Implement overlapping type family instances.

An ordered, overlapping type family instance is introduced by 'type
instance
where', followed by equations. See the new section in the user manual
(7.7.2.2) for details. The canonical example is Boolean equality at the
type
level:

type family Equals (a :: k) (b :: k) :: Bool
type instance where
  Equals a a = True
  Equals a b = False

A branched family instance, such as this one, checks its equations in
order
and applies only the first the matches. As explained in the note
[Instance
checking within groups] in FamInstEnv.lhs, we must be careful not to
simplify,
say, (Equals Int b) to False, because b might later unify with Int.

This commit includes all of the commits on the overlapping-tyfams
branch. SPJ
requested that I combine all my commits over the past several months
into one
monolithic commit. The following GHC repos are affected: ghc, testsuite,
utils/haddock, libraries/template-haskell, and libraries/dph.

Here are some details for the interested:

- The definition of CoAxiom has been moved from TyCon.lhs to a
  new file CoAxiom.lhs. I made this decision because of the
  number of definitions necessary to support BranchList.

- BranchList is a GADT whose type tracks whether it is a
  singleton list or not-necessarily-a-singleton-list. The reason
  I introduced this type is to increase static checking of places
  where GHC code assumes that a FamInst or CoAxiom is indeed a
  singleton. This assumption takes place roughly 10 times
  throughout the code. I was worried that a future change to GHC
  would invalidate the assumption, and GHC might subtly fail to
  do the right thing. By explicitly labeling CoAxioms and
  FamInsts as being Unbranched (singleton) or
  Branched (not-necessarily-singleton), we make this assumption
  explicit and checkable. Furthermore, to enforce the accuracy of
  this label, the list of branches of a CoAxiom or FamInst is
  stored using a BranchList, whose constructors constrain its
  type index appropriately.

I think that the decision to use BranchList is probably the most
controversial decision I made from a code design point of view.
Although I provide conversions to/from ordinary lists, it is more
efficient to use the brList... functions provided in CoAxiom than
always to convert. The use of these functions does not wander far
from the core CoAxiom/FamInst logic.

BranchLists are motivated and explained in the note [Branched axioms] in
CoAxiom.lhs.

- The CoAxiom type has changed significantly. You can see the new
  type in CoAxiom.lhs. It uses a CoAxBranch type to track
  branches of the CoAxiom. Correspondingly various functions
  producing and consuming CoAxioms had to change, including the
  binary layout of interface files.

- To get branched axioms to work correctly, it is important to have a
  notion
  of type "apartness": two types are apart if they cannot unify, and no
  substitution of variables can ever get them to unify, even after type
family
  simplification. (This is different than the normal failure to unify
because
  of the type family bit.) This notion in encoded in tcApartTys, in
Unify.lhs.
  Because apartness is finer-grained than unification, the tcUnifyTys
now
  calls tcApartTys.

- CoreLinting axioms has been updated, both to reflect the new
  form of CoAxiom and to enforce the apartness rules of branch
  application. The formalization of the new rules is in
  docs/core-spec/core-spec.pdf.

- The FamInst type (in types/FamInstEnv.lhs) has changed
  significantly, paralleling the changes to CoAxiom. Of course,
  this forced minor changes in many files.

- There are several new Notes in FamInstEnv.lhs, including one
  discussing confluent overlap and why we're not doing it.

- lookupFamInstEnv, lookupFamInstEnvConflicts, and
  lookup_fam_inst_env' (the function that actually does the work)
  have all been more-or-less completely rewritten. There is a
  Note [lookup_fam_inst_env' implementation] describing the
  implementation. One of the changes that affects other files is
  to change the type of matches from a pair of (FamInst, [Type])
  to a new datatype (which now includes the index of the matching
  branch). This seemed a better design.

- The TySynInstD constructor in Template Haskell was updated to
  use the new datatype TySynEqn. I also bumped the TH version
  number, requiring changes to DPH cabal files. (That's why the
  DPH repo has an overlapping-tyfams branch.)

- As SPJ requested, I refactored some of the code in HsDecls:

 * splitting up TyDecl into SynDecl and DataDecl, correspondingly
   changing HsTyDefn to HsDataDefn (with only one constructor)

 * splitting FamInstD into TyFamInstD and DataFamInstD and
   splitting FamInstDecl into DataFamInstDecl and TyFamInstDecl

 * making the ClsInstD take a ClsInstDecl, for parallelism with
   InstDecl's other constructors

 * changing constructor TyFamily into FamDecl

 * creating a FamilyDecl type that stores the details for a family
   declaration; this is useful because FamilyDecls can appear in classes
but
   other decls cannot

 * restricting the associated types and associated type defaults for a
 * class
   to be the new, more restrictive types

 * splitting cid_fam_insts into cid_tyfam_insts and cid_datafam_insts,
   according to the new types

 * perhaps one or two more that I'm overlooking

None of these changes has far-reaching implications.

- The user manual, section 7.7.2.2, is updated to describe the new type
  family
  instances.

4 files changed, 70 insertions, 24 deletions

diff --git a/docs/core-spec/CoreLint.ott b/docs/core-spec/CoreLint.ott
index b142901ede..beaf52a7d9 100644
--- a/docs/core-spec/CoreLint.ott
+++ b/docs/core-spec/CoreLint.ott
@@ -222,15 +222,19 @@ k0 <: k1
 --------------------- :: InstCo
 G |-co g t0 : s[m |-> t0] ~#k t[n |-> t0]
 
-</ G |-co gi : si ~#ki ti // i />
-</ substi @ // i /> = inits(</ [ ni |-> si ] // i />)
-</ ni = zi_k'i // i />
-</ ki <: substi(k'i) // i />
-s' = s </ [ ni |-> si ] // i />
-t' = t </ [ ni |-> ti ] // i />
-G |-ty s' : k
+C = T </ axBranchkk // kk />
+0 <= ind < length </ axBranchkk // kk />
+forall </ ni // i />. (</ s1j // j /> ~> t1) = (</ axBranchkk // kk />)[ind]
+</ G |-co gi : s'i ~#k'i t'i // i />
+</ substi @ // i /> = inits(</ [ ni |-> s'i ] // i />)
+</ ni = zi_ki // i />
+</ k'i <: substi(ki) // i />
+no_conflict(C, </ s2j // j />, ind-1)
+</ s2j = s1j </ [ni |-> s'i] // i/> // j />
+t2 = t1 </ [ni |-> t'i] // i />
+G |-ty t2 : k
 ------------------------------------------------------ :: AxiomInstCo
-G |-co (forall </ ni // i />. (s ~ t)) </ gi // i /> : s' ~#k t'
+G |-co C ind </ gi // i /> : T </ s2j // j /> ~#k t2
 
 defn G |- ki k ok ::  :: lintKind :: 'K_'
   {{ com Kind validity, \coderef{coreSyn/CoreLint.lhs}{lintKind} }}
@@ -397,4 +401,18 @@ Constraint <: OpenKind
 Constraint <: *
 
 ------------------ :: LiftedConstraint
-* <: Constraint
\ No newline at end of file
+* <: Constraint
+
+defn no_conflict ( C , </ sj // j /> , ind ) ::  :: check_no_conflict :: 'NoConflict_'
+  {{ com Branched axiom conflict checking, \coderef{coreSyn/CoreLint.lhs}{lintCoercion\#check\_no\_conflict} }}
+by
+
+------------------------------------------------ :: NoBranch
+no_conflict(C, </ si // i/>, -1)
+
+C = T </ axBranchkk // kk />
+forall </ ni // i />. (</ tj // j /> ~> t') = (</ axBranchkk // kk />)[ind]
+apart(</ sj // j />, </ tj // j />)
+no_conflict(C, </ sj // j />, ind-1)
+------------------------------------------------ :: Branch
+no_conflict(C, </ sj // j />, ind)
diff --git a/docs/core-spec/CoreSyn.ott b/docs/core-spec/CoreSyn.ott
index f3e8a61eb0..4c59849bb6 100644
--- a/docs/core-spec/CoreSyn.ott
+++ b/docs/core-spec/CoreSyn.ott
@@ -16,7 +16,7 @@ metavar alpha {{ tex \alpha }}, beta {{ tex \beta }} ::=
 metavar N ::=   {{ com Type-level constructor names }}
 metavar K ::=   {{ com Term-level data constructor names }}
 
-indexvar i, j ::= {{ com Indices to be used in lists }}
+indexvar i, j, kk {{ tex k }} ::= {{ com Indices to be used in lists }}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%  Syntax  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -101,7 +101,7 @@ g {{ tex \gamma }} :: 'Coercion_' ::= {{ com Coercions, \coderef{types/Coercion.
   | g1 g2                   ::   :: AppCo         {{ com Application }}
   | forall n . g            ::   :: ForAllCo      {{ com Polymorphism }}
   | n                       ::   :: CoVarCo       {{ com Variable }}
-  | C </ gi // i />         ::   :: AxiomInstCo   {{ com Axiom application }}
+  | C ind </ gj // j />     ::   :: AxiomInstCo   {{ com Axiom application }}
   | t1 ==>! t2              ::   :: UnsafeCo      {{ com Unsafe coercion }}
   | sym g                   ::   :: SymCo         {{ com Symmetry }}
   | g1 ; g2                 ::   :: TransCo       {{ com Transitivity }}
@@ -116,9 +116,13 @@ LorR :: 'LeftOrRight_' ::= {{ com left or right deconstructor, \coderef{types/Co
   | Right            ::   :: CRight               {{ com Right projection }}
 
 C :: 'CoAxiom_' ::= {{ com Axioms, \coderef{types/TyCon.lhs}{CoAxiom} }}
-  | forall </ ni // i /> . ( s ~ t )   ::   :: CoAxiom  {{ com Axiom }}
+  | T </ axBranchi // ; // i />    ::   :: CoAxiom  {{ com Axiom }}
   | ( C )                              :: M :: Parens   {{ com Parentheses }}
 
+axBranch, b :: 'CoAxBranch_' ::= {{ com Axiom branches, \coderef{types/TyCon.lhs}{CoAxBranch} }}
+  | forall </ ni // i /> . ( </ tj // j /> ~> s )  ::   :: CoAxBranch  {{ com Axiom branch }}
+  | ( </ axBranchi // i /> ) [ ind ]               :: M :: lookup      {{ com List lookup }}
+
 %% TYCONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 T :: 'TyCon_' ::= {{ com Type constructors, \coderef{types/TyCon.lhs}{TyCon} }}
@@ -162,10 +166,13 @@ subst :: 'Subst_' ::= {{ com List of type substitutions }}
   | [ n |-> t ]        ::   :: Mapping
   | </ substi // i />  ::   :: List
 
-nat {{ tex \mathbb{N} }} :: 'Nat_' ::= {{ com Natural numbers }}
-  | i                       ::   :: index
-  | length </ ti // i />    :: M :: length
-  | tyConArity T            :: M :: tyConArity
+ind :: 'Ind_' ::= {{ com Indices, numbers }}
+  | i                           ::   :: index
+  | length </ ti // i />        :: M :: length_t
+  | length </ axBranchi // i /> :: M :: length_axBranch
+  | tyConArity T                :: M :: tyConArity
+  | ind - 1                     :: M :: decrement
+  | -1                          :: M :: minusOne
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%  Terminals  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -220,6 +227,8 @@ terminals :: 'terminals_' ::=
   | dataConRepType :: :: dataConRepType   {{ tex \textsf{dataConRepType} }}
   | isNewTyCon   ::   :: isNewTyCon       {{ tex \textsf{isNewTyCon} }}
   | Constraint   ::   :: Constraint       {{ tex \textsf{Constraint} }}
+  | no_conflict  ::   :: no_conflict      {{ tex \textsf{no\_conflict} }}
+  | apart        ::   :: apart            {{ tex \textsf{apart} }}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%  Formulae  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -233,8 +242,8 @@ formula :: 'formula_' ::=
   | t1 /= t2                           ::   :: type_inequality
   | e1 /=e e2                          ::   :: expr_inequality
     {{ tex [[e1]] \neq [[e2]] }}
-  | rf                                 ::   :: rf_formula
-  | tlf                                ::   :: tlf_formula
+  | 0 <= ind1 < ind2                   ::   :: in_bounds
+    {{ tex 0 \leq [[ind1]] < [[ind2]] }}
   | g1 = g2                            ::   :: co_rewrite
   | no_duplicates </ zi // i />        ::   :: no_duplicates_name
   | no_duplicates </ bindingi // i />  ::   :: no_duplicates_binding
@@ -247,8 +256,8 @@ formula :: 'formula_' ::=
   | vars1 = vars2                      ::   :: vars_rewrite
   | </ Gi @ // i /> = inits ( </ nj // j /> ) :: :: context_folding
   | </ substi @ // i /> = inits ( </ [ nj |-> tj ] // j /> ) :: :: subst_folding
-  | nat1 = nat2                        ::   :: eq_nat
-  | nat1 < nat2                        ::   :: lt
+  | ind1 = ind2                        ::   :: eq_ind
+  | ind1 < ind2                        ::   :: lt
   | G |- tylit lit : k                 ::   :: lintTyLit
     {{ tex [[G]] \labeledjudge{tylit} [[lit]] : [[k]] }}
   | isNewTyCon T                       ::   :: isNewTyCon
@@ -258,6 +267,9 @@ formula :: 'formula_' ::=
   | t is_a_coercion                    ::   :: is_a_coercion
     {{ tex \exists \tau_1, \tau_2, \kappa \text{ s.t.~} [[t]] =
            \tau_1 \mathop{ {\sim}_{\#}^{\kappa} } \tau_2 }}
+  | axBranch1 = axBranch2              ::   :: branch_rewrite
+  | C1 = C2                            ::   :: axiom_rewrite
+  | apart ( </ ti // i /> , </ sj // j /> ) :: :: apart
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%  Subrules and Parsing  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -280,4 +292,5 @@ TyCon_PromotedTyCon right Coercion_AppCo
 Subst_Mapping <= Type_TySubstList
 Subst_List <= Type_TySubstList
 
-Subst_Mapping <= Type_TySubstListPost
\ No newline at end of file
+Subst_Mapping <= Type_TySubstListPost
+
diff --git a/docs/core-spec/core-spec.mng b/docs/core-spec/core-spec.mng
index 4a76e46c91..4b1e986c6d 100644
--- a/docs/core-spec/core-spec.mng
+++ b/docs/core-spec/core-spec.mng
@@ -145,7 +145,10 @@ Is it a left projection or a right projection?
 
 Axioms:
 
-\gram{\ottC}
+\gram{
+\ottC\ottinterrule
+\ottaxBranch
+}
 
 \subsection{Type constructors}
 
@@ -268,8 +271,7 @@ folding the substitution over the kinds for kind-checking.
 
 \subsection{Name consistency}
 
-There are two very similar checks for names, one declared as a local function
-within \coderef{coreSyn/CoreLint.lhs}{lintSingleBinding}:
+There are two very similar checks for names, one declared as a local function:
 
 \ottdefnlintSingleBindingXXlintBinder{}
 
@@ -303,4 +305,17 @@ within \coderef{coreSyn/CoreLint.lhs}{lintSingleBinding}:
 
 \ottdefnisSubKind{}
 
+\subsection{Branched axiom conflict checking}
+
+The following judgment is used within \ottdrulename{Co\_AxiomInstCo} to make
+sure that a type family application cannot unify with any previous branch
+in the axiom.
+
+\ottdefncheckXXnoXXconflict{}
+
+The judgment $[[apart]]$ checks to see whether two lists of types are surely apart.
+It checks to see if \coderef{types/Unify.lhs}{tcApartTys} returns \texttt{SurelyApart}.
+Two types are apart if neither type is a type family application and if they do not
+unify.
+
 \end{document}
diff --git a/docs/core-spec/core-spec.pdf b/docs/core-spec/core-spec.pdf
index 0e427c9c81..be13ca22c5 100644
--- a/docs/core-spec/core-spec.pdf
+++ b/docs/core-spec/core-spec.pdf