content: {-
  (c) The University of Glasgow 2006
  (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
  -}
  
  {-# LANGUAGE NoPolyKinds #-}
  
  -- | GHC.Core holds all the main data types for use by for the Glasgow Haskell Compiler midsection
  module GHC.Core (
          -- * Main data types
          Expr(..), Alt(..), Bind(..), AltCon(..), Arg,
          CoreProgram, CoreExpr, CoreAlt, CoreBind, CoreArg, CoreBndr,
          TaggedExpr, TaggedAlt, TaggedBind, TaggedArg, TaggedBndr(..), deTagExpr,
  
          -- * In/Out type synonyms
          InId, InBind, InExpr, InAlt, InArg, InType, InKind,
                 InBndr, InVar, InCoercion, InTyVar, InCoVar, InTyCoVar,
          OutId, OutBind, OutExpr, OutAlt, OutArg, OutType, OutKind,
                 OutBndr, OutVar, OutCoercion, OutTyVar, OutCoVar,
                 OutTyCoVar, MOutCoercion,
  
          -- ** 'Expr' construction
          mkLet, mkLets, mkLetNonRec, mkLetRec, mkLams,
          mkApps, mkTyApps, mkCoApps, mkVarApps, mkTyArg,
  
          mkIntLit, mkIntLitWrap,
          mkWordLit, mkWordLitWrap,
          mkWord8Lit,
          mkWord32LitWord32, mkWord64LitWord64, mkInt64LitInt64,
          mkCharLit, mkStringLit,
          mkFloatLit, mkFloatLitFloat,
          mkDoubleLit, mkDoubleLitDouble,
  
          mkConApp, mkConApp2, mkTyBind, mkCoBind,
          varToCoreExpr, varsToCoreExprs,
  
          mkBinds,
  
          isId, cmpAltCon, cmpAlt, ltAlt,
  
          -- ** Simple 'Expr' access functions and predicates
          bindersOf, bindersOfBinds, rhssOfBind, rhssOfBinds, rhssOfAlts,
          foldBindersOfBindStrict, foldBindersOfBindsStrict,
          collectBinders, collectTyBinders, collectTyAndValBinders,
          collectNBinders, collectNValBinders_maybe,
          collectArgs, collectValArgs, stripNArgs, collectArgsTicks, flattenBinds,
          collectFunSimple,
  
          exprToType,
          wrapLamBody,
  
          isValArg, isTypeArg, isCoArg, isTyCoArg, valArgCount, valBndrCount,
          isRuntimeArg, isRuntimeVar,
  
          -- * Unfolding data types
          Unfolding(..),  UnfoldingCache(..), UnfoldingGuidance(..), UnfoldingSource(..),
  
          -- ** Constructing 'Unfolding's
          noUnfolding, bootUnfolding, evaldUnfolding, mkOtherCon,
          unSaturatedOk, needSaturated, boringCxtOk, boringCxtNotOk,
  
          -- ** Predicates and deconstruction on 'Unfolding'
          expandUnfolding_maybe,
          maybeUnfoldingTemplate, otherCons,
          isValueUnfolding, isEvaldUnfolding, isCheapUnfolding,
          isExpandableUnfolding, isConLikeUnfolding, isCompulsoryUnfolding,
          isStableUnfolding, isStableUserUnfolding, isStableSystemUnfolding,
          isInlineUnfolding, isBootUnfolding, isBetterUnfoldingThan,
          hasCoreUnfolding, hasSomeUnfolding,
          canUnfold, neverUnfoldGuidance, isStableSource,
  
          -- * Annotated expression data types
          AnnExpr, AnnExpr'(..), AnnBind(..), AnnAlt(..),
  
          -- ** Operations on annotated expressions
          collectAnnArgs, collectAnnArgsTicks,
  
          -- ** Operations on annotations
          deAnnotate, deAnnotate', deAnnAlt, deAnnBind,
          collectAnnBndrs, collectNAnnBndrs,
  
          -- * Orphanhood
          IsOrphan(..), isOrphan, notOrphan, chooseOrphanAnchor,
  
          -- * Core rule data types
          CoreRule(..),
          RuleName, RuleFun, IdUnfoldingFun, InScopeEnv(..), RuleOpts,
  
          -- ** Operations on 'CoreRule's
          ruleArity, ruleName, ruleIdName, ruleActivation,
          setRuleIdName, ruleModule,
          isBuiltinRule, isLocalRule, isAutoRule,
      ) where
  
  import GHC.Prelude
  import GHC.Platform
  
  import GHC.Types.Var.Env( InScopeSet )
  import GHC.Types.Var
  import GHC.Core.Type
  import GHC.Core.Coercion
  import GHC.Core.Rules.Config ( RuleOpts )
  import GHC.Types.Name
  import GHC.Types.Name.Set
  import GHC.Types.Literal
  import GHC.Types.Tickish
  import GHC.Core.DataCon
  import GHC.Unit.Module
  import GHC.Types.Basic
  import GHC.Types.Unique.Set
  
  import GHC.Utils.Binary
  import GHC.Utils.Misc
  import GHC.Utils.Outputable
  import GHC.Utils.Panic
  
  import Data.Data hiding (TyCon)
  import Data.Int
  import Data.List.NonEmpty (nonEmpty)
  import qualified Data.List.NonEmpty as NE
  import Data.Word
  
  import Control.DeepSeq
  
  infixl 4 `mkApps`, `mkTyApps`, `mkVarApps`, `App`, `mkCoApps`
  -- Left associative, so that we can say (f `mkTyApps` xs `mkVarApps` ys)
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{The main data types}
  *                                                                      *
  ************************************************************************
  
  These data types are the heart of the compiler
  -}
  
  -- | This is the data type that represents GHCs core intermediate language. Currently
  -- GHC uses System FC <https://www.microsoft.com/en-us/research/publication/system-f-with-type-equality-coercions/> for this purpose,
  -- which is closely related to the simpler and better known System F <http://en.wikipedia.org/wiki/System_F>.
  --
  -- We get from Haskell source to this Core language in a number of stages:
  --
  -- 1. The source code is parsed into an abstract syntax tree, which is represented
  --    by the data type 'GHC.Hs.Expr.HsExpr' with the names being 'GHC.Types.Name.Reader.RdrNames'
  --
  -- 2. This syntax tree is /renamed/, which attaches a 'GHC.Types.Unique.Unique' to every 'GHC.Types.Name.Reader.RdrName'
  --    (yielding a 'GHC.Types.Name.Name') to disambiguate identifiers which are lexically identical.
  --    For example, this program:
  --
  -- @
  --      f x = let f x = x + 1
  --            in f (x - 2)
  -- @
  --
  --    Would be renamed by having 'Unique's attached so it looked something like this:
  --
  -- @
  --      f_1 x_2 = let f_3 x_4 = x_4 + 1
  --                in f_3 (x_2 - 2)
  -- @
  --    But see Note [Shadowing in Core] below.
  --
  -- 3. The resulting syntax tree undergoes type checking (which also deals with instantiating
  --    type class arguments) to yield a 'GHC.Hs.Expr.HsExpr' type that has 'GHC.Types.Id.Id' as it's names.
  --
  -- 4. Finally the syntax tree is /desugared/ from the expressive 'GHC.Hs.Expr.HsExpr' type into
  --    this 'Expr' type, which has far fewer constructors and hence is easier to perform
  --    optimization, analysis and code generation on.
  --
  -- The type parameter @b@ is for the type of binders in the expression tree.
  --
  -- The language consists of the following elements:
  --
  -- *  Variables
  --    See Note [Variable occurrences in Core]
  --
  -- *  Primitive literals
  --
  -- *  Applications: note that the argument may be a 'Type'.
  --    See Note [Representation polymorphism invariants]
  --
  -- *  Lambda abstraction
  --    See Note [Representation polymorphism invariants]
  --
  -- *  Recursive and non recursive @let@s. Operationally
  --    this corresponds to allocating a thunk for the things
  --    bound and then executing the sub-expression.
  --
  --    See Note [Core letrec invariant]
  --    See Note [Core let-can-float invariant]
  --    See Note [Representation polymorphism invariants]
  --    See Note [Core type and coercion invariant]
  --
  -- *  Case expression. Operationally this corresponds to evaluating
  --    the scrutinee (expression examined) to weak head normal form
  --    and then examining at most one level of resulting constructor (i.e. you
  --    cannot do nested pattern matching directly with this).
  --
  --    The binder gets bound to the value of the scrutinee,
  --    and the 'Type' must be that of all the case alternatives
  --
  --    IMPORTANT: see Note [Case expression invariants]
  --
  -- *  Cast an expression to a particular type.
  --    This is used to implement @newtype@s (a @newtype@ constructor or
  --    destructor just becomes a 'Cast' in Core) and GADTs.
  --
  -- *  Ticks. These are used to represent all the source annotation we
  --    support: profiling SCCs, HPC ticks, and GHCi breakpoints.
  --
  -- *  A type: this should only show up at the top level of an Arg
  --
  -- *  A coercion
  
  {- Note [Why does Case have a 'Type' field?]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  The obvious alternative is
     exprType (Case scrut bndr alts)
       | (_,_,rhs1):_ <- alts
       = exprType rhs1
  
  But caching the type in the Case constructor
    exprType (Case scrut bndr ty alts) = ty
  is better for at least three reasons:
  
  * It works when there are no alternatives (see case invariant 1 above)
  
  * It might be faster in deeply-nested situations.
  
  * It might not be quite the same as (exprType rhs) for one
    of the RHSs in alts. Consider a phantom type synonym
         type S a = Int
     and we want to form the case expression
          case x of { K (a::*) -> (e :: S a) }
     Then exprType of the RHS is (S a), but we cannot make that be
     the 'ty' in the Case constructor because 'a' is simply not in
     scope there. Instead we must expand the synonym to Int before
     putting it in the Case constructor.  See GHC.Core.Utils.mkSingleAltCase.
  
     So we'd have to do synonym expansion in exprType which would
     be inefficient.
  
  * The type stored in the case is checked with lintInTy. This checks
    (among other things) that it does not mention any variables that are
    not in scope. If we did not have the type there, it would be a bit
    harder for Core Lint to reject case blah of Ex x -> x where
        data Ex = forall a. Ex a.
  -}
  
  -- If you edit this type, you may need to update the GHC formalism
  -- See Note [GHC Formalism] in GHC.Core.Lint
  data Expr b
    = Var   Id
    | Lit   Literal
    | App   (Expr b) (Arg b)
    | Lam   b (Expr b)
    | Let   (Bind b) (Expr b)
    | Case  (Expr b) b Type [Alt b]   -- See Note [Case expression invariants]
                                      -- and Note [Why does Case have a 'Type' field?]
    | Cast  (Expr b) CoercionR        -- The Coercion has Representational role
    | Tick  CoreTickish (Expr b)
    | Type  Type
    | Coercion Coercion
    deriving Data
  
  -- | Type synonym for expressions that occur in function argument positions.
  -- Only 'Arg' should contain a 'Type' at top level, general 'Expr' should not
  type Arg b = Expr b
  
  -- | A case split alternative. Consists of the constructor leading to the alternative,
  -- the variables bound from the constructor, and the expression to be executed given that binding.
  -- The default alternative is @(DEFAULT, [], rhs)@
  
  -- If you edit this type, you may need to update the GHC formalism
  -- See Note [GHC Formalism] in GHC.Core.Lint
  data Alt b
      = Alt AltCon [b] (Expr b)
      deriving (Data)
  
  -- | A case alternative constructor (i.e. pattern match)
  
  -- If you edit this type, you may need to update the GHC formalism
  -- See Note [GHC Formalism] in GHC.Core.Lint
  data AltCon
    = DataAlt DataCon   --  ^ A plain data constructor: @case e of { Foo x -> ... }@.
                        -- Invariant: the 'DataCon' is always from a @data@ type, and never from a @newtype@
  
    | LitAlt  Literal   -- ^ A literal: @case e of { 1 -> ... }@
                        -- Invariant: always an *unlifted* literal
                        -- See Note [Literal alternatives]
  
    | DEFAULT           -- ^ Trivial alternative: @case e of { _ -> ... }@
     deriving (Eq, Data)
  
  -- This instance is a bit shady. It can only be used to compare AltCons for
  -- a single type constructor. Fortunately, it seems quite unlikely that we'll
  -- ever need to compare AltCons for different type constructors.
  -- The instance adheres to the order described in Note [Case expression invariants]
  instance Ord AltCon where
    compare (DataAlt con1) (DataAlt con2) =
      assert (dataConTyCon con1 == dataConTyCon con2) $
      compare (dataConTag con1) (dataConTag con2)
    compare (DataAlt _) _ = GT
    compare _ (DataAlt _) = LT
    compare (LitAlt l1) (LitAlt l2) = compare l1 l2
    compare (LitAlt _) DEFAULT = GT
    compare DEFAULT DEFAULT = EQ
    compare DEFAULT _ = LT
  
  -- | Binding, used for top level bindings in a module and local bindings in a @let@.
  
  -- If you edit this type, you may need to update the GHC formalism
  -- See Note [GHC Formalism] in GHC.Core.Lint
  data Bind b = NonRec b (Expr b)
              | Rec [(b, (Expr b))]
    deriving Data
  
  -- | Helper function. You can use the result of 'mkBinds' with 'mkLets' for
  -- instance.
  --
  --   * @'mkBinds' 'Recursive' binds@ makes a single mutually-recursive
  --     bindings with all the rhs/lhs pairs in @binds@
  --   * @'mkBinds' 'NonRecursive' binds@ makes one non-recursive binding
  --     for each rhs/lhs pairs in @binds@
  mkBinds :: RecFlag -> [(b, (Expr b))] -> [Bind b]
  mkBinds Recursive binds = [Rec binds]
  mkBinds NonRecursive binds = map (uncurry NonRec) binds
  
  {-
  Note [Literal alternatives]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Literal alternatives (LitAlt lit) are always for *un-lifted* literals.
  We have one literal, a literal Integer, that is lifted, and we don't
  allow in a LitAlt, because LitAlt cases don't do any evaluation. Also
  (see #5603) if you say
      case 3 of
        IS x -> ...
        IP _ -> ...
        IN _ -> ...
  (where IS, IP, IN are the constructors for Integer) we don't want the
  simplifier calling findAlt with argument (LitAlt 3).  No no.  Integer
  literals are an opaque encoding of an algebraic data type, not of
  an unlifted literal, like all the others.
  
  Also, we do not permit case analysis with literal patterns on floating-point
  types. See #9238 and Note [Rules for floating-point comparisons] in
  GHC.Core.Opt.ConstantFold for the rationale for this restriction.
  
  -------------------------- GHC.Core INVARIANTS ---------------------------
  
  Note [Variable occurrences in Core]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Variable /occurrences/ are never CoVars, though /bindings/ can be.
  All CoVars appear in Coercions.
  
  For example
    \(c :: Age~#Int) (d::Int). d |> (sym c)
  Here 'c' is a CoVar, which is lambda-bound, but it /occurs/ in
  a Coercion, (sym c).
  
  Note [Shadowing in Core]
  ~~~~~~~~~~~~~~~~~~~~~~~~
  You might wonder if there is an invariant that a Core expression has no
  "shadowing".  For example, is this illegal?
       \x. \x. blah     -- x is shadowed
  Answer; no!  Core does /not/ have a no-shadowing invariant.
  
  Neither the simplifier nor any other pass GUARANTEES that shadowing is
  avoided. Thus, all passes SHOULD work fine even in the presence of
  arbitrary shadowing in their inputs.
  
  So the Unique in a Var is not really unique at all.  Still, it's very
  useful to give a constant-time equality/ordering for Vars, and to give
  a key that can be used to make sets of Vars (VarSet), or mappings from
  Vars to other things (VarEnv).   Moreover, if you do want to eliminate
  shadowing, you can give a new Unique to an Id without changing its
  printable name, which makes debugging easier.
  
  It would in many ways be easier to have a no-shadowing invariant.  And the
  Simplifier does its best to clone variables that are shadowed.  But it is
  extremely difficult to GUARANTEE it:
  
  * We use `GHC.Types.Id.mkTemplateLocal` to make up local binders, with uniques
    that are locally-unique (enough for the purpose) but not globally unique.
    It is convenient not to have to plumb a unique supply to these functions.
  
  * It is very difficult for the Simplifier to gurantee a no-shadowing result.
    See Note [Shadowing in the Simplifier] in GHC.Core.Opt.Simplify.Iteration.
  
  * See Note [Shadowing in CSE] in GHC.Core.Opt.CSE
  
  * See Note [Shadowing in SpecConstr] in GHC.Core.Opt.SpecContr
  
  Note [Core letrec invariant]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  The Core letrec invariant:
  
    The right hand sides of all /top-level/ or /recursive/
    bindings must be of lifted type
  
  See "Type#type_classification" in GHC.Core.Type
  for the meaning of "lifted" vs. "unlifted".
  
  For the non-top-level, non-recursive case see
  Note [Core let-can-float invariant].
  
  At top level, however, there are two exceptions to this rule:
  
  (TL1) A top-level binding is allowed to bind primitive string literal,
        (which is unlifted).  See Note [Core top-level string literals].
  
  (TL2) In Core, we generate a top-level binding for every non-newtype data
  constructor worker or wrapper
        e.g.   data T = MkT Int
        we generate
               MkT :: Int -> T
               MkT = \x. MkT x
        (This binding looks recursive, but isn't; it defines a top-level, curried
        function whose body just allocates and returns the data constructor.)
  
        But if (a) the data constructor is nullary and (b) the data type is unlifted,
        this binding is unlifted.
        e.g.   data S :: UnliftedType where { S1 :: S, S2 :: S -> S }
        we generate
               S1 :: S   -- A top-level unlifted binding
               S1 = S1
        We allow this top-level unlifted binding to exist.
  
  Note [Core let-can-float invariant]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  The let-can-float invariant:
  
      The right hand side of a /non-top-level/, /non-recursive/ binding
      may be of unlifted type, but only if
      the expression is ok-for-speculation
      or the 'Let' is for a join point.
  
      (For top-level or recursive lets see Note [Core letrec invariant].)
  
  This means that the let can be floated around
  without difficulty. For example, this is OK:
  
     y::Int# = x +# 1#
  
  But this is not, as it may affect termination if the
  expression is floated out:
  
     y::Int# = fac 4#
  
  In this situation you should use @case@ rather than a @let@. The function
  'GHC.Core.Utils.needsCaseBinding' can help you determine which to generate, or
  alternatively use 'GHC.Core.Make.mkCoreLet' rather than this constructor directly,
  which will generate a @case@ if necessary
  
  The let-can-float invariant is initially enforced by mkCoreLet in GHC.Core.Make.
  
  Historical Note [The let/app invariant]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Before 2022 GHC used the "let/app invariant", which applied the let-can-float rules
  to the argument of an application, as well as to the RHS of a let.  This made some
  kind of sense, because 'let' can always be encoded as application:
     let x=rhs in b   =    (\x.b) rhs
  
  But the let/app invariant got in the way of RULES; see #19313.  For example
    up :: Int# -> Int#
    {-# RULES "up/down" forall x. up (down x) = x #-}
  The LHS of this rule doesn't satisfy the let/app invariant.
  
  Indeed RULES is a big reason that GHC doesn't use ANF, where the argument of an
  application is always a variable or a constant.  To allow RULES to work nicely
  we need to allow lots of things in the arguments of a call.
  
  TL;DR: we relaxed the let/app invariant to become the let-can-float invariant.
  
  Note [Core top-level string literals]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  As an exception to the usual rule that top-level binders must be lifted,
  we allow binding primitive string literals (of type Addr#) at the
  top level. This allows us to share string literals earlier in the pipeline and
  crucially allows other optimizations in the Core2Core pipeline to fire.
  Consider,
  
    f n = let a::Addr# = "foo"#
          in \x -> blah
  
  In order to be able to inline `f`, we would like to float `a` to the top.
  Another option would be to inline `a`, but that would lead to duplicating string
  literals, which we want to avoid. See #8472.
  
  The solution is simply to allow top-level unlifted binders. We can't allow
  arbitrary unlifted expression at the top-level though, unlifted binders cannot
  be thunks, so we just allow string literals.
  
  We allow the top-level primitive string literals to be wrapped in Ticks
  in the same way they can be wrapped when nested in an expression.
  CoreToSTG currently discards Ticks around top-level primitive string literals.
  See #14779.
  
  Also see Note [Compilation plan for top-level string literals].
  
  Note [Compilation plan for top-level string literals]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Here is a summary on how top-level string literals are handled by various
  parts of the compilation pipeline.
  
  * In the source language, there is no way to bind a primitive string literal
    at the top level.
  
  * In Core, we have a special rule that permits top-level Addr# bindings. See
    Note [Core top-level string literals]. Core-to-core passes may introduce
    new top-level string literals.
  
    See GHC.Core.Utils.exprIsTopLevelBindable, and exprIsTickedString
  
  * In STG, top-level string literals are explicitly represented in the syntax
    tree.
  
  * A top-level string literal may end up exported from a module. In this case,
    in the object file, the content of the exported literal is given a label with
    the _bytes suffix.
  
  Note [NON-BOTTOM-DICTS invariant]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  It is a global invariant (not checkable by Lint) that
  
       every non-newtype dictionary-typed expression is non-bottom.
  
  These conditions are captured by GHC.Core.Type.isTerminatingType.
  
  How are we so sure about this?  Dictionaries are built by GHC in only two ways:
  
  * A dictionary function (DFun), arising from an instance declaration.
    DFuns do no computation: they always return a data constructor immediately.
    See DFunUnfolding in GHC.Core.  So the result of a call to a DFun is always
    non-bottom.
  
    Exception: newtype dictionaries.
  
    Plus: see the Very Nasty Wrinkle in Note [Speculative evaluation]
    in GHC.CoreToStg.Prep
  
  * A superclass selection from some other dictionary. This is harder to guarantee:
    see Note [Recursive superclasses] and Note [Solving superclass constraints]
    in GHC.Tc.TyCl.Instance.
  
  A bad Core-to-Core pass could invalidate this reasoning, but that's too bad.
  It's still an invariant of Core programs generated by GHC from Haskell, and
  Core-to-Core passes maintain it.
  
  Why is it useful to know that dictionaries are non-bottom?
  
  1. It justifies the use of `-XDictsStrict`;
     see `GHC.Core.Types.Demand.strictifyDictDmd`
  
  2. It means that (eq_sel d) is ok-for-speculation and thus
       case (eq_sel d) of _ -> blah
     can be discarded by the Simplifier.  See these Notes:
     Note [exprOkForSpeculation and type classes] in GHC.Core.Utils
     Note[Speculative evaluation] in GHC.CoreToStg.Prep
  
  Note [Case expression invariants]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Case expressions are one of the more complicated elements of the Core
  language, and come with a number of invariants.  All of them should be
  checked by Core Lint.
  
  1. The list of alternatives may be empty;
     See Note [Empty case alternatives]
  
  2. The 'DEFAULT' case alternative must be first in the list,
     if it occurs at all.  Checked in GHC.Core.Lint.checkCaseAlts.
  
  3. The remaining cases are in order of (strictly) increasing
       tag  (for 'DataAlts') or
       lit  (for 'LitAlts').
     This makes finding the relevant constructor easy, and makes
     comparison easier too.   Checked in GHC.Core.Lint.checkCaseAlts.
  
  4. The list of alternatives must be exhaustive. An /exhaustive/ case
     does not necessarily mention all constructors:
  
     @
          data Foo = Red | Green | Blue
          ... case x of
                Red   -> True
                other -> f (case x of
                                Green -> ...
                                Blue  -> ... ) ...
     @
  
     The inner case does not need a @Red@ alternative, because @x@
     can't be @Red@ at that program point.
  
     This is not checked by Core Lint -- it's very hard to do so.
     E.g. suppose that inner case was floated out, thus:
           let a = case x of
                     Green -> ...
                     Blue  -> ... )
           case x of
             Red   -> True
             other -> f a
     Now it's really hard to see that the Green/Blue case is
     exhaustive.  But it is.
  
     If you have a case-expression that really /isn't/ exhaustive,
     we may generate seg-faults.  Consider the Green/Blue case
     above.  Since there are only two branches we may generate
     code that tests for Green, and if not Green simply /assumes/
     Blue (since, if the case is exhaustive, that's all that
     remains).  Of course, if it's not Blue and we start fetching
     fields that should be in a Blue constructor, we may die
     horribly. See also Note [Core Lint guarantee] in GHC.Core.Lint.
  
  5. Floating-point values must not be scrutinised against literals.
     See #9238 and Note [Rules for floating-point comparisons]
     in GHC.Core.Opt.ConstantFold for rationale.  Checked in lintCaseExpr;
     see the call to isFloatingPrimTy.
  
  6. The 'ty' field of (Case scrut bndr ty alts) is the type of the
     /entire/ case expression.  Checked in lintAltExpr.
     See also Note [Why does Case have a 'Type' field?].
  
  7. The type of the scrutinee must be the same as the type
     of the case binder, obviously.  Checked in lintCaseExpr.
  
  8. The multiplicity of the binders in constructor patterns must be the
     multiplicity of the corresponding field /scaled by the multiplicity of the
     case binder/. Checked in lintCoreAlt.
  
  Note [Core type and coercion invariant]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  We allow a /non-recursive/, /non-top-level/ let to bind type and
  coercion variables.  These can be very convenient for postponing type
  substitutions until the next run of the simplifier.
  
  * A type variable binding must have a RHS of (Type ty)
  
  * A coercion variable binding must have a RHS of (Coercion co)
  
    It is possible to have terms that return a coercion, but we use
    case-binding for those; e.g.
       case (eq_sel d) of (co :: a ~# b) -> blah
    where eq_sel :: (a~b) -> (a~#b)
  
    Or even
        case (df @Int) of (co :: a ~# b) -> blah
    Which is very exotic, and I think never encountered; but see
    Note [Equality superclasses in quantified constraints]
    in GHC.Tc.Solver.Dict
  
  Note [Representation polymorphism invariants]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  GHC allows us to abstract over calling conventions using **representation polymorphism**.
  For example, we have:
  
    ($) :: forall (r :: RuntimeRep) (a :: Type) (b :: TYPE r). (a -> b) -> a -> b
  
  In this example, the type `b` is representation-polymorphic: it has kind `TYPE r`,
  where the type variable `r :: RuntimeRep` abstracts over the runtime representation
  of values of type `b`.
  
  To ensure that programs containing representation-polymorphism remain compilable,
  we enforce the following representation-polymorphism invariants:
  
  The paper "Levity Polymorphism" [PLDI'17] states the first two invariants:
  
    I1. The type of a bound variable must have a fixed runtime representation
        (except for join points: See Note [Invariants on join points])
    I2. The type of a function argument must have a fixed runtime representation.
  
  Example of I1:
  
    \(r::RuntimeRep). \(a::TYPE r). \(x::a). e
  
      This contravenes I1 because x's type has kind (TYPE r), which has 'r' free.
      We thus wouldn't know how to compile this lambda abstraction.
  
  Example of I2:
  
    f (undefined :: (a :: TYPE r))
  
      This contravenes I2: we are applying the function `f` to a value
      with an unknown runtime representation.
  
  Note that these two invariants require us to check other types than just the
  types of bound variables and types of function arguments, due to transformations
  that GHC performs. For example, the definition
  
    myCoerce :: forall {r} (a :: TYPE r) (b :: TYPE r). Coercible a b => a -> b
    myCoerce = coerce
  
  is invalid, because `coerce` has no binding (see GHC.Types.Id.Make.coerceId).
  So, before code-generation, GHC saturates the RHS of 'myCoerce' by performing
  an eta-expansion (see GHC.CoreToStg.Prep.maybeSaturate):
  
    myCoerce = \ (x :: TYPE r) -> coerce x
  
  However, this transformation would be invalid, because now the binding of x
  in the lambda abstraction would violate I1.
  
  See Note [Representation-polymorphism checking built-ins] in GHC.Tc.Utils.Concrete
  and Note [Linting representation-polymorphic builtins] in GHC.Core.Lint for
  more details.
  
  Note that we currently require something slightly stronger than a fixed runtime
  representation: we check whether bound variables and function arguments have a
  /fixed RuntimeRep/ in the sense of Note [Fixed RuntimeRep] in GHC.Tc.Utils.Concrete.
  See Note [Representation polymorphism checking] in GHC.Tc.Utils.Concrete
  for an overview of how we enforce these invariants in the typechecker.
  
  Note [Empty case alternatives]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  The alternatives of a case expression should be exhaustive.  But
  this exhaustive list can be empty!
  
  * A case expression can have empty alternatives if (and only if) the
    scrutinee is bound to raise an exception or diverge. When do we know
    this?  See Note [Bottoming expressions] in GHC.Core.Utils.
  
  * The possibility of empty alternatives is one reason we need a type on
    the case expression: if the alternatives are empty we can't get the
    type from the alternatives!
  
  * In the case of empty types (see Note [Bottoming expressions]), say
      data T
    we do NOT want to replace
      case (x::T) of Bool {}   -->   error Bool "Inaccessible case"
    because x might raise an exception, and *that*'s what we want to see!
    (#6067 is an example.) To preserve semantics we'd have to say
       x `seq` error Bool "Inaccessible case"
    but the 'seq' is just such a case, so we are back to square 1.
  
  * We can use the empty-alternative construct to coerce error values from
    one type to another.  For example
  
      f :: Int -> Int
      f n = error "urk"
  
      g :: Int -> (# Char, Bool #)
      g x = case f x of { 0 -> ..., n -> ... }
  
    Then if we inline f in g's RHS we get
      case (error Int "urk") of (# Char, Bool #) { ... }
    and we can discard the alternatives since the scrutinee is bottom to give
      case (error Int "urk") of (# Char, Bool #) {}
  
    This is nicer than using an unsafe coerce between Int ~ (# Char,Bool #),
    if for no other reason that we don't need to instantiate the (~) at an
    unboxed type.
  
  * We treat a case expression with empty alternatives as trivial iff
    its scrutinee is (see GHC.Core.Utils.exprIsTrivial).  This is actually
    important; see Note [Empty case is trivial] in GHC.Core.Utils
  
  * We lower empty cases in GHC.CoreToStg.coreToStgExpr to an eval on the
    scrutinee.
  
  Historical Note: We used to lower EmptyCase in CorePrep by way of an
  unsafeCoercion on the scrutinee, but that yielded panics in CodeGen when
  we were beginning to eta expand in arguments, plus required to mess with
  heterogenously-kinded coercions. It's simpler to stick to it just a bit longer.
  
  Note [Join points]
  ~~~~~~~~~~~~~~~~~~
  In Core, a *join point* is a specially tagged function whose only occurrences
  are saturated tail calls. A tail call can appear in these places:
  
    1. In the branches (not the scrutinee) of a case
    2. Underneath a let (value or join point)
    3. Inside another join point
  
  We write a join-point declaration as
    join j @a @b x y = e1 in e2,
  like a let binding but with "join" instead (or "join rec" for "let rec"). Note
  that we put the parameters before the = rather than using lambdas; this is
  because it's relevant how many parameters the join point takes *as a join
  point.* This number is called the *join arity,* distinct from arity because it
  counts types as well as values. Note that a join point may return a lambda! So
    join j x = x + 1
  is different from
    join j = \x -> x + 1
  The former has join arity 1, while the latter has join arity 0.
  
  The identifier for a join point is called a join id or a *label.* An invocation
  is called a *jump.* We write a jump using the jump keyword:
  
    jump j 3
  
  The words *label* and *jump* are evocative of assembly code (or Cmm) for a
  reason: join points are indeed compiled as labeled blocks, and jumps become
  actual jumps (plus argument passing and stack adjustment). There is no closure
  allocated and only a fraction of the function-call overhead. Hence we would
  like as many functions as possible to become join points (see OccurAnal) and
  the type rules for join points ensure we preserve the properties that make them
  efficient.
  
  In the actual AST, a join point is indicated by the IdDetails of the binder: a
  local value binding gets 'VanillaId' but a join point gets a 'JoinId' with its
  join arity.
  
  For more details, see the paper:
  
    Luke Maurer, Paul Downen, Zena Ariola, and Simon Peyton Jones. "Compiling
    without continuations." Submitted to PLDI'17.
  
    https://www.microsoft.com/en-us/research/publication/compiling-without-continuations/
  
  Note [Invariants on join points]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Join points must follow these invariants:
  
    1. All occurrences must be tail calls. Each of these tail calls must pass the
       same number of arguments, counting both types and values; we call this the
       "join arity" (to distinguish from regular arity, which only counts values).
  
       See Note [Join points are less general than the paper]
  
    2. For join arity n, the right-hand side must begin with at least n lambdas.
       No ticks, no casts, just lambdas!  C.f. GHC.Core.Utils.joinRhsArity.
  
       2a. Moreover, this same constraint applies to any unfolding of
           the binder.  Reason: if we want to push a continuation into
           the RHS we must push it into the unfolding as well.
  
       2b. The Arity (in the IdInfo) of a join point varies independently of the
           join-arity. For example, we could have
               j x = case x of { T -> \y.y; F -> \y.3 }
           Its join-arity is 1, but its idArity is 2; and we do not eta-expand
           join points: see Note [Do not eta-expand join points] in
                            GHC.Core.Opt.Simplify.Utils.
  
           Allowing the idArity to be bigger than the join-arity is
           important in arityType; see GHC.Core.Opt.Arity
           Note [Arity for recursive join bindings]
  
           Historical note: see #17294.
  
    3. If the binding is recursive, then all other bindings in the recursive group
       must also be join points.
  
    4. The binding's type must not be polymorphic in its return type (as defined
       in Note [The polymorphism rule of join points]).
  
  However, join points have simpler invariants in other ways
  
    5. A join point can have an unboxed type without the RHS being
       ok-for-speculation (i.e. drop the let-can-float invariant)
       e.g.  let j :: Int# = factorial x in ...
  
    6. The RHS of join point is not required to have a fixed runtime representation,
       e.g.  let j :: r :: TYPE l = fail (##) in ...
       This happened in an intermediate program #13394
  
  Examples:
  
    join j1  x = 1 + x in jump j (jump j x)  -- Fails 1: non-tail call
    join j1' x = 1 + x in if even a
                            then jump j1 a
                            else jump j1 a b -- Fails 1: inconsistent calls
    join j2  x = flip (+) x in j2 1 2        -- Fails 2: not enough lambdas
    join j2' x = \y -> x + y in j3 1         -- Passes: extra lams ok
    join j @a (x :: a) = x                   -- Fails 4: polymorphic in ret type
  
  Invariant 1 applies to left-hand sides of rewrite rules, so a rule for a join
  point must have an exact call as its LHS.
  
  Strictly speaking, invariant 3 is redundant, since a call from inside a lazy
  binding isn't a tail call. Since a let-bound value can't invoke a free join
  point, then, they can't be mutually recursive. (A Core binding group *can*
  include spurious extra bindings if the occurrence analyser hasn't run, so
  invariant 3 does still need to be checked.) For the rigorous definition of
  "tail call", see Section 3 of the paper (Note [Join points]).
  
  Invariant 4 is subtle; see Note [The polymorphism rule of join points].
  
  Invariant 6 is to enable code like this:
  
    f = \(r :: RuntimeRep) (a :: TYPE r) (x :: T).
        join j :: a
             j = error @r @a "bloop"
        in case x of
             A -> j
             B -> j
             C -> error @r @a "blurp"
  
  Core Lint will check these invariants, anticipating that any binder whose
  OccInfo is marked AlwaysTailCalled will become a join point as soon as the
  simplifier (or simpleOptPgm) runs.
  
  Note [Join points are less general than the paper]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  In the paper "Compiling without continuations", this expression is
  perfectly valid:
  
      join { j = \_ -> e }
      in (case blah of       )
         (  True  -> j void# ) arg
         (  False -> blah    )
  
  assuming 'j' has arity 1.   Here the call to 'j' does not look like a
  tail call, but actually everything is fine. See Section 3, "Managing \Delta"
  in the paper.
  
  In GHC, however, we adopt a slightly more restrictive subset, in which
  join point calls must be tail calls.  I think we /could/ loosen it up, but
  in fact the simplifier ensures that we always get tail calls, and it makes
  the back end a bit easier I think.  Generally, just less to think about;
  nothing deeper than that.
  
  Note [The type of a join point]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  A join point has the same type it would have as a function. That is, if it takes
  an Int and a Bool and its body produces a String, its type is `Int -> Bool ->
  String`. Natural as this may seem, it can be awkward. A join point shouldn't be
  thought to "return" in the same sense a function does---a jump is one-way. This
  is crucial for understanding how case-of-case interacts with join points:
  
    case (join
            j :: Int -> Bool -> String
            j x y = ...
          in
            jump j z w) of
      "" -> True
      _  -> False
  
  The simplifier will pull the case into the join point (see Note [Join points
  and case-of-case] in GHC.Core.Opt.Simplify):
  
    join
      j :: Int -> Bool -> Bool -- changed!
      j x y = case ... of "" -> True
                          _  -> False
    in
      jump j z w
  
  The body of the join point now returns a Bool, so the label `j` has to
  have its type updated accordingly, which is done by
  GHC.Core.Opt.Simplify.Env.adjustJoinPointType. Inconvenient though
  this may be, it has the advantage that 'GHC.Core.Utils.exprType' can
  still return a type for any expression, including a jump.
  
  Relationship to the paper
  
  This plan differs from the paper (see Note [Invariants on join
  points]). In the paper, we instead give j the type `Int -> Bool ->
  forall a. a`. Then each jump carries the "return type" as a parameter,
  exactly the way other non-returning functions like `error` work:
  
    case (join
            j :: Int -> Bool -> forall a. a
            j x y = ...
          in
            jump j z w @String) of
      "" -> True
      _  -> False
  
  Now we can move the case inward and we only have to change the jump:
  
    join
      j :: Int -> Bool -> forall a. a
      j x y = case ... of "" -> True
                          _  -> False
    in
      jump j z w @Bool
  
  (Core Lint would still check that the body of the join point has the right type;
  that type would simply not be reflected in the join id.)
  
  Note [The polymorphism rule of join points]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Invariant 4 of Note [Invariants on join points] forbids a join point to be
  polymorphic in its return type. That is, if its type is
  
    forall a1 ... ak. t1 -> ... -> tn -> r
  
  where its join arity is k+n, none of the type parameters ai may occur free in r.
  
  In some way, this falls out of the fact that given
  
    join
       j @a1 ... @ak x1 ... xn = e1
    in e2
  
  then all calls to `j` are in tail-call positions of `e`, and expressions in
  tail-call positions in `e` have the same type as `e`.
  Therefore the type of `e1` -- the return type of the join point -- must be the
  same as the type of e2.
  Since the type variables aren't bound in `e2`, its type can't include them, and
  thus neither can the type of `e1`.
  
  This unfortunately prevents the `go` in the following code from being a
  join-point:
  
    iter :: forall a. Int -> (a -> a) -> a -> a
    iter @a n f x = go @a n f x
      where
        go :: forall a. Int -> (a -> a) -> a -> a
        go @a 0 _ x = x
        go @a n f x = go @a (n-1) f (f x)
  
  In this case, a static argument transformation would fix that (see
  ticket #14620):
  
    iter :: forall a. Int -> (a -> a) -> a -> a
    iter @a n f x = go' @a n f x
      where
        go' :: Int -> (a -> a) -> a -> a
        go' 0 _ x = x
        go' n f x = go' (n-1) f (f x)
  
  In general, loopification could be employed to do that (see #14068.)
  
  Can we simply drop the requirement, and allow `go` to be a join-point? We
  could, and it would work. But we could not longer apply the case-of-join-point
  transformation universally. This transformation would do:
  
    case (join go @a n f x = case n of 0 -> x
                                       n -> go @a (n-1) f (f x)
          in go @Bool n neg True) of
      True -> e1; False -> e2
  
   ===>
  
    join go @a n f x = case n of 0 -> case x of True -> e1; False -> e2
                                 n -> go @a (n-1) f (f x)
    in go @Bool n neg True
  
  but that is ill-typed, as `x` is type `a`, not `Bool`.
  
  
  This also justifies why we do not consider the `e` in `e |> co` to be in
  tail position: A cast changes the type, but the type must be the same. But
  operationally, casts are vacuous, so this is a bit unfortunate! See #14610 for
  ideas how to fix this.
  
  Note [Strict fields in Core]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  In Core, evaluating a data constructor worker evaluates its strict fields.
  
  In other words, let's say we have the following data type
  
    data T a b = MkT !a b
  
  Now if `xs` reduces to `error "boom"`, then `MkT xs b` will throw that error.
  Consequently, it is sound to seq the field before the call to the constructor,
  e.g., with `case xs of xs' { __DEFAULT -> MkT xs' b }`.
  Let's call this transformation "field eval insertion".
  
  Note in particular that the data constructor application `MkT xs b` above is
  *not* a value, unless `xs` is!
  
  This has pervasive effect on the Core pipeline:
  
  (SFC1) `exprIsHNF`/`exprIsConLike`/`exprOkForSpeculation` need to assert that the
      strict arguments of a DataCon worker are values/ok-for-spec themselves.
  
  (SFC2) `exprIsConApp_maybe` inserts field evals in the `FloatBind`s it returns, so
      that the Simplifier, Constant-folding, the pattern-match checker, etc. all
      see the inserted field evals when they match on strict workers.
  
      For example,
        exprIsConApp_maybe (MkT e1 e2)
          = Just ([FloatCase e1 x], MkT, [x,e2])
      Meaning that (MkT e1 e2) is indeed a data constructor application, but if
      you want to decompose it (which is the purpose of exprIsConApp_maybe) you
      must evaluate e1 first.
      In case of case-of-known constructor, we get the rewrite
        case MkT e1 e2 of MkT xs' b' -> b'
        ==>
        case e1 of xs' { __DEFAULT -> e2 }
      which crucially retains the eval on e1.
  
  (SFC3) The demand signature of a data constructor is strict in strict field
      position and lazy in non-strict fields. Likewise the demand *transformer*
      of a DataCon worker can stricten up demands on strict field args.
      See Note [Demand transformer for data constructors].
  
  (SFC4) In the absence of `-fpedantic-bottoms`, it is still possible that some seqs
      are ultimately dropped or delayed due to eta-expansion.
      See Note [Dealing with bottom].
  
  Strict field semantics is exploited and lowered in STG during EPT enforcement;
  see Note [EPT enforcement lowers strict constructor worker semantics] for the
  connection.
  
  It might be tempting to think that strict fields could be implemented in terms
  of unlifted fields. However, unlifted fields behave differently when the data
  constructor is partially applied; see Note [exprIsHNF for function applications]
  for an example.
  
  Historical Note:
  The delightfully simple description of strict field semantics is the result of
  a long saga (#20749, the bits about strict data constructors in #21497, #22475),
  where we tried a more lenient (but actually not) semantics first that would
  allow both strict and lazy implementations of DataCon workers. This was favoured
  because the "pervasive effect" throughout the compiler was deemed too large
  (when it really turned out to be quite modest).
  Alas, this semantics would require us to implement `exprIsHNF` in *exactly* the
  same way as above, otherwise the analysis would not be conservative wrt. the
  lenient semantics (which includes the strict one). It is also much harder to
  explain and maintain, as it turned out.
  
  ************************************************************************
  *                                                                      *
              In/Out type synonyms
  *                                                                      *
  ********************************************************************* -}
  
  {- Many passes apply a substitution, and it's very handy to have type
     synonyms to remind us whether or not the substitution has been applied -}
  
  -- Pre-cloning or substitution
  type InBndr     = CoreBndr
  type InType     = Type
  type InKind     = Kind
  type InBind     = CoreBind
  type InExpr     = CoreExpr
  type InAlt      = CoreAlt
  type InArg      = CoreArg
  type InCoercion = Coercion
  
  -- Post-cloning or substitution
  type OutBndr     = CoreBndr
  type OutType     = Type
  type OutKind     = Kind
  type OutCoercion = Coercion
  type OutBind     = CoreBind
  type OutExpr     = CoreExpr
  type OutAlt      = CoreAlt
  type OutArg      = CoreArg
  type MOutCoercion = MCoercion
  
  
  {-
  ************************************************************************
  *                                                                      *
                  Orphans
  *                                                                      *
  ************************************************************************
  -}
  
  -- | Is this instance an orphan?  If it is not an orphan, contains an 'OccName'
  -- witnessing the instance's non-orphanhood.
  -- See Note [Orphans]
  data IsOrphan
    = IsOrphan
    | NotOrphan !OccName -- The OccName 'n' witnesses the instance's non-orphanhood
                        -- In that case, the instance is fingerprinted as part
                        -- of the definition of 'n's definition
      deriving Data
  
  -- | Returns true if 'IsOrphan' is orphan.
  isOrphan :: IsOrphan -> Bool
  isOrphan IsOrphan = True
  isOrphan _ = False
  
  -- | Returns true if 'IsOrphan' is not an orphan.
  notOrphan :: IsOrphan -> Bool
  notOrphan NotOrphan{} = True
  notOrphan _ = False
  
  chooseOrphanAnchor :: NameSet -> IsOrphan
  -- Something (rule, instance) is relate to all the Names in this
  -- list. Choose one of them to be an "anchor" for the orphan.  We make
  -- the choice deterministic to avoid gratuitous changes in the ABI
  -- hash (#4012).  Specifically, use lexicographic comparison of
  -- OccName rather than comparing Uniques
  --
  -- NB: 'minimum' use Ord, and (Ord OccName) works lexicographically
  --
  chooseOrphanAnchor local_names = case nonEmpty $ nonDetEltsUniqSet local_names of
      Nothing -> IsOrphan
      Just local_names -> NotOrphan (minimum (NE.map nameOccName local_names))
      -- It's OK to use nonDetEltsUFM here, see comments above
  
  instance Binary IsOrphan where
      put_ bh IsOrphan = putByte bh 0
      put_ bh (NotOrphan n) = do
          putByte bh 1
          put_ bh n
      get bh = do
          h <- getByte bh
          case h of
              0 -> return IsOrphan
              _ -> do
                  n <- get bh
                  return $ NotOrphan n
  
  instance NFData IsOrphan where
    rnf IsOrphan = ()
    rnf (NotOrphan n) = rnf n
  
  {-
  Note [Orphans]
  ~~~~~~~~~~~~~~
  Class instances, rules, and family instances are divided into orphans
  and non-orphans.  Roughly speaking, an instance/rule is an orphan if
  its left hand side mentions nothing defined in this module.  Orphan-hood
  has two major consequences
  
   * A module that contains orphans is called an "orphan module".  If
     the module being compiled depends (transitively) on an orphan
     module M, then M.hi is read in regardless of whether M is otherwise
     needed. This is to ensure that we don't miss any instance decls in
     M.  But it's painful, because it means we need to keep track of all
     the orphan modules below us.
  
   * The "visible orphan modules" are all the orphan module in the transitive
     closure of the imports of this module.
  
   * During instance lookup, we filter orphan instances depending on
     whether or not the instance is in a visible orphan module.
  
   * A non-orphan is not finger-printed separately.  Instead, for
     fingerprinting purposes it is treated as part of the entity it
     mentions on the LHS.  For example
        data T = T1 | T2
        instance Eq T where ....
     The instance (Eq T) is incorporated as part of T's fingerprint.
  
     In contrast, orphans are all fingerprinted together in the
     mi_orph_hash field of the ModIface.
  
     See GHC.Iface.Recomp.addFingerprints.
  
  Orphan-hood is computed
    * For class instances:
      when we make a ClsInst in GHC.Core.InstEnv.mkLocalClsInst
        (because it is needed during instance lookup)
      See Note [When exactly is an instance decl an orphan?]
          in GHC.Core.InstEnv
  
    * For rules
      when we generate a CoreRule (GHC.Core.Rules.mkRule)
  
    * For family instances:
      when we generate an IfaceFamInst (GHC.Iface.Make.instanceToIfaceInst)
  
  Orphan-hood is persisted into interface files, in ClsInst, FamInst,
  and CoreRules.
  
  -}
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Rewrite rules}
  *                                                                      *
  ************************************************************************
  
  The CoreRule type and its friends are dealt with mainly in GHC.Core.Rules, but
  GHC.Core.FVs, GHC.Core.Subst, GHC.Core.Ppr, GHC.Core.Tidy also inspect the
  representation.
  -}
  
  
  -- | A 'CoreRule' is:
  --
  -- * \"Local\" if the function it is a rule for is defined in the
  --   same module as the rule itself.
  --
  -- * \"Orphan\" if nothing on the LHS is defined in the same module
  --   as the rule itself
  data CoreRule
    = Rule {
          ru_name :: RuleName,            -- ^ Name of the rule, for communication with the user
          ru_act  :: Activation,          -- ^ When the rule is active
  
          -- Rough-matching stuff
          -- see comments with InstEnv.ClsInst( is_cls, is_rough )
          ru_fn    :: !Name,               -- ^ Name of the 'GHC.Types.Id.Id' at the head of this rule
          ru_rough :: [Maybe Name],       -- ^ Name at the head of each argument to the left hand side
  
          -- Proper-matching stuff
          -- see comments with InstEnv.ClsInst( is_tvs, is_tys )
          ru_bndrs :: [CoreBndr],         -- ^ Variables quantified over
          ru_args  :: [CoreExpr],         -- ^ Left hand side arguments
  
          -- And the right-hand side
          ru_rhs   :: CoreExpr,           -- ^ Right hand side of the rule
                                          -- Occurrence info is guaranteed correct
                                          -- See Note [OccInfo in unfoldings and rules]
  
          -- Locality
          ru_auto :: Bool,   -- ^ @True@  <=> this rule is auto-generated
                             --               (notably by Specialise or SpecConstr)
                             --   @False@ <=> generated at the user's behest
                             -- See Note [Trimming auto-rules] in "GHC.Iface.Tidy"
                             -- for the sole purpose of this field.
  
          ru_origin :: !Module,   -- ^ 'Module' the rule was defined in, used
                                  -- to test if we should see an orphan rule.
  
          ru_orphan :: !IsOrphan, -- ^ Whether or not the rule is an orphan.
  
          ru_local :: Bool        -- ^ @True@ iff the fn at the head of the rule is
                                  -- defined in the same module as the rule
                                  -- and is not an implicit 'Id' (like a record selector,
                                  -- class operation, or data constructor).  This
                                  -- is different from 'ru_orphan', where a rule
                                  -- can avoid being an orphan if *any* Name in
                                  -- LHS of the rule was defined in the same
                                  -- module as the rule.
      }
  
    -- | Built-in rules are used for constant folding
    -- and suchlike.  They have no free variables.
    -- A built-in rule is always visible (there is no such thing as
    -- an orphan built-in rule.)
    | BuiltinRule {
          ru_name  :: RuleName,   -- ^ As above
          ru_fn    :: Name,       -- ^ As above
          ru_nargs :: Int,        -- ^ Number of arguments that 'ru_try' consumes,
                                  -- if it fires, including type arguments
          ru_try   :: RuleFun
                  -- ^ This function does the rewrite.  It given too many
                  -- arguments, it simply discards them; the returned 'CoreExpr'
                  -- is just the rewrite of 'ru_fn' applied to the first 'ru_nargs' args
      }
                  -- See Note [Extra args in the target] in GHC.Core.Rules
  
  type RuleFun = RuleOpts -> InScopeEnv -> Id -> [CoreExpr] -> Maybe CoreExpr
  
  -- | The 'InScopeSet' in the 'InScopeEnv' is a /superset/ of variables that are
  -- currently in scope. See Note [The InScopeSet invariant].
  data InScopeEnv = ISE InScopeSet IdUnfoldingFun
  
  type IdUnfoldingFun = Id -> Unfolding
  -- A function that embodies how to unfold an Id if you need
  -- to do that in the Rule.  The reason we need to pass this info in
  -- is that whether an Id is unfoldable depends on the simplifier phase
  
  isBuiltinRule :: CoreRule -> Bool
  isBuiltinRule (BuiltinRule {}) = True
  isBuiltinRule _                = False
  
  isAutoRule :: CoreRule -> Bool
  isAutoRule (BuiltinRule {}) = False
  isAutoRule (Rule { ru_auto = is_auto }) = is_auto
  
  -- | The number of arguments the 'ru_fn' must be applied
  -- to before the rule can match on it
  ruleArity :: CoreRule -> FullArgCount
  ruleArity (BuiltinRule {ru_nargs = n}) = n
  ruleArity (Rule {ru_args = args})      = length args
  
  ruleName :: CoreRule -> RuleName
  ruleName = ru_name
  
  ruleModule :: CoreRule -> Maybe Module
  ruleModule Rule { ru_origin } = Just ru_origin
  ruleModule BuiltinRule {} = Nothing
  
  ruleActivation :: CoreRule -> Activation
  ruleActivation (BuiltinRule { })       = AlwaysActive
  ruleActivation (Rule { ru_act = act }) = act
  
  -- | The 'Name' of the 'GHC.Types.Id.Id' at the head of the rule left hand side
  ruleIdName :: CoreRule -> Name
  ruleIdName = ru_fn
  
  isLocalRule :: CoreRule -> Bool
  isLocalRule (BuiltinRule {})               = False
  isLocalRule (Rule { ru_local = is_local }) = is_local
  
  -- | Set the 'Name' of the 'GHC.Types.Id.Id' at the head of the rule left hand side
  setRuleIdName :: Name -> CoreRule -> CoreRule
  setRuleIdName nm ru = ru { ru_fn = nm }
  
  {-
  ************************************************************************
  *                                                                      *
                  Unfoldings
  *                                                                      *
  ************************************************************************
  
  The @Unfolding@ type is declared here to avoid numerous loops
  
  Note [Never put `OtherCon` unfoldings on lambda binders]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Based on #21496 we never attach unfoldings of any kind to lambda binders.
  It's just too easy for the call site to change and invalidate the unfolding.
  E.g. the caller of the lambda drops a seq (e.g. because the lambda is strict in it's binder)
  which in turn makes the OtherCon[] unfolding a lie.
  So unfoldings on lambda binders can never really be trusted when on lambda binders if there
  is the chance of the call site to change. So it's easiest to just never attach any
  to lambda binders to begin with, as well as stripping them off if we e.g. float out
  and expression while abstracting over some arguments.
  -}
  
  -- | Records the /unfolding/ of an identifier, which is approximately the form the
  -- identifier would have if we substituted its definition in for the identifier.
  -- This type should be treated as abstract everywhere except in "GHC.Core.Unfold"
  data Unfolding
    = NoUnfolding        -- ^ We have no information about the unfolding.
  
    | BootUnfolding      -- ^ We have no information about the unfolding, because
                         -- this 'Id' came from an @hi-boot@ file.
                         -- See Note [Inlining and hs-boot files] in "GHC.CoreToIface"
                         -- for what this is used for.
  
    | OtherCon [AltCon]  -- ^ It ain't one of these constructors.
                         -- @OtherCon xs@ also indicates that something has been evaluated
                         -- and hence there's no point in re-evaluating it.
                         -- @OtherCon []@ is used even for non-data-type values
                         -- to indicated evaluated-ness.  Notably:
                         --
                         -- > data C = C !(Int -> Int)
                         -- > case x of { C f -> ... }
                         --
                         -- Here, @f@ gets an @OtherCon []@ unfolding.
  
    | DFunUnfolding {     -- The Unfolding of a DFunId
                          -- See Note [DFun unfoldings]
                          --     df = /\a1..am. \d1..dn. MkD t1 .. tk
                          --                                 (op1 a1..am d1..dn)
                          --                                 (op2 a1..am d1..dn)
          df_bndrs :: [Var],      -- The bound variables [a1..m],[d1..dn]
          df_con   :: DataCon,    -- The dictionary data constructor (never a newtype datacon)
          df_args  :: [CoreExpr]  -- Args of the data con: types, superclasses and methods,
      }                           -- in positional order
  
    | CoreUnfolding { -- An unfolding for an Id with no pragma,
                      -- or perhaps a NOINLINE pragma
                      -- (For NOINLINE, the phase, if any, is in the
                      -- InlinePragInfo for this Id.)
          uf_tmpl     :: CoreExpr,         -- The unfolding itself (aka "template")
                                           -- Always occ-analysed;
                                           -- See Note [OccInfo in unfoldings and rules]
  
          uf_src      :: UnfoldingSource,  -- Where the unfolding came from
          uf_is_top   :: Bool,             -- True <=> top level binding
          uf_cache    :: UnfoldingCache,   -- Cache of flags computable from the expr
                                           -- See Note [Tying the 'CoreUnfolding' knot]
          uf_guidance :: UnfoldingGuidance -- Tells about the *size* of the template.
      }
    -- ^ An unfolding with redundant cached information. Parameters:
    --
    --  uf_tmpl: Template used to perform unfolding;
    --           NB: Occurrence info is guaranteed correct:
    --               see Note [OccInfo in unfoldings and rules]
    --
    --  uf_is_top: Is this a top level binding?
    --
    --  uf_is_value: 'exprIsHNF' template (cached); it is ok to discard a 'seq' on
    --     this variable
    --
    --  uf_is_work_free:  Does this waste only a little work if we expand it inside an inlining?
    --     Basically this is a cached version of 'exprIsWorkFree'
    --
    --  uf_guidance:  Tells us about the /size/ of the unfolding template
  
  
  -- | Properties of a 'CoreUnfolding' that could be computed on-demand from its template.
  -- See Note [UnfoldingCache]
  data UnfoldingCache
    = UnfoldingCache {
          uf_is_value   :: !Bool,         -- exprIsHNF template (cached); it is ok to discard
                                          --      a `seq` on this variable
          uf_is_conlike :: !Bool,         -- True <=> applicn of constructor or CONLIKE function
                                          --      Cached version of exprIsConLike
          uf_is_work_free :: !Bool,       -- True <=> doesn't waste (much) work to expand
                                          --          inside an inlining
                                          --      Cached version of exprIsCheap
          uf_expandable :: !Bool          -- True <=> can expand in RULE matching
                                          --      Cached version of exprIsExpandable
      }
    deriving (Eq)
  
  -- | 'UnfoldingGuidance' says when unfolding should take place
  data UnfoldingGuidance
    = UnfWhen {   -- Inline without thinking about the *size* of the uf_tmpl
                  -- Used (a) for small *and* cheap unfoldings
                  --      (b) for INLINE functions
                  -- See Note [INLINE for small functions] in GHC.Core.Unfold
        ug_arity    :: Arity,     -- Number of value arguments expected
  
        ug_unsat_ok  :: Bool,     -- True <=> ok to inline even if unsaturated
        ug_boring_ok :: Bool      -- True <=> ok to inline even if the context is boring
                  -- So True,True means "always"
      }
  
    | UnfIfGoodArgs {     -- Arose from a normal Id; the info here is the
                          -- result of a simple analysis of the RHS
  
        ug_args ::  [Int],  -- Discount if the argument is evaluated.
                            -- (i.e., a simplification will definitely
                            -- be possible).  One elt of the list per *value* arg.
  
        ug_size :: Int,     -- The "size" of the unfolding.
  
        ug_res :: Int       -- Scrutinee discount: the discount to subtract if the thing is in
      }                     -- a context (case (thing args) of ...),
                            -- (where there are the right number of arguments.)
  
    | UnfNever        -- The RHS is big, so don't inline it
    deriving (Eq)
  
  {- Note [UnfoldingCache]
  ~~~~~~~~~~~~~~~~~~~~~~~~
  The UnfoldingCache field of an Unfolding holds four (strict) booleans,
  all derived from the uf_tmpl field of the unfolding.
  
  * We serialise the UnfoldingCache to and from interface files, for
    reasons described in  Note [Tying the 'CoreUnfolding' knot] in
    GHC.IfaceToCore
  
  * Because it is a strict data type, we must be careful not to
    pattern-match on it until we actually want its values.  E.g
    GHC.Core.Unfold.callSiteInline/tryUnfolding are careful not to force
    it unnecessarily.  Just saves a bit of work.
  
  * When `seq`ing Core to eliminate space leaks, to suffices to `seq` on
    the cache, but not its fields, because it is strict in all fields.
  
  Note [Historical note: unfoldings for wrappers]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  We used to have a nice clever scheme in interface files for
  wrappers. A wrapper's unfolding can be reconstructed from its worker's
  id and its strictness. This decreased .hi file size (sometimes
  significantly, for modules like GHC.Classes with many high-arity w/w
  splits) and had a slight corresponding effect on compile times.
  
  However, when we added the second demand analysis, this scheme lead to
  some Core lint errors. The second analysis could change the strictness
  signatures, which sometimes resulted in a wrapper's regenerated
  unfolding applying the wrapper to too many arguments.
  
  Instead of repairing the clever .hi scheme, we abandoned it in favor
  of simplicity. The .hi sizes are usually insignificant (excluding the
  +1M for base libraries), and compile time barely increases (~+1% for
  nofib). The nicer upshot is that the UnfoldingSource no longer mentions
  an Id, so, eg, substitutions need not traverse them.
  
  
  Note [DFun unfoldings]
  ~~~~~~~~~~~~~~~~~~~~~~
  The Arity in a DFunUnfolding is total number of args (type and value)
  that the DFun needs to produce a dictionary.  That's not necessarily
  related to the ordinary arity of the dfun Id, esp if the class has
  one method, so the dictionary is represented by a newtype.  Example
  
       class C a where { op :: a -> Int }
       instance C a -> C [a] where op xs = op (head xs)
  
  The instance translates to
  
       $dfCList :: forall a. C a => C [a]  -- Arity 2!
       $dfCList = /\a.\d. $copList {a} d |> co
  
       $copList :: forall a. C a => [a] -> Int  -- Arity 2!
       $copList = /\a.\d.\xs. op {a} d (head xs)
  
  Now we might encounter (op (dfCList {ty} d) a1 a2)
  and we want the (op (dfList {ty} d)) rule to fire, because $dfCList
  has all its arguments, even though its (value) arity is 2.  That's
  why we record the number of expected arguments in the DFunUnfolding.
  
  Note that although it's an Arity, it's most convenient for it to give
  the *total* number of arguments, both type and value.  See the use
  site in exprIsConApp_maybe.
  -}
  
  -- Constants for the UnfWhen constructor
  needSaturated, unSaturatedOk :: Bool
  needSaturated = False
  unSaturatedOk = True
  
  boringCxtNotOk, boringCxtOk :: Bool
  boringCxtOk    = True
  boringCxtNotOk = False
  
  ------------------------------------------------
  noUnfolding :: Unfolding
  -- ^ There is no known 'Unfolding'
  evaldUnfolding :: Unfolding
  -- ^ This unfolding marks the associated thing as being evaluated
  
  noUnfolding    = NoUnfolding
  evaldUnfolding = OtherCon []
  
  -- | There is no known 'Unfolding', because this came from an
  -- hi-boot file.
  bootUnfolding :: Unfolding
  bootUnfolding = BootUnfolding
  
  mkOtherCon :: [AltCon] -> Unfolding
  mkOtherCon = OtherCon
  
  -- | Retrieves the template of an unfolding if possible
  -- maybeUnfoldingTemplate is used mainly when specialising, and we do
  -- want to specialise DFuns, so it's important to return a template
  -- for DFunUnfoldings
  maybeUnfoldingTemplate :: Unfolding -> Maybe CoreExpr
  maybeUnfoldingTemplate (CoreUnfolding { uf_tmpl = expr })
    = Just expr
  maybeUnfoldingTemplate (DFunUnfolding { df_bndrs = bndrs, df_con = con, df_args = args })
    = Just (mkLams bndrs (mkApps (Var (dataConWorkId con)) args))
  maybeUnfoldingTemplate _
    = Nothing
  
  -- | The constructors that the unfolding could never be:
  -- returns @[]@ if no information is available
  otherCons :: Unfolding -> [AltCon]
  otherCons (OtherCon cons) = cons
  otherCons _               = []
  
  -- | Determines if it is certainly the case that the unfolding will
  -- yield a value (something in HNF): returns @False@ if unsure
  isValueUnfolding :: Unfolding -> Bool
          -- Returns False for OtherCon
  isValueUnfolding (CoreUnfolding { uf_cache = cache }) = uf_is_value cache
  isValueUnfolding (DFunUnfolding {})                   = True
  isValueUnfolding _                                    = False
  
  -- | Determines if it possibly the case that the unfolding will
  -- yield a value. Unlike 'isValueUnfolding' it returns @True@
  -- for 'OtherCon'
  isEvaldUnfolding :: Unfolding -> Bool
          -- Returns True for OtherCon
  isEvaldUnfolding (OtherCon _)                         = True
  isEvaldUnfolding (DFunUnfolding {})                   = True
  isEvaldUnfolding (CoreUnfolding { uf_cache = cache }) = uf_is_value cache
  isEvaldUnfolding _                                    = False
  
  -- | @True@ if the unfolding is a constructor application, the application
  -- of a CONLIKE function or 'OtherCon'
  isConLikeUnfolding :: Unfolding -> Bool
  isConLikeUnfolding (CoreUnfolding { uf_cache = cache }) = uf_is_conlike cache
  isConLikeUnfolding _                                    = False
  
  -- | Is the thing we will unfold into certainly cheap?
  isCheapUnfolding :: Unfolding -> Bool
  isCheapUnfolding (CoreUnfolding { uf_cache = cache }) = uf_is_work_free cache
  isCheapUnfolding _                                    = False
  
  isExpandableUnfolding :: Unfolding -> Bool
  isExpandableUnfolding (CoreUnfolding { uf_cache = cache }) = uf_expandable cache
  isExpandableUnfolding _                                    = False
  
  expandUnfolding_maybe :: Unfolding -> Maybe CoreExpr
  -- Expand an expandable unfolding; this is used in rule matching
  --   See Note [Expanding variables] in GHC.Core.Rules
  -- The key point here is that CONLIKE things can be expanded
  expandUnfolding_maybe (CoreUnfolding { uf_cache = cache, uf_tmpl = rhs })
    | uf_expandable cache
      = Just rhs
  expandUnfolding_maybe _ = Nothing
  
  isCompulsoryUnfolding :: Unfolding -> Bool
  isCompulsoryUnfolding (CoreUnfolding { uf_src = src }) = isCompulsorySource src
  isCompulsoryUnfolding _                                = False
  
  isStableUnfolding :: Unfolding -> Bool
  -- True of unfoldings that should not be overwritten
  -- by a CoreUnfolding for the RHS of a let-binding
  isStableUnfolding (CoreUnfolding { uf_src = src }) = isStableSource src
  isStableUnfolding (DFunUnfolding {})               = True
  isStableUnfolding _                                = False
  
  isStableUserUnfolding :: Unfolding -> Bool
  -- True of unfoldings that arise from an INLINE or INLINEABLE pragma
  isStableUserUnfolding (CoreUnfolding { uf_src = src }) = isStableUserSource src
  isStableUserUnfolding _                                = False
  
  isStableSystemUnfolding :: Unfolding -> Bool
  -- True of unfoldings that arise from an INLINE or INLINEABLE pragma
  isStableSystemUnfolding (CoreUnfolding { uf_src = src }) = isStableSystemSource src
  isStableSystemUnfolding _                                = False
  
  isInlineUnfolding :: Unfolding -> Bool
  -- ^ True of a /stable/ unfolding that is
  --   (a) always inlined; that is, with an `UnfWhen` guidance, or
  --   (b) a DFunUnfolding which never needs to be inlined
  isInlineUnfolding (CoreUnfolding { uf_src = src, uf_guidance = guidance })
    | isStableSource src
    , UnfWhen {} <- guidance
    = True
  
  isInlineUnfolding (DFunUnfolding {})
    = True
  
  -- Default case
  isInlineUnfolding _ = False
  
  
  -- | Only returns False if there is no unfolding information available at all
  hasSomeUnfolding :: Unfolding -> Bool
  hasSomeUnfolding NoUnfolding   = False
  hasSomeUnfolding BootUnfolding = False
  hasSomeUnfolding _             = True
  
  isBootUnfolding :: Unfolding -> Bool
  isBootUnfolding BootUnfolding = True
  isBootUnfolding _             = False
  
  neverUnfoldGuidance :: UnfoldingGuidance -> Bool
  neverUnfoldGuidance UnfNever = True
  neverUnfoldGuidance _        = False
  
  hasCoreUnfolding :: Unfolding -> Bool
  -- An unfolding "has Core" if it contains a Core expression, which
  -- may mention free variables. See Note [Fragile unfoldings]
  hasCoreUnfolding (CoreUnfolding {}) = True
  hasCoreUnfolding (DFunUnfolding {}) = True
  hasCoreUnfolding _                  = False
    -- NoUnfolding, BootUnfolding, OtherCon have no Core
  
  canUnfold :: Unfolding -> Bool
  canUnfold (CoreUnfolding { uf_guidance = g }) = not (neverUnfoldGuidance g)
  canUnfold _                                   = False
  
  isBetterUnfoldingThan :: Unfolding -> Unfolding -> Bool
  -- See Note [Better unfolding]
  isBetterUnfoldingThan NoUnfolding   _ = False
  isBetterUnfoldingThan BootUnfolding _ = False
  
  isBetterUnfoldingThan (CoreUnfolding {uf_cache = uc1}) unf2
    = case unf2 of
        CoreUnfolding {uf_cache = uc2} -> uf_is_value uc1 && not (uf_is_value uc2)
        OtherCon _                     -> uf_is_value uc1
        _                              -> True
           -- Default case: CoreUnfolding better than NoUnfolding etc
           -- Better than DFunUnfolding? I don't care.
  
  isBetterUnfoldingThan (DFunUnfolding {}) unf2
    | DFunUnfolding {} <- unf2 = False
    | otherwise                = True
  
  isBetterUnfoldingThan (OtherCon cs1) unf2
    = case unf2 of
        CoreUnfolding {uf_cache = uc}             -- If unf1 is OtherCon and unf2 is
                         -> not (uf_is_value uc)  -- just a thunk, unf1 is better
  
        OtherCon cs2     -> not (null cs1) && null cs2  -- A bit crude
        DFunUnfolding {} -> False
        NoUnfolding      -> True
        BootUnfolding    -> True
  
  {- Note [Fragile unfoldings]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  An unfolding is "fragile" if it mentions free variables (and hence would
  need substitution) or might be affected by optimisation.  The non-fragile
  ones are
  
     NoUnfolding, BootUnfolding
  
     OtherCon {}    If we know this binder (say a lambda binder) will be
                    bound to an evaluated thing, we want to retain that
                    info in simpleOptExpr; see #13077.
  
  We consider even a StableUnfolding as fragile, because it needs substitution.
  
  Note [Better unfolding]
  ~~~~~~~~~~~~~~~~~~~~~~~
  (unf1 `isBetterUnfoldingThan` unf2) is used when we have
      let x = <rhs> in   -- unf2
      let $j y = ...x...
      in case x of
            K a -> ...$j v....
  
  At the /call site/ of $j, `x` has a better unfolding than it does at the
  /defnition site/ of $j; so we are keener to inline $j.  See
  Note [Inlining join points] in GHC.Core.Opt.Simplify.Inline for discussion.
  
  The notion of "better" is encapsulated here.
  
  Note [Stable unfoldings]
  ~~~~~~~~~~~~~~~~~~~~~~~~
  When you say
        {-# INLINE f #-}
        f x = <rhs>
  you intend that calls (f e) are replaced by <rhs>[e/x] So we
  should capture (\x.<rhs>) in the Unfolding of 'f', and never meddle
  with it.  Meanwhile, we can optimise <rhs> to our heart's content,
  leaving the original unfolding intact in Unfolding of 'f'. For example
          all xs = foldr (&&) True xs
          any p = all . map p  {-# INLINE any #-}
  We optimise any's RHS fully, but leave the stable unfolding for `any`
  saying "all . map p", which deforests well at the call site.
  
  So INLINE pragma gives rise to a stable unfolding, which captures the
  original RHS.
  
  Moreover, it's only used when 'f' is applied to the
  specified number of arguments; that is, the number of argument on
  the LHS of the '=' sign in the original source definition.
  For example, (.) is now defined in the libraries like this
     {-# INLINE (.) #-}
     (.) f g = \x -> f (g x)
  so that it'll inline when applied to two arguments. If 'x' appeared
  on the left, thus
     (.) f g x = f (g x)
  it'd only inline when applied to three arguments.  This slightly-experimental
  change was requested by Roman, but it seems to make sense.
  
  Note [OccInfo in unfoldings and rules]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  In unfoldings and rules, we guarantee that the template is occ-analysed, so
  that the occurrence info on the binders is correct. That way, when the
  Simplifier inlines an unfolding, it doesn't need to occ-analysis it first.
  (The Simplifier is designed to simplify occ-analysed expressions.)
  
  Given this decision it's vital that we do *always* do it.
  
  * If we don't, we may get more simplifier iterations than necessary,
    because once-occ info isn't there
  
  * More seriously, we may get an infinite loop if there's a Rec without a
    loop breaker marked.
  
  * Or we may get code that mentions variables not in scope: #22761
    e.g. Suppose we have a stable unfolding : \y. let z = p+1 in 3
    Then the pre-simplifier occ-anal will occ-anal the unfolding
    (redundantly perhaps, but we need its free vars); this will not report
    the use of `p`; so p's binding will be discarded, and yet `p` is still
    mentioned.
  
    Better to occ-anal the unfolding at birth, which will drop the
    z-binding as dead code.  (Remember, it's the occurrence analyser that
    drops dead code.)
  
  * Another example is #8892:
      \x -> letrec { f = ...g...; g* = f } in body
    where g* is (for some strange reason) the loop breaker.  If we don't
    occ-anal it when reading it in, we won't mark g as a loop breaker, and we
    may inline g entirely in body, dropping its binding, and leaving the
    occurrence in f out of scope. This happened in #8892, where the unfolding
    in question was a DFun unfolding.
  
  
  ************************************************************************
  *                                                                      *
                    AltCon
  *                                                                      *
  ************************************************************************
  -}
  
  -- The Ord is needed for the FiniteMap used in the lookForConstructor
  -- in GHC.Core.Opt.Simplify.Env.  If you declared that lookForConstructor
  -- *ignores* constructor-applications with LitArg args, then you could get rid
  -- of this Ord.
  
  instance Outputable AltCon where
    ppr (DataAlt dc) = ppr dc
    ppr (LitAlt lit) = ppr lit
    ppr DEFAULT      = text "__DEFAULT"
  
  cmpAlt :: Alt a -> Alt a -> Ordering
  cmpAlt (Alt con1 _ _) (Alt con2 _ _) = con1 `cmpAltCon` con2
  
  ltAlt :: Alt a -> Alt a -> Bool
  ltAlt a1 a2 = (a1 `cmpAlt` a2) == LT
  
  cmpAltCon :: AltCon -> AltCon -> Ordering
  -- ^ Compares 'AltCon's within a single list of alternatives
  -- DEFAULT comes out smallest, so that sorting by AltCon puts
  -- alternatives in the order required: see Note [Case expression invariants]
  cmpAltCon DEFAULT      DEFAULT     = EQ
  cmpAltCon DEFAULT      _           = LT
  
  cmpAltCon (DataAlt d1) (DataAlt d2) = dataConTag d1 `compare` dataConTag d2
  cmpAltCon (DataAlt _)  DEFAULT      = GT
  cmpAltCon (LitAlt  l1) (LitAlt  l2) = l1 `compare` l2
  cmpAltCon (LitAlt _)   DEFAULT      = GT
  
  cmpAltCon con1 con2 = pprPanic "cmpAltCon" (ppr con1 $$ ppr con2)
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Useful synonyms}
  *                                                                      *
  ************************************************************************
  
  Note [CoreProgram]
  ~~~~~~~~~~~~~~~~~~
  The top level bindings of a program, a CoreProgram, are represented as
  a list of CoreBind
  
   * Later bindings in the list can refer to earlier ones, but not vice
     versa.  So this is OK
        NonRec { x = 4 }
        Rec { p = ...q...x...
            ; q = ...p...x }
        Rec { f = ...p..x..f.. }
        NonRec { g = ..f..q...x.. }
     But it would NOT be ok for 'f' to refer to 'g'.
  
   * The occurrence analyser does strongly-connected component analysis
     on each Rec binding, and splits it into a sequence of smaller
     bindings where possible.  So the program typically starts life as a
     single giant Rec, which is then dependency-analysed into smaller
     chunks.
  -}
  
  -- If you edit this type, you may need to update the GHC formalism
  -- See Note [GHC Formalism] in GHC.Core.Lint
  type CoreProgram = [CoreBind]   -- See Note [CoreProgram]
  
  -- | The common case for the type of binders and variables when
  -- we are manipulating the Core language within GHC
  type CoreBndr = Var
  -- | Expressions where binders are 'CoreBndr's
  type CoreExpr = Expr CoreBndr
  -- | Argument expressions where binders are 'CoreBndr's
  type CoreArg  = Arg  CoreBndr
  -- | Binding groups where binders are 'CoreBndr's
  type CoreBind = Bind CoreBndr
  -- | Case alternatives where binders are 'CoreBndr's
  type CoreAlt  = Alt  CoreBndr
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Tagging}
  *                                                                      *
  ************************************************************************
  -}
  
  -- | Binders are /tagged/ with a t
  data TaggedBndr t = TB CoreBndr t       -- TB for "tagged binder"
  
  type TaggedBind t = Bind (TaggedBndr t)
  type TaggedExpr t = Expr (TaggedBndr t)
  type TaggedArg  t = Arg  (TaggedBndr t)
  type TaggedAlt  t = Alt  (TaggedBndr t)
  
  instance Outputable b => Outputable (TaggedBndr b) where
    ppr (TB b l) = char '<' <> ppr b <> comma <> ppr l <> char '>'
  
  deTagExpr :: TaggedExpr t -> CoreExpr
  deTagExpr (Var v)                   = Var v
  deTagExpr (Lit l)                   = Lit l
  deTagExpr (Type ty)                 = Type ty
  deTagExpr (Coercion co)             = Coercion co
  deTagExpr (App e1 e2)               = App (deTagExpr e1) (deTagExpr e2)
  deTagExpr (Lam (TB b _) e)          = Lam b (deTagExpr e)
  deTagExpr (Let bind body)           = Let (deTagBind bind) (deTagExpr body)
  deTagExpr (Case e (TB b _) ty alts) = Case (deTagExpr e) b ty (map deTagAlt alts)
  deTagExpr (Tick t e)                = Tick t (deTagExpr e)
  deTagExpr (Cast e co)               = Cast (deTagExpr e) co
  
  deTagBind :: TaggedBind t -> CoreBind
  deTagBind (NonRec (TB b _) rhs) = NonRec b (deTagExpr rhs)
  deTagBind (Rec prs)             = Rec [(b, deTagExpr rhs) | (TB b _, rhs) <- prs]
  
  deTagAlt :: TaggedAlt t -> CoreAlt
  deTagAlt (Alt con bndrs rhs) = Alt con [b | TB b _ <- bndrs] (deTagExpr rhs)
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Core-constructing functions with checking}
  *                                                                      *
  ************************************************************************
  -}
  
  -- | Apply a list of argument expressions to a function expression in a nested fashion. Prefer to
  -- use 'GHC.Core.Make.mkCoreApps' if possible
  mkApps    :: Expr b -> [Arg b]  -> Expr b
  -- | Apply a list of type argument expressions to a function expression in a nested fashion
  mkTyApps  :: Expr b -> [Type]   -> Expr b
  -- | Apply a list of coercion argument expressions to a function expression in a nested fashion
  mkCoApps  :: Expr b -> [Coercion] -> Expr b
  -- | Apply a list of type or value variables to a function expression in a nested fashion
  mkVarApps :: Expr b -> [Var] -> Expr b
  -- | Apply a list of argument expressions to a data constructor in a nested fashion. Prefer to
  -- use 'GHC.Core.Make.mkCoreConApps' if possible
  mkConApp      :: DataCon -> [Arg b] -> Expr b
  
  mkApps    f args = foldl' App                       f args
  mkCoApps  f args = foldl' (\ e a -> App e (Coercion a)) f args
  mkVarApps f vars = foldl' (\ e a -> App e (varToCoreExpr a)) f vars
  mkConApp con args = mkApps (Var (dataConWorkId con)) args
  
  mkTyApps  f args = foldl' (\ e a -> App e (mkTyArg a)) f args
  
  mkConApp2 :: DataCon -> [Type] -> [Var] -> Expr b
  mkConApp2 con tys arg_ids = Var (dataConWorkId con)
                              `mkApps` map Type tys
                              `mkApps` map varToCoreExpr arg_ids
  
  mkTyArg :: Type -> Expr b
  mkTyArg ty
    | Just co <- isCoercionTy_maybe ty = Coercion co
    | otherwise                        = Type ty
  
  -- | Create a machine integer literal expression of type @Int#@ from an @Integer@.
  -- If you want an expression of type @Int@ use 'GHC.Core.Make.mkIntExpr'
  mkIntLit :: Platform -> Integer -> Expr b
  mkIntLit platform n = Lit (mkLitInt platform n)
  
  -- | Create a machine integer literal expression of type @Int#@ from an
  -- @Integer@, wrapping if necessary.
  -- If you want an expression of type @Int@ use 'GHC.Core.Make.mkIntExpr'
  mkIntLitWrap :: Platform -> Integer -> Expr b
  mkIntLitWrap platform n = Lit (mkLitIntWrap platform n)
  
  -- | Create a machine word literal expression of type  @Word#@ from an @Integer@.
  -- If you want an expression of type @Word@ use 'GHC.Core.Make.mkWordExpr'
  mkWordLit :: Platform -> Integer -> Expr b
  mkWordLit platform w = Lit (mkLitWord platform w)
  
  -- | Create a machine word literal expression of type  @Word#@ from an
  -- @Integer@, wrapping if necessary.
  -- If you want an expression of type @Word@ use 'GHC.Core.Make.mkWordExpr'
  mkWordLitWrap :: Platform -> Integer -> Expr b
  mkWordLitWrap platform w = Lit (mkLitWordWrap platform w)
  
  mkWord8Lit :: Integer -> Expr b
  mkWord8Lit    w = Lit (mkLitWord8 w)
  
  mkWord32LitWord32 :: Word32 -> Expr b
  mkWord32LitWord32 w = Lit (mkLitWord32 (toInteger w))
  
  mkWord64LitWord64 :: Word64 -> Expr b
  mkWord64LitWord64 w = Lit (mkLitWord64 (toInteger w))
  
  mkInt64LitInt64 :: Int64 -> Expr b
  mkInt64LitInt64 w = Lit (mkLitInt64 (toInteger w))
  
  -- | Create a machine character literal expression of type @Char#@.
  -- If you want an expression of type @Char@ use 'GHC.Core.Make.mkCharExpr'
  mkCharLit :: Char -> Expr b
  -- | Create a machine string literal expression of type @Addr#@.
  -- If you want an expression of type @String@ use 'GHC.Core.Make.mkStringExpr'
  mkStringLit :: String -> Expr b
  
  mkCharLit   c = Lit (mkLitChar c)
  mkStringLit s = Lit (mkLitString s)
  
  -- | Create a machine single precision literal expression of type @Float#@ from a @Rational@.
  -- If you want an expression of type @Float@ use 'GHC.Core.Make.mkFloatExpr'
  mkFloatLit :: Rational -> Expr b
  -- | Create a machine single precision literal expression of type @Float#@ from a @Float@.
  -- If you want an expression of type @Float@ use 'GHC.Core.Make.mkFloatExpr'
  mkFloatLitFloat :: Float -> Expr b
  
  mkFloatLit      f = Lit (mkLitFloat f)
  mkFloatLitFloat f = Lit (mkLitFloat (toRational f))
  
  -- | Create a machine double precision literal expression of type @Double#@ from a @Rational@.
  -- If you want an expression of type @Double@ use 'GHC.Core.Make.mkDoubleExpr'
  mkDoubleLit :: Rational -> Expr b
  -- | Create a machine double precision literal expression of type @Double#@ from a @Double@.
  -- If you want an expression of type @Double@ use 'GHC.Core.Make.mkDoubleExpr'
  mkDoubleLitDouble :: Double -> Expr b
  
  mkDoubleLit       d = Lit (mkLitDouble d)
  mkDoubleLitDouble d = Lit (mkLitDouble (toRational d))
  
  -- | Bind all supplied binding groups over an expression in a nested let expression. Assumes
  -- that the rhs satisfies the let-can-float invariant.  Prefer to use
  -- 'GHC.Core.Make.mkCoreLets' if possible, which does guarantee the invariant
  mkLets        :: [Bind b] -> Expr b -> Expr b
  -- | Bind all supplied binders over an expression in a nested lambda expression. Prefer to
  -- use 'GHC.Core.Make.mkCoreLams' if possible
  mkLams        :: [b] -> Expr b -> Expr b
  
  mkLams binders body = foldr Lam body binders
  mkLets binds body   = foldr mkLet body binds
  
  mkLet :: Bind b -> Expr b -> Expr b
  -- The desugarer sometimes generates an empty Rec group
  -- which Lint rejects, so we kill it off right away
  mkLet (Rec []) body = body
  mkLet bind     body = Let bind body
  
  -- | @mkLetNonRec bndr rhs body@ wraps @body@ in a @let@ binding @bndr@.
  mkLetNonRec :: b -> Expr b -> Expr b -> Expr b
  mkLetNonRec b rhs body = Let (NonRec b rhs) body
  
  -- | @mkLetRec binds body@ wraps @body@ in a @let rec@ with the given set of
  -- @binds@ if binds is non-empty.
  mkLetRec :: [(b, Expr b)] -> Expr b -> Expr b
  mkLetRec [] body = body
  mkLetRec bs body = Let (Rec bs) body
  
  -- | Create a binding group where a type variable is bound to a type.
  -- Per Note [Core type and coercion invariant],
  -- this can only be used to bind something in a non-recursive @let@ expression
  mkTyBind :: TyVar -> Type -> CoreBind
  mkTyBind tv ty      = NonRec tv (Type ty)
  
  -- | Create a binding group where a type variable is bound to a type.
  -- Per Note [Core type and coercion invariant],
  -- this can only be used to bind something in a non-recursive @let@ expression
  mkCoBind :: CoVar -> Coercion -> CoreBind
  mkCoBind cv co      = NonRec cv (Coercion co)
  
  -- | Convert a binder into either a 'Var' or 'Type' 'Expr' appropriately
  varToCoreExpr :: CoreBndr -> Expr b
  varToCoreExpr v | isTyVar v = Type (mkTyVarTy v)
                  | isCoVar v = Coercion (mkCoVarCo v)
                  | otherwise = assert (isId v) $ Var v
  
  varsToCoreExprs :: [CoreBndr] -> [Expr b]
  varsToCoreExprs vs = map varToCoreExpr vs
  
  {-
  ************************************************************************
  *                                                                      *
     Getting a result type
  *                                                                      *
  ************************************************************************
  
  These are defined here to avoid a module loop between GHC.Core.Utils and GHC.Core.FVs
  
  -}
  
  -- | If the expression is a 'Type', converts. Otherwise,
  -- panics. NB: This does /not/ convert 'Coercion' to 'CoercionTy'.
  exprToType :: CoreExpr -> Type
  exprToType (Type ty)     = ty
  exprToType _bad          = pprPanic "exprToType" empty
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Simple access functions}
  *                                                                      *
  ************************************************************************
  -}
  
  -- | Extract every variable by this group
  bindersOf  :: Bind b -> [b]
  -- If you edit this function, you may need to update the GHC formalism
  -- See Note [GHC Formalism] in GHC.Core.Lint
  bindersOf (NonRec binder _) = [binder]
  bindersOf (Rec pairs)       = [binder | (binder, _) <- pairs]
  
  -- | 'bindersOf' applied to a list of binding groups
  bindersOfBinds :: [Bind b] -> [b]
  bindersOfBinds binds = foldr ((++) . bindersOf) [] binds
  
  -- We inline this to avoid unknown function calls.
  {-# INLINE foldBindersOfBindStrict #-}
  foldBindersOfBindStrict :: (a -> b -> a) -> a -> Bind b -> a
  foldBindersOfBindStrict f
    = \z bind -> case bind of
        NonRec b _rhs -> f z b
        Rec pairs -> foldl' f z $ map fst pairs
  
  {-# INLINE foldBindersOfBindsStrict #-}
  foldBindersOfBindsStrict :: (a -> b -> a) -> a -> [Bind b] -> a
  foldBindersOfBindsStrict f = \z binds -> foldl' fold_bind z binds
    where
      fold_bind = (foldBindersOfBindStrict f)
  
  
  rhssOfBind :: Bind b -> [Expr b]
  rhssOfBind (NonRec _ rhs) = [rhs]
  rhssOfBind (Rec pairs)    = [rhs | (_,rhs) <- pairs]
  
  rhssOfBinds :: [Bind b] -> [Expr b]
  rhssOfBinds []             = []
  rhssOfBinds (NonRec _ rhs : bs) = rhs : rhssOfBinds bs
  rhssOfBinds (Rec pairs    : bs) = map snd pairs ++ rhssOfBinds bs
  
  rhssOfAlts :: [Alt b] -> [Expr b]
  rhssOfAlts alts = [e | Alt _ _ e <- alts]
  
  -- | Collapse all the bindings in the supplied groups into a single
  -- list of lhs\/rhs pairs suitable for binding in a 'Rec' binding group
  flattenBinds :: [Bind b] -> [(b, Expr b)]
  flattenBinds (NonRec b r : binds) = (b,r) : flattenBinds binds
  flattenBinds (Rec prs1   : binds) = prs1 ++ flattenBinds binds
  flattenBinds []                   = []
  
  -- | We often want to strip off leading lambdas before getting down to
  -- business. Variants are 'collectTyBinders', 'collectValBinders',
  -- and 'collectTyAndValBinders'
  collectBinders         :: Expr b   -> ([b],     Expr b)
  collectTyBinders       :: CoreExpr -> ([TyVar], CoreExpr)
  collectValBinders      :: CoreExpr -> ([Id],    CoreExpr)
  collectTyAndValBinders :: CoreExpr -> ([TyVar], [Id], CoreExpr)
  
  -- | Strip off exactly N leading lambdas (type or value).
  -- Good for use with join points.
  -- Panic if there aren't enough
  collectNBinders :: JoinArity -> Expr b -> ([b], Expr b)
  
  collectBinders expr
    = go [] expr
    where
      go bs (Lam b e) = go (b:bs) e
      go bs e          = (reverse bs, e)
  
  collectTyBinders expr
    = go [] expr
    where
      go tvs (Lam b e) | isTyVar b = go (b:tvs) e
      go tvs e                     = (reverse tvs, e)
  
  collectValBinders expr
    = go [] expr
    where
      go ids (Lam b e) | isId b = go (b:ids) e
      go ids body               = (reverse ids, body)
  
  collectTyAndValBinders expr
    = (tvs, ids, body)
    where
      (tvs, body1) = collectTyBinders expr
      (ids, body)  = collectValBinders body1
  
  collectNBinders orig_n orig_expr
    = go orig_n [] orig_expr
    where
      go 0 bs expr      = (reverse bs, expr)
      go n bs (Lam b e) = go (n-1) (b:bs) e
      go _ _  _         = pprPanic "collectNBinders" $ int orig_n
  
  -- | Strip off exactly N leading value lambdas
  -- returning all the binders found up to that point
  -- Return Nothing if there aren't enough
  collectNValBinders_maybe :: Arity -> CoreExpr -> Maybe ([Var], CoreExpr)
  collectNValBinders_maybe orig_n orig_expr
    = go orig_n [] orig_expr
    where
      go 0 bs expr      = Just (reverse bs, expr)
      go n bs (Lam b e) | isId b    = go (n-1) (b:bs) e
                        | otherwise = go n     (b:bs) e
      go _ _  _         = Nothing
  
  -- | Takes a nested application expression and returns the function
  -- being applied and the arguments to which it is applied
  collectArgs :: Expr b -> (Expr b, [Arg b])
  collectArgs expr
    = go expr []
    where
      go (App f a) as = go f (a:as)
      go e         as = (e, as)
  
  -- | Takes a nested application expression and returns the function
  -- being applied and the arguments to which it is applied
  collectValArgs :: Expr b -> (Expr b, [Arg b])
  collectValArgs expr
    = go expr []
    where
      go (App f a) as
        | isValArg a  = go f (a:as)
        | otherwise   = go f as
      go e         as = (e, as)
  
  -- | Takes a nested application expression and returns the function
  -- being applied. Looking through casts and ticks to find it.
  collectFunSimple :: Expr b -> Expr b
  collectFunSimple expr
    = go expr
    where
      go expr' =
        case expr' of
          App f _a    -> go f
          Tick _t e   -> go e
          Cast e _co  -> go e
          e           -> e
  
  -- | fmap on the body of a lambda.
  --   wrapLamBody f (\x -> body) == (\x -> f body)
  wrapLamBody :: (CoreExpr -> CoreExpr) -> CoreExpr -> CoreExpr
  wrapLamBody f expr = go expr
    where
    go (Lam v body) = Lam v $ go body
    go expr = f expr
  
  -- | Attempt to remove the last N arguments of a function call.
  -- Strip off any ticks or coercions encountered along the way and any
  -- at the end.
  stripNArgs :: Word -> Expr a -> Maybe (Expr a)
  stripNArgs !n (Tick _ e) = stripNArgs n e
  stripNArgs n (Cast f _) = stripNArgs n f
  stripNArgs 0 e = Just e
  stripNArgs n (App f _) = stripNArgs (n - 1) f
  stripNArgs _ _ = Nothing
  
  -- | Like @collectArgs@, but also looks through floatable
  -- ticks if it means that we can find more arguments.
  collectArgsTicks :: (CoreTickish -> Bool) -> Expr b
                   -> (Expr b, [Arg b], [CoreTickish])
  collectArgsTicks skipTick expr
    = go expr [] []
    where
      go (App f a)  as ts = go f (a:as) ts
      go (Tick t e) as ts
        | skipTick t      = go e as (t:ts)
      go e          as ts = (e, as, reverse ts)
  
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Predicates}
  *                                                                      *
  ************************************************************************
  
  At one time we optionally carried type arguments through to runtime.
  @isRuntimeVar v@ returns if (Lam v _) really becomes a lambda at runtime,
  i.e. if type applications are actual lambdas because types are kept around
  at runtime.  Similarly isRuntimeArg.
  -}
  
  -- | Will this variable exist at runtime?
  isRuntimeVar :: Var -> Bool
  isRuntimeVar = isId
  
  -- | Will this argument expression exist at runtime?
  isRuntimeArg :: CoreExpr -> Bool
  isRuntimeArg = isValArg
  
  -- | Returns @True@ for value arguments, false for type args
  -- NB: coercions are value arguments (zero width, to be sure,
  -- like State#, but still value args).
  isValArg :: Expr b -> Bool
  isValArg e = not (isTypeArg e)
  
  -- | Returns @True@ iff the expression is a 'Type' or 'Coercion'
  -- expression at its top level
  isTyCoArg :: Expr b -> Bool
  isTyCoArg (Type {})     = True
  isTyCoArg (Coercion {}) = True
  isTyCoArg _             = False
  
  -- | Returns @True@ iff the expression is a 'Coercion'
  -- expression at its top level
  isCoArg :: Expr b -> Bool
  isCoArg (Coercion {}) = True
  isCoArg _             = False
  
  -- | Returns @True@ iff the expression is a 'Type' expression at its
  -- top level.  Note this does NOT include 'Coercion's.
  isTypeArg :: Expr b -> Bool
  isTypeArg (Type {}) = True
  isTypeArg _         = False
  
  -- | The number of binders that bind values rather than types
  valBndrCount :: [CoreBndr] -> Int
  valBndrCount = count isId
  
  -- | The number of argument expressions that are values rather than types at their top level
  valArgCount :: [Arg b] -> Int
  valArgCount = count isValArg
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Annotated core}
  *                                                                      *
  ************************************************************************
  -}
  
  -- | Annotated core: allows annotation at every node in the tree
  type AnnExpr bndr annot = (annot, AnnExpr' bndr annot)
  
  -- | A clone of the 'Expr' type but allowing annotation at every tree node
  data AnnExpr' bndr annot
    = AnnVar      Id
    | AnnLit      Literal
    | AnnLam      bndr (AnnExpr bndr annot)
    | AnnApp      (AnnExpr bndr annot) (AnnExpr bndr annot)
    | AnnCase     (AnnExpr bndr annot) bndr Type [AnnAlt bndr annot]
    | AnnLet      (AnnBind bndr annot) (AnnExpr bndr annot)
    | AnnCast     (AnnExpr bndr annot) (annot, Coercion)
                     -- Put an annotation on the (root of) the coercion
    | AnnTick     CoreTickish (AnnExpr bndr annot)
    | AnnType     Type
    | AnnCoercion Coercion
  
  -- | A clone of the 'Alt' type but allowing annotation at every tree node
  data AnnAlt bndr annot = AnnAlt AltCon [bndr] (AnnExpr bndr annot)
  
  -- | A clone of the 'Bind' type but allowing annotation at every tree node
  data AnnBind bndr annot
    = AnnNonRec bndr (AnnExpr bndr annot)
    | AnnRec    [(bndr, AnnExpr bndr annot)]
  
  -- | Takes a nested application expression and returns the function
  -- being applied and the arguments to which it is applied
  collectAnnArgs :: AnnExpr b a -> (AnnExpr b a, [AnnExpr b a])
  collectAnnArgs expr
    = go expr []
    where
      go (_, AnnApp f a) as = go f (a:as)
      go e               as = (e, as)
  
  collectAnnArgsTicks :: (CoreTickish -> Bool) -> AnnExpr b a
                         -> (AnnExpr b a, [AnnExpr b a], [CoreTickish])
  collectAnnArgsTicks tickishOk expr
    = go expr [] []
    where
      go (_, AnnApp f a)  as ts = go f (a:as) ts
      go (_, AnnTick t e) as ts | tickishOk t
                                = go e as (t:ts)
      go e                as ts = (e, as, reverse ts)
  
  deAnnotate :: AnnExpr bndr annot -> Expr bndr
  deAnnotate (_, e) = deAnnotate' e
  
  deAnnotate' :: AnnExpr' bndr annot -> Expr bndr
  deAnnotate' (AnnType t)           = Type t
  deAnnotate' (AnnCoercion co)      = Coercion co
  deAnnotate' (AnnVar  v)           = Var v
  deAnnotate' (AnnLit  lit)         = Lit lit
  deAnnotate' (AnnLam  binder body) = Lam binder (deAnnotate body)
  deAnnotate' (AnnApp  fun arg)     = App (deAnnotate fun) (deAnnotate arg)
  deAnnotate' (AnnCast e (_,co))    = Cast (deAnnotate e) co
  deAnnotate' (AnnTick tick body)   = Tick tick (deAnnotate body)
  
  deAnnotate' (AnnLet bind body)
    = Let (deAnnBind bind) (deAnnotate body)
  deAnnotate' (AnnCase scrut v t alts)
    = Case (deAnnotate scrut) v t (map deAnnAlt alts)
  
  deAnnAlt :: AnnAlt bndr annot -> Alt bndr
  deAnnAlt (AnnAlt con args rhs) = Alt con args (deAnnotate rhs)
  
  deAnnBind  :: AnnBind b annot -> Bind b
  deAnnBind (AnnNonRec var rhs) = NonRec var (deAnnotate rhs)
  deAnnBind (AnnRec pairs) = Rec [(v,deAnnotate rhs) | (v,rhs) <- pairs]
  
  -- | As 'collectBinders' but for 'AnnExpr' rather than 'Expr'
  collectAnnBndrs :: AnnExpr bndr annot -> ([bndr], AnnExpr bndr annot)
  collectAnnBndrs e
    = collect [] e
    where
      collect bs (_, AnnLam b body) = collect (b:bs) body
      collect bs body               = (reverse bs, body)
  
  -- | As 'collectNBinders' but for 'AnnExpr' rather than 'Expr'
  collectNAnnBndrs :: Int -> AnnExpr bndr annot -> ([bndr], AnnExpr bndr annot)
  collectNAnnBndrs orig_n e
    = collect orig_n [] e
    where
      collect 0 bs body               = (reverse bs, body)
      collect n bs (_, AnnLam b body) = collect (n-1) (b:bs) body
      collect _ _  _                  = pprPanic "collectNBinders" $ int orig_n
  