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

    {-# LANGUAGE CPP, DeriveDataTypeable, DeriveFunctor #-}

    -- | CoreSyn holds all the main data types for use by for the Glasgow Haskell Compiler midsection
    module CoreSyn (
            -- * Main data types
            Expr(..), Alt, Bind(..), AltCon(..), Arg,
            Tickish(..), TickishScoping(..), TickishPlacement(..),
            CoreProgram, CoreExpr, CoreAlt, CoreBind, CoreArg, CoreBndr,
            TaggedExpr, TaggedAlt, TaggedBind, TaggedArg, TaggedBndr(..), deTagExpr,

            -- ** 'Expr' construction
            mkLets, mkLams,
            mkApps, mkTyApps, mkCoApps, mkVarApps,

            mkIntLit, mkIntLitInt,
            mkWordLit, mkWordLitWord,
            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, collectValBinders, collectTyAndValBinders,
            collectArgs, collectArgsTicks, flattenBinds,

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

            tickishCounts, tickishScoped, tickishScopesLike, tickishFloatable,
            tickishCanSplit, mkNoCount, mkNoScope,
            tickishIsCode, tickishPlace,
            tickishContains,

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

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

            -- ** Predicates and deconstruction on 'Unfolding'
            unfoldingTemplate, expandUnfolding_maybe,
            maybeUnfoldingTemplate, otherCons,
            isValueUnfolding, isEvaldUnfolding, isCheapUnfolding,
            isExpandableUnfolding, isConLikeUnfolding, isCompulsoryUnfolding,
            isStableUnfolding, hasStableCoreUnfolding_maybe,
            isClosedUnfolding, hasSomeUnfolding,
            canUnfold, neverUnfoldGuidance, isStableSource,

            -- * Strictness
            seqExpr, seqExprs, seqUnfolding,

            -- * Annotated expression data types
            AnnExpr, AnnExpr'(..), AnnBind(..), AnnAlt,

            -- ** Operations on annotated expressions
            collectAnnArgs, collectAnnArgsTicks,

            -- ** Operations on annotations
            deAnnotate, deAnnotate', deAnnAlt, collectAnnBndrs,

            -- * Core rule data types
            CoreRule(..),   -- CoreSubst, CoreTidy, CoreFVs, PprCore only
            RuleName, RuleFun, IdUnfoldingFun, InScopeEnv,

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

            -- * Core vectorisation declarations data type
            CoreVect(..)
        ) where

    #include "HsVersions.h"

    import CostCentre
    import VarEnv( InScopeSet )
    import Var
    import Type
    import Coercion
    import Name
    import Literal
    import DataCon
    import Module
    import TyCon
    import BasicTypes
    import DynFlags
    import FastString
    import Outputable
    import Util
    import SrcLoc     ( RealSrcSpan, containsSpan )

    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 <http://research.microsoft.com/~simonpj/papers/ext-f/> 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 'HsExpr.HsExpr' with the names being 'RdrName.RdrNames'
    --
    -- 2. This syntax tree is /renamed/, which attaches a 'Unique.Unique' to every 'RdrName.RdrName'
    --    (yielding a '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 'HsExpr.HsExpr' type that has 'Id.Id' as it's names.
    --
    -- 4. Finally the syntax tree is /desugared/ from the expressive 'HsExpr.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
    --
    -- *  Primitive literals
    --
    -- *  Applications: note that the argument may be a 'Type'.
    --
    --    See "CoreSyn#let_app_invariant" for another invariant
    --
    -- *  Lambda abstraction
    --
    -- *  Recursive and non recursive @let@s. Operationally
    --    this corresponds to allocating a thunk for the things
    --    bound and then executing the sub-expression.
    --
    --    #top_level_invariant#
    --    #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/).
    --
    --    See Note [CoreSyn let/app invariant]
    --
    --    #type_let#
    --    We allow a /non-recursive/ let to bind a type variable, thus:
    --
    --    > Let (NonRec tv (Type ty)) body
    --
    --    This can be very convenient for postponing type substitutions until
    --    the next run of the simplifier.
    --
    --    At the moment, the rest of the compiler only deals with type-let
    --    in a Let expression, rather than at top level.  We may want to revist
    --    this choice.
    --
    -- *  Case split. 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
    --
    --    #case_invariants#
    --    This is one of the more complicated elements of the Core language,
    --    and comes with a number of restrictions:
    --
    --    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.
    --
    --    3. The remaining cases are in order of increasing
    --         tag  (for 'DataAlts') or
    --         lit  (for 'LitAlts').
    --       This makes finding the relevant constructor easy,
    --       and makes comparison easier too.
    --
    --    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.
    --
    -- *  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.
    --
    -- *  Notes. These allow general information to be added to expressions
    --    in the syntax tree
    --
    -- *  A type: this should only show up at the top level of an Arg
    --
    -- *  A coercion

    -- If you edit this type, you may need to update the GHC formalism
    -- See Note [GHC Formalism] in coreSyn/CoreLint.lhs
    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 #case_invariant#
      | Cast  (Expr b) Coercion
      | Tick  (Tickish Id) (Expr b)
      | Type  Type
      | Coercion Coercion
      deriving (Data, Typeable)

    -- | 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 coreSyn/CoreLint.lhs
    type Alt b = (AltCon, [b], Expr b)

    -- | 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 coreSyn/CoreLint.lhs
    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, Ord, Data, Typeable)

    -- | 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 coreSyn/CoreLint.lhs
    data Bind b = NonRec b (Expr b)
                | Rec [(b, (Expr b))]
      deriving (Data, Typeable)

    {-
    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 an 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 Trac #5603) if you say
        case 3 of
          S# x -> ...
          J# _ _ -> ...
    (where S#, J# 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.

    -------------------------- CoreSyn INVARIANTS ---------------------------

    Note [CoreSyn top-level invariant]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    See #toplevel_invariant#

    Note [CoreSyn letrec invariant]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    See #letrec_invariant#

    Note [CoreSyn let/app invariant]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The let/app invariant
         the right hand side of 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.

    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
    'CoreUtils.needsCaseBinding' can help you determine which to generate, or
    alternatively use 'MkCore.mkCoreLet' rather than this constructor directly,
    which will generate a @case@ if necessary

    Th let/app invariant is initially enforced by DsUtils.mkCoreLet and mkCoreApp

    Note [CoreSyn case invariants]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    See #case_invariants#

    Note [CoreSyn 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 [Type let]
    ~~~~~~~~~~~~~~~
    See #type_let#

    Note [Empty case alternatives]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The alternatives of a case expression should be exhaustive.  A case expression
    can have empty alternatives if (and only if) the scrutinee is bound to raise
    an exception or diverge.  So:
       Case (error Int "Hello") b Bool []
    is fine, and has type Bool.  This 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!  I'll write this
       case (error Int "Hello") of Bool {}
    with the return type just before the alternatives.

    Here's another example:
      data T
      f :: T -> Bool
      f = \(x:t). case x of Bool {}
    Since T has no data constructors, the case alternatives are of course
    empty.  However note that 'x' is not bound to a visibly-bottom value;
    it's the *type* that tells us it's going to diverge.  Its a bit of a
    degnerate situation but we do NOT want to replace
       case x of Bool {}   -->   error Bool "Inaccessible case"
    because x might raise an exception, and *that*'s what we want to see!
    (Trac #6067 is an example.) To preserve semantics we'd have to say
       x `seq` error Bool "Inaccessible case"
     but the 'seq' is just a case, so we are back to square 1.  Or I suppose
    we could say
       x |> UnsafeCoerce T Bool
    but that loses all trace of the fact that this originated with an empty
    set of alternatives.

    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.

    ************************************************************************
    *                                                                      *
                  Ticks
    *                                                                      *
    ************************************************************************
    -}

    -- | Allows attaching extra information to points in expressions

    -- If you edit this type, you may need to update the GHC formalism
    -- See Note [GHC Formalism] in coreSyn/CoreLint.lhs
    data Tickish id =
        -- | An @{-# SCC #-}@ profiling annotation, either automatically
        -- added by the desugarer as a result of -auto-all, or added by
        -- the user.
        ProfNote {
          profNoteCC    :: CostCentre, -- ^ the cost centre
          profNoteCount :: !Bool,      -- ^ bump the entry count?
          profNoteScope :: !Bool       -- ^ scopes over the enclosed expression
                                       -- (i.e. not just a tick)
        }

      -- | A "tick" used by HPC to track the execution of each
      -- subexpression in the original source code.
      | HpcTick {
          tickModule :: Module,
          tickId     :: !Int
        }

      -- | A breakpoint for the GHCi debugger.  This behaves like an HPC
      -- tick, but has a list of free variables which will be available
      -- for inspection in GHCi when the program stops at the breakpoint.
      --
      -- NB. we must take account of these Ids when (a) counting free variables,
      -- and (b) substituting (don't substitute for them)
      | Breakpoint
        { breakpointId     :: !Int
        , breakpointFVs    :: [id]  -- ^ the order of this list is important:
                                    -- it matches the order of the lists in the
                                    -- appropriate entry in HscTypes.ModBreaks.
                                    --
                                    -- Careful about substitution!  See
                                    -- Note [substTickish] in CoreSubst.
        }

      -- | A source note.
      --
      -- Source notes are pure annotations: Their presence should neither
      -- influence compilation nor execution. The semantics are given by
      -- causality: The presence of a source note means that a local
      -- change in the referenced source code span will possibly provoke
      -- the generated code to change. On the flip-side, the functionality
      -- of annotated code *must* be invariant against changes to all
      -- source code *except* the spans referenced in the source notes
      -- (see "Causality of optimized Haskell" paper for details).
      --
      -- Therefore extending the scope of any given source note is always
      -- valid. Note that it is still undesirable though, as this reduces
      -- their usefulness for debugging and profiling. Therefore we will
      -- generally try only to make use of this property where it is
      -- neccessary to enable optimizations.
      | SourceNote
        { sourceSpan :: RealSrcSpan -- ^ Source covered
        , sourceName :: String      -- ^ Name for source location
                                    --   (uses same names as CCs)
        }

      deriving (Eq, Ord, Data, Typeable)

    -- | A "counting tick" (where tickishCounts is True) is one that
    -- counts evaluations in some way.  We cannot discard a counting tick,
    -- and the compiler should preserve the number of counting ticks as
    -- far as possible.
    --
    -- However, we still allow the simplifier to increase or decrease
    -- sharing, so in practice the actual number of ticks may vary, except
    -- that we never change the value from zero to non-zero or vice versa.
    tickishCounts :: Tickish id -> Bool
    tickishCounts n@ProfNote{} = profNoteCount n
    tickishCounts HpcTick{}    = True
    tickishCounts Breakpoint{} = True
    tickishCounts _            = False

    -- | Specifies the scoping behaviour of ticks. This governs the
    -- behaviour of ticks that care about the covered code and the cost
    -- associated with it. Important for ticks relating to profiling.
    data TickishScoping =
        -- | No scoping: The tick does not care about what code it
        -- covers. Transformations can freely move code inside as well as
        -- outside without any additional annotation obligations
        NoScope

        -- | Soft scoping: We want all code that is covered to stay
        -- covered.  Note that this scope type does not forbid
        -- transformations from happening, as as long as all results of
        -- the transformations are still covered by this tick or a copy of
        -- it. For example
        --
        --   let x = tick<...> (let y = foo in bar) in baz
        --     ===>
        --   let x = tick<...> bar; y = tick<...> foo in baz
        --
        -- Is a valid transformation as far as "bar" and "foo" is
        -- concerned, because both still are scoped over by the tick.
        --
        -- Note though that one might object to the "let" not being
        -- covered by the tick any more. However, we are generally lax
        -- with this - constant costs don't matter too much, and given
        -- that the "let" was effectively merged we can view it as having
        -- lost its identity anyway.
        --
        -- Also note that this scoping behaviour allows floating a tick
        -- "upwards" in pretty much any situation. For example:
        --
        --   case foo of x -> tick<...> bar
        --     ==>
        --   tick<...> case foo of x -> bar
        --
        -- While this is always leagl, we want to make a best effort to
        -- only make us of this where it exposes transformation
        -- opportunities.
      | SoftScope

        -- | Cost centre scoping: We don't want any costs to move to other
        -- cost-centre stacks. This means we not only want no code or cost
        -- to get moved out of their cost centres, but we also object to
        -- code getting associated with new cost-centre ticks - or
        -- changing the order in which they get applied.
        --
        -- A rule of thumb is that we don't want any code to gain new
        -- annotations. However, there are notable exceptions, for
        -- example:
        --
        --   let f = \y -> foo in tick<...> ... (f x) ...
        --     ==>
        --   tick<...> ... foo[x/y] ...
        --
        -- In-lining lambdas like this is always legal, because inlining a
        -- function does not change the cost-centre stack when the
        -- function is called.
      | CostCentreScope

      deriving (Eq)

    -- | Returns the intended scoping rule for a Tickish
    tickishScoped :: Tickish id -> TickishScoping
    tickishScoped n@ProfNote{}
      | profNoteScope n        = CostCentreScope
      | otherwise              = NoScope
    tickishScoped HpcTick{}    = NoScope
    tickishScoped Breakpoint{} = CostCentreScope
       -- Breakpoints are scoped: eventually we're going to do call
       -- stacks, but also this helps prevent the simplifier from moving
       -- breakpoints around and changing their result type (see #1531).
    tickishScoped SourceNote{} = SoftScope

    -- | Returns whether the tick scoping rule is at least as permissive
    -- as the given scoping rule.
    tickishScopesLike :: Tickish id -> TickishScoping -> Bool
    tickishScopesLike t scope = tickishScoped t `like` scope
      where NoScope         `like` _               = True
            _               `like` NoScope         = False
            SoftScope       `like` _               = True
            _               `like` SoftScope       = False
            CostCentreScope `like` _               = True

    -- | Returns @True@ for ticks that can be floated upwards easily even
    -- where it might change execution counts, such as:
    --
    --   Just (tick<...> foo)
    --     ==>
    --   tick<...> (Just foo)
    --
    -- This is a combination of @tickishSoftScope@ and
    -- @tickishCounts@. Note that in principle splittable ticks can become
    -- floatable using @mkNoTick@ -- even though there's currently no
    -- tickish for which that is the case.
    tickishFloatable :: Tickish id -> Bool
    tickishFloatable t = t `tickishScopesLike` SoftScope && not (tickishCounts t)

    -- | Returns @True@ for a tick that is both counting /and/ scoping and
    -- can be split into its (tick, scope) parts using 'mkNoScope' and
    -- 'mkNoTick' respectively.
    tickishCanSplit :: Tickish id -> Bool
    tickishCanSplit ProfNote{profNoteScope = True, profNoteCount = True}
                       = True
    tickishCanSplit _  = False

    mkNoCount :: Tickish id -> Tickish id
    mkNoCount n | not (tickishCounts n)   = n
                | not (tickishCanSplit n) = panic "mkNoCount: Cannot split!"
    mkNoCount n@ProfNote{}                = n {profNoteCount = False}
    mkNoCount _                           = panic "mkNoCount: Undefined split!"

    mkNoScope :: Tickish id -> Tickish id
    mkNoScope n | tickishScoped n == NoScope  = n
                | not (tickishCanSplit n)     = panic "mkNoScope: Cannot split!"
    mkNoScope n@ProfNote{}                    = n {profNoteScope = False}
    mkNoScope _                               = panic "mkNoScope: Undefined split!"

    -- | Return @True@ if this source annotation compiles to some backend
    -- code. Without this flag, the tickish is seen as a simple annotation
    -- that does not have any associated evaluation code.
    --
    -- What this means that we are allowed to disregard the tick if doing
    -- so means that we can skip generating any code in the first place. A
    -- typical example is top-level bindings:
    --
    --   foo = tick<...> \y -> ...
    --     ==>
    --   foo = \y -> tick<...> ...
    --
    -- Here there is just no operational difference between the first and
    -- the second version. Therefore code generation should simply
    -- translate the code as if it found the latter.
    tickishIsCode :: Tickish id -> Bool
    tickishIsCode SourceNote{} = False
    tickishIsCode _tickish     = True  -- all the rest for now

    -- | Governs the kind of expression that the tick gets placed on when
    -- annotating for example using @mkTick@. If we find that we want to
    -- put a tickish on an expression ruled out here, we try to float it
    -- inwards until we find a suitable expression.
    data TickishPlacement =

        -- | Place ticks exactly on run-time expressions. We can still
        -- move the tick through pure compile-time constructs such as
        -- other ticks, casts or type lambdas. This is the most
        -- restrictive placement rule for ticks, as all tickishs have in
        -- common that they want to track runtime processes. The only
        -- legal placement rule for counting ticks.
        PlaceRuntime

        -- | As @PlaceRuntime@, but we float the tick through all
        -- lambdas. This makes sense where there is little difference
        -- between annotating the lambda and annotating the lambda's code.
      | PlaceNonLam

        -- | In addition to floating through lambdas, cost-centre style
        -- tickishs can also be moved from constructors, non-function
        -- variables and literals. For example:
        --
        --   let x = scc<...> C (scc<...> y) (scc<...> 3) in ...
        --
        -- Neither the constructor application, the variable or the
        -- literal are likely to have any cost worth mentioning. And even
        -- if y names a thunk, the call would not care about the
        -- evaluation context. Therefore removing all annotations in the
        -- above example is safe.
      | PlaceCostCentre

      deriving (Eq)

    -- | Placement behaviour we want for the ticks
    tickishPlace :: Tickish id -> TickishPlacement
    tickishPlace n@ProfNote{}
      | profNoteCount n        = PlaceRuntime
      | otherwise              = PlaceCostCentre
    tickishPlace HpcTick{}     = PlaceRuntime
    tickishPlace Breakpoint{}  = PlaceRuntime
    tickishPlace SourceNote{}  = PlaceNonLam

    -- | Returns whether one tick "contains" the other one, therefore
    -- making the second tick redundant.
    tickishContains :: Eq b => Tickish b -> Tickish b -> Bool
    tickishContains (SourceNote sp1 n1) (SourceNote sp2 n2)
      = n1 == n2 && containsSpan sp1 sp2
    tickishContains t1 t2
      = t1 == t2

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Transformation rules}
    *                                                                      *
    ************************************************************************

    The CoreRule type and its friends are dealt with mainly in CoreRules,
    but CoreFVs, Subst, PprCore, CoreTidy 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 '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
                                    --   @False@ <=> generated at the users behest
                                    --   Main effect: reporting of orphan-hood

            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)

                    -- NB: ru_local is *not* used to decide orphan-hood
                    --      c.g. MkIface.coreRuleToIfaceRule
        }

      -- | Built-in rules are used for constant folding
      -- and suchlike.  They have no free variables.
      | 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 Rules.lhs

    type RuleFun = DynFlags -> 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

    ruleActivation :: CoreRule -> Activation
    ruleActivation (BuiltinRule { })       = AlwaysActive
    ruleActivation (Rule { ru_act = act }) = act

    -- | The 'Name' of the '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 'Id.Id' at the head of the rule left hand side
    setRuleIdName :: Name -> CoreRule -> CoreRule
    setRuleIdName nm ru = ru { ru_fn = nm }

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Vectorisation declarations}
    *                                                                      *
    ************************************************************************

    Representation of desugared vectorisation declarations that are fed to the vectoriser (via
    'ModGuts').
    -}

    data CoreVect = Vect      Id   CoreExpr
                  | NoVect    Id
                  | VectType  Bool TyCon (Maybe TyCon)
                  | VectClass TyCon                     -- class tycon
                  | VectInst  Id                        -- instance dfun (always SCALAR)  !!!FIXME: should be superfluous now

    {-
    ************************************************************************
    *                                                                      *
                    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 "CoreUnfold"
    data Unfolding
      = NoUnfolding        -- ^ We have no information about the unfolding

      | 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 [InlineRules]

      | InlineCompulsory   -- Something that *has* no binding, so you *must* inline it
                           -- Only a few primop-like things have this property
                           -- (see MkId.lhs, 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 CoreUnfold
          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 substract 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 []

    mkOtherCon :: [AltCon] -> Unfolding
    mkOtherCon = OtherCon

    seqUnfolding :: Unfolding -> ()
    seqUnfolding (CoreUnfolding { uf_tmpl = e, uf_is_top = top,
                    uf_is_value = b1, uf_is_work_free = b2,
                    uf_expandable = b3, uf_is_conlike = b4,
                    uf_guidance = g})
      = seqExpr e `seq` top `seq` b1 `seq` b2 `seq` b3 `seq` b4 `seq` seqGuidance g

    seqUnfolding _ = ()

    seqGuidance :: UnfoldingGuidance -> ()
    seqGuidance (UnfIfGoodArgs ns n b) = n `seq` sum ns `seq` b `seq` ()
    seqGuidance _                      = ()

    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 Rules.lhs
    -- 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

    hasStableCoreUnfolding_maybe :: Unfolding -> Maybe Bool
    -- Just True  <=> has stable inlining, very keen to inline (eg. INLINE pragma)
    -- Just False <=> has stable inlining, open to inlining it (eg. INLINEABLE pragma)
    -- Nothing    <=> not stable, or cannot inline it anyway
    hasStableCoreUnfolding_maybe (CoreUnfolding { uf_src = src, uf_guidance = guide })
       | isStableSource src
       = case guide of
           UnfWhen {}       -> Just True
           UnfIfGoodArgs {} -> Just False
           UnfNever         -> Nothing
    hasStableCoreUnfolding_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

    isClosedUnfolding :: Unfolding -> Bool          -- No free variables
    isClosedUnfolding (CoreUnfolding {}) = False
    isClosedUnfolding (DFunUnfolding {}) = False
    isClosedUnfolding _                  = True

    -- | Only returns False if there is no unfolding information available at all
    hasSomeUnfolding :: Unfolding -> Bool
    hasSomeUnfolding NoUnfolding = False
    hasSomeUnfolding _           = True

    neverUnfoldGuidance :: UnfoldingGuidance -> Bool
    neverUnfoldGuidance UnfNever = True
    neverUnfoldGuidance _        = False

    canUnfold :: Unfolding -> Bool
    canUnfold (CoreUnfolding { uf_guidance = g }) = not (neverUnfoldGuidance g)
    canUnfold _                                   = False

    {-
    Note [InlineRules]
    ~~~~~~~~~~~~~~~~~
    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 CoreUnfold.

    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 simpifier 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 SimplEnv.  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      = ptext (sLit "__DEFAULT")

    cmpAlt :: (AltCon, a, b) -> (AltCon, a, b) -> Ordering
    cmpAlt (con1, _, _) (con2, _, _) = con1 `cmpAltCon` con2

    ltAlt :: (AltCon, a, b) -> (AltCon, a, b) -> Bool
    ltAlt a1 a2 = (a1 `cmpAlt` a2) == LT

    cmpAltCon :: AltCon -> AltCon -> Ordering
    -- ^ Compares 'AltCon's within a single list of alternatives
    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 coreSyn/CoreLint.lhs
    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 '>'

    instance Outputable b => OutputableBndr (TaggedBndr b) where
      pprBndr _ b = ppr b   -- Simple
      pprInfixOcc  b = ppr b
      pprPrefixOcc b = ppr b

    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 (con, bndrs, rhs) = (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 'MkCore.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 'MkCore.mkCoreConApps' if possible
    mkConApp      :: DataCon -> [Arg b] -> Expr b

    mkApps    f args = foldl App                       f args
    mkTyApps  f args = foldl (\ e a -> App e (Type a)) 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

    mkConApp2 :: DataCon -> [Type] -> [Var] -> Expr b
    mkConApp2 con tys arg_ids = Var (dataConWorkId con)
                                `mkApps` map Type tys
                                `mkApps` map varToCoreExpr arg_ids

    -- | Create a machine integer literal expression of type @Int#@ from an @Integer@.
    -- If you want an expression of type @Int@ use 'MkCore.mkIntExpr'
    mkIntLit      :: DynFlags -> Integer -> Expr b
    -- | Create a machine integer literal expression of type @Int#@ from an @Int@.
    -- If you want an expression of type @Int@ use 'MkCore.mkIntExpr'
    mkIntLitInt   :: DynFlags -> Int     -> Expr b

    mkIntLit    dflags n = Lit (mkMachInt dflags n)
    mkIntLitInt dflags n = Lit (mkMachInt dflags (toInteger n))

    -- | Create a machine word literal expression of type  @Word#@ from an @Integer@.
    -- If you want an expression of type @Word@ use 'MkCore.mkWordExpr'
    mkWordLit     :: DynFlags -> Integer -> Expr b
    -- | Create a machine word literal expression of type  @Word#@ from a @Word@.
    -- If you want an expression of type @Word@ use 'MkCore.mkWordExpr'
    mkWordLitWord :: DynFlags -> Word -> Expr b

    mkWordLit     dflags w = Lit (mkMachWord dflags w)
    mkWordLitWord dflags w = Lit (mkMachWord dflags (toInteger w))

    mkWord64LitWord64 :: Word64 -> Expr b
    mkWord64LitWord64 w = Lit (mkMachWord64 (toInteger w))

    mkInt64LitInt64 :: Int64 -> Expr b
    mkInt64LitInt64 w = Lit (mkMachInt64 (toInteger w))

    -- | Create a machine character literal expression of type @Char#@.
    -- If you want an expression of type @Char@ use 'MkCore.mkCharExpr'
    mkCharLit :: Char -> Expr b
    -- | Create a machine string literal expression of type @Addr#@.
    -- If you want an expression of type @String@ use 'MkCore.mkStringExpr'
    mkStringLit :: String -> Expr b

    mkCharLit   c = Lit (mkMachChar c)
    mkStringLit s = Lit (mkMachString s)

    -- | Create a machine single precision literal expression of type @Float#@ from a @Rational@.
    -- If you want an expression of type @Float@ use 'MkCore.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 'MkCore.mkFloatExpr'
    mkFloatLitFloat :: Float -> Expr b

    mkFloatLit      f = Lit (mkMachFloat f)
    mkFloatLitFloat f = Lit (mkMachFloat (toRational f))

    -- | Create a machine double precision literal expression of type @Double#@ from a @Rational@.
    -- If you want an expression of type @Double@ use 'MkCore.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 'MkCore.mkDoubleExpr'
    mkDoubleLitDouble :: Double -> Expr b

    mkDoubleLit       d = Lit (mkMachDouble d)
    mkDoubleLitDouble d = Lit (mkMachDouble (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 'MkCore.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 'MkCore.mkCoreLams' if possible
    mkLams        :: [b] -> Expr b -> Expr b

    mkLams binders body = foldr Lam body binders
    mkLets binds body   = foldr Let body binds

    -- | Create a binding group where a type variable is bound to a type. Per "CoreSyn#type_let",
    -- 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 "CoreSyn#type_let",
    -- 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

    {-
    ************************************************************************
    *                                                                      *
    \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 coreSyn/CoreLint.lhs
    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 | (_,_,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. This function is your friend.
    collectBinders               :: Expr b -> ([b],         Expr b)
    -- | Collect as many type bindings as possible from the front of a nested lambda
    collectTyBinders             :: CoreExpr -> ([TyVar],     CoreExpr)
    -- | Collect as many value bindings as possible from the front of a nested lambda
    collectValBinders            :: CoreExpr -> ([Id],        CoreExpr)
    -- | Collect type binders from the front of the lambda first,
    -- then follow up by collecting as many value bindings as possible
    -- from the resulting stripped expression
    collectTyAndValBinders       :: CoreExpr -> ([TyVar], [Id], CoreExpr)

    collectBinders expr
      = go [] expr
      where
        go bs (Lam b e) = go (b:bs) e
        go bs e          = (reverse bs, e)

    collectTyAndValBinders expr
      = (tvs, ids, body)
      where
        (tvs, body1) = collectTyBinders expr
        (ids, body)  = collectValBinders body1

    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)

    -- | Takes a nested application expression and returns the 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)

    -- | Like @collectArgs@, but also collects looks through floatable
    -- ticks if it means that we can find more arguments.
    collectArgsTicks :: (Tickish Id -> Bool) -> Expr b
                     -> (Expr b, [Arg b], [Tickish Id])
    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 '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{Seq stuff}
    *                                                                      *
    ************************************************************************
    -}

    seqExpr :: CoreExpr -> ()
    seqExpr (Var v)         = v `seq` ()
    seqExpr (Lit lit)       = lit `seq` ()
    seqExpr (App f a)       = seqExpr f `seq` seqExpr a
    seqExpr (Lam b e)       = seqBndr b `seq` seqExpr e
    seqExpr (Let b e)       = seqBind b `seq` seqExpr e
    seqExpr (Case e b t as) = seqExpr e `seq` seqBndr b `seq` seqType t `seq` seqAlts as
    seqExpr (Cast e co)     = seqExpr e `seq` seqCo co
    seqExpr (Tick n e)      = seqTickish n `seq` seqExpr e
    seqExpr (Type t)        = seqType t
    seqExpr (Coercion co)   = seqCo co

    seqExprs :: [CoreExpr] -> ()
    seqExprs [] = ()
    seqExprs (e:es) = seqExpr e `seq` seqExprs es

    seqTickish :: Tickish Id -> ()
    seqTickish ProfNote{ profNoteCC = cc } = cc `seq` ()
    seqTickish HpcTick{} = ()
    seqTickish Breakpoint{ breakpointFVs = ids } = seqBndrs ids
    seqTickish SourceNote{} = ()

    seqBndr :: CoreBndr -> ()
    seqBndr b = b `seq` ()

    seqBndrs :: [CoreBndr] -> ()
    seqBndrs [] = ()
    seqBndrs (b:bs) = seqBndr b `seq` seqBndrs bs

    seqBind :: Bind CoreBndr -> ()
    seqBind (NonRec b e) = seqBndr b `seq` seqExpr e
    seqBind (Rec prs)    = seqPairs prs

    seqPairs :: [(CoreBndr, CoreExpr)] -> ()
    seqPairs [] = ()
    seqPairs ((b,e):prs) = seqBndr b `seq` seqExpr e `seq` seqPairs prs

    seqAlts :: [CoreAlt] -> ()
    seqAlts [] = ()
    seqAlts ((c,bs,e):alts) = c `seq` seqBndrs bs `seq` seqExpr e `seq` seqAlts alts

    seqRules :: [CoreRule] -> ()
    seqRules [] = ()
    seqRules (Rule { ru_bndrs = bndrs, ru_args = args, ru_rhs = rhs } : rules)
      = seqBndrs bndrs `seq` seqExprs (rhs:args) `seq` seqRules rules
    seqRules (BuiltinRule {} : rules) = seqRules rules

    {-
    ************************************************************************
    *                                                                      *
    \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     (Tickish Id) (AnnExpr bndr annot)
      | AnnType     Type
      | AnnCoercion Coercion

    -- | A clone of the 'Alt' type but allowing annotation at every tree node
    type AnnAlt bndr annot = (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 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 :: (Tickish Var -> Bool) -> AnnExpr b a
                           -> (AnnExpr b a, [AnnExpr b a], [Tickish Var])
    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)
      where
        deAnnBind (AnnNonRec var rhs) = NonRec var (deAnnotate rhs)
        deAnnBind (AnnRec pairs) = Rec [(v,deAnnotate rhs) | (v,rhs) <- pairs]

    deAnnotate' (AnnCase scrut v t alts)
      = Case (deAnnotate scrut) v t (map deAnnAlt alts)

    deAnnAlt :: AnnAlt bndr annot -> Alt bndr
    deAnnAlt (con,args,rhs) = (con,args,deAnnotate rhs)

    -- | 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)