{- |

Module : $Header$

Copyright : (c) University of Cambridge, Cambridge, England

adaption (c) Till Mossakowski, Uni Bremen 2002-2005

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

Maintainer : maeder@tzi.de

Stability : provisional

Portability : portable

Data structures for Isabelle signatures and theories.

Adapted from Isabelle.

-}

module Isabelle.IsaSign where

import qualified Data.Map as Map

-------------------- not quite from src/Pure/term.ML ------------------------

----------------------------- Names -----------------------------------------

-- | type names

type TName = String

-- | names for values or constants (non-classes and non-types)

data VName = VName

{ new :: String -- ^ name within Isabelle

, altSyn :: Maybe AltSyntax -- ^ mixfix template syntax

} deriving Show

data AltSyntax = AltSyntax String [Int] Int deriving Show

mkVName :: String -> VName

mkVName s = VName { new = s, altSyn = Nothing }

-- | the original (Haskell) name

orig :: VName -> String

orig = new

instance Eq VName where

v1 == v2 = new v1 == new v2

instance Ord VName where

v1 <= v2 = new v1 <= new v2

{- | Indexnames can be quickly renamed by adding an offset to the integer part,

for resolution. -}

data Indexname = Indexname

{ unindexed :: String

, indexOffset :: Int

} deriving (Ord, Eq, Show)

{- Types are classified by sorts. -}

data IsaClass = IsaClass String

deriving (Ord, Eq, Show)

type Sort = [IsaClass]

{- The sorts attached to TFrees and TVars specify the sort of that variable -}

data Typ = Type { typeId :: TName,

typeSort :: Sort,

typeArgs :: [Typ] }

| TFree { typeId :: TName,

typeSort :: Sort }

| TVar { indexname :: Indexname,

typeSort :: Sort }

deriving (Eq, Ord, Show)

{-Terms. Bound variables are indicated by depth number.

Free variables, (scheme) variables and constants have names.

A term is "closed" if every bound variable of level "lev"

is enclosed by at least "lev" abstractions.

It is possible to create meaningless terms containing loose bound vars

or type mismatches. But such terms are not allowed in rules. -}

data Continuity = IsCont | NotCont deriving (Eq, Ord ,Show)

data Term =

Const { termName :: VName,

termType :: Typ }

| Free { termName :: VName }

| Abs { absVar :: Term,

termId :: Term,

continuity :: Continuity } -- lambda abstraction

| App { funId :: Term,

argId :: Term,

continuity :: Continuity } -- application

| If { ifId :: Term,

thenId :: Term,

elseId :: Term,

continuity :: Continuity }

| Case { termId :: Term,

caseSubst :: [(Term, Term)] }

| Let { letSubst :: [(Term, Term)],

inId :: Term }

| IsaEq { firstTerm :: Term,

secondTerm :: Term }

| Tuplex [Term] Continuity

deriving (Eq, Ord, Show)

data Sentence = Sentence { isSimp :: Bool -- True for "[simp]"

, isRefuteAux :: Bool

, senTerm :: Term

, thmProof :: Maybe String }

| ConstDef { senTerm :: Term }

| RecDef { keyWord :: String

, senTerms :: [[Term]] }

deriving (Eq, Ord, Show)

mkSen :: Term -> Sentence

mkSen t = Sentence

{ isSimp = False

, isRefuteAux = False

, thmProof = Nothing

, senTerm = t }

mkRefuteSen :: Term -> Sentence

mkRefuteSen t = (mkSen t) { isRefuteAux = True }

isRefute :: Sentence -> Bool

isRefute s = case s of

Sentence { isRefuteAux = b } -> b

_ -> False

-------------------- from src/Pure/sorts.ML ------------------------

{-- type classes and sorts --}

{- Classes denote (possibly empty) collections of types that are

partially ordered by class inclusion. They are represented

symbolically by strings.

Sorts are intersections of finitely many classes. They are

represented by lists of classes. Normal forms of sorts are sorted

lists of minimal classes (wrt. current class inclusion).

(already defined in Pure/term.ML)

classrel:

table representing the proper subclass relation; entries (c, cs)

represent the superclasses cs of c;

arities:

table of association lists of all type arities; (t, ars) means

that type constructor t has the arities ars; an element (c, Ss) of

ars represents the arity t::(Ss)c;

-}

type Classrel = Map.Map IsaClass (Maybe [IsaClass])

type Arities = Map.Map TName [(IsaClass, [(Typ, Sort)])]

type Abbrs = Map.Map TName ([TName], Typ)

data TypeSig =

TySg {

classrel:: Classrel, -- domain of the map yields the classes

defaultSort:: Sort,

log_types:: [TName],

univ_witness:: Maybe (Typ, Sort),

abbrs:: Abbrs, -- constructor name, variable names, type.

arities:: Arities }

-- actually isa-instances. the former field tycons can be computed.

deriving (Eq, Show)

emptyTypeSig :: TypeSig

emptyTypeSig = TySg {

classrel = Map.empty,

defaultSort = [],

log_types = [],

univ_witness = Nothing,

abbrs = Map.empty,

arities = Map.empty }

-------------------- from src/Pure/sign.ML ------------------------

data BaseSig = Main_thy -- ^ main theory of higher order logic (HOL)

| MainHC_thy -- ^ extend main theory of HOL logic for HasCASL

| HOLCF_thy -- ^ higher order logic for continuous functions

| HsHOLCF_thy -- ^ HOLCF for Haskell

| HsHOL_thy -- ^ HOL for Haskell

| MHsHOL_thy

| MHsHOLCF_thy

deriving (Eq, Ord, Show)

{- possibly simply supply a theory like MainHC as string

or recursively as Isabelle.Sign -}

data Sign = Sign

{ theoryName :: String,

baseSig :: BaseSig, -- like Main etc.

tsig :: TypeSig,

constTab :: ConstTab, -- value cons with type

domainTab :: DomainTab,

showLemmas :: Bool

} deriving (Eq, Show)

{- list of datatype definitions

each of these consists of a list of (mutually recursive) datatypes

each datatype consists of its name (Typ) and a list of constructors

each constructor consists of its name (String) and list of argument types

-}

type ConstTab = Map.Map VName Typ

-- same types for data types and domains

type DomainTab = [[DomainEntry]]

type DomainEntry = (Typ, [(VName, [Typ])])

emptySign :: Sign

emptySign = Sign { theoryName = "thy",

baseSig = Main_thy,

tsig = emptyTypeSig,

constTab = Map.empty,

domainTab = [],

showLemmas = False }

------------------------ Sentence -------------------------------------

{- Instances in Haskell have form:

instance (MyClass a, MyClass b) => MyClass (MyTypeConst a b)

In Isabelle:

instance MyTypeConst :: (MyClass, MyClass) MyClass

Note that the Isabelle syntax does not allows for multi-parameter classes.

Rather, it subsumes the syntax for arities.

Type constraints are applied to value constructors in Haskell as follows:

MyValCon :: (MyClass a, MyClass b) => MyTypeConst a b

In Isabelle:

MyValCon :: MyTypeConst (a::MyClass) (b::MyClass)

In both cases, the typing expressions may be encoded as schemes.

Schemes and instances allows for the inference of type constraints over

values of functions.

-}