{- HetCATS/HasCASL/Le.hs

$Id$

Authors: Christian Maeder

Year: 2002

abstract syntax after/during static analysis

-}

module Le where

import Id

import Set

type TypeId = Id

-- "*", "->", etc. are predefined type constructors

-- the unit type is the empty product

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

-- Kinds

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

data Kind = Star ExtClass | Kfun Kind Kind

instance Eq Kind where

Star _ == Star _ = True

Kfun f1 a1 == Kfun f2 a2 = f1 == f2 && a1 == a2

_ == _ = False

instance Ord Kind where

Star _ <= Star _ = True

Kfun f1 a1 <= Kfun f2 a2 = if f1 <= f2 then

if f2 <= f1 then a1 <= a2

else True

else False

Star _ <= Kfun _ _ = True

Kfun _ _ <= Star _ = False

type ClassId = Id

data Class = Universe

| ClassName ClassId

| Intersection (Set ClassId)

data Variance = CoVar | ContraVar | InVar

data ExtClass = ExtClass Class Variance

star :: Kind

star = Star $ ExtClass Universe InVar

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

-- Types

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

data Tyvar = Tyvar { typeVarId :: TypeId, typeKind :: Kind } deriving (Eq, Ord)

data Tycon = Tycon TypeId Kind

deriving Eq

data Type = TVar Tyvar | TCon Tycon | TAp Type Type | TGen Int

deriving Eq

data Pred = IsIn Id Type

deriving Eq

data Qual t = [Pred] :=> t

deriving Eq

data Scheme = Scheme [Kind] (Qual Type)

deriving Eq

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

-- Symbols

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

data SymbType = OpType Scheme

| TypeKind Kind

| Class

data Symbol = Symbol {symbId :: Id, sumbType :: SymbType}

-- the list of items which are part of a "sort-gen" (or free type)

type GenItems = [Symbol]

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

-- Items

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

data GenKind = Free | Generated | Loose deriving (Show,Eq)

data VarDecl = VarDecl { varId :: Id, varType :: Type }

data TypeBody = Alias Type -- non-recursive

| Datatype [Alternative] GenKind GenItems

| SubtypeDefn VarDecl Type Term -- a formula

-- type variables correspond to the kind

data TypeDefn = TypeDefn [Tyvar] TypeBody

-- full function type of constructor (result sort is the data type)

data Alternative = Construct Id Type [Component]

| Subtype Type

-- full function type of a selector (result sort is component sort)

data Component = Component (Maybe Id) Type

data ClassItem = ClassItem { classId :: Id

, subClasses :: [ClassId]

, superClasses :: [ClassId]

, classDefn :: Maybe Class

, classBody :: [SigItem]

}

data TypeRel = TypeRel [Tyvar] Type Type

data TypeItem = TypeItem{ typeConstrId :: Id

, itemKind :: Kind

, subtypes :: [TypeRel]

, supertypes :: [TypeRel]

, typeDefn :: Maybe TypeDefn

}

type ConsId = Symbol

type SelId = Symbol

data OpDefn = OpDef [VarDecl] Term

| Constr ConsId

| Select [ConsId] SelId

data BinOpAttr = Assoc | Comm | Idem deriving (Show)

data OpAttr = BinOpAttr BinOpAttr | UnitOpAttr Term

data OpItem = OpItem { opId :: Id

, opType :: Scheme

, opAttrs :: [OpAttr]

, opDefn :: Maybe OpDefn

}

data TypeOp = OfType | AsType | InType deriving (Eq)

data Binder = LambdaTotal | LambdaPartial

| Forall

| Exists | ExistsUnique

deriving (Eq)

data Term = BaseName Id Scheme [Type] -- instance

| VarId Id Type Class

| Application Term Term

| Binding Binder [VarDecl] Term

| Typed Term TypeOp Type

data SigItem = AClassItem ClassItem

| ATypeItem TypeItem

| AnOpItem OpItem