{- |

Module : $Header$

Description : Abstract syntax of CASL basic specifications

Copyright : (c) Klaus L�ttich, Christian Maeder, Uni Bremen 2002-2006

License : similar to LGPL, see HetCATS/LICENSE.txt or LIZENZ.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.List (nub)

-- DrIFT command

{-! global: UpPos !-}

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

deriving Show

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 [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

data SortsKind = NonEmptySorts | PossiblyEmptySorts deriving Show

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 [Annoted DATATYPE_DECL] Range

-- type, semi colons

| Ext_SIG_ITEMS s

deriving Show

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

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

data FunKind = Total | Partial deriving (Show, Eq, Ord)

data OP_TYPE = Op_type FunKind [SORT] SORT Range

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

deriving (Show, Eq, Ord)

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 FunKind [ARG_DECL] SORT Range

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

deriving Show

data ARG_DECL = Arg_decl [VAR] SORT Range

-- pos: commas, colon

deriving Show

data OP_ATTR f = Assoc_op_attr | Comm_op_attr | Idem_op_attr

| Unit_op_attr (TERM f)

deriving (Show, Eq, Ord)

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

data PRED_TYPE = Pred_type [SORT] Range

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

deriving (Show, Eq, Ord)

data PRED_HEAD = Pred_head [ARG_DECL] Range

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

deriving Show

data DATATYPE_DECL = Datatype_decl SORT [Annoted ALTERNATIVE] Range

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

deriving Show

data ALTERNATIVE = Alt_construct FunKind OP_NAME [COMPONENTS] Range

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

| Subsorts [SORT] Range

-- pos: sort, commas

deriving Show

data COMPONENTS = Cons_select FunKind [OP_NAME] SORT Range

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

| Sort SORT

deriving Show

data VAR_DECL = Var_decl [VAR] SORT Range

-- pos: commas, colon

deriving (Show, Eq, Ord)

{- 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 FORMULA f = Quantification QUANTIFIER [VAR_DECL] (FORMULA f) Range

-- pos: QUANTIFIER, semi colons, dot

| Conjunction [FORMULA f] Range

-- pos: "/\"s

| Disjunction [FORMULA f] Range

-- pos: "\/"s

| Implication (FORMULA f) (FORMULA f) Bool Range

-- pos: "=>" or "if" (True -> "=>")

| Equivalence (FORMULA f) (FORMULA f) Range

-- pos: "<=>"

| Negation (FORMULA f) Range

-- pos: not

| True_atom Range

-- pos: true

| False_atom Range

-- pos: false

| Predication PRED_SYMB [TERM f] Range

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

| Definedness (TERM f) Range

-- pos: def

| Existl_equation (TERM f) (TERM f) Range

-- pos: =e=

| Strong_equation (TERM f) (TERM f) Range

-- pos: =

| 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?

| ExtFORMULA f

-- needed for CASL extensions

deriving (Show, Eq, Ord)

is_True_atom, is_False_atom :: FORMULA f -> Bool

is_True_atom (True_atom _) = True

is_True_atom _ = False

is_False_atom (False_atom _) = True

is_False_atom _ = 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, Eq, Ord)

-- | 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 length (nub sorts) == length sorts

-- no duplicate sorts, i.e. injective sort map? Then we can ignore indices

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

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

-- and afterwards rename them into the sorts they denote

else (map indSort1 indices,map indOp indOps1,map sortMap indSorts)

where

sorts = map newSort constrs

indices = [0..length sorts-1]

indSorts = zip indices sorts

indSort (i,s) = if i<0 then s else indSort1 i

indSort1 i = origSort $ head (drop i constrs)

sortMap (i,s) = (indSort1 i,s)

indOps = zip indices (map opSymbs constrs)

indOps1 = concat (map (\(i,ops) -> map ((,) i) ops) indOps)

indOp (res,(Qual_op_name on (Op_type k args1 res1 pos1) pos,args)) =

Qual_op_name on

(Op_type k (map indSort (zip args args1))

(indSort (res,res1)) pos1) pos

indOp _ = error

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

-- | from a free Sort_gex_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 length (nub sorts) == length sorts

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

then Just $ map getOpProfile constrs

else Nothing

where

sorts = map newSort constrs

getOpProfile constr = (newSort constr,map fst $ opSymbs constr)

data QUANTIFIER = Universal | Existential | Unique_existential

deriving (Show, Eq, Ord)

data PRED_SYMB = Pred_name PRED_NAME

| Qual_pred_name PRED_NAME PRED_TYPE Range

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

deriving (Show, Eq, Ord)

data TERM f = Simple_id SIMPLE_ID -- "Var" might be a better constructor

| 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: "{", "}"

deriving (Show, Eq, Ord)

data OP_SYMB = Op_name OP_NAME

| Qual_op_name OP_NAME OP_TYPE Range

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

deriving (Show, Eq, Ord)

type CASLFORMULA = FORMULA ()

type CASLTERM = TERM ()

type OP_NAME = Id

type PRED_NAME = Id

type SORT = Id

type VAR = SIMPLE_ID

-----

data SYMB_ITEMS = Symb_items SYMB_KIND [SYMB] Range

-- pos: SYMB_KIND, commas

deriving (Show, Eq)

data SYMB_MAP_ITEMS = Symb_map_items SYMB_KIND [SYMB_OR_MAP] Range

-- pos: SYMB_KIND, commas

deriving (Show, Eq)

data SYMB_KIND = Implicit | Sorts_kind

| Ops_kind | Preds_kind

deriving (Show, Eq)

data SYMB = Symb_id Id

| Qual_id Id TYPE Range

-- pos: colon

deriving (Show, Eq)

data TYPE = O_type OP_TYPE

| P_type PRED_TYPE

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

deriving (Show, Eq)

data SYMB_OR_MAP = Symb SYMB

| Symb_map SYMB SYMB Range

-- pos: "|->"

deriving (Show, Eq)