l) == length l

{- | from a Sort_gex_ax, recover:

a traditional sort generation constraint plus a sort mapping -}

recover_Sort_gen_ax :: [Constraint] ->

([SORT], [OP_SYMB], [(SORT, SORT)])

recover_Sort_gen_ax constrs =

if isInjectiveList sorts

-- we can ignore indices

then (sorts, map fst (concatMap opSymbs constrs), [])

{- otherwise, we have to introduce new sorts for the indices

and afterwards rename them into the sorts they denote -}

else (origSorts, indOps, zip origSorts sorts)

where

sorts = map newSort constrs

origSorts = map origSort constrs

indSort s i = if i < 0 then s else origSorts !! i

indOps = concatMap (\ c -> map (indOp $ origSort c) $ opSymbs c) constrs

indOp res (Qual_op_name opn (Op_type k args1 _ pos1) pos, args) =

Qual_op_name opn

(Op_type k (zipWith indSort args1 args) res pos1) pos

indOp _ _ = error

"CASL/AS_Basic_CASL: Internal error: Unqualified OP_SYMB in Sort_gen_ax"

{- | from a Sort_gen_ax, recover:

the sorts, each paired with the constructors -}

recoverSortGen :: [Constraint] -> [(SORT, [OP_SYMB])]

recoverSortGen = map $ \ c -> (newSort c, map fst $ opSymbs c)

{- | from a free Sort_gen_ax, recover:

the sorts, each paired with the constructors

fails (i.e. delivers Nothing) if the sort map is not injective -}

recover_free_Sort_gen_ax :: [Constraint] -> Maybe [(SORT, [OP_SYMB])]

recover_free_Sort_gen_ax constrs =

if isInjectiveList $ map newSort constrs

then Just $ recoverSortGen constrs

else Nothing

-- | determine whether a formula is a sort generation constraint

isSortGen :: FORMULA f -> Bool

isSortGen f = case f of

Sort_gen_ax _ _ -> True

_ -> False

data QUANTIFIER = Universal | Existential | Unique_existential

deriving (Show, Eq, Ord, Typeable, Data)

data PRED_SYMB = Pred_name PRED_NAME

| Qual_pred_name PRED_NAME PRED_TYPE Range

-- pos: "(", pred, colon, ")"

deriving (Show, Eq, Ord, Typeable, Data)

predSymbName :: PRED_SYMB -> PRED_NAME

predSymbName p = case p of

Pred_name n -> n

Qual_pred_name n _ _ -> n

data TERM f = Qual_var VAR SORT Range -- pos: "(", var, colon, ")"

| Application OP_SYMB [TERM f] Range

-- pos: parens around TERM f if any and seperating commas

| Sorted_term (TERM f) SORT Range

-- pos: colon

| Cast (TERM f) SORT Range

-- pos: "as"

| Conditional (TERM f) (FORMULA f) (TERM f) Range

-- pos: "when", "else"

| Unparsed_term String Range -- SML-CATS

-- A new intermediate state

| Mixfix_qual_pred PRED_SYMB -- as part of a mixfix formula

| Mixfix_term [TERM f] -- not starting with Mixfix_sorted_term/cast

| Mixfix_token Token -- NO-BRACKET-TOKEN, LITERAL, PLACE

| Mixfix_sorted_term SORT Range

-- pos: colon

| Mixfix_cast SORT Range

-- pos: "as"

| Mixfix_parenthesized [TERM f] Range

{- non-emtpy term list

pos: "(", commas, ")" -}

| Mixfix_bracketed [TERM f] Range

-- pos: "[", commas, "]"

| Mixfix_braced [TERM f] Range

{- also for list-notation

pos: "{", "}" -}

| ExtTERM f

deriving (Show, Eq, Ord, Typeable, Data)

-- | state after mixfix- but before overload resolution

varOrConst :: Token -> TERM f

varOrConst t = Application (Op_name $ simpleIdToId t) [] $ tokPos t

data OP_SYMB = Op_name OP_NAME

| Qual_op_name OP_NAME OP_TYPE Range

-- pos: "(", op, colon, ")"

deriving (Show, Eq, Ord, Typeable, Data)

opSymbName :: OP_SYMB -> OP_NAME

opSymbName o = case o of

Op_name n -> n

Qual_op_name n _ _ -> n

-- * short cuts for terms and formulas

-- | create binding if variables are non-null

mkForallRange :: [VAR_DECL] -> FORMULA f -> Range -> FORMULA f

mkForallRange vl f ps =

if null vl then f else Quantification Universal vl f ps

mkForall :: [VAR_DECL] -> FORMULA f -> FORMULA f

mkForall vl f = mkForallRange vl f nullRange

-- | create an existential binding

mkExist :: [VAR_DECL] -> FORMULA f -> FORMULA f

mkExist vs f = Quantification Existential vs f nullRange

-- | convert a singleton variable declaration into a qualified variable

toQualVar :: VAR_DECL -> TERM f

toQualVar (Var_decl v s ps) =

if isSingle v then Qual_var (head v) s ps else error "toQualVar"

mkRel :: Relation -> FORMULA f -> FORMULA f -> FORMULA f

mkRel r f f' = Relation f r f' nullRange

mkImpl :: FORMULA f -> FORMULA f -> FORMULA f

mkImpl = mkRel Implication

mkAnyEq :: Equality -> TERM f -> TERM f -> FORMULA f

mkAnyEq e f f' = Equation f e f' nullRange

mkExEq :: TERM f -> TERM f -> FORMULA f

mkExEq = mkAnyEq Existl

mkStEq :: TERM f -> TERM f -> FORMULA f

mkStEq = mkAnyEq Strong

mkEqv :: FORMULA f -> FORMULA f -> FORMULA f

mkEqv = mkRel Equivalence

mkAppl :: OP_SYMB -> [TERM f] -> TERM f

mkAppl op_symb fs = Application op_symb fs nullRange

mkPredication :: PRED_SYMB -> [TERM f] -> FORMULA f

mkPredication symb fs = Predication symb fs nullRange

-- | turn sorted variable into variable delcaration

mkVarDecl :: VAR -> SORT -> VAR_DECL

mkVarDecl v s = Var_decl [v] s nullRange

-- | turn sorted variable into term

mkVarTerm :: VAR -> SORT -> TERM f

mkVarTerm v = toQualVar . mkVarDecl v

-- | optimized conjunction

conjunctRange :: [FORMULA f] -> Range -> FORMULA f

conjunctRange fs ps = case fs of

[] -> Atom True ps

[phi] -> phi

_ -> Junction Con fs ps

conjunct :: [FORMULA f] -> FORMULA f

conjunct fs = conjunctRange fs nullRange

disjunctRange :: [FORMULA f] -> Range -> FORMULA f

disjunctRange fs ps = case fs of

[] -> Atom False ps

[phi] -> phi

_ -> Junction Dis fs ps

disjunct :: [FORMULA f] -> FORMULA f

disjunct fs = disjunctRange fs nullRange

mkQualOp :: OP_NAME -> OP_TYPE -> OP_SYMB

mkQualOp f ty = Qual_op_name f ty nullRange

mkQualPred :: PRED_NAME -> PRED_TYPE -> PRED_SYMB

mkQualPred f ty = Qual_pred_name f ty nullRange

negateForm :: FORMULA f -> Range -> FORMULA f

negateForm f r = case f of

Atom b ps -> Atom (not b) ps

Negation nf _ -> nf

_ -> Negation f r

mkNeg :: FORMULA f -> FORMULA f

mkNeg f = negateForm f nullRange

mkVarDeclStr :: String -> SORT -> VAR_DECL

mkVarDeclStr = mkVarDecl . mkSimpleId

-- * type synonyms

type CASLFORMULA = FORMULA ()

type CASLTERM = TERM ()

type OP_NAME = Id

type PRED_NAME = Id

type SORT = Id

type VAR = Token

data SYMB_ITEMS = Symb_items SYMB_KIND [SYMB] Range

-- pos: SYMB_KIND, commas

deriving (Show, Eq, Ord, Typeable, Data)

symbItemsName :: SYMB_ITEMS -> [String]

symbItemsName (Symb_items _ syms _ ) =

map (\x -> case x of

Symb_id i -> show i

Qual_id i _ _ -> show i) syms

data SYMB_MAP_ITEMS = Symb_map_items SYMB_KIND [SYMB_OR_MAP] Range

-- pos: SYMB_KIND, commas

deriving (Show, Eq, Ord, Typeable, Data)

data SYMB_KIND = Implicit | Sorts_kind

| Ops_kind | Preds_kind

deriving (Show, Eq, Ord, Typeable, Data)

data SYMB = Symb_id Id

| Qual_id Id TYPE Range

-- pos: colon

deriving (Show, Eq, Ord, Typeable, Data)

data TYPE = O_type OP_TYPE

| P_type PRED_TYPE

| A_type SORT -- ambiguous pred or (constant total) op

deriving (Show, Eq, Ord, Typeable, Data)

data SYMB_OR_MAP = Symb SYMB

| Symb_map SYMB SYMB Range

-- pos: "|->"

deriving (Show, Eq, Ord, Typeable, Data)