.. _instance-decls: .. _instance-resolution: Instance declarations and resolution ------------------------------------ An instance declaration has the form :: instance (assertion1, ..., assertionn) => class type1 ... typem where ... The part before the "``=>``" is the *context*, while the part after the "``=>``" is the *head* of the instance declaration. When GHC tries to resolve, say, the constraint ``C Int Bool``, it tries to match every instance declaration against the constraint, by instantiating the head of the instance declaration. Consider these declarations: :: instance context1 => C Int a where ... -- (A) instance context2 => C a Bool where ... -- (B) GHC's default behaviour is that *exactly one instance must match the constraint it is trying to resolve*. For example, the constraint ``C Int Bool`` matches instances (A) and (B), and hence would be rejected; while ``C Int Char`` matches only (A) and hence (A) is chosen. Notice that - When matching, GHC takes no account of the context of the instance declaration (``context1`` etc). - It is fine for there to be a *potential* of overlap (by including both declarations (A) and (B), say); an error is only reported if a particular constraint matches more than one. See also :ref:`instance-overlap` for flags that loosen the instance resolution rules. .. _flexible-instance-head: Relaxed rules for the instance head ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. extension:: TypeSynonymInstances :shortdesc: Enable type synonyms in instance heads. Implied by :extension:`FlexibleInstances`. :since: 6.8.1 Allow definition of type class instances for type synonyms. .. extension:: FlexibleInstances :shortdesc: Enable flexible instances. Implies :extension:`TypeSynonymInstances`. :implies: :extension:`TypeSynonymInstances` :since: 6.8.1 Allow definition of type class instances with arbitrary nested types in the instance head. In Haskell 98 the head of an instance declaration must be of the form ``C (T a1 ... an)``, where ``C`` is the class, ``T`` is a data type constructor, and the ``a1 ... an`` are distinct type variables. In the case of multi-parameter type classes, this rule applies to each parameter of the instance head (Arguably it should be okay if just one has this form and the others are type variables, but that's the rules at the moment). GHC relaxes this rule in two ways: - With the :extension:`TypeSynonymInstances` extension, instance heads may use type synonyms. As always, using a type synonym is just shorthand for writing the RHS of the type synonym definition. For example: :: type Point a = (a,a) instance C (Point a) where ... is legal. The instance declaration is equivalent to :: instance C (a,a) where ... As always, type synonyms must be fully applied. You cannot, for example, write: :: instance Monad Point where ... - The :extension:`FlexibleInstances` extension allows the head of the instance declaration to mention arbitrary nested types. For example, this becomes a legal instance declaration :: instance C (Maybe Int) where ... See also the `rules on overlap <#instance-overlap>`__. The :extension:`FlexibleInstances` extension implies :extension:`TypeSynonymInstances`. However, the instance declaration must still conform to the rules for instance termination: see :ref:`instance-termination`. .. _formal-instance-syntax: Formal syntax for instance declaration types ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The top of an instance declaration only permits very specific forms of types. To make more precise what forms of types are or are not permitted, we provide a BNF-style grammar for the tops of instance declarations below. .. code-block:: none inst_top ::= 'instance' opt_forall opt_ctxt inst_head opt_where opt_forall ::= | 'forall' tv_bndrs '.' tv_bndrs ::= | tv_bndr tv_bndrs tv_bndr ::= tyvar | '(' tyvar '::' ctype ')' opt_ctxt ::= | btype '=>' | '(' ctxt ')' '=>' ctxt ::= ctype | ctype ',' ctxt inst_head ::= '(' inst_head ')' | prefix_cls_tycon arg_types | arg_type infix_cls_tycon arg_type | '(' arg_type infix_cls_tycon arg_type ')' arg_types arg_type ::= | arg_type arg_types opt_where ::= | 'where' Where: - ``btype`` is a type that is not allowed to have an outermost ``forall``/``=>`` unless it is surrounded by parentheses. For example, ``forall a. a`` and ``Eq a => a`` are not legal ``btype``\s, but ``(forall a. a)`` and ``(Eq a => a)`` are legal. - ``ctype`` is a ``btype`` that has no restrictions on an outermost ``forall``/``=>``, so ``forall a. a`` and ``Eq a => a`` are legal ``ctype``\s. - ``arg_type`` is a type that is not allowed to have ``forall``\s or ``=>``\s - ``prefix_cls_tycon`` is a class type constructor written prefix (e.g., ``Show`` or ``(&&&)``), while ``infix_cls_tycon`` is a class type constructor written infix (e.g., ``\`Show\``` or ``&&&``). This is a simplified grammar that does not fully delve into all of the implementation details of GHC's parser (such as the placement of Haddock comments), but it is sufficient to attain an understanding of what is syntactically allowed. Some further various observations about this grammar: - Instance declarations are not allowed to be declared with nested ``forall``\s or ``=>``\s. For example, this would be rejected: :: instance forall a. forall b. C (Either a b) where ... As a result, ``inst_top`` puts all of its quantification and constraints up front with ``opt_forall`` and ``opt_context``. - Furthermore, instance declarations types do not permit outermost parentheses that surround the ``opt_forall`` or ``opt_ctxt``, if at least one of them are used. For example, ``instance (forall a. C a)`` would be rejected, since GHC would treat the ``forall`` as being nested. Note that it is acceptable to use parentheses in a ``inst_head``. For instance, ``instance (C a)`` is accepted, as is ``instance forall a. (C a)``. .. _instance-rules: .. _instance-termination: .. _undecidable-instances: Instance termination rules ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. extension:: UndecidableInstances :shortdesc: Enable undecidable instances. :since: 6.8.1 Permit definition of instances which may lead to type-checker non-termination. Regardless of :extension:`FlexibleInstances` and :extension:`FlexibleContexts`, instance declarations must conform to some rules that ensure that instance resolution will terminate. The restrictions can be lifted with :extension:`UndecidableInstances` (see :ref:`undecidable-instances`). The rules are these: 1. The Paterson Conditions: for each class constraint ``(C t1 ... tn)`` in the context 1. No type variable has more occurrences in the constraint than in the head 2. The constraint has fewer constructors and variables (taken together and counting repetitions) than the head 3. The constraint mentions no type functions. A type function application can in principle expand to a type of arbitrary size, and so are rejected out of hand 2. The Coverage Condition. For each functional dependency, ⟨tvs⟩\ :sub:`left` ``->`` ⟨tvs⟩\ :sub:`right`, of the class, every type variable in S(⟨tvs⟩\ :sub:`right`) must appear in S(⟨tvs⟩\ :sub:`left`), where S is the substitution mapping each type variable in the class declaration to the corresponding type in the instance head. These restrictions ensure that instance resolution terminates: each reduction step makes the problem smaller by at least one constructor. You can find lots of background material about the reason for these restrictions in the paper `Understanding functional dependencies via Constraint Handling Rules `__. For example, these are okay: :: instance C Int [a] -- Multiple parameters instance Eq (S [a]) -- Structured type in head -- Repeated type variable in head instance C4 a a => C4 [a] [a] instance Stateful (ST s) (MutVar s) -- Head can consist of type variables only instance C a instance (Eq a, Show b) => C2 a b -- Non-type variables in context instance Show (s a) => Show (Sized s a) instance C2 Int a => C3 Bool [a] instance C2 Int a => C3 [a] b But these are not: :: -- Context assertion no smaller than head instance C a => C a where ... -- (C b b) has more occurrences of b than the head instance C b b => Foo [b] where ... The same restrictions apply to instances generated by ``deriving`` clauses. Thus the following is accepted: :: data MinHeap h a = H a (h a) deriving (Show) because the derived instance :: instance (Show a, Show (h a)) => Show (MinHeap h a) conforms to the above rules. The restrictions on functional dependencies (:ref:`functional-dependencies`) are particularly troublesome. It is tempting to introduce type variables in the context that do not appear in the head, something that is excluded by the normal rules. For example: :: class HasConverter a b | a -> b where convert :: a -> b data Foo a = MkFoo a instance (HasConverter a b,Show b) => Show (Foo a) where show (MkFoo value) = show (convert value) This is dangerous territory, however. Here, for example, is a program that would make the typechecker loop: :: class D a class F a b | a->b instance F [a] [[a]] instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head Similarly, it can be tempting to lift the coverage condition: :: class Mul a b c | a b -> c where (.*.) :: a -> b -> c instance Mul Int Int Int where (.*.) = (*) instance Mul Int Float Float where x .*. y = fromIntegral x * y instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v The third instance declaration does not obey the coverage condition; and indeed the (somewhat strange) definition: :: f = \ b x y -> if b then x .*. [y] else y makes instance inference go into a loop, because it requires the constraint ``(Mul a [b] b)``. The :extension:`UndecidableInstances` extension is also used to lift some of the restrictions imposed on type family instances. See :ref:`type-family-decidability`. .. _instance-overlap: Overlapping instances ~~~~~~~~~~~~~~~~~~~~~ .. extension:: OverlappingInstances :shortdesc: Enable overlapping instances. :since: 6.8.1 Deprecated extension to weaken checks intended to ensure instance resolution termination. .. extension:: IncoherentInstances :shortdesc: Enable incoherent instances. Implies :extension:`OverlappingInstances`. :since: 6.8.1 Deprecated extension to weaken checks intended to ensure instance resolution termination. In general, as discussed in :ref:`instance-resolution`, *GHC requires that it be unambiguous which instance declaration should be used to resolve a type-class constraint*. GHC also provides a way to loosen the instance resolution, by allowing more than one instance to match, *provided there is a most specific one*. Moreover, it can be loosened further, by allowing more than one instance to match irrespective of whether there is a most specific one. This section gives the details. To control the choice of instance, it is possible to specify the overlap behavior for individual instances with a pragma, written immediately after the ``instance`` keyword. The pragma may be one of: ``{-# OVERLAPPING #-}``, ``{-# OVERLAPPABLE #-}``, ``{-# OVERLAPS #-}``, or ``{-# INCOHERENT #-}``. The matching behaviour is also influenced by two module-level language extension flags: :extension:`OverlappingInstances` and :extension:`IncoherentInstances`. These extensions are now deprecated (since GHC 7.10) in favour of the fine-grained per-instance pragmas. A more precise specification is as follows. The willingness to be overlapped or incoherent is a property of the *instance declaration* itself, controlled as follows: - An instance is *incoherent* if: it has an ``INCOHERENT`` pragma; or if the instance has no pragma and it appears in a module compiled with :extension:`IncoherentInstances`. - An instance is *overlappable* if: it has an ``OVERLAPPABLE`` or ``OVERLAPS`` pragma; or if the instance has no pragma and it appears in a module compiled with :extension:`OverlappingInstances`; or if the instance is incoherent. - An instance is *overlapping* if: it has an ``OVERLAPPING`` or ``OVERLAPS`` pragma; or if the instance has no pragma and it appears in a module compiled with :extension:`OverlappingInstances`; or if the instance is incoherent. Now suppose that, in some client module, we are searching for an instance of the *target constraint* ``(C ty1 .. tyn)``. The search works like this: - Find all instances :math:`I` that *match* the target constraint; that is, the target constraint is a substitution instance of :math:`I`. These instance declarations are the *candidates*. - If no candidates remain, the search fails - Eliminate any candidate :math:`IX` for which there is another candidate :math:`IY` such that both of the following hold: - :math:`IY` is strictly more specific than :math:`IX`. That is, :math:`IY` is a substitution instance of :math:`IX` but not vice versa. - Either :math:`IX` is *overlappable*, or :math:`IY` is *overlapping*. (This "either/or" design, rather than a "both/and" design, allow a client to deliberately override an instance from a library, without requiring a change to the library.) - If all the remaining candidates are incoherent, the search succeeds, returning an arbitrary surviving candidate. - If more than one non-incoherent candidate remains, the search fails. - Otherwise there is exactly one non-incoherent candidate; call it the "prime candidate". - Now find all instances, or in-scope given constraints, that *unify* with the target constraint, but do not *match* it. Such non-candidate instances might match when the target constraint is further instantiated. If all of them are incoherent top-level instances, the search succeeds, returning the prime candidate. Otherwise the search fails. Notice that these rules are not influenced by flag settings in the client module, where the instances are *used*. These rules make it possible for a library author to design a library that relies on overlapping instances without the client having to know. Errors are reported *lazily* (when attempting to solve a constraint), rather than *eagerly* (when the instances themselves are defined). Consider, for example :: instance C Int b where .. instance C a Bool where .. These potentially overlap, but GHC will not complain about the instance declarations themselves, regardless of flag settings. If we later try to solve the constraint ``(C Int Char)`` then only the first instance matches, and all is well. Similarly with ``(C Bool Bool)``. But if we try to solve ``(C Int Bool)``, both instances match and an error is reported. As a more substantial example of the rules in action, consider :: instance {-# OVERLAPPABLE #-} context1 => C Int b where ... -- (A) instance {-# OVERLAPPABLE #-} context2 => C a Bool where ... -- (B) instance {-# OVERLAPPABLE #-} context3 => C a [b] where ... -- (C) instance {-# OVERLAPPING #-} context4 => C Int [Int] where ... -- (D) (These all need :extension:`FlexibleInstances`.) Now suppose that the type inference engine needs to solve the constraint ``C Int [Int]``. This constraint matches instances (A), (C) and (D), but the last is more specific, and hence is chosen. If (D) did not exist then (A) and (C) would still be matched, but neither is most specific. In that case, the program would be rejected, unless :extension:`IncoherentInstances` is enabled, in which case it would be accepted and (A) or (C) would be chosen arbitrarily. An instance declaration is *more specific* than another iff the head of former is a substitution instance of the latter. For example (D) is "more specific" than (C) because you can get from (C) to (D) by substituting ``a := Int`` and ``b := Int``. The final bullet (about unifying instances) makes GHC conservative about committing to an overlapping instance. For example: :: f :: [b] -> [b] f x = ... Suppose that from the RHS of ``f`` we get the constraint ``C b [b]``. But GHC does not commit to instance (C), because in a particular call of ``f``, ``b`` might be instantiated to ``Int``, in which case instance (D) would be more specific still. So GHC rejects the program. If, however, you enable the extension :extension:`IncoherentInstances` when compiling the module that contains (D), GHC will instead pick (C), without complaining about the problem of subsequent instantiations. Notice that we gave a type signature to ``f``, so GHC had to *check* that ``f`` has the specified type. Suppose instead we do not give a type signature, asking GHC to *infer* it instead. In this case, GHC will refrain from simplifying the constraint ``C Int [b]`` (for the same reason as before) but, rather than rejecting the program, it will infer the type :: f :: C b [b] => [b] -> [b] That postpones the question of which instance to pick to the call site for ``f`` by which time more is known about the type ``b``. You will need the :extension:`FlexibleContexts` extension. Exactly the same situation can arise in instance declarations themselves. Suppose we have :: class Foo a where f :: a -> a instance Foo [b] where f x = ... and, as before, the constraint ``C Int [b]`` arises from ``f``'s right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve the constraint ``C Int [b]``, because it matches more than one instance declaration. The solution is to postpone the choice by adding the constraint to the context of the instance declaration, thus: :: instance C Int [b] => Foo [b] where f x = ... (You need :extension:`FlexibleContexts` to do this.) In the unification check in the final bullet, GHC also uses the "in-scope given constraints". Consider for example :: instance C a Int g :: forall b c. C b Int => blah g = ...needs (C c Int)... Here GHC will not solve the constraint ``(C c Int)`` from the top-level instance, because a particular call of ``g`` might instantiate both ``b`` and ``c`` to the same type, which would allow the constraint to be solved in a different way. This latter restriction is principally to make the constraint-solver complete. (Interested folk can read ``Note [Instance and Given overlap]`` in ``TcInteract``.) It is easy to avoid: in a type signature avoid a constraint that matches a top-level instance. The flag :ghc-flag:`-Wsimplifiable-class-constraints` warns about such signatures. .. warning:: Overlapping instances must be used with care. They can give rise to incoherence (i.e. different instance choices are made in different parts of the program) even without :extension:`IncoherentInstances`. Consider: :: {-# LANGUAGE OverlappingInstances #-} module Help where class MyShow a where myshow :: a -> String instance MyShow a => MyShow [a] where myshow xs = concatMap myshow xs showHelp :: MyShow a => [a] -> String showHelp xs = myshow xs {-# LANGUAGE FlexibleInstances, OverlappingInstances #-} module Main where import Help data T = MkT instance MyShow T where myshow x = "Used generic instance" instance MyShow [T] where myshow xs = "Used more specific instance" main = do { print (myshow [MkT]); print (showHelp [MkT]) } In function ``showHelp`` GHC sees no overlapping instances, and so uses the ``MyShow [a]`` instance without complaint. In the call to ``myshow`` in ``main``, GHC resolves the ``MyShow [T]`` constraint using the overlapping instance declaration in module ``Main``. As a result, the program prints .. code-block:: none "Used more specific instance" "Used generic instance" (An alternative possible behaviour, not currently implemented, would be to reject module ``Help`` on the grounds that a later instance declaration might overlap the local one.) .. _instance-sigs: Instance signatures: type signatures in instance declarations ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. extension:: InstanceSigs :shortdesc: Enable instance signatures. :since: 7.6.1 Allow type signatures for members in instance definitions. In Haskell, you can't write a type signature in an instance declaration, but it is sometimes convenient to do so, and the language extension :extension:`InstanceSigs` allows you to do so. For example: :: data T a = MkT a a instance Eq a => Eq (T a) where (==) :: T a -> T a -> Bool -- The signature (==) (MkT x1 x2) (MkTy y1 y2) = x1==y1 && x2==y2 Some details - The type signature in the instance declaration must be more polymorphic than (or the same as) the one in the class declaration, instantiated with the instance type. For example, this is fine: :: instance Eq a => Eq (T a) where (==) :: forall b. b -> b -> Bool (==) x y = True Here the signature in the instance declaration is more polymorphic than that required by the instantiated class method. - The code for the method in the instance declaration is typechecked against the type signature supplied in the instance declaration, as you would expect. So if the instance signature is more polymorphic than required, the code must be too. - One stylistic reason for wanting to write a type signature is simple documentation. Another is that you may want to bring scoped type variables into scope. For example: :: class C a where foo :: b -> a -> (a, [b]) instance C a => C (T a) where foo :: forall b. b -> T a -> (T a, [b]) foo x (T y) = (T y, xs) where xs :: [b] xs = [x,x,x] Provided that you also specify :extension:`ScopedTypeVariables` (:ref:`scoped-type-variables`), the ``forall b`` scopes over the definition of ``foo``, and in particular over the type signature for ``xs``.