GHC/Core.hs

    {-
    (c) The University of Glasgow 2006
    (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
    -}

    {-# LANGUAGE CPP, DeriveDataTypeable, FlexibleContexts #-}
    {-# LANGUAGE NamedFieldPuns #-}
    {-# LANGUAGE BangPatterns #-}

    {-# OPTIONS_GHC -Wno-incomplete-uni-patterns   #-}
    {-# OPTIONS_GHC -Wno-incomplete-record-updates #-}

    -- | 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,
            OutId, OutBind, OutExpr, OutAlt, OutArg, OutType, OutKind,
                   OutBndr, OutVar, OutCoercion, OutTyVar, OutCoVar, MOutCoercion,

            -- ** 'Expr' construction
            mkLet, mkLets, mkLetNonRec, mkLetRec, mkLams,
            mkApps, mkTyApps, mkCoApps, mkVarApps, mkTyArg,

            mkIntLit, mkIntLitWrap,
            mkWordLit, mkWordLitWrap,
            mkWord8Lit,
            mkWord64LitWord64, mkInt64LitInt64,
            mkCharLit, mkStringLit,
            mkFloatLit, mkFloatLitFloat,
            mkDoubleLit, mkDoubleLitDouble,

            mkConApp, mkConApp2, mkTyBind, mkCoBind,
            varToCoreExpr, varsToCoreExprs,

            isId, cmpAltCon, cmpAlt, ltAlt,

            -- ** Simple 'Expr' access functions and predicates
            bindersOf, bindersOfBinds, rhssOfBind, rhssOfAlts,
            collectBinders, collectTyBinders, collectTyAndValBinders,
            collectNBinders,
            collectArgs, stripNArgs, collectArgsTicks, flattenBinds,

            exprToType, exprToCoercion_maybe,
            applyTypeToArg,

            isValArg, isTypeArg, isCoArg, isTyCoArg, valArgCount, valBndrCount,
            isRuntimeArg, isRuntimeVar,

            -- * Unfolding data types
            Unfolding(..),  UnfoldingGuidance(..), UnfoldingSource(..),

            -- ** Constructing 'Unfolding's
            noUnfolding, bootUnfolding, evaldUnfolding, mkOtherCon,
            unSaturatedOk, needSaturated, boringCxtOk, boringCxtNotOk,

            -- ** Predicates and deconstruction on 'Unfolding'
            unfoldingTemplate, expandUnfolding_maybe,
            maybeUnfoldingTemplate, otherCons,
            isValueUnfolding, isEvaldUnfolding, isCheapUnfolding,
            isExpandableUnfolding, isConLikeUnfolding, isCompulsoryUnfolding,
            isStableUnfolding, hasCoreUnfolding, hasSomeUnfolding,
            isBootUnfolding,
            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(..), RuleBase,
            RuleName, RuleFun, IdUnfoldingFun, InScopeEnv,
            RuleEnv(..), RuleOpts(..), mkRuleEnv, emptyRuleEnv,

            -- ** Operations on 'CoreRule's
            ruleArity, ruleName, ruleIdName, ruleActivation,
            setRuleIdName, ruleModule,
            isBuiltinRule, isLocalRule, isAutoRule,
        ) where

    #include "HsVersions.h"

    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.Types.Name
    import GHC.Types.Name.Set
    import GHC.Types.Name.Env( NameEnv, emptyNameEnv )
    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 GHC.Driver.Ppr

    import Data.Data hiding (TyCon)
    import Data.Int
    import Data.Word

    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] 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 [Core let/app invariant]
    --    See Note [Levity polymorphism invariants]
    --
    -- *  Lambda abstraction
    --    See Note [Levity 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/app invariant]
    --    See Note [Levity 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) Coercion
      | 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 [Core case 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

    {-
    Note [Shadowing]
    ~~~~~~~~~~~~~~~~
    While various passes attempt to rename on-the-fly in a manner that
    avoids "shadowing" (thereby simplifying downstream optimizations),
    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.

    In particular, scrutinee variables `x` in expressions of the form
    `Case e x t` are often renamed to variables with a prefix
    "wild_". These "wild" variables may appear in the body of the
    case-expression, and further, may be shadowed within the body.

    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.

    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 [Core letrec invariant]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The right hand sides of all top-level and recursive @let@s
    /must/ be of lifted type (see "Type#type_classification" for
    the meaning of /lifted/ vs. /unlifted/).

    There is one exception to this rule, top-level @let@s are
    allowed to bind primitive string literals: see
    Note [Core top-level string literals].

    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#) 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.

    * 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 [Core let/app invariant]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The let/app invariant
         the right hand side of a non-recursive 'Let', and
         the argument of an 'App',
        /may/ be of unlifted type, but only if
        the expression is ok-for-speculation
        or the 'Let' is for a join point.

    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/app invariant is initially enforced by mkCoreLet and mkCoreApp in
    GHC.Core.Make.

    For discussion of some implications of the let/app invariant primops see
    Note [Checking versus non-checking primops] in GHC.Builtin.PrimOps.

    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 isFloatingTy.

    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.Canonical

    Note [Core case invariants]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    See Note [Case expression invariants]

    Note [Levity polymorphism invariants]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The levity-polymorphism invariants are these (as per "Levity Polymorphism",
    PLDI '17):

    * The type of a term-binder must not be levity-polymorphic,
      unless it is a let(rec)-bound join point
         (see Note [Invariants on join points])

    * The type of the argument of an App must not be levity-polymorphic.

    A type (t::TYPE r) is "levity polymorphic" if 'r' has any free variables.

    For example
      \(r::RuntimeRep). \(a::TYPE r). \(x::a). e
    is illegal because x's type has kind (TYPE r), which has 'r' free.

    See Note [Levity polymorphism checking] in GHC.HsToCore.Monad to see where these
    invariants are established for user-written code.

    Note [Core let goal]
    ~~~~~~~~~~~~~~~~~~~~
    * The simplifier tries to ensure that if the RHS of a let is a constructor
      application, its arguments are trivial, so that the constructor can be
      inlined vigorously.

    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

    * An empty case is replaced by its scrutinee during the CoreToStg
      conversion; remember STG is un-typed, so there is no need for
      the empty case to do the type conversion.

    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 is the number of value
             binders in the top n lambdas, where n is the join arity.

             So arity <= join arity; the former counts only value binders
             while the latter counts all binders.
             e.g. Suppose $j has join arity 1
                   let j = \x y. e in case x of { A -> j 1; B -> j 2 }
             Then its ordinary arity is also 1, not 2.

             The arity of a join point isn't very important; but short of setting
             it to zero, it is helpful to have an invariant.  E.g. #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/app invariant)
         e.g.  let j :: Int# = factorial x in ...

      6. A join point can have a levity-polymorphic RHS
         e.g.  let j :: r :: TYPE l = fail void# 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.

    ************************************************************************
    *                                                                      *
                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
      | isEmptyNameSet local_names = IsOrphan
      | otherwise                  = NotOrphan (minimum occs)
      where
        occs = map nameOccName $ nonDetEltsUniqSet 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

    {-
    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.

     * 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
        (because it is needed during instance lookup)

      * For rules and family instances:
           when we generate an IfaceRule (GHC.Iface.Make.coreRuleToIfaceRule)
                         or IfaceFamInst (GHC.Iface.Make.instanceToIfaceInst)
    -}

    {-
    ************************************************************************
    *                                                                      *
    \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.
    -}

    -- | Gathers a collection of 'CoreRule's. Maps (the name of) an 'Id' to its rules
    type RuleBase = NameEnv [CoreRule]
            -- The rules are unordered;
            -- we sort out any overlaps on lookup

    -- | A full rule environment which we can apply rules from.  Like a 'RuleBase',
    -- but it also includes the set of visible orphans we use to filter out orphan
    -- rules which are not visible (even though we can see them...)
    data RuleEnv
        = RuleEnv { re_base          :: RuleBase
                  , re_visible_orphs :: ModuleSet
                  }

    mkRuleEnv :: RuleBase -> [Module] -> RuleEnv
    mkRuleEnv rules vis_orphs = RuleEnv rules (mkModuleSet vis_orphs)

    emptyRuleEnv :: RuleEnv
    emptyRuleEnv = RuleEnv emptyNameEnv emptyModuleSet

    -- | 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 rule matching] in GHC.Core.Rules

    -- | Rule options
    data RuleOpts = RuleOpts
       { roPlatform                :: !Platform -- ^ Target platform
       , roNumConstantFolding      :: !Bool     -- ^ Enable more advanced numeric constant folding
       , roExcessRationalPrecision :: !Bool     -- ^ Cut down precision of Rational values to that of Float/Double if disabled
       , roBignumRules             :: !Bool     -- ^ Enable rules for bignums
       }

    type RuleFun = RuleOpts -> InScopeEnv -> Id -> [CoreExpr] -> Maybe CoreExpr
    type InScopeEnv = (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 -> Int
    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 = ru_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
    -}

    -- | 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,        -- Template; occurrence info is correct
            uf_src        :: UnfoldingSource, -- Where the unfolding came from
            uf_is_top     :: Bool,          -- True <=> top level binding
            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
            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

    ------------------------------------------------
    data UnfoldingSource
      = -- See also Note [Historical note: unfoldings for wrappers]

        InlineRhs          -- The current rhs of the function
                           -- Replace uf_tmpl each time around

      | InlineStable       -- From an INLINE or INLINABLE pragma
                           --   INLINE     if guidance is UnfWhen
                           --   INLINABLE  if guidance is UnfIfGoodArgs/UnfoldNever
                           -- (well, technically an INLINABLE might be made
                           -- UnfWhen if it was small enough, and then
                           -- it will behave like INLINE outside the current
                           -- module, but that is the way automatic unfoldings
                           -- work so it is consistent with the intended
                           -- meaning of INLINABLE).
                           --
                           -- uf_tmpl may change, but only as a result of
                           -- gentle simplification, it doesn't get updated
                           -- to the current RHS during compilation as with
                           -- InlineRhs.
                           --
                           -- See Note [InlineStable]

      | InlineCompulsory   -- Something that *has* no binding, so you *must* inline it
                           -- Only a few primop-like things have this property
                           -- (see "GHC.Types.Id.Make", calls to mkCompulsoryUnfolding).
                           -- Inline absolutely always, however boring the context.

    -- | '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 [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

    isStableSource :: UnfoldingSource -> Bool
    -- Keep the unfolding template
    isStableSource InlineCompulsory   = True
    isStableSource InlineStable       = True
    isStableSource InlineRhs          = False

    -- | Retrieves the template of an unfolding: panics if none is known
    unfoldingTemplate :: Unfolding -> CoreExpr
    unfoldingTemplate = uf_tmpl

    -- | Retrieves the template of an unfolding if possible
    -- maybeUnfoldingTemplate is used mainly wnen 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_is_value = is_evald }) = is_evald
    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 (CoreUnfolding { uf_is_value = is_evald }) = is_evald
    isEvaldUnfolding _                                          = False

    -- | @True@ if the unfolding is a constructor application, the application
    -- of a CONLIKE function or 'OtherCon'
    isConLikeUnfolding :: Unfolding -> Bool
    isConLikeUnfolding (OtherCon _)                             = True
    isConLikeUnfolding (CoreUnfolding { uf_is_conlike = con })  = con
    isConLikeUnfolding _                                        = False

    -- | Is the thing we will unfold into certainly cheap?
    isCheapUnfolding :: Unfolding -> Bool
    isCheapUnfolding (CoreUnfolding { uf_is_work_free = is_wf }) = is_wf
    isCheapUnfolding _                                           = False

    isExpandableUnfolding :: Unfolding -> Bool
    isExpandableUnfolding (CoreUnfolding { uf_expandable = is_expable }) = is_expable
    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_expandable = True, uf_tmpl = rhs }) = Just rhs
    expandUnfolding_maybe _                                                       = Nothing

    isCompulsoryUnfolding :: Unfolding -> Bool
    isCompulsoryUnfolding (CoreUnfolding { uf_src = InlineCompulsory }) = True
    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

    -- | 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

    {- 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 [InlineStable]
    ~~~~~~~~~~~~~~~~~
    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 InlineRule saying "all . map p",
    which deforests well at the call site.

    So INLINE pragma gives rise to an InlineRule, 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.

    See also Note [Inlining an InlineRule] in GHC.Core.Unfold.

    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.  This is important,
    because the Simplifier does not re-analyse the template when using it. If
    the occurrence info is wrong
      - 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

    ************************************************************************
    *                                                                      *
                      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 = WARN( True, text "Comparing incomparable AltCons" <+>
                                      ppr con1 <+> ppr con2 )
                          LT

    {-
    ************************************************************************
    *                                                                      *
    \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)

    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/app 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

    -}

    applyTypeToArg :: Type -> CoreExpr -> Type
    -- ^ Determines the type resulting from applying an expression with given type
    -- to a given argument expression
    applyTypeToArg fun_ty arg = piResultTy fun_ty (exprToType arg)

    -- | 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

    -- | If the expression is a 'Coercion', converts.
    exprToCoercion_maybe :: CoreExpr -> Maybe Coercion
    exprToCoercion_maybe (Coercion co) = Just co
    exprToCoercion_maybe _             = Nothing

    {-
    ************************************************************************
    *                                                                      *
    \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

    rhssOfBind :: Bind b -> [Expr b]
    rhssOfBind (NonRec _ rhs) = [rhs]
    rhssOfBind (Rec pairs)    = [rhs | (_,rhs) <- pairs]

    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.
    collectNBinders        :: Int -> 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

    -- | 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)

    -- | 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 collects 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