types/TyCon.lhs

% % (c) The University of Glasgow 2006 % (c) The GRASP/AQUA Project, Glasgow University, 1992-1998 % The @TyCon@ datatype \begin{code}

    module TyCon(
            -- * Main TyCon data types
            TyCon, FieldLabel,

            AlgTyConRhs(..), visibleDataCons,
            TyConParent(..), isNoParent,
            SynTyConRhs(..), Role(..),

            -- ** Constructing TyCons
            mkAlgTyCon,
            mkClassTyCon,
            mkFunTyCon,
            mkPrimTyCon,
            mkKindTyCon,
            mkLiftedPrimTyCon,
            mkTupleTyCon,
            mkSynTyCon,
            mkForeignTyCon,
            mkPromotedDataCon,
            mkPromotedTyCon,

            -- ** Predicates on TyCons
            isAlgTyCon,
            isClassTyCon, isFamInstTyCon,
            isFunTyCon,
            isPrimTyCon,
            isTupleTyCon, isUnboxedTupleTyCon, isBoxedTupleTyCon,
            isSynTyCon, isTypeSynonymTyCon,
            isDecomposableTyCon,
            isForeignTyCon,
            isPromotedDataCon, isPromotedTyCon,
            isPromotedDataCon_maybe, isPromotedTyCon_maybe,
            promotableTyCon_maybe, promoteTyCon,

            isDataTyCon, isProductTyCon, isDataProductTyCon_maybe,
            isEnumerationTyCon,
            isNewTyCon, isAbstractTyCon,
            isFamilyTyCon, isOpenFamilyTyCon,
            isSynFamilyTyCon, isDataFamilyTyCon,
            isOpenSynFamilyTyCon, isClosedSynFamilyTyCon_maybe,
            isBuiltInSynFamTyCon_maybe,
            isUnLiftedTyCon,
            isGadtSyntaxTyCon, isDistinctTyCon, isDistinctAlgRhs,
            isTyConAssoc, tyConAssoc_maybe,
            isRecursiveTyCon,
            isImplicitTyCon,

            -- ** Extracting information out of TyCons
            tyConName,
            tyConKind,
            tyConUnique,
            tyConTyVars,
            tyConCType, tyConCType_maybe,
            tyConDataCons, tyConDataCons_maybe,
            tyConSingleDataCon_maybe, tyConSingleAlgDataCon_maybe,
            tyConFamilySize,
            tyConStupidTheta,
            tyConArity,
            tyConRoles,
            tyConParent,
            tyConTuple_maybe, tyConClass_maybe,
            tyConFamInst_maybe, tyConFamInstSig_maybe, tyConFamilyCoercion_maybe,
            synTyConDefn_maybe, synTyConRhs_maybe,
            tyConExtName,           -- External name for foreign types
            algTyConRhs,
            newTyConRhs, newTyConEtadArity, newTyConEtadRhs, unwrapNewTyCon_maybe,
            tupleTyConBoxity, tupleTyConSort, tupleTyConArity,

            -- ** Manipulating TyCons
            tcExpandTyCon_maybe, coreExpandTyCon_maybe,
            makeTyConAbstract,
            newTyConCo, newTyConCo_maybe,
            pprPromotionQuote,

            -- * Primitive representations of Types
            PrimRep(..), PrimElemRep(..),
            tyConPrimRep, isVoidRep, isGcPtrRep,
            primRepSizeW, primElemRepSizeB,

            -- * Recursion breaking
            RecTcChecker, initRecTc, checkRecTc

    ) where

    #include "HsVersions.h"

    import {-# SOURCE #-} TypeRep ( Kind, Type, PredType )
    import {-# SOURCE #-} DataCon ( DataCon, isVanillaDataCon )

    import Var
    import Class
    import BasicTypes
    import DynFlags
    import ForeignCall
    import Name
    import NameSet
    import CoAxiom
    import PrelNames
    import Maybes
    import Outputable
    import FastString
    import Constants
    import Util
    import qualified Data.Data as Data
    import Data.Typeable (Typeable)

\end{code} ----------------------------------------------- Notes about type families ----------------------------------------------- Note [Type synonym families] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * Type synonym families, also known as "type functions", map directly onto the type functions in FC: type family F a :: * type instance F Int = Bool ..etc... * Reply "yes" to isSynFamilyTyCon, and isFamilyTyCon * From the user's point of view (F Int) and Bool are simply equivalent types. * A Haskell 98 type synonym is a degenerate form of a type synonym family. * Type functions can't appear in the LHS of a type function: type instance F (F Int) = ... -- BAD! * Translation of type family decl: type family F a :: * translates to a SynTyCon 'F', whose SynTyConRhs is OpenSynFamilyTyCon type family G a :: * where G Int = Bool G Bool = Char G a = () translates to a SynTyCon 'G', whose SynTyConRhs is ClosedSynFamilyTyCon, with the appropriate CoAxiom representing the equations * In the future we might want to support * injective type families (allow decomposition) but we don't at the moment [2013] Note [Data type families] ~~~~~~~~~~~~~~~~~~~~~~~~~ See also Note [Wrappers for data instance tycons] in MkId.lhs * Data type families are declared thus data family T a :: * data instance T Int = T1 | T2 Bool Here T is the "family TyCon". * Reply "yes" to isDataFamilyTyCon, and isFamilyTyCon * The user does not see any "equivalent types" as he did with type synonym families. He just sees constructors with types T1 :: T Int T2 :: Bool -> T Int * Here's the FC version of the above declarations: data T a data R:TInt = T1 | T2 Bool axiom ax_ti : T Int ~ R:TInt The R:TInt is the "representation TyCons". It has an AlgTyConParent of FamInstTyCon T [Int] ax_ti * The data contructor T2 has a wrapper (which is what the source-level "T2" invokes): $WT2 :: Bool -> T Int $WT2 b = T2 b `cast` sym ax_ti * A data instance can declare a fully-fledged GADT: data instance T (a,b) where X1 :: T (Int,Bool) X2 :: a -> b -> T (a,b) Here's the FC version of the above declaration: data R:TPair a where X1 :: R:TPair Int Bool X2 :: a -> b -> R:TPair a b axiom ax_pr :: T (a,b) ~ R:TPair a b $WX1 :: forall a b. a -> b -> T (a,b) $WX1 a b (x::a) (y::b) = X2 a b x y `cast` sym (ax_pr a b) The R:TPair are the "representation TyCons". We have a bit of work to do, to unpick the result types of the data instance declaration for T (a,b), to get the result type in the representation; e.g. T (a,b) --> R:TPair a b The representation TyCon R:TList, has an AlgTyConParent of FamInstTyCon T [(a,b)] ax_pr * Notice that T is NOT translated to a FC type function; it just becomes a "data type" with no constructors, which can be coerced inot into R:TInt, R:TPair by the axioms. These axioms axioms come into play when (and *only* when) you - use a data constructor - do pattern matching Rather like newtype, in fact As a result - T behaves just like a data type so far as decomposition is concerned - (T Int) is not implicitly converted to R:TInt during type inference. Indeed the latter type is unknown to the programmer. - There *is* an instance for (T Int) in the type-family instance environment, but it is only used for overlap checking - It's fine to have T in the LHS of a type function: type instance F (T a) = [a] It was this last point that confused me! The big thing is that you should not think of a data family T as a *type function* at all, not even an injective one! We can't allow even injective type functions on the LHS of a type function: type family injective G a :: * type instance F (G Int) = Bool is no good, even if G is injective, because consider type instance G Int = Bool type instance F Bool = Char So a data type family is not an injective type function. It's just a data type with some axioms that connect it to other data types. Note [Associated families and their parent class] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ *Associated* families are just like *non-associated* families, except that they have a TyConParent of AssocFamilyTyCon, which identifies the parent class. However there is an important sharing relationship between * the tyConTyVars of the parent Class * the tyConTyvars of the associated TyCon class C a b where data T p a type F a q b Here the 'a' and 'b' are shared with the 'Class'; that is, they have the same Unique. This is important. In an instance declaration we expect * all the shared variables to be instantiated the same way * the non-shared variables of the associated type should not be instantiated at all instance C [x] (Tree y) where data T p [x] = T1 x | T2 p type F [x] q (Tree y) = (x,y,q) Note [TyCon Role signatures] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Every tycon has a role signature, assigning a role to each of the tyConTyVars (or of equal length to the tyConArity, if there are no tyConTyVars). An example demonstrates these best: say we have a tycon T, with parameters a at nominal, b at representational, and c at phantom. Then, to prove representational equality between T a1 b1 c1 and T a2 b2 c2, we need to have nominal equality between a1 and a2, representational equality between b1 and b2, and nothing in particular (i.e., phantom equality) between c1 and c2. This might happen, say, with the following declaration: data T a b c where MkT :: b -> T Int b c Data and class tycons have their roles inferred (see inferRoles in TcTyDecls), as do vanilla synonym tycons. Family tycons have all parameters at role N, though it is conceivable that we could relax this restriction. (->)'s and tuples' parameters are at role R. Each primitive tycon declares its roles; it's worth noting that (~#)'s parameters are at role N. Promoted data constructors' type arguments are at role R. All kind arguments are at role N. %************************************************************************ %* * \subsection{The data type} %* * %************************************************************************ \begin{code}

    -- | TyCons represent type constructors. Type constructors are introduced by things such as:
    --
    -- 1) Data declarations: @data Foo = ...@ creates the @Foo@ type constructor of kind @*@
    --
    -- 2) Type synonyms: @type Foo = ...@ creates the @Foo@ type constructor
    --
    -- 3) Newtypes: @newtype Foo a = MkFoo ...@ creates the @Foo@ type constructor of kind @* -> *@
    --
    -- 4) Class declarations: @class Foo where@ creates the @Foo@ type constructor of kind @*@
    --
    -- This data type also encodes a number of primitive, built in type constructors such as those
    -- for function and tuple types.

    -- If you edit this type, you may need to update the GHC formalism
    -- See Note [GHC Formalism] in coreSyn/CoreLint.lhs
    data TyCon
      = -- | The function type constructor, @(->)@
        FunTyCon {
            tyConUnique :: Unique,
            tyConName   :: Name,
            tc_kind   :: Kind,
            tyConArity  :: Arity
        }

      -- | Algebraic type constructors, which are defined to be those
      -- arising @data@ type and @newtype@ declarations.  All these
      -- constructors are lifted and boxed. See 'AlgTyConRhs' for more
      -- information.
      | AlgTyCon {
            tyConUnique :: Unique,
            tyConName   :: Name,
            tc_kind     :: Kind,
            tyConArity  :: Arity,

            tyConTyVars :: [TyVar],   -- ^ The kind and type variables used in the type constructor.
                                      -- Invariant: length tyvars = arity
                                      -- Precisely, this list scopes over:
                                      --
                                      -- 1. The 'algTcStupidTheta'
                                      -- 2. The cached types in 'algTyConRhs.NewTyCon'
                                      -- 3. The family instance types if present
                                      --
                                      -- Note that it does /not/ scope over the data constructors.
            tc_roles     :: [Role],   -- ^ The role for each type variable
                                      -- This list has the same length as tyConTyVars
                                      -- See also Note [TyCon Role signatures]

            tyConCType   :: Maybe CType, -- The C type that should be used
                                         -- for this type when using the FFI
                                         -- and CAPI

            algTcGadtSyntax  :: Bool,       -- ^ Was the data type declared with GADT syntax?
                                            -- If so, that doesn't mean it's a true GADT;
                                            -- only that the "where" form was used.
                                            -- This field is used only to guide pretty-printing

            algTcStupidTheta :: [PredType], -- ^ The \"stupid theta\" for the data type
                                            -- (always empty for GADTs).
                                            -- A \"stupid theta\" is the context to the left
                                            -- of an algebraic type declaration,
                                            -- e.g. @Eq a@ in the declaration
                                            --    @data Eq a => T a ...@.

            algTcRhs :: AlgTyConRhs,  -- ^ Contains information about the
                                      -- data constructors of the algebraic type

            algTcRec :: RecFlag,      -- ^ Tells us whether the data type is part
                                      -- of a mutually-recursive group or not

            algTcParent :: TyConParent,     -- ^ Gives the class or family declaration 'TyCon'
                                            -- for derived 'TyCon's representing class
                                            -- or family instances, respectively.
                                            -- See also 'synTcParent'

            tcPromoted :: Maybe TyCon    -- ^ Promoted TyCon, if any
        }

      -- | Represents the infinite family of tuple type constructors,
      --   @()@, @(a,b)@, @(# a, b #)@ etc.
      | TupleTyCon {
            tyConUnique    :: Unique,
            tyConName      :: Name,
            tc_kind        :: Kind,
            tyConArity     :: Arity,
            tyConTupleSort :: TupleSort,
            tyConTyVars    :: [TyVar],
            dataCon        :: DataCon, -- ^ Corresponding tuple data constructor
            tcPromoted     :: Maybe TyCon    -- Nothing for unboxed tuples
        }

      -- | Represents type synonyms
      | SynTyCon {
            tyConUnique  :: Unique,
            tyConName    :: Name,
            tc_kind    :: Kind,
            tyConArity   :: Arity,

            tyConTyVars  :: [TyVar],        -- Bound tyvars
            tc_roles     :: [Role],

            synTcRhs     :: SynTyConRhs,       -- ^ Contains information about the
                                               -- expansion of the synonym

            synTcParent  :: TyConParent     -- ^ Gives the family declaration 'TyCon'
                                            -- of 'TyCon's representing family instances

        }

      -- | Primitive types; cannot be defined in Haskell. This includes
      -- the usual suspects (such as @Int#@) as well as foreign-imported
      -- types and kinds
      | PrimTyCon {
            tyConUnique   :: Unique,
            tyConName     :: Name,
            tc_kind       :: Kind,
            tyConArity    :: Arity,
            tc_roles      :: [Role],

            primTyConRep  :: PrimRep,       -- ^ Many primitive tycons are unboxed, but some are
                                            --   boxed (represented by pointers). This 'PrimRep'
                                            --   holds that information.
                                            -- Only relevant if tc_kind = *

            isUnLifted   :: Bool,           -- ^ Most primitive tycons are unlifted
                                            --   (may not contain bottom)
                                            --   but foreign-imported ones may be lifted

            tyConExtName :: Maybe FastString   -- ^ @Just e@ for foreign-imported types,
                                               --   holds the name of the imported thing
        }

      -- | Represents promoted data constructor.
      | PromotedDataCon {         -- See Note [Promoted data constructors]
            tyConUnique :: Unique, -- ^ Same Unique as the data constructor
            tyConName   :: Name,   -- ^ Same Name as the data constructor
            tyConArity  :: Arity,
            tc_roles    :: [Role], -- ^ Roles: N for kind vars, R for type vars
            tc_kind     :: Kind,   -- ^ Translated type of the data constructor
            dataCon     :: DataCon -- ^ Corresponding data constructor
        }

      -- | Represents promoted type constructor.
      | PromotedTyCon {
            tyConUnique :: Unique, -- ^ Same Unique as the type constructor
            tyConName   :: Name,   -- ^ Same Name as the type constructor
            tyConArity  :: Arity,  -- ^ n if ty_con :: * -> ... -> *  n times
            tc_kind     :: Kind,   -- ^ Always TysPrim.superKind
            ty_con      :: TyCon   -- ^ Corresponding type constructor
        }

      deriving Typeable

    -- | Names of the fields in an algebraic record type
    type FieldLabel = Name

    -- | Represents right-hand-sides of 'TyCon's for algebraic types
    data AlgTyConRhs

        -- | Says that we know nothing about this data type, except that
        -- it's represented by a pointer.  Used when we export a data type
        -- abstractly into an .hi file.
      = AbstractTyCon
          Bool      -- True  <=> It's definitely a distinct data type,
                    --           equal only to itself; ie not a newtype
                    -- False <=> Not sure
                    -- See Note [AbstractTyCon and type equality]

        -- | Represents an open type family without a fixed right hand
        -- side.  Additional instances can appear at any time.
        --
        -- These are introduced by either a top level declaration:
        --
        -- > data T a :: *
        --
        -- Or an associated data type declaration, within a class declaration:
        --
        -- > class C a b where
        -- >   data T b :: *
      | DataFamilyTyCon

        -- | Information about those 'TyCon's derived from a @data@
        -- declaration. This includes data types with no constructors at
        -- all.
      | DataTyCon {
            data_cons :: [DataCon],
                              -- ^ The data type constructors; can be empty if the user
                              --   declares the type to have no constructors
                              --
                              -- INVARIANT: Kept in order of increasing 'DataCon' tag
                              --      (see the tag assignment in DataCon.mkDataCon)

            is_enum :: Bool   -- ^ Cached value: is this an enumeration type?
                              --   See Note [Enumeration types]
        }

      -- | Information about those 'TyCon's derived from a @newtype@ declaration
      | NewTyCon {
            data_con :: DataCon,    -- ^ The unique constructor for the @newtype@.
                                    --   It has no existentials

            nt_rhs :: Type,         -- ^ Cached value: the argument type of the constructor,
                                    -- which is just the representation type of the 'TyCon'
                                    -- (remember that @newtype@s do not exist at runtime
                                    -- so need a different representation type).
                                    --
                                    -- The free 'TyVar's of this type are the 'tyConTyVars'
                                    -- from the corresponding 'TyCon'

            nt_etad_rhs :: ([TyVar], Type),
                            -- ^ Same as the 'nt_rhs', but this time eta-reduced.
                            -- Hence the list of 'TyVar's in this field may be
                            -- shorter than the declared arity of the 'TyCon'.

                            -- See Note [Newtype eta]
            nt_co :: CoAxiom Unbranched
                                 -- The axiom coercion that creates the @newtype@ from
                                 -- the representation 'Type'.

                                 -- See Note [Newtype coercions]
                                 -- Invariant: arity = #tvs in nt_etad_rhs;
                                 -- See Note [Newtype eta]
                                 -- Watch out!  If any newtypes become transparent
                                 -- again check Trac #1072.
        }

\end{code} Note [AbstractTyCon and type equality] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ TODO \begin{code}

    -- | Extract those 'DataCon's that we are able to learn about.  Note
    -- that visibility in this sense does not correspond to visibility in
    -- the context of any particular user program!
    visibleDataCons :: AlgTyConRhs -> [DataCon]
    visibleDataCons (AbstractTyCon {})            = []
    visibleDataCons DataFamilyTyCon {}            = []
    visibleDataCons (DataTyCon{ data_cons = cs }) = cs
    visibleDataCons (NewTyCon{ data_con = c })    = [c]

    -- ^ Both type classes as well as family instances imply implicit
    -- type constructors.  These implicit type constructors refer to their parent
    -- structure (ie, the class or family from which they derive) using a type of
    -- the following form.  We use 'TyConParent' for both algebraic and synonym
    -- types, but the variant 'ClassTyCon' will only be used by algebraic 'TyCon's.
    data TyConParent
      = -- | An ordinary type constructor has no parent.
        NoParentTyCon

      -- | Type constructors representing a class dictionary.
      -- See Note [ATyCon for classes] in TypeRep
      | ClassTyCon
            Class           -- INVARIANT: the classTyCon of this Class is the current tycon

      -- | An *associated* type of a class.
      | AssocFamilyTyCon
            Class           -- The class in whose declaration the family is declared
                            -- See Note [Associated families and their parent class]

      -- | Type constructors representing an instance of a *data* family. Parameters:
      --
      --  1) The type family in question
      --
      --  2) Instance types; free variables are the 'tyConTyVars'
      --  of the current 'TyCon' (not the family one). INVARIANT:
      --  the number of types matches the arity of the family 'TyCon'
      --
      --  3) A 'CoTyCon' identifying the representation
      --  type with the type instance family
      | FamInstTyCon          -- See Note [Data type families]
            (CoAxiom Unbranched)  -- The coercion constructor,
                                  -- always of kind   T ty1 ty2 ~ R:T a b c
                                  -- where T is the family TyCon,
                                  -- and R:T is the representation TyCon (ie this one)
                                  -- and a,b,c are the tyConTyVars of this TyCon

              -- Cached fields of the CoAxiom, but adjusted to
              -- use the tyConTyVars of this TyCon
            TyCon   -- The family TyCon
            [Type]  -- Argument types (mentions the tyConTyVars of this TyCon)
                    -- Match in length the tyConTyVars of the family TyCon

            -- E.g.  data intance T [a] = ...
            -- gives a representation tycon:
            --      data R:TList a = ...
            --      axiom co a :: T [a] ~ R:TList a
            -- with R:TList's algTcParent = FamInstTyCon T [a] co

    instance Outputable TyConParent where
        ppr NoParentTyCon           = text "No parent"
        ppr (ClassTyCon cls)        = text "Class parent" <+> ppr cls
        ppr (AssocFamilyTyCon cls)  = text "Class parent (assoc. family)" <+> ppr cls
        ppr (FamInstTyCon _ tc tys) = text "Family parent (family instance)" <+> ppr tc <+> sep (map ppr tys)

    -- | Checks the invariants of a 'TyConParent' given the appropriate type class name, if any
    okParent :: Name -> TyConParent -> Bool
    okParent _       NoParentTyCon               = True
    okParent tc_name (AssocFamilyTyCon cls)      = tc_name `elem` map tyConName (classATs cls)
    okParent tc_name (ClassTyCon cls)            = tc_name == tyConName (classTyCon cls)
    okParent _       (FamInstTyCon _ fam_tc tys) = tyConArity fam_tc == length tys

    isNoParent :: TyConParent -> Bool
    isNoParent NoParentTyCon = True
    isNoParent _             = False

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

    -- | Information pertaining to the expansion of a type synonym (@type@)
    data SynTyConRhs
      = -- | An ordinary type synonyn.
        SynonymTyCon
           Type           -- This 'Type' is the rhs, and may mention from 'tyConTyVars'.
                          -- It acts as a template for the expansion when the 'TyCon'
                          -- is applied to some types.

       -- | An open type synonym family  e.g. @type family F x y :: * -> *@
       | OpenSynFamilyTyCon

       -- | A closed type synonym family  e.g. @type family F x where { F Int = Bool }@
       | ClosedSynFamilyTyCon
           (CoAxiom Branched) -- The one axiom for this family

       -- | A closed type synonym family declared in an hs-boot file with
       -- type family F a where ..
       | AbstractClosedSynFamilyTyCon

       | BuiltInSynFamTyCon BuiltInSynFamily

\end{code} Note [Closed type families] ~~~~~~~~~~~~~~~~~~~~~~~~~ * In an open type family you can add new instances later. This is the usual case. * In a closed type family you can only put equations where the family is defined. Note [Promoted data constructors] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ A data constructor can be promoted to become a type constructor, via the PromotedTyCon alternative in TyCon. * Only data constructors with (a) no kind polymorphism (b) no constraints in its type (eg GADTs) are promoted. Existentials are ok; see Trac #7347. * The TyCon promoted from a DataCon has the *same* Name and Unique as the DataCon. Eg. If the data constructor Data.Maybe.Just(unique 78, say) is promoted to a TyCon whose name is Data.Maybe.Just(unique 78) * The *kind* of a promoted DataCon may be polymorphic. Example: type of DataCon Just :: forall (a:*). a -> Maybe a kind of (promoted) tycon Just :: forall (a:box). a -> Maybe a The kind is not identical to the type, because of the */box kind signature on the forall'd variable; so the tc_kind field of PromotedTyCon is not identical to the dataConUserType of the DataCon. But it's the same modulo changing the variable kinds, done by DataCon.promoteType. * Small note: We promote the *user* type of the DataCon. Eg data T = MkT {-# UNPACK #-} !(Bool, Bool) The promoted kind is MkT :: (Bool,Bool) -> T *not* MkT :: Bool -> Bool -> T Note [Enumeration types] ~~~~~~~~~~~~~~~~~~~~~~~~ We define datatypes with no constructors to *not* be enumerations; this fixes trac #2578, Otherwise we end up generating an empty table for __closure_tbl which is used by tagToEnum# to map Int# to constructors in an enumeration. The empty table apparently upset the linker. Moreover, all the data constructor must be enumerations, meaning they have type (forall abc. T a b c). GADTs are not enumerations. For example consider data T a where T1 :: T Int T2 :: T Bool T3 :: T a What would [T1 ..] be? [T1,T3] :: T Int? Easiest thing is to exclude them. See Trac #4528. Note [Newtype coercions] ~~~~~~~~~~~~~~~~~~~~~~~~ The NewTyCon field nt_co is a CoAxiom which is used for coercing from the representation type of the newtype, to the newtype itself. For example, newtype T a = MkT (a -> a) the NewTyCon for T will contain nt_co = CoT where CoT t : T t ~ t -> t. In the case that the right hand side is a type application ending with the same type variables as the left hand side, we "eta-contract" the coercion. So if we had newtype S a = MkT [a] then we would generate the arity 0 axiom CoS : S ~ []. The primary reason we do this is to make newtype deriving cleaner. In the paper we'd write axiom CoT : (forall t. T t) ~ (forall t. [t]) and then when we used CoT at a particular type, s, we'd say CoT @ s which encodes as (TyConApp instCoercionTyCon [TyConApp CoT [], s]) Note [Newtype eta] ~~~~~~~~~~~~~~~~~~ Consider newtype Parser a = MkParser (IO a) derriving( Monad ) Are these two types equal (to Core)? Monad Parser Monad IO which we need to make the derived instance for Monad Parser. Well, yes. But to see that easily we eta-reduce the RHS type of Parser, in this case to ([], Froogle), so that even unsaturated applications of Parser will work right. This eta reduction is done when the type constructor is built, and cached in NewTyCon. The cached field is only used in coreExpandTyCon_maybe. Here's an example that I think showed up in practice Source code: newtype T a = MkT [a] newtype Foo m = MkFoo (forall a. m a -> Int) w1 :: Foo [] w1 = ... w2 :: Foo T w2 = MkFoo (\(MkT x) -> case w1 of MkFoo f -> f x) After desugaring, and discarding the data constructors for the newtypes, we get: w2 :: Foo T w2 = w1 And now Lint complains unless Foo T == Foo [], and that requires T==[] This point carries over to the newtype coercion, because we need to say w2 = w1 `cast` Foo CoT so the coercion tycon CoT must have kind: T ~ [] and arity: 0 %************************************************************************ %* * \subsection{PrimRep} %* * %************************************************************************ Note [rep swamp] GHC has a rich selection of types that represent "primitive types" of one kind or another. Each of them makes a different set of distinctions, and mostly the differences are for good reasons, although it's probably true that we could merge some of these. Roughly in order of "includes more information": - A Width (cmm/CmmType) is simply a binary value with the specified number of bits. It may represent a signed or unsigned integer, a floating-point value, or an address. data Width = W8 | W16 | W32 | W64 | W80 | W128 - Size, which is used in the native code generator, is Width + floating point information. data Size = II8 | II16 | II32 | II64 | FF32 | FF64 | FF80 it is necessary because e.g. the instruction to move a 64-bit float on x86 (movsd) is different from the instruction to move a 64-bit integer (movq), so the mov instruction is parameterised by Size. - CmmType wraps Width with more information: GC ptr, float, or other value. data CmmType = CmmType CmmCat Width data CmmCat -- "Category" (not exported) = GcPtrCat -- GC pointer | BitsCat -- Non-pointer | FloatCat -- Float It is important to have GcPtr information in Cmm, since we generate info tables containing pointerhood for the GC from this. As for why we have float (and not signed/unsigned) here, see Note [Signed vs unsigned]. - ArgRep makes only the distinctions necessary for the call and return conventions of the STG machine. It is essentially CmmType + void. - PrimRep makes a few more distinctions than ArgRep: it divides non-GC-pointers into signed/unsigned and addresses, information that is necessary for passing these values to foreign functions. There's another tension here: whether the type encodes its size in bytes, or whether its size depends on the machine word size. Width and CmmType have the size built-in, whereas ArgRep and PrimRep do not. This means to turn an ArgRep/PrimRep into a CmmType requires DynFlags. On the other hand, CmmType includes some "nonsense" values, such as CmmType GcPtrCat W32 on a 64-bit machine. \begin{code}

    -- | A 'PrimRep' is an abstraction of a type.  It contains information that
    -- the code generator needs in order to pass arguments, return results,
    -- and store values of this type.
    data PrimRep
      = VoidRep
      | PtrRep
      | IntRep              -- ^ Signed, word-sized value
      | WordRep             -- ^ Unsigned, word-sized value
      | Int64Rep            -- ^ Signed, 64 bit value (with 32-bit words only)
      | Word64Rep           -- ^ Unsigned, 64 bit value (with 32-bit words only)
      | AddrRep             -- ^ A pointer, but /not/ to a Haskell value (use 'PtrRep')
      | FloatRep
      | DoubleRep
      | VecRep Int PrimElemRep  -- ^ A vector
      deriving( Eq, Show )

    data PrimElemRep
      = Int8ElemRep
      | Int16ElemRep
      | Int32ElemRep
      | Int64ElemRep
      | Word8ElemRep
      | Word16ElemRep
      | Word32ElemRep
      | Word64ElemRep
      | FloatElemRep
      | DoubleElemRep
       deriving( Eq, Show )

    instance Outputable PrimRep where
      ppr r = text (show r)

    instance Outputable PrimElemRep where
      ppr r = text (show r)

    isVoidRep :: PrimRep -> Bool
    isVoidRep VoidRep = True
    isVoidRep _other  = False

    isGcPtrRep :: PrimRep -> Bool
    isGcPtrRep PtrRep = True
    isGcPtrRep _      = False

    -- | Find the size of a 'PrimRep', in words
    primRepSizeW :: DynFlags -> PrimRep -> Int
    primRepSizeW _      IntRep           = 1
    primRepSizeW _      WordRep          = 1
    primRepSizeW dflags Int64Rep         = wORD64_SIZE `quot` wORD_SIZE dflags
    primRepSizeW dflags Word64Rep        = wORD64_SIZE `quot` wORD_SIZE dflags
    primRepSizeW _      FloatRep         = 1    -- NB. might not take a full word
    primRepSizeW dflags DoubleRep        = dOUBLE_SIZE dflags `quot` wORD_SIZE dflags
    primRepSizeW _      AddrRep          = 1
    primRepSizeW _      PtrRep           = 1
    primRepSizeW _      VoidRep          = 0
    primRepSizeW dflags (VecRep len rep) = len * primElemRepSizeB rep `quot` wORD_SIZE dflags

    primElemRepSizeB :: PrimElemRep -> Int
    primElemRepSizeB Int8ElemRep   = 1
    primElemRepSizeB Int16ElemRep  = 2
    primElemRepSizeB Int32ElemRep  = 4
    primElemRepSizeB Int64ElemRep  = 8
    primElemRepSizeB Word8ElemRep  = 1
    primElemRepSizeB Word16ElemRep = 2
    primElemRepSizeB Word32ElemRep = 4
    primElemRepSizeB Word64ElemRep = 8
    primElemRepSizeB FloatElemRep  = 4
    primElemRepSizeB DoubleElemRep = 8

\end{code} %************************************************************************ %* * \subsection{TyCon Construction} %* * %************************************************************************ Note: the TyCon constructors all take a Kind as one argument, even though they could, in principle, work out their Kind from their other arguments. But to do so they need functions from Types, and that makes a nasty module mutual-recursion. And they aren't called from many places. So we compromise, and move their Kind calculation to the call site. \begin{code}

    -- | Given the name of the function type constructor and it's kind, create the
    -- corresponding 'TyCon'. It is reccomended to use 'TypeRep.funTyCon' if you want
    -- this functionality
    mkFunTyCon :: Name -> Kind -> TyCon
    mkFunTyCon name kind
      = FunTyCon {
            tyConUnique = nameUnique name,
            tyConName   = name,
            tc_kind   = kind,
            tyConArity  = 2
        }

    -- | This is the making of an algebraic 'TyCon'. Notably, you have to
    -- pass in the generic (in the -XGenerics sense) information about the
    -- type constructor - you can get hold of it easily (see Generics
    -- module)
    mkAlgTyCon :: Name
               -> Kind              -- ^ Kind of the resulting 'TyCon'
               -> [TyVar]           -- ^ 'TyVar's scoped over: see 'tyConTyVars'.
                                    --   Arity is inferred from the length of this list
               -> [Role]            -- ^ The roles for each TyVar
               -> Maybe CType       -- ^ The C type this type corresponds to
                                    --   when using the CAPI FFI
               -> [PredType]        -- ^ Stupid theta: see 'algTcStupidTheta'
               -> AlgTyConRhs       -- ^ Information about dat aconstructors
               -> TyConParent
               -> RecFlag           -- ^ Is the 'TyCon' recursive?
               -> Bool              -- ^ Was the 'TyCon' declared with GADT syntax?
               -> Maybe TyCon       -- ^ Promoted version
               -> TyCon
    mkAlgTyCon name kind tyvars roles cType stupid rhs parent is_rec gadt_syn prom_tc
      = AlgTyCon {
            tyConName        = name,
            tyConUnique      = nameUnique name,
            tc_kind          = kind,
            tyConArity       = length tyvars,
            tyConTyVars      = tyvars,
            tc_roles         = roles,
            tyConCType       = cType,
            algTcStupidTheta = stupid,
            algTcRhs         = rhs,
            algTcParent      = ASSERT2( okParent name parent, ppr name $$ ppr parent ) parent,
            algTcRec         = is_rec,
            algTcGadtSyntax  = gadt_syn,
            tcPromoted       = prom_tc
        }

    -- | Simpler specialization of 'mkAlgTyCon' for classes
    mkClassTyCon :: Name -> Kind -> [TyVar] -> [Role] -> AlgTyConRhs -> Class -> RecFlag -> TyCon
    mkClassTyCon name kind tyvars roles rhs clas is_rec
      = mkAlgTyCon name kind tyvars roles Nothing [] rhs (ClassTyCon clas)
                   is_rec False
                   Nothing    -- Class TyCons are not pormoted

    mkTupleTyCon :: Name
                 -> Kind    -- ^ Kind of the resulting 'TyCon'
                 -> Arity   -- ^ Arity of the tuple
                 -> [TyVar] -- ^ 'TyVar's scoped over: see 'tyConTyVars'
                 -> DataCon
                 -> TupleSort    -- ^ Whether the tuple is boxed or unboxed
                 -> Maybe TyCon  -- ^ Promoted version
                 -> TyCon
    mkTupleTyCon name kind arity tyvars con sort prom_tc
      = TupleTyCon {
            tyConUnique = nameUnique name,
            tyConName = name,
            tc_kind = kind,
            tyConArity = arity,
            tyConTupleSort = sort,
            tyConTyVars = tyvars,
            dataCon = con,
            tcPromoted = prom_tc
        }

    -- ^ Foreign-imported (.NET) type constructors are represented
    -- as primitive, but /lifted/, 'TyCons' for now. They are lifted
    -- because the Haskell type @T@ representing the (foreign) .NET
    -- type @T@ is actually implemented (in ILX) as a @thunk<T>@
    mkForeignTyCon :: Name
                   -> Maybe FastString -- ^ Name of the foreign imported thing, maybe
                   -> Kind
                   -> TyCon
    mkForeignTyCon name ext_name kind
      = PrimTyCon {
            tyConName    = name,
            tyConUnique  = nameUnique name,
            tc_kind    = kind,
            tyConArity   = 0,
            tc_roles     = [],
            primTyConRep = PtrRep, -- they all do
            isUnLifted   = False,
            tyConExtName = ext_name
        }

    -- | Create an unlifted primitive 'TyCon', such as @Int#@
    mkPrimTyCon :: Name  -> Kind -> [Role] -> PrimRep -> TyCon
    mkPrimTyCon name kind roles rep
      = mkPrimTyCon' name kind roles rep True

    -- | Kind constructors
    mkKindTyCon :: Name -> Kind -> TyCon
    mkKindTyCon name kind
      = mkPrimTyCon' name kind [] VoidRep True

    -- | Create a lifted primitive 'TyCon' such as @RealWorld@
    mkLiftedPrimTyCon :: Name  -> Kind -> [Role] -> PrimRep -> TyCon
    mkLiftedPrimTyCon name kind roles rep
      = mkPrimTyCon' name kind roles rep False

    mkPrimTyCon' :: Name  -> Kind -> [Role] -> PrimRep -> Bool -> TyCon
    mkPrimTyCon' name kind roles rep is_unlifted
      = PrimTyCon {
            tyConName    = name,
            tyConUnique  = nameUnique name,
            tc_kind    = kind,
            tyConArity   = length roles,
            tc_roles     = roles,
            primTyConRep = rep,
            isUnLifted   = is_unlifted,
            tyConExtName = Nothing
        }

    -- | Create a type synonym 'TyCon'
    mkSynTyCon :: Name -> Kind -> [TyVar] -> [Role] -> SynTyConRhs -> TyConParent -> TyCon
    mkSynTyCon name kind tyvars roles rhs parent
      = SynTyCon {
            tyConName = name,
            tyConUnique = nameUnique name,
            tc_kind = kind,
            tyConArity = length tyvars,
            tyConTyVars = tyvars,
            tc_roles = roles,
            synTcRhs = rhs,
            synTcParent = parent
        }

    -- | Create a promoted data constructor 'TyCon'
    -- Somewhat dodgily, we give it the same Name
    -- as the data constructor itself; when we pretty-print
    -- the TyCon we add a quote; see the Outputable TyCon instance
    mkPromotedDataCon :: DataCon -> Name -> Unique -> Kind -> [Role] -> TyCon
    mkPromotedDataCon con name unique kind roles
      = PromotedDataCon {
            tyConName   = name,
            tyConUnique = unique,
            tyConArity  = arity,
            tc_roles    = roles,
            tc_kind     = kind,
            dataCon     = con
      }
      where
        arity = length roles

    -- | Create a promoted type constructor 'TyCon'
    -- Somewhat dodgily, we give it the same Name
    -- as the type constructor itself
    mkPromotedTyCon :: TyCon -> Kind -> TyCon
    mkPromotedTyCon tc kind
      = PromotedTyCon {
            tyConName   = getName tc,
            tyConUnique = getUnique tc,
            tyConArity  = tyConArity tc,
            tc_kind     = kind,
            ty_con      = tc
      }

\end{code} \begin{code}

    isFunTyCon :: TyCon -> Bool
    isFunTyCon (FunTyCon {}) = True
    isFunTyCon _             = False

    -- | Test if the 'TyCon' is algebraic but abstract (invisible data constructors)
    isAbstractTyCon :: TyCon -> Bool
    isAbstractTyCon (AlgTyCon { algTcRhs = AbstractTyCon {} }) = True
    isAbstractTyCon _ = False

    -- | Make an algebraic 'TyCon' abstract. Panics if the supplied 'TyCon' is not algebraic
    makeTyConAbstract :: TyCon -> TyCon
    makeTyConAbstract tc@(AlgTyCon { algTcRhs = rhs })
      = tc { algTcRhs = AbstractTyCon (isDistinctAlgRhs rhs) }
    makeTyConAbstract tc = pprPanic "makeTyConAbstract" (ppr tc)

    -- | Does this 'TyCon' represent something that cannot be defined in Haskell?
    isPrimTyCon :: TyCon -> Bool
    isPrimTyCon (PrimTyCon {}) = True
    isPrimTyCon _              = False

    -- | Is this 'TyCon' unlifted (i.e. cannot contain bottom)? Note that this can only
    -- be true for primitive and unboxed-tuple 'TyCon's
    isUnLiftedTyCon :: TyCon -> Bool
    isUnLiftedTyCon (PrimTyCon  {isUnLifted = is_unlifted}) = is_unlifted
    isUnLiftedTyCon (TupleTyCon {tyConTupleSort = sort})    = not (isBoxed (tupleSortBoxity sort))
    isUnLiftedTyCon _                                       = False

    -- | Returns @True@ if the supplied 'TyCon' resulted from either a
    -- @data@ or @newtype@ declaration
    isAlgTyCon :: TyCon -> Bool
    isAlgTyCon (AlgTyCon {})   = True
    isAlgTyCon (TupleTyCon {}) = True
    isAlgTyCon _               = False

    isDataTyCon :: TyCon -> Bool
    -- ^ Returns @True@ for data types that are /definitely/ represented by
    -- heap-allocated constructors.  These are scrutinised by Core-level
    -- @case@ expressions, and they get info tables allocated for them.
    --
    -- Generally, the function will be true for all @data@ types and false
    -- for @newtype@s, unboxed tuples and type family 'TyCon's. But it is
    -- not guaranteed to return @True@ in all cases that it could.
    --
    -- NB: for a data type family, only the /instance/ 'TyCon's
    --     get an info table.  The family declaration 'TyCon' does not
    isDataTyCon (AlgTyCon {algTcRhs = rhs})
      = case rhs of
            DataTyCon {}       -> True
            NewTyCon {}        -> False
            DataFamilyTyCon {} -> False
            AbstractTyCon {}   -> False      -- We don't know, so return False
    isDataTyCon (TupleTyCon {tyConTupleSort = sort}) = isBoxed (tupleSortBoxity sort)
    isDataTyCon _ = False

    -- | 'isDistinctTyCon' is true of 'TyCon's that are equal only to
    -- themselves, even via coercions (except for unsafeCoerce).
    -- This excludes newtypes, type functions, type synonyms.
    -- It relates directly to the FC consistency story:
    --     If the axioms are consistent,
    --     and  co : S tys ~ T tys, and S,T are "distinct" TyCons,
    --     then S=T.
    -- Cf Note [Pruning dead case alternatives] in Unify
    isDistinctTyCon :: TyCon -> Bool
    isDistinctTyCon (AlgTyCon {algTcRhs = rhs}) = isDistinctAlgRhs rhs
    isDistinctTyCon (FunTyCon {})               = True
    isDistinctTyCon (TupleTyCon {})             = True
    isDistinctTyCon (PrimTyCon {})              = True
    isDistinctTyCon (PromotedDataCon {})        = True
    isDistinctTyCon _                           = False

    isDistinctAlgRhs :: AlgTyConRhs -> Bool
    isDistinctAlgRhs (DataTyCon {})           = True
    isDistinctAlgRhs (DataFamilyTyCon {})     = True
    isDistinctAlgRhs (AbstractTyCon distinct) = distinct
    isDistinctAlgRhs (NewTyCon {})            = False

    -- | Is this 'TyCon' that for a @newtype@
    isNewTyCon :: TyCon -> Bool
    isNewTyCon (AlgTyCon {algTcRhs = NewTyCon {}}) = True
    isNewTyCon _                                   = False

    -- | Take a 'TyCon' apart into the 'TyVar's it scopes over, the 'Type' it expands
    -- into, and (possibly) a coercion from the representation type to the @newtype@.
    -- Returns @Nothing@ if this is not possible.
    unwrapNewTyCon_maybe :: TyCon -> Maybe ([TyVar], Type, CoAxiom Unbranched)
    unwrapNewTyCon_maybe (AlgTyCon { tyConTyVars = tvs,
                                     algTcRhs = NewTyCon { nt_co = co,
                                                           nt_rhs = rhs }})
                               = Just (tvs, rhs, co)
    unwrapNewTyCon_maybe _     = Nothing

    isProductTyCon :: TyCon -> Bool
    -- True of datatypes or newtypes that have
    --   one, vanilla, data constructor
    isProductTyCon tc@(AlgTyCon {}) = case algTcRhs tc of
                                        DataTyCon{ data_cons = [data_con] }
                                                    -> isVanillaDataCon data_con
                                        NewTyCon {} -> True
                                        _           -> False
    isProductTyCon (TupleTyCon {})  = True
    isProductTyCon _                = False

    isDataProductTyCon_maybe :: TyCon -> Maybe DataCon
    -- True of datatypes (not newtypes) with
    --   one, vanilla, data constructor
    isDataProductTyCon_maybe (AlgTyCon { algTcRhs = DataTyCon { data_cons = cons } })
      | [con] <- cons         -- Singleton
      , isVanillaDataCon con  -- Vanilla
      = Just con
    isDataProductTyCon_maybe (TupleTyCon { dataCon = con })
      = Just con
    isDataProductTyCon_maybe _ = Nothing

    -- | Is this a 'TyCon' representing a regular H98 type synonym (@type@)?
    isTypeSynonymTyCon :: TyCon -> Bool
    isTypeSynonymTyCon (SynTyCon { synTcRhs = SynonymTyCon {} }) = True
    isTypeSynonymTyCon _ = False

    -- | Is this 'TyCon' a type synonym or type family?
    isSynTyCon :: TyCon -> Bool
    isSynTyCon (SynTyCon {}) = True
    isSynTyCon _             = False

    -- As for newtypes, it is in some contexts important to distinguish between
    -- closed synonyms and synonym families, as synonym families have no unique
    -- right hand side to which a synonym family application can expand.
    --

    isDecomposableTyCon :: TyCon -> Bool
    -- True iff we can decompose (T a b c) into ((T a b) c)
    --   I.e. is it injective?
    -- Specifically NOT true of synonyms (open and otherwise)
    -- Ultimately we may have injective associated types
    -- in which case this test will become more interesting
    --
    -- It'd be unusual to call isInjectiveTyCon on a regular H98
    -- type synonym, because you should probably have expanded it first
    -- But regardless, it's not decomposable
    isDecomposableTyCon (SynTyCon {}) = False
    isDecomposableTyCon _other        = True

    -- | Is this an algebraic 'TyCon' declared with the GADT syntax?
    isGadtSyntaxTyCon :: TyCon -> Bool
    isGadtSyntaxTyCon (AlgTyCon { algTcGadtSyntax = res }) = res
    isGadtSyntaxTyCon _                                    = False

    -- | Is this an algebraic 'TyCon' which is just an enumeration of values?
    isEnumerationTyCon :: TyCon -> Bool
    -- See Note [Enumeration types] in TyCon
    isEnumerationTyCon (AlgTyCon {algTcRhs = DataTyCon { is_enum = res }}) = res
    isEnumerationTyCon (TupleTyCon {tyConArity = arity}) = arity == 0
    isEnumerationTyCon _                                                   = False

    -- | Is this a 'TyCon', synonym or otherwise, that defines a family?
    isFamilyTyCon :: TyCon -> Bool
    isFamilyTyCon (SynTyCon {synTcRhs = OpenSynFamilyTyCon })              = True
    isFamilyTyCon (SynTyCon {synTcRhs = ClosedSynFamilyTyCon {} })         = True
    isFamilyTyCon (SynTyCon {synTcRhs = AbstractClosedSynFamilyTyCon {} }) = True
    isFamilyTyCon (SynTyCon {synTcRhs = BuiltInSynFamTyCon {} })           = True
    isFamilyTyCon (AlgTyCon {algTcRhs = DataFamilyTyCon {}})               = True
    isFamilyTyCon _ = False

    -- | Is this a 'TyCon', synonym or otherwise, that defines an family with
    -- instances?
    isOpenFamilyTyCon :: TyCon -> Bool
    isOpenFamilyTyCon (SynTyCon {synTcRhs = OpenSynFamilyTyCon }) = True
    isOpenFamilyTyCon (AlgTyCon {algTcRhs = DataFamilyTyCon })    = True
    isOpenFamilyTyCon _ = False

    -- | Is this a synonym 'TyCon' that can have may have further instances appear?
    isSynFamilyTyCon :: TyCon -> Bool
    isSynFamilyTyCon (SynTyCon {synTcRhs = OpenSynFamilyTyCon {}})           = True
    isSynFamilyTyCon (SynTyCon {synTcRhs = ClosedSynFamilyTyCon {}})         = True
    isSynFamilyTyCon (SynTyCon {synTcRhs = AbstractClosedSynFamilyTyCon {}}) = True
    isSynFamilyTyCon (SynTyCon {synTcRhs = BuiltInSynFamTyCon {}})           = True
    isSynFamilyTyCon _ = False

    isOpenSynFamilyTyCon :: TyCon -> Bool
    isOpenSynFamilyTyCon (SynTyCon {synTcRhs = OpenSynFamilyTyCon }) = True
    isOpenSynFamilyTyCon _ = False

    -- leave out abstract closed families here
    isClosedSynFamilyTyCon_maybe :: TyCon -> Maybe (CoAxiom Branched)
    isClosedSynFamilyTyCon_maybe
      (SynTyCon {synTcRhs = ClosedSynFamilyTyCon ax}) = Just ax
    isClosedSynFamilyTyCon_maybe _ = Nothing

    isBuiltInSynFamTyCon_maybe :: TyCon -> Maybe BuiltInSynFamily
    isBuiltInSynFamTyCon_maybe
      SynTyCon {synTcRhs = BuiltInSynFamTyCon ops } = Just ops
    isBuiltInSynFamTyCon_maybe _ = Nothing

    -- | Is this a synonym 'TyCon' that can have may have further instances appear?
    isDataFamilyTyCon :: TyCon -> Bool
    isDataFamilyTyCon (AlgTyCon {algTcRhs = DataFamilyTyCon {}}) = True
    isDataFamilyTyCon _ = False

    -- | Are we able to extract informationa 'TyVar' to class argument list
    -- mappping from a given 'TyCon'?
    isTyConAssoc :: TyCon -> Bool
    isTyConAssoc tc = isJust (tyConAssoc_maybe tc)

    tyConAssoc_maybe :: TyCon -> Maybe Class
    tyConAssoc_maybe tc = case tyConParent tc of
                            AssocFamilyTyCon cls -> Just cls
                            _                    -> Nothing

    -- The unit tycon didn't used to be classed as a tuple tycon
    -- but I thought that was silly so I've undone it
    -- If it can't be for some reason, it should be a AlgTyCon
    isTupleTyCon :: TyCon -> Bool
    -- ^ Does this 'TyCon' represent a tuple?
    --
    -- NB: when compiling @Data.Tuple@, the tycons won't reply @True@ to
    -- 'isTupleTyCon', because they are built as 'AlgTyCons'.  However they
    -- get spat into the interface file as tuple tycons, so I don't think
    -- it matters.
    isTupleTyCon (TupleTyCon {}) = True
    isTupleTyCon _               = False

    -- | Is this the 'TyCon' for an unboxed tuple?
    isUnboxedTupleTyCon :: TyCon -> Bool
    isUnboxedTupleTyCon (TupleTyCon {tyConTupleSort = sort}) = not (isBoxed (tupleSortBoxity sort))
    isUnboxedTupleTyCon _                                    = False

    -- | Is this the 'TyCon' for a boxed tuple?
    isBoxedTupleTyCon :: TyCon -> Bool
    isBoxedTupleTyCon (TupleTyCon {tyConTupleSort = sort}) = isBoxed (tupleSortBoxity sort)
    isBoxedTupleTyCon _                                    = False

    -- | Extract the boxity of the given 'TyCon', if it is a 'TupleTyCon'.
    -- Panics otherwise
    tupleTyConBoxity :: TyCon -> Boxity
    tupleTyConBoxity tc = tupleSortBoxity (tyConTupleSort tc)

    -- | Extract the 'TupleSort' of the given 'TyCon', if it is a 'TupleTyCon'.
    -- Panics otherwise
    tupleTyConSort :: TyCon -> TupleSort
    tupleTyConSort tc = tyConTupleSort tc

    -- | Extract the arity of the given 'TyCon', if it is a 'TupleTyCon'.
    -- Panics otherwise
    tupleTyConArity :: TyCon -> Arity
    tupleTyConArity tc = tyConArity tc

    -- | Is this a recursive 'TyCon'?
    isRecursiveTyCon :: TyCon -> Bool
    isRecursiveTyCon (AlgTyCon {algTcRec = Recursive}) = True
    isRecursiveTyCon _                                 = False

    promotableTyCon_maybe :: TyCon -> Maybe TyCon
    promotableTyCon_maybe (AlgTyCon { tcPromoted = prom })   = prom
    promotableTyCon_maybe (TupleTyCon { tcPromoted = prom }) = prom
    promotableTyCon_maybe _                                  = Nothing

    promoteTyCon :: TyCon -> TyCon
    promoteTyCon tc = case promotableTyCon_maybe tc of
                        Just prom_tc -> prom_tc
                        Nothing      -> pprPanic "promoteTyCon" (ppr tc)

    -- | Is this the 'TyCon' of a foreign-imported type constructor?
    isForeignTyCon :: TyCon -> Bool
    isForeignTyCon (PrimTyCon {tyConExtName = Just _}) = True
    isForeignTyCon _                                   = False

    -- | Is this a PromotedTyCon?
    isPromotedTyCon :: TyCon -> Bool
    isPromotedTyCon (PromotedTyCon {}) = True
    isPromotedTyCon _                  = False

    -- | Retrieves the promoted TyCon if this is a PromotedTyCon;
    isPromotedTyCon_maybe :: TyCon -> Maybe TyCon
    isPromotedTyCon_maybe (PromotedTyCon { ty_con = tc }) = Just tc
    isPromotedTyCon_maybe _ = Nothing

    -- | Is this a PromotedDataCon?
    isPromotedDataCon :: TyCon -> Bool
    isPromotedDataCon (PromotedDataCon {}) = True
    isPromotedDataCon _                    = False

    -- | Retrieves the promoted DataCon if this is a PromotedDataCon;
    isPromotedDataCon_maybe :: TyCon -> Maybe DataCon
    isPromotedDataCon_maybe (PromotedDataCon { dataCon = dc }) = Just dc
    isPromotedDataCon_maybe _ = Nothing

    -- | Identifies implicit tycons that, in particular, do not go into interface
    -- files (because they are implicitly reconstructed when the interface is
    -- read).
    --
    -- Note that:
    --
    -- * Associated families are implicit, as they are re-constructed from
    --   the class declaration in which they reside, and
    --
    -- * Family instances are /not/ implicit as they represent the instance body
    --   (similar to a @dfun@ does that for a class instance).
    isImplicitTyCon :: TyCon -> Bool
    isImplicitTyCon (FunTyCon {})        = True
    isImplicitTyCon (TupleTyCon {})      = True
    isImplicitTyCon (PrimTyCon {})       = True
    isImplicitTyCon (PromotedDataCon {}) = True
    isImplicitTyCon (PromotedTyCon {})   = True
    isImplicitTyCon (AlgTyCon { algTcParent = AssocFamilyTyCon {} }) = True
    isImplicitTyCon (AlgTyCon {})                                    = False
    isImplicitTyCon (SynTyCon { synTcParent = AssocFamilyTyCon {} }) = True
    isImplicitTyCon (SynTyCon {})                                    = False

    tyConCType_maybe :: TyCon -> Maybe CType
    tyConCType_maybe tc@(AlgTyCon {}) = tyConCType tc
    tyConCType_maybe _ = Nothing

\end{code} ----------------------------------------------- -- Expand type-constructor applications ----------------------------------------------- \begin{code}

    tcExpandTyCon_maybe, coreExpandTyCon_maybe
            :: TyCon
            -> [tyco]                 -- ^ Arguments to 'TyCon'
            -> Maybe ([(TyVar,tyco)],
                      Type,
                      [tyco])         -- ^ Returns a 'TyVar' substitution, the body type
                                      -- of the synonym (not yet substituted) and any arguments
                                      -- remaining from the application

    -- ^ Used to create the view the /typechecker/ has on 'TyCon's.
    -- We expand (closed) synonyms only, cf. 'coreExpandTyCon_maybe'
    tcExpandTyCon_maybe (SynTyCon {tyConTyVars = tvs,
                                   synTcRhs = SynonymTyCon rhs }) tys
       = expand tvs rhs tys
    tcExpandTyCon_maybe _ _ = Nothing

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

    -- ^ Used to create the view /Core/ has on 'TyCon's. We expand
    -- not only closed synonyms like 'tcExpandTyCon_maybe',
    -- but also non-recursive @newtype@s
    coreExpandTyCon_maybe tycon tys = tcExpandTyCon_maybe tycon tys

    ----------------
    expand  :: [TyVar] -> Type                 -- Template
            -> [a]                             -- Args
            -> Maybe ([(TyVar,a)], Type, [a])  -- Expansion
    expand tvs rhs tys
      = case n_tvs `compare` length tys of
            LT -> Just (tvs `zip` tys, rhs, drop n_tvs tys)
            EQ -> Just (tvs `zip` tys, rhs, [])
            GT -> Nothing
       where
         n_tvs = length tvs

\end{code} \begin{code}

    tyConKind :: TyCon -> Kind
    tyConKind = tc_kind

    -- | As 'tyConDataCons_maybe', but returns the empty list of constructors if no constructors
    -- could be found
    tyConDataCons :: TyCon -> [DataCon]
    -- It's convenient for tyConDataCons to return the
    -- empty list for type synonyms etc
    tyConDataCons tycon = tyConDataCons_maybe tycon `orElse` []

    -- | Determine the 'DataCon's originating from the given 'TyCon', if the 'TyCon' is the
    -- sort that can have any constructors (note: this does not include abstract algebraic types)
    tyConDataCons_maybe :: TyCon -> Maybe [DataCon]
    tyConDataCons_maybe (AlgTyCon {algTcRhs = DataTyCon { data_cons = cons }}) = Just cons
    tyConDataCons_maybe (AlgTyCon {algTcRhs = NewTyCon { data_con = con }})    = Just [con]
    tyConDataCons_maybe (TupleTyCon {dataCon = con})                           = Just [con]
    tyConDataCons_maybe _                                                      = Nothing

    -- | Determine the number of value constructors a 'TyCon' has. Panics if the 'TyCon'
    -- is not algebraic or a tuple
    tyConFamilySize  :: TyCon -> Int
    tyConFamilySize (AlgTyCon   {algTcRhs = DataTyCon {data_cons = cons}}) =
      length cons
    tyConFamilySize (AlgTyCon   {algTcRhs = NewTyCon {}})        = 1
    tyConFamilySize (AlgTyCon   {algTcRhs = DataFamilyTyCon {}}) = 0
    tyConFamilySize (TupleTyCon {})                              = 1
    tyConFamilySize other = pprPanic "tyConFamilySize:" (ppr other)

    -- | Extract an 'AlgTyConRhs' with information about data constructors from an algebraic or tuple
    -- 'TyCon'. Panics for any other sort of 'TyCon'
    algTyConRhs :: TyCon -> AlgTyConRhs
    algTyConRhs (AlgTyCon {algTcRhs = rhs}) = rhs
    algTyConRhs (TupleTyCon {dataCon = con, tyConArity = arity})
        = DataTyCon { data_cons = [con], is_enum = arity == 0 }
    algTyConRhs other = pprPanic "algTyConRhs" (ppr other)

    -- | Get the list of roles for the type parameters of a TyCon
    tyConRoles :: TyCon -> [Role]
    -- See also Note [TyCon Role signatures]
    tyConRoles tc
      = case tc of
        { FunTyCon {}                          -> const_role Representational
        ; AlgTyCon { tc_roles = roles }        -> roles
        ; TupleTyCon {}                        -> const_role Representational
        ; SynTyCon { tc_roles = roles }        -> roles
        ; PrimTyCon { tc_roles = roles }       -> roles
        ; PromotedDataCon { tc_roles = roles } -> roles
        ; PromotedTyCon {}                     -> const_role Nominal
        }
      where
        const_role r = replicate (tyConArity tc) r

\end{code} \begin{code}

    -- | Extract the bound type variables and type expansion of a type synonym 'TyCon'. Panics if the
    -- 'TyCon' is not a synonym
    newTyConRhs :: TyCon -> ([TyVar], Type)
    newTyConRhs (AlgTyCon {tyConTyVars = tvs, algTcRhs = NewTyCon { nt_rhs = rhs }}) = (tvs, rhs)
    newTyConRhs tycon = pprPanic "newTyConRhs" (ppr tycon)

    -- | The number of type parameters that need to be passed to a newtype to resolve it. May be less than in the definition if it can be eta-contracted.
    newTyConEtadArity :: TyCon -> Int
    newTyConEtadArity (AlgTyCon {algTcRhs = NewTyCon { nt_etad_rhs = tvs_rhs }})
            = length (fst tvs_rhs)
    newTyConEtadArity tycon = pprPanic "newTyConEtadArity" (ppr tycon)

    -- | Extract the bound type variables and type expansion of an eta-contracted type synonym 'TyCon'.
    -- Panics if the 'TyCon' is not a synonym
    newTyConEtadRhs :: TyCon -> ([TyVar], Type)
    newTyConEtadRhs (AlgTyCon {algTcRhs = NewTyCon { nt_etad_rhs = tvs_rhs }}) = tvs_rhs
    newTyConEtadRhs tycon = pprPanic "newTyConEtadRhs" (ppr tycon)

    -- | Extracts the @newtype@ coercion from such a 'TyCon', which can be used to construct something
    -- with the @newtype@s type from its representation type (right hand side). If the supplied 'TyCon'
    -- is not a @newtype@, returns @Nothing@
    newTyConCo_maybe :: TyCon -> Maybe (CoAxiom Unbranched)
    newTyConCo_maybe (AlgTyCon {algTcRhs = NewTyCon { nt_co = co }}) = Just co
    newTyConCo_maybe _                                               = Nothing

    newTyConCo :: TyCon -> CoAxiom Unbranched
    newTyConCo tc = case newTyConCo_maybe tc of
                     Just co -> co
                     Nothing -> pprPanic "newTyConCo" (ppr tc)

    -- | Find the primitive representation of a 'TyCon'
    tyConPrimRep :: TyCon -> PrimRep
    tyConPrimRep (PrimTyCon {primTyConRep = rep}) = rep
    tyConPrimRep tc = ASSERT(not (isUnboxedTupleTyCon tc)) PtrRep

\end{code} \begin{code}

    -- | Find the \"stupid theta\" of the 'TyCon'. A \"stupid theta\" is the context to the left of
    -- an algebraic type declaration, e.g. @Eq a@ in the declaration @data Eq a => T a ...@
    tyConStupidTheta :: TyCon -> [PredType]
    tyConStupidTheta (AlgTyCon {algTcStupidTheta = stupid}) = stupid
    tyConStupidTheta (TupleTyCon {})                        = []
    tyConStupidTheta tycon = pprPanic "tyConStupidTheta" (ppr tycon)

\end{code} \begin{code}

    -- | Extract the 'TyVar's bound by a vanilla type synonym (not familiy)
    -- and the corresponding (unsubstituted) right hand side.
    synTyConDefn_maybe :: TyCon -> Maybe ([TyVar], Type)
    synTyConDefn_maybe (SynTyCon {tyConTyVars = tyvars, synTcRhs = SynonymTyCon ty})
      = Just (tyvars, ty)
    synTyConDefn_maybe _ = Nothing

    -- | Extract the information pertaining to the right hand side of a type synonym (@type@) declaration.
    synTyConRhs_maybe :: TyCon -> Maybe SynTyConRhs
    synTyConRhs_maybe (SynTyCon {synTcRhs = rhs}) = Just rhs
    synTyConRhs_maybe _                           = Nothing

\end{code} \begin{code}

    -- | If the given 'TyCon' has a /single/ data constructor, i.e. it is a @data@ type with one
    -- alternative, a tuple type or a @newtype@ then that constructor is returned. If the 'TyCon'
    -- has more than one constructor, or represents a primitive or function type constructor then
    -- @Nothing@ is returned. In any other case, the function panics
    tyConSingleDataCon_maybe :: TyCon -> Maybe DataCon
    tyConSingleDataCon_maybe (TupleTyCon {dataCon = c})                            = Just c
    tyConSingleDataCon_maybe (AlgTyCon {algTcRhs = DataTyCon { data_cons = [c] }}) = Just c
    tyConSingleDataCon_maybe (AlgTyCon {algTcRhs = NewTyCon { data_con = c }})     = Just c
    tyConSingleDataCon_maybe _                                                     = Nothing

    tyConSingleAlgDataCon_maybe :: TyCon -> Maybe DataCon
    -- Returns (Just con) for single-constructor *algebraic* data types
    -- *not* newtypes
    tyConSingleAlgDataCon_maybe (TupleTyCon {dataCon = c})                            = Just c
    tyConSingleAlgDataCon_maybe (AlgTyCon {algTcRhs = DataTyCon { data_cons = [c] }}) = Just c
    tyConSingleAlgDataCon_maybe _                                                     = Nothing

\end{code} \begin{code}

    -- | Is this 'TyCon' that for a class instance?
    isClassTyCon :: TyCon -> Bool
    isClassTyCon (AlgTyCon {algTcParent = ClassTyCon _}) = True
    isClassTyCon _                                       = False

    -- | If this 'TyCon' is that for a class instance, return the class it is for.
    -- Otherwise returns @Nothing@
    tyConClass_maybe :: TyCon -> Maybe Class
    tyConClass_maybe (AlgTyCon {algTcParent = ClassTyCon clas}) = Just clas
    tyConClass_maybe _                                          = Nothing

    tyConTuple_maybe :: TyCon -> Maybe TupleSort
    tyConTuple_maybe (TupleTyCon {tyConTupleSort = sort}) = Just sort
    tyConTuple_maybe _                                    = Nothing

    ----------------------------------------------------------------------------
    tyConParent :: TyCon -> TyConParent
    tyConParent (AlgTyCon {algTcParent = parent}) = parent
    tyConParent (SynTyCon {synTcParent = parent}) = parent
    tyConParent _                                 = NoParentTyCon

    ----------------------------------------------------------------------------
    -- | Is this 'TyCon' that for a data family instance?
    isFamInstTyCon :: TyCon -> Bool
    isFamInstTyCon tc = case tyConParent tc of
                          FamInstTyCon {} -> True
                          _               -> False

    tyConFamInstSig_maybe :: TyCon -> Maybe (TyCon, [Type], CoAxiom Unbranched)
    tyConFamInstSig_maybe tc
      = case tyConParent tc of
          FamInstTyCon ax f ts -> Just (f, ts, ax)
          _                    -> Nothing

    -- | If this 'TyCon' is that of a family instance, return the family in question
    -- and the instance types. Otherwise, return @Nothing@
    tyConFamInst_maybe :: TyCon -> Maybe (TyCon, [Type])
    tyConFamInst_maybe tc
      = case tyConParent tc of
          FamInstTyCon _ f ts -> Just (f, ts)
          _                   -> Nothing

    -- | If this 'TyCon' is that of a family instance, return a 'TyCon' which represents
    -- a coercion identifying the representation type with the type instance family.
    -- Otherwise, return @Nothing@
    tyConFamilyCoercion_maybe :: TyCon -> Maybe (CoAxiom Unbranched)
    tyConFamilyCoercion_maybe tc
      = case tyConParent tc of
          FamInstTyCon co _ _ -> Just co
          _                   -> Nothing

\end{code} %************************************************************************ %* * \subsection[TyCon-instances]{Instance declarations for @TyCon@} %* * %************************************************************************ @TyCon@s are compared by comparing their @Unique@s. The strictness analyser needs @Ord@. It is a lexicographic order with the property @(a<=b) || (b<=a)@. \begin{code}

    instance Eq TyCon where
        a == b = case (a `compare` b) of { EQ -> True;   _ -> False }
        a /= b = case (a `compare` b) of { EQ -> False;  _ -> True  }

    instance Ord TyCon where
        a <= b = case (a `compare` b) of { LT -> True;  EQ -> True;  GT -> False }
        a <  b = case (a `compare` b) of { LT -> True;  EQ -> False; GT -> False }
        a >= b = case (a `compare` b) of { LT -> False; EQ -> True;  GT -> True  }
        a >  b = case (a `compare` b) of { LT -> False; EQ -> False; GT -> True  }
        compare a b = getUnique a `compare` getUnique b

    instance Uniquable TyCon where
        getUnique tc = tyConUnique tc

    instance Outputable TyCon where
      -- At the moment a promoted TyCon has the same Name as its
      -- corresponding TyCon, so we add the quote to distinguish it here
      ppr tc = pprPromotionQuote tc <> ppr (tyConName tc)

    pprPromotionQuote :: TyCon -> SDoc
    pprPromotionQuote (PromotedDataCon {}) = char '\''   -- Quote promoted DataCons in types
    pprPromotionQuote (PromotedTyCon {})   = ifPprDebug (char '\'')
    pprPromotionQuote _                    = empty       -- However, we don't quote TyCons in kinds
                                                         -- e.g.   type family T a :: Bool -> *
                                                         -- cf Trac #5952.  Except with -dppr-debug

    instance NamedThing TyCon where
        getName = tyConName

    instance Data.Data TyCon where
        -- don't traverse?
        toConstr _   = abstractConstr "TyCon"
        gunfold _ _  = error "gunfold"
        dataTypeOf _ = mkNoRepType "TyCon"

\end{code} %************************************************************************ %* * Walking over recursive TyCons %* * %************************************************************************ Note [Expanding newtypes and products] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ When expanding a type to expose a data-type constructor, we need to be careful about newtypes, lest we fall into an infinite loop. Here are the key examples: newtype Id x = MkId x newtype Fix f = MkFix (f (Fix f)) newtype T = MkT (T -> T) Type Expansion -------------------------- T T -> T Fix Maybe Maybe (Fix Maybe) Id (Id Int) Int Fix Id NO NO NO Notice that we can expand T, even though it's recursive. And we can expand Id (Id Int), even though the Id shows up twice at the outer level. So, when expanding, we keep track of when we've seen a recursive newtype at outermost level; and bale out if we see it again. We sometimes want to do the same for product types, so that the strictness analyser doesn't unbox infinitely deeply. The function that manages this is checkRecTc. \begin{code}

    newtype RecTcChecker = RC NameSet

    initRecTc :: RecTcChecker
    initRecTc = RC emptyNameSet

    checkRecTc :: RecTcChecker -> TyCon -> Maybe RecTcChecker
    -- Nothing      => Recursion detected
    -- Just rec_tcs => Keep going
    checkRecTc (RC rec_nts) tc
      | not (isRecursiveTyCon tc)     = Just (RC rec_nts)
      | tc_name `elemNameSet` rec_nts = Nothing
      | otherwise                     = Just (RC (addOneToNameSet rec_nts tc_name))
      where
        tc_name = tyConName tc

\end{code}