\begin{code}
module CoreUtils (
- coreExprType, coreAltsType,
+ -- Construction
+ mkNote, mkInlineMe, mkSCC, mkCoerce,
+ bindNonRec, needsCaseBinding,
+ mkIfThenElse, mkAltExpr, mkPiType, mkPiTypes,
- exprIsBottom, exprIsDupable, exprIsTrivial, exprIsWHNF, exprIsCheap,
- exprOkForSpeculation,
- FormSummary(..), mkFormSummary, whnfOrBottom, exprArity,
- cheapEqExpr, eqExpr, applyTypeToArgs
+ -- Taking expressions apart
+ findDefault, findAlt, hasDefault,
+
+ -- Properties of expressions
+ exprType, coreAltsType,
+ exprIsBottom, exprIsDupable, exprIsTrivial, exprIsCheap,
+ exprIsValue,exprOkForSpeculation, exprIsBig,
+ exprIsConApp_maybe, exprIsAtom,
+ idAppIsBottom, idAppIsCheap,
+
+
+ -- Arity and eta expansion
+ manifestArity, exprArity,
+ exprEtaExpandArity, etaExpand,
+
+ -- Size
+ coreBindsSize,
+
+ -- Hashing
+ hashExpr,
+
+ -- Equality
+ cheapEqExpr, eqExpr, applyTypeToArgs, applyTypeToArg
) where
#include "HsVersions.h"
+import GlaExts -- For `xori`
+
import CoreSyn
import PprCore ( pprCoreExpr )
-import Var ( IdOrTyVar, isId, isTyVar )
-import VarSet
+import Var ( Var, isId, isTyVar )
import VarEnv
-import Name ( isLocallyDefined )
-import Const ( Con, isWHNFCon, conIsTrivial, conIsCheap, conIsDupable,
- conType, conOkForSpeculation, conStrictness
+import Name ( hashName )
+import Literal ( hashLiteral, literalType, litIsDupable, isZeroLit )
+import DataCon ( DataCon, dataConRepArity, dataConArgTys, isExistentialDataCon, dataConTyCon )
+import PrimOp ( PrimOp(..), primOpOkForSpeculation, primOpIsCheap )
+import Id ( Id, idType, globalIdDetails, idNewStrictness, idLBVarInfo,
+ mkWildId, idArity, idName, idUnfolding, idInfo, isOneShotLambda,
+ isDataConId_maybe, mkSysLocal, isDataConId, isBottomingId
)
-import Id ( Id, idType, setIdType, idUnique, idAppIsBottom,
- getIdArity,
- getIdSpecialisation, setIdSpecialisation,
- getInlinePragma, setInlinePragma,
- getIdUnfolding, setIdUnfolding, idInfo
+import IdInfo ( LBVarInfo(..),
+ GlobalIdDetails(..),
+ megaSeqIdInfo )
+import NewDemand ( appIsBottom )
+import Type ( Type, mkFunTy, mkForAllTy, splitFunTy_maybe, splitFunTy,
+ applyTys, isUnLiftedType, seqType, mkTyVarTy,
+ splitForAllTy_maybe, isForAllTy, splitNewType_maybe,
+ splitTyConApp_maybe, eqType, funResultTy, applyTy,
+ funResultTy, applyTy
)
-import IdInfo ( arityLowerBound, InlinePragInfo(..), lbvarInfo, LBVarInfo(..) )
-import Type ( Type, mkFunTy, mkForAllTy,
- splitFunTy_maybe, tyVarsOfType, tyVarsOfTypes,
- isNotUsgTy, mkUsgTy, unUsgTy, UsageAnn(..),
- tidyTyVar, applyTys, isUnLiftedType
- )
-import Demand ( isPrim, isLazy )
-import Unique ( buildIdKey, augmentIdKey )
-import Util ( zipWithEqual, mapAccumL )
+import TyCon ( tyConArity )
+import TysWiredIn ( boolTy, trueDataCon, falseDataCon )
+import CostCentre ( CostCentre )
+import BasicTypes ( Arity )
+import Unique ( Unique )
import Outputable
import TysPrim ( alphaTy ) -- Debugging only
+import Util ( equalLength, lengthAtLeast )
\end{code}
%************************************************************************
\begin{code}
-coreExprType :: CoreExpr -> Type
-
-coreExprType (Var var) = idType var
-coreExprType (Let _ body) = coreExprType body
-coreExprType (Case _ _ alts) = coreAltsType alts
-coreExprType (Note (Coerce ty _) e) = ty
-coreExprType (Note (TermUsg u) e) = mkUsgTy u (unUsgTy (coreExprType e))
-coreExprType (Note other_note e) = coreExprType e
-coreExprType e@(Con con args) = applyTypeToArgs e (conType con) args
-
-coreExprType (Lam binder expr)
- | isId binder = (case (lbvarInfo . idInfo) binder of
- IsOneShotLambda -> mkUsgTy UsOnce
- otherwise -> id) $
- idType binder `mkFunTy` coreExprType expr
- | isTyVar binder = mkForAllTy binder (coreExprType expr)
-
-coreExprType e@(App _ _)
+exprType :: CoreExpr -> Type
+
+exprType (Var var) = idType var
+exprType (Lit lit) = literalType lit
+exprType (Let _ body) = exprType body
+exprType (Case _ _ alts) = coreAltsType alts
+exprType (Note (Coerce ty _) e) = ty -- **! should take usage from e
+exprType (Note other_note e) = exprType e
+exprType (Lam binder expr) = mkPiType binder (exprType expr)
+exprType e@(App _ _)
= case collectArgs e of
- (fun, args) -> applyTypeToArgs e (coreExprType fun) args
+ (fun, args) -> applyTypeToArgs e (exprType fun) args
-coreExprType other = pprTrace "coreExprType" (pprCoreExpr other) alphaTy
+exprType other = pprTrace "exprType" (pprCoreExpr other) alphaTy
coreAltsType :: [CoreAlt] -> Type
-coreAltsType ((_,_,rhs) : _) = coreExprType rhs
+coreAltsType ((_,_,rhs) : _) = exprType rhs
+\end{code}
+
+@mkPiType@ makes a (->) type or a forall type, depending on whether
+it is given a type variable or a term variable. We cleverly use the
+lbvarinfo field to figure out the right annotation for the arrove in
+case of a term variable.
+
+\begin{code}
+mkPiType :: Var -> Type -> Type -- The more polymorphic version
+mkPiTypes :: [Var] -> Type -> Type -- doesn't work...
+
+mkPiTypes vs ty = foldr mkPiType ty vs
+
+mkPiType v ty
+ | isId v = mkFunTy (idType v) ty
+ | otherwise = mkForAllTy v ty
\end{code}
\begin{code}
--- The first argument is just for debugging
+applyTypeToArg :: Type -> CoreExpr -> Type
+applyTypeToArg fun_ty (Type arg_ty) = applyTy fun_ty arg_ty
+applyTypeToArg fun_ty other_arg = funResultTy fun_ty
+
applyTypeToArgs :: CoreExpr -> Type -> [CoreExpr] -> Type
+-- A more efficient version of applyTypeToArg
+-- when we have several args
+-- The first argument is just for debugging
applyTypeToArgs e op_ty [] = op_ty
applyTypeToArgs e op_ty (Type ty : args)
= -- Accumulate type arguments so we can instantiate all at once
- ASSERT2( all isNotUsgTy tys, ppr e <+> text "of" <+> ppr op_ty <+> text "to" <+> ppr (Type ty : args) <+> text "i.e." <+> ppr tys )
- applyTypeToArgs e (applyTys op_ty tys) rest_args
+ go [ty] args
where
- (tys, rest_args) = go [ty] args
- go tys (Type ty : args) = go (ty:tys) args
- go tys rest_args = (reverse tys, rest_args)
+ go rev_tys (Type ty : args) = go (ty:rev_tys) args
+ go rev_tys rest_args = applyTypeToArgs e op_ty' rest_args
+ where
+ op_ty' = applyTys op_ty (reverse rev_tys)
applyTypeToArgs e op_ty (other_arg : args)
= case (splitFunTy_maybe op_ty) of
\end{code}
+
%************************************************************************
%* *
-\subsection{Figuring out things about expressions}
+\subsection{Attaching notes}
%* *
%************************************************************************
+mkNote removes redundant coercions, and SCCs where possible
+
\begin{code}
-data FormSummary
- = VarForm -- Expression is a variable (or scc var, etc)
-
- | ValueForm -- Expression is a value: i.e. a value-lambda,constructor, or literal
- -- May 1999: I'm experimenting with allowing "cheap" non-values
- -- here.
-
- | BottomForm -- Expression is guaranteed to be bottom. We're more gung
- -- ho about inlining such things, because it can't waste work
- | OtherForm -- Anything else
-
-instance Outputable FormSummary where
- ppr VarForm = ptext SLIT("Var")
- ppr ValueForm = ptext SLIT("Value")
- ppr BottomForm = ptext SLIT("Bot")
- ppr OtherForm = ptext SLIT("Other")
-
-whnfOrBottom :: FormSummary -> Bool
-whnfOrBottom VarForm = True
-whnfOrBottom ValueForm = True
-whnfOrBottom BottomForm = True
-whnfOrBottom OtherForm = False
+mkNote :: Note -> CoreExpr -> CoreExpr
+mkNote (Coerce to_ty from_ty) expr = mkCoerce to_ty from_ty expr
+mkNote (SCC cc) expr = mkSCC cc expr
+mkNote InlineMe expr = mkInlineMe expr
+mkNote note expr = Note note expr
+
+-- Slide InlineCall in around the function
+-- No longer necessary I think (SLPJ Apr 99)
+-- mkNote InlineCall (App f a) = App (mkNote InlineCall f) a
+-- mkNote InlineCall (Var v) = Note InlineCall (Var v)
+-- mkNote InlineCall expr = expr
\end{code}
+Drop trivial InlineMe's. This is somewhat important, because if we have an unfolding
+that looks like (Note InlineMe (Var v)), the InlineMe doesn't go away because it may
+not be *applied* to anything.
+
+We don't use exprIsTrivial here, though, because we sometimes generate worker/wrapper
+bindings like
+ fw = ...
+ f = inline_me (coerce t fw)
+As usual, the inline_me prevents the worker from getting inlined back into the wrapper.
+We want the split, so that the coerces can cancel at the call site.
+
+However, we can get left with tiresome type applications. Notably, consider
+ f = /\ a -> let t = e in (t, w)
+Then lifting the let out of the big lambda gives
+ t' = /\a -> e
+ f = /\ a -> let t = inline_me (t' a) in (t, w)
+The inline_me is to stop the simplifier inlining t' right back
+into t's RHS. In the next phase we'll substitute for t (since
+its rhs is trivial) and *then* we could get rid of the inline_me.
+But it hardly seems worth it, so I don't bother.
+
\begin{code}
-mkFormSummary :: CoreExpr -> FormSummary
-mkFormSummary expr
- = go (0::Int) expr -- The "n" is the number of *value* arguments so far
+mkInlineMe (Var v) = Var v
+mkInlineMe e = Note InlineMe e
+\end{code}
+
+
+
+\begin{code}
+mkCoerce :: Type -> Type -> CoreExpr -> CoreExpr
+
+mkCoerce to_ty from_ty (Note (Coerce to_ty2 from_ty2) expr)
+ = ASSERT( from_ty `eqType` to_ty2 )
+ mkCoerce to_ty from_ty2 expr
+
+mkCoerce to_ty from_ty expr
+ | to_ty `eqType` from_ty = expr
+ | otherwise = ASSERT( from_ty `eqType` exprType expr )
+ Note (Coerce to_ty from_ty) expr
+\end{code}
+
+\begin{code}
+mkSCC :: CostCentre -> Expr b -> Expr b
+ -- Note: Nested SCC's *are* preserved for the benefit of
+ -- cost centre stack profiling
+mkSCC cc (Lit lit) = Lit lit
+mkSCC cc (Lam x e) = Lam x (mkSCC cc e) -- Move _scc_ inside lambda
+mkSCC cc (Note (SCC cc') e) = Note (SCC cc) (Note (SCC cc') e)
+mkSCC cc (Note n e) = Note n (mkSCC cc e) -- Move _scc_ inside notes
+mkSCC cc expr = Note (SCC cc) expr
+\end{code}
+
+
+%************************************************************************
+%* *
+\subsection{Other expression construction}
+%* *
+%************************************************************************
+
+\begin{code}
+bindNonRec :: Id -> CoreExpr -> CoreExpr -> CoreExpr
+-- (bindNonRec x r b) produces either
+-- let x = r in b
+-- or
+-- case r of x { _DEFAULT_ -> b }
+--
+-- depending on whether x is unlifted or not
+-- It's used by the desugarer to avoid building bindings
+-- that give Core Lint a heart attack. Actually the simplifier
+-- deals with them perfectly well.
+bindNonRec bndr rhs body
+ | needsCaseBinding (idType bndr) rhs = Case rhs bndr [(DEFAULT,[],body)]
+ | otherwise = Let (NonRec bndr rhs) body
+
+needsCaseBinding ty rhs = isUnLiftedType ty && not (exprOkForSpeculation rhs)
+ -- Make a case expression instead of a let
+ -- These can arise either from the desugarer,
+ -- or from beta reductions: (\x.e) (x +# y)
+\end{code}
+
+\begin{code}
+mkAltExpr :: AltCon -> [CoreBndr] -> [Type] -> CoreExpr
+ -- This guy constructs the value that the scrutinee must have
+ -- when you are in one particular branch of a case
+mkAltExpr (DataAlt con) args inst_tys
+ = mkConApp con (map Type inst_tys ++ map varToCoreExpr args)
+mkAltExpr (LitAlt lit) [] []
+ = Lit lit
+
+mkIfThenElse :: CoreExpr -> CoreExpr -> CoreExpr -> CoreExpr
+mkIfThenElse guard then_expr else_expr
+ = Case guard (mkWildId boolTy)
+ [ (DataAlt trueDataCon, [], then_expr),
+ (DataAlt falseDataCon, [], else_expr) ]
+\end{code}
+
+
+%************************************************************************
+%* *
+\subsection{Taking expressions apart}
+%* *
+%************************************************************************
+
+The default alternative must be first, if it exists at all.
+This makes it easy to find, though it makes matching marginally harder.
+
+\begin{code}
+hasDefault :: [CoreAlt] -> Bool
+hasDefault ((DEFAULT,_,_) : alts) = True
+hasDefault _ = False
+
+findDefault :: [CoreAlt] -> ([CoreAlt], Maybe CoreExpr)
+findDefault ((DEFAULT,args,rhs) : alts) = ASSERT( null args ) (alts, Just rhs)
+findDefault alts = (alts, Nothing)
+
+findAlt :: AltCon -> [CoreAlt] -> CoreAlt
+findAlt con alts
+ = case alts of
+ (deflt@(DEFAULT,_,_):alts) -> go alts deflt
+ other -> go alts panic_deflt
+
where
- go n (Con con _) | isWHNFCon con = ValueForm
- | otherwise = OtherForm
-
- go n (Note _ e) = go n e
-
- go n (Let (NonRec b r) e) | exprIsCheap r = go n e -- let f = f' alpha in (f,g)
- -- should be treated as a value
- go n (Let _ e) = OtherForm
-
- -- We want selectors to look like values
- -- e.g. case x of { (a,b) -> a }
- -- should give a ValueForm, so that it will be inlined
- -- vigorously
- go n expr@(Case _ _ _) | exprIsCheap expr = ValueForm
- | otherwise = OtherForm
-
- go 0 (Lam x e) | isId x = ValueForm -- NB: \x.bottom /= bottom!
- | otherwise = go 0 e
- go n (Lam x e) | isId x = go (n-1) e -- Applied lambda
- | otherwise = go n e
-
- go n (App fun (Type _)) = go n fun -- Ignore type args
- go n (App fun arg) = go (n+1) fun
-
- go n (Var f) | idAppIsBottom f n = BottomForm
- go 0 (Var f) = VarForm
- go n (Var f) | n < arityLowerBound (getIdArity f) = ValueForm
- | otherwise = OtherForm
+ panic_deflt = pprPanic "Missing alternative" (ppr con $$ vcat (map ppr alts))
+
+ go [] deflt = deflt
+ go (alt@(con1,_,_) : alts) deflt | con == con1 = alt
+ | otherwise = ASSERT( not (con1 == DEFAULT) )
+ go alts deflt
\end{code}
-@exprIsTrivial@ is true of expressions we are unconditionally
- happy to duplicate; simple variables and constants,
- and type applications.
+
+%************************************************************************
+%* *
+\subsection{Figuring out things about expressions}
+%* *
+%************************************************************************
+
+@exprIsTrivial@ is true of expressions we are unconditionally happy to
+ duplicate; simple variables and constants, and type
+ applications. Note that primop Ids aren't considered
+ trivial unless
@exprIsBottom@ is true of expressions that are guaranteed to diverge
+There used to be a gruesome test for (hasNoBinding v) in the
+Var case:
+ exprIsTrivial (Var v) | hasNoBinding v = idArity v == 0
+The idea here is that a constructor worker, like $wJust, is
+really short for (\x -> $wJust x), becuase $wJust has no binding.
+So it should be treated like a lambda. Ditto unsaturated primops.
+But now constructor workers are not "have-no-binding" Ids. And
+completely un-applied primops and foreign-call Ids are sufficiently
+rare that I plan to allow them to be duplicated and put up with
+saturating them.
+
\begin{code}
-exprIsTrivial (Type _) = True
-exprIsTrivial (Var v) = True
-exprIsTrivial (App e arg) = isTypeArg arg && exprIsTrivial e
-exprIsTrivial (Note _ e) = exprIsTrivial e
-exprIsTrivial (Con con args) = conIsTrivial con && all isTypeArg args
-exprIsTrivial (Lam b body) | isTyVar b = exprIsTrivial body
-exprIsTrivial other = False
+exprIsTrivial (Var v) = True -- See notes above
+exprIsTrivial (Type _) = True
+exprIsTrivial (Lit lit) = True
+exprIsTrivial (App e arg) = not (isRuntimeArg arg) && exprIsTrivial e
+exprIsTrivial (Note _ e) = exprIsTrivial e
+exprIsTrivial (Lam b body) = not (isRuntimeVar b) && exprIsTrivial body
+exprIsTrivial other = False
+
+exprIsAtom :: CoreExpr -> Bool
+-- Used to decide whether to let-binding an STG argument
+-- when compiling to ILX => type applications are not allowed
+exprIsAtom (Var v) = True -- primOpIsDupable?
+exprIsAtom (Lit lit) = True
+exprIsAtom (Type ty) = True
+exprIsAtom (Note (SCC _) e) = False
+exprIsAtom (Note _ e) = exprIsAtom e
+exprIsAtom other = False
\end{code}
@exprIsDupable@ is true of expressions that can be duplicated at a modest
- cost in space. This will only happen in different case
+ cost in code size. This will only happen in different case
branches, so there's no issue about duplicating work.
+
+ That is, exprIsDupable returns True of (f x) even if
+ f is very very expensive to call.
+
Its only purpose is to avoid fruitless let-binding
and then inlining of case join points
\begin{code}
-exprIsDupable (Type _) = True
-exprIsDupable (Con con args) = conIsDupable con &&
- all exprIsDupable args &&
- valArgCount args <= dupAppSize
-
-exprIsDupable (Note _ e) = exprIsDupable e
-exprIsDupable expr = case collectArgs expr of
- (Var f, args) -> valArgCount args <= dupAppSize
- other -> False
+exprIsDupable (Type _) = True
+exprIsDupable (Var v) = True
+exprIsDupable (Lit lit) = litIsDupable lit
+exprIsDupable (Note InlineMe e) = True
+exprIsDupable (Note _ e) = exprIsDupable e
+exprIsDupable expr
+ = go expr 0
+ where
+ go (Var v) n_args = True
+ go (App f a) n_args = n_args < dupAppSize
+ && exprIsDupable a
+ && go f (n_args+1)
+ go other n_args = False
dupAppSize :: Int
dupAppSize = 4 -- Size of application we are prepared to duplicate
it is obviously in weak head normal form, or is cheap to get to WHNF.
[Note that that's not the same as exprIsDupable; an expression might be
big, and hence not dupable, but still cheap.]
-By ``cheap'' we mean a computation we're willing to push inside a lambda
-in order to bring a couple of lambdas together. That might mean it gets
-evaluated more than once, instead of being shared. The main examples of things
-which aren't WHNF but are ``cheap'' are:
+
+By ``cheap'' we mean a computation we're willing to:
+ push inside a lambda, or
+ inline at more than one place
+That might mean it gets evaluated more than once, instead of being
+shared. The main examples of things which aren't WHNF but are
+``cheap'' are:
* case e of
pi -> ei
+ (where e, and all the ei are cheap)
- where e, and all the ei are cheap; and
-
- * let x = e
- in b
-
- where e and b are cheap; and
+ * let x = e in b
+ (where e and b are cheap)
* op x1 ... xn
+ (where op is a cheap primitive operator)
- where op is a cheap primitive operator
+ * error "foo"
+ (because we are happy to substitute it inside a lambda)
-\begin{code}
-exprIsCheap :: CoreExpr -> Bool
-exprIsCheap (Type _) = True
-exprIsCheap (Var _) = True
-exprIsCheap (Con con args) = conIsCheap con && all exprIsCheap args
-exprIsCheap (Note _ e) = exprIsCheap e
-exprIsCheap (Lam x e) = if isId x then True else exprIsCheap e
-exprIsCheap (Let bind body) = all exprIsCheap (rhssOfBind bind) && exprIsCheap body
-exprIsCheap (Case scrut _ alts) = exprIsCheap scrut &&
- all (\(_,_,rhs) -> exprIsCheap rhs) alts
-
-exprIsCheap other_expr -- look for manifest partial application
- = case collectArgs other_expr of
- (f, args) -> isPap f (valArgCount args) && all exprIsCheap args
-\end{code}
+Notice that a variable is considered 'cheap': we can push it inside a lambda,
+because sharing will make sure it is only evaluated once.
\begin{code}
-isPap :: CoreExpr -- Function
- -> Int -- Number of value args
- -> Bool
-isPap (Var f) n_val_args
- = idAppIsBottom f n_val_args
- -- Application of a function which
- -- always gives bottom; we treat this as
- -- a WHNF, because it certainly doesn't
- -- need to be shared!
-
- || n_val_args == 0 -- Just a type application of
+exprIsCheap :: CoreExpr -> Bool
+exprIsCheap (Lit lit) = True
+exprIsCheap (Type _) = True
+exprIsCheap (Var _) = True
+exprIsCheap (Note InlineMe e) = True
+exprIsCheap (Note _ e) = exprIsCheap e
+exprIsCheap (Lam x e) = isRuntimeVar x || exprIsCheap e
+exprIsCheap (Case e _ alts) = exprIsCheap e &&
+ and [exprIsCheap rhs | (_,_,rhs) <- alts]
+ -- Experimentally, treat (case x of ...) as cheap
+ -- (and case __coerce x etc.)
+ -- This improves arities of overloaded functions where
+ -- there is only dictionary selection (no construction) involved
+exprIsCheap (Let (NonRec x _) e)
+ | isUnLiftedType (idType x) = exprIsCheap e
+ | otherwise = False
+ -- strict lets always have cheap right hand sides, and
+ -- do no allocation.
+
+exprIsCheap other_expr
+ = go other_expr 0 True
+ where
+ go (Var f) n_args args_cheap
+ = (idAppIsCheap f n_args && args_cheap)
+ -- A constructor, cheap primop, or partial application
+
+ || idAppIsBottom f n_args
+ -- Application of a function which
+ -- always gives bottom; we treat this as cheap
+ -- because it certainly doesn't need to be shared!
+
+ go (App f a) n_args args_cheap
+ | not (isRuntimeArg a) = go f n_args args_cheap
+ | otherwise = go f (n_args + 1) (exprIsCheap a && args_cheap)
+
+ go other n_args args_cheap = False
+
+idAppIsCheap :: Id -> Int -> Bool
+idAppIsCheap id n_val_args
+ | n_val_args == 0 = True -- Just a type application of
-- a variable (f t1 t2 t3)
-- counts as WHNF
-
- || n_val_args < arityLowerBound (getIdArity f)
-
-isPap fun n_val_args = False
+ | otherwise = case globalIdDetails id of
+ DataConId _ -> True
+ RecordSelId _ -> True -- I'm experimenting with making record selection
+ -- look cheap, so we will substitute it inside a
+ -- lambda. Particularly for dictionary field selection
+
+ PrimOpId op -> primOpIsCheap op -- In principle we should worry about primops
+ -- that return a type variable, since the result
+ -- might be applied to something, but I'm not going
+ -- to bother to check the number of args
+ other -> n_val_args < idArity id
\end{code}
-exprOkForSpeculation returns True of an UNLIFTED-TYPE expression that it is safe
-to evaluate even if normal order eval might not evaluate the expression
-at all. E.G.
+exprOkForSpeculation returns True of an expression that it is
+
+ * safe to evaluate even if normal order eval might not
+ evaluate the expression at all, or
+
+ * safe *not* to evaluate even if normal order would do so
+
+It returns True iff
+
+ the expression guarantees to terminate,
+ soon,
+ without raising an exception,
+ without causing a side effect (e.g. writing a mutable variable)
+
+E.G.
let x = case y# +# 1# of { r# -> I# r# }
in E
==>
\begin{code}
exprOkForSpeculation :: CoreExpr -> Bool
-exprOkForSpeculation (Var v) = True -- Unlifted type => already evaluated
-
-exprOkForSpeculation (Note _ e) = exprOkForSpeculation e
-exprOkForSpeculation (Let (NonRec b r) e) = isUnLiftedType (idType b) &&
- exprOkForSpeculation r &&
- exprOkForSpeculation e
-exprOkForSpeculation (Let (Rec _) _) = False
-exprOkForSpeculation (Case _ _ _) = False -- Conservative
-exprOkForSpeculation (App _ _) = False
-
-exprOkForSpeculation (Con con args)
- = conOkForSpeculation con &&
- and (zipWith ok (filter isValArg args) (fst (conStrictness con)))
+exprOkForSpeculation (Lit _) = True
+exprOkForSpeculation (Type _) = True
+exprOkForSpeculation (Var v) = isUnLiftedType (idType v)
+exprOkForSpeculation (Note _ e) = exprOkForSpeculation e
+exprOkForSpeculation other_expr
+ = case collectArgs other_expr of
+ (Var f, args) -> spec_ok (globalIdDetails f) args
+ other -> False
+
where
- ok arg demand | isLazy demand = True
- | isPrim demand = exprOkForSpeculation arg
- | otherwise = False
-
-exprOkForSpeculation other = panic "exprOkForSpeculation"
- -- Lam, Type
+ spec_ok (DataConId _) args
+ = True -- The strictness of the constructor has already
+ -- been expressed by its "wrapper", so we don't need
+ -- to take the arguments into account
+
+ spec_ok (PrimOpId op) args
+ | isDivOp op, -- Special case for dividing operations that fail
+ [arg1, Lit lit] <- args -- only if the divisor is zero
+ = not (isZeroLit lit) && exprOkForSpeculation arg1
+ -- Often there is a literal divisor, and this
+ -- can get rid of a thunk in an inner looop
+
+ | otherwise
+ = primOpOkForSpeculation op &&
+ all exprOkForSpeculation args
+ -- A bit conservative: we don't really need
+ -- to care about lazy arguments, but this is easy
+
+ spec_ok other args = False
+
+isDivOp :: PrimOp -> Bool
+-- True of dyadic operators that can fail
+-- only if the second arg is zero
+-- This function probably belongs in PrimOp, or even in
+-- an automagically generated file.. but it's such a
+-- special case I thought I'd leave it here for now.
+isDivOp IntQuotOp = True
+isDivOp IntRemOp = True
+isDivOp WordQuotOp = True
+isDivOp WordRemOp = True
+isDivOp IntegerQuotRemOp = True
+isDivOp IntegerDivModOp = True
+isDivOp FloatDivOp = True
+isDivOp DoubleDivOp = True
+isDivOp other = False
\end{code}
go n (Case e _ _) = go 0 e -- Just check the scrut
go n (App e _) = go (n+1) e
go n (Var v) = idAppIsBottom v n
- go n (Con _ _) = False
+ go n (Lit _) = False
go n (Lam _ _) = False
+
+idAppIsBottom :: Id -> Int -> Bool
+idAppIsBottom id n_val_args = appIsBottom (idNewStrictness id) n_val_args
\end{code}
-exprIsWHNF reports True for head normal forms. Note that does not necessarily
-mean *normal* forms; constructors might have non-trivial argument expressions, for
-example. We use a let binding for WHNFs, rather than a case binding, even if it's
-used strictly. We try to expose WHNFs by floating lets out of the RHS of lets.
+@exprIsValue@ returns true for expressions that are certainly *already*
+evaluated to *head* normal form. This is used to decide whether it's ok
+to change
+
+ case x of _ -> e ===> e
+
+and to decide whether it's safe to discard a `seq`
+
+So, it does *not* treat variables as evaluated, unless they say they are.
+
+But it *does* treat partial applications and constructor applications
+as values, even if their arguments are non-trivial, provided the argument
+type is lifted;
+ e.g. (:) (f x) (map f xs) is a value
+ map (...redex...) is a value
+Because `seq` on such things completes immediately
-We treat applications of buildId and augmentId as honorary WHNFs, because we
-want them to get exposed
+For unlifted argument types, we have to be careful:
+ C (f x :: Int#)
+Suppose (f x) diverges; then C (f x) is not a value. True, but
+this form is illegal (see the invariants in CoreSyn). Args of unboxed
+type must be ok-for-speculation (or trivial).
\begin{code}
-exprIsWHNF :: CoreExpr -> Bool -- True => Variable, value-lambda, constructor, PAP
-exprIsWHNF (Type ty) = True -- Types are honorary WHNFs; we don't mind
+exprIsValue :: CoreExpr -> Bool -- True => Value-lambda, constructor, PAP
+exprIsValue (Type ty) = True -- Types are honorary Values; we don't mind
-- copying them
-exprIsWHNF (Var v) = True
-exprIsWHNF (Lam b e) = isId b || exprIsWHNF e
-exprIsWHNF (Note _ e) = exprIsWHNF e
-exprIsWHNF (Let _ e) = False
-exprIsWHNF (Case _ _ _) = False
-exprIsWHNF (Con con _) = isWHNFCon con
-exprIsWHNF e@(App _ _) = case collectArgs e of
- (Var v, args) -> n_val_args == 0 ||
- fun_arity > n_val_args ||
- v_uniq == buildIdKey ||
- v_uniq == augmentIdKey
- where
- n_val_args = valArgCount args
- fun_arity = arityLowerBound (getIdArity v)
- v_uniq = idUnique v
-
- _ -> False
+exprIsValue (Lit l) = True
+exprIsValue (Lam b e) = isRuntimeVar b || exprIsValue e
+exprIsValue (Note _ e) = exprIsValue e
+exprIsValue (Var v) = idArity v > 0 || isEvaldUnfolding (idUnfolding v)
+ -- The idArity case catches data cons and primops that
+ -- don't have unfoldings
+ -- A worry: what if an Id's unfolding is just itself:
+ -- then we could get an infinite loop...
+exprIsValue other_expr
+ | (Var fun, args) <- collectArgs other_expr,
+ isDataConId fun || valArgCount args < idArity fun
+ = check (idType fun) args
+ | otherwise
+ = False
+ where
+ -- 'check' checks that unlifted-type args are in
+ -- fact guaranteed non-divergent
+ check fun_ty [] = True
+ check fun_ty (Type _ : args) = case splitForAllTy_maybe fun_ty of
+ Just (_, ty) -> check ty args
+ check fun_ty (arg : args)
+ | isUnLiftedType arg_ty = exprOkForSpeculation arg
+ | otherwise = check res_ty args
+ where
+ (arg_ty, res_ty) = splitFunTy fun_ty
+\end{code}
+
+\begin{code}
+exprIsConApp_maybe :: CoreExpr -> Maybe (DataCon, [CoreExpr])
+exprIsConApp_maybe (Note (Coerce to_ty from_ty) expr)
+ = -- Maybe this is over the top, but here we try to turn
+ -- coerce (S,T) ( x, y )
+ -- effectively into
+ -- ( coerce S x, coerce T y )
+ -- This happens in anger in PrelArrExts which has a coerce
+ -- case coerce memcpy a b of
+ -- (# r, s #) -> ...
+ -- where the memcpy is in the IO monad, but the call is in
+ -- the (ST s) monad
+ case exprIsConApp_maybe expr of {
+ Nothing -> Nothing ;
+ Just (dc, args) ->
+
+ case splitTyConApp_maybe to_ty of {
+ Nothing -> Nothing ;
+ Just (tc, tc_arg_tys) | tc /= dataConTyCon dc -> Nothing
+ | isExistentialDataCon dc -> Nothing
+ | otherwise ->
+ -- Type constructor must match
+ -- We knock out existentials to keep matters simple(r)
+ let
+ arity = tyConArity tc
+ val_args = drop arity args
+ to_arg_tys = dataConArgTys dc tc_arg_tys
+ mk_coerce ty arg = mkCoerce ty (exprType arg) arg
+ new_val_args = zipWith mk_coerce to_arg_tys val_args
+ in
+ ASSERT( all isTypeArg (take arity args) )
+ ASSERT( equalLength val_args to_arg_tys )
+ Just (dc, map Type tc_arg_tys ++ new_val_args)
+ }}
+
+exprIsConApp_maybe (Note _ expr)
+ = exprIsConApp_maybe expr
+ -- We ignore InlineMe notes in case we have
+ -- x = __inline_me__ (a,b)
+ -- All part of making sure that INLINE pragmas never hurt
+ -- Marcin tripped on this one when making dictionaries more inlinable
+ --
+ -- In fact, we ignore all notes. For example,
+ -- case _scc_ "foo" (C a b) of
+ -- C a b -> e
+ -- should be optimised away, but it will be only if we look
+ -- through the SCC note.
+
+exprIsConApp_maybe expr = analyse (collectArgs expr)
+ where
+ analyse (Var fun, args)
+ | Just con <- isDataConId_maybe fun,
+ args `lengthAtLeast` dataConRepArity con
+ -- Might be > because the arity excludes type args
+ = Just (con,args)
+
+ -- Look through unfoldings, but only cheap ones, because
+ -- we are effectively duplicating the unfolding
+ analyse (Var fun, [])
+ | let unf = idUnfolding fun,
+ isCheapUnfolding unf
+ = exprIsConApp_maybe (unfoldingTemplate unf)
+
+ analyse other = Nothing
+\end{code}
+
+
+
+%************************************************************************
+%* *
+\subsection{Eta reduction and expansion}
+%* *
+%************************************************************************
+
+\begin{code}
+exprEtaExpandArity :: CoreExpr -> Arity
+-- The Int is number of value args the thing can be
+-- applied to without doing much work
+--
+-- This is used when eta expanding
+-- e ==> \xy -> e x y
+--
+-- It returns 1 (or more) to:
+-- case x of p -> \s -> ...
+-- because for I/O ish things we really want to get that \s to the top.
+-- We are prepared to evaluate x each time round the loop in order to get that
+
+-- It's all a bit more subtle than it looks. Consider one-shot lambdas
+-- let x = expensive in \y z -> E
+-- We want this to have arity 2 if the \y-abstraction is a 1-shot lambda
+-- Hence the ArityType returned by arityType
+
+-- NB: this is particularly important/useful for IO state
+-- transformers, where we often get
+-- let x = E in \ s -> ...
+-- and the \s is a real-world state token abstraction. Such
+-- abstractions are almost invariably 1-shot, so we want to
+-- pull the \s out, past the let x=E.
+-- The hack is in Id.isOneShotLambda
+--
+-- Consider also
+-- f = \x -> error "foo"
+-- Here, arity 1 is fine. But if it is
+-- f = \x -> case e of
+-- True -> error "foo"
+-- False -> \y -> x+y
+-- then we want to get arity 2.
+-- Hence the ABot/ATop in ArityType
+
+
+exprEtaExpandArity e = arityDepth (arityType e)
+
+-- A limited sort of function type
+data ArityType = AFun Bool ArityType -- True <=> one-shot
+ | ATop -- Know nothing
+ | ABot -- Diverges
+
+arityDepth :: ArityType -> Arity
+arityDepth (AFun _ ty) = 1 + arityDepth ty
+arityDepth ty = 0
+
+andArityType ABot at2 = at2
+andArityType ATop at2 = ATop
+andArityType (AFun t1 at1) (AFun t2 at2) = AFun (t1 && t2) (andArityType at1 at2)
+andArityType at1 at2 = andArityType at2 at1
+
+arityType :: CoreExpr -> ArityType
+ -- (go1 e) = [b1,..,bn]
+ -- means expression can be rewritten \x_b1 -> ... \x_bn -> body
+ -- where bi is True <=> the lambda is one-shot
+
+arityType (Note n e) = arityType e
+-- Not needed any more: etaExpand is cleverer
+-- | ok_note n = arityType e
+-- | otherwise = ATop
+
+arityType (Var v)
+ = mk (idArity v)
+ where
+ mk :: Arity -> ArityType
+ mk 0 | isBottomingId v = ABot
+ | otherwise = ATop
+ mk n = AFun False (mk (n-1))
+
+ -- When the type of the Id encodes one-shot-ness,
+ -- use the idinfo here
+
+ -- Lambdas; increase arity
+arityType (Lam x e) | isId x = AFun (isOneShotLambda x) (arityType e)
+ | otherwise = arityType e
+
+ -- Applications; decrease arity
+arityType (App f (Type _)) = arityType f
+arityType (App f a) = case arityType f of
+ AFun one_shot xs | one_shot -> xs
+ | exprIsCheap a -> xs
+ other -> ATop
+
+ -- Case/Let; keep arity if either the expression is cheap
+ -- or it's a 1-shot lambda
+arityType (Case scrut _ alts) = case foldr1 andArityType [arityType rhs | (_,_,rhs) <- alts] of
+ xs@(AFun one_shot _) | one_shot -> xs
+ xs | exprIsCheap scrut -> xs
+ | otherwise -> ATop
+
+arityType (Let b e) = case arityType e of
+ xs@(AFun one_shot _) | one_shot -> xs
+ xs | all exprIsCheap (rhssOfBind b) -> xs
+ | otherwise -> ATop
+
+arityType other = ATop
+
+{- NOT NEEDED ANY MORE: etaExpand is cleverer
+ok_note InlineMe = False
+ok_note other = True
+ -- Notice that we do not look through __inline_me__
+ -- This may seem surprising, but consider
+ -- f = _inline_me (\x -> e)
+ -- We DO NOT want to eta expand this to
+ -- f = \x -> (_inline_me (\x -> e)) x
+ -- because the _inline_me gets dropped now it is applied,
+ -- giving just
+ -- f = \x -> e
+ -- A Bad Idea
+-}
\end{code}
+
\begin{code}
-exprArity :: CoreExpr -> Int -- How many value lambdas are at the top
-exprArity (Lam b e) | isTyVar b = exprArity e
- | otherwise = 1 + exprArity e
-exprArity other = 0
+etaExpand :: Arity -- Result should have this number of value args
+ -> [Unique]
+ -> CoreExpr -> Type -- Expression and its type
+ -> CoreExpr
+-- (etaExpand n us e ty) returns an expression with
+-- the same meaning as 'e', but with arity 'n'.
+--
+-- Given e' = etaExpand n us e ty
+-- We should have
+-- ty = exprType e = exprType e'
+
+etaExpand n us expr ty
+ | manifestArity expr >= n = expr -- The no-op case
+ | otherwise = eta_expand n us expr ty
+ where
+
+-- manifestArity sees how many leading value lambdas there are
+manifestArity :: CoreExpr -> Arity
+manifestArity (Lam v e) | isId v = 1 + manifestArity e
+ | otherwise = manifestArity e
+manifestArity (Note _ e) = manifestArity e
+manifestArity e = 0
+
+-- etaExpand deals with for-alls. For example:
+-- etaExpand 1 E
+-- where E :: forall a. a -> a
+-- would return
+-- (/\b. \y::a -> E b y)
+--
+-- It deals with coerces too, though they are now rare
+-- so perhaps the extra code isn't worth it
+
+eta_expand n us expr ty
+ | n == 0 &&
+ -- The ILX code generator requires eta expansion for type arguments
+ -- too, but alas the 'n' doesn't tell us how many of them there
+ -- may be. So we eagerly eta expand any big lambdas, and just
+ -- cross our fingers about possible loss of sharing in the
+ -- ILX case.
+ -- The Right Thing is probably to make 'arity' include
+ -- type variables throughout the compiler. (ToDo.)
+ not (isForAllTy ty)
+ -- Saturated, so nothing to do
+ = expr
+
+eta_expand n us (Note note@(Coerce _ ty) e) _
+ = Note note (eta_expand n us e ty)
+
+ -- Use mkNote so that _scc_s get pushed inside any lambdas that
+ -- are generated as part of the eta expansion. We rely on this
+ -- behaviour in CorePrep, when we eta expand an already-prepped RHS.
+eta_expand n us (Note note e) ty
+ = mkNote note (eta_expand n us e ty)
+
+ -- Short cut for the case where there already
+ -- is a lambda; no point in gratuitously adding more
+eta_expand n us (Lam v body) ty
+ | isTyVar v
+ = Lam v (eta_expand n us body (applyTy ty (mkTyVarTy v)))
+
+ | otherwise
+ = Lam v (eta_expand (n-1) us body (funResultTy ty))
+
+eta_expand n us expr ty
+ = case splitForAllTy_maybe ty of {
+ Just (tv,ty') -> Lam tv (eta_expand n us (App expr (Type (mkTyVarTy tv))) ty')
+
+ ; Nothing ->
+
+ case splitFunTy_maybe ty of {
+ Just (arg_ty, res_ty) -> Lam arg1 (eta_expand (n-1) us2 (App expr (Var arg1)) res_ty)
+ where
+ arg1 = mkSysLocal SLIT("eta") uniq arg_ty
+ (uniq:us2) = us
+
+ ; Nothing ->
+
+ case splitNewType_maybe ty of {
+ Just ty' -> mkCoerce ty ty' (eta_expand n us (mkCoerce ty' ty expr) ty') ;
+ Nothing -> pprTrace "Bad eta expand" (ppr expr $$ ppr ty) expr
+ }}}
\end{code}
+exprArity is a cheap-and-cheerful version of exprEtaExpandArity.
+It tells how many things the expression can be applied to before doing
+any work. It doesn't look inside cases, lets, etc. The idea is that
+exprEtaExpandArity will do the hard work, leaving something that's easy
+for exprArity to grapple with. In particular, Simplify uses exprArity to
+compute the ArityInfo for the Id.
+
+Originally I thought that it was enough just to look for top-level lambdas, but
+it isn't. I've seen this
+
+ foo = PrelBase.timesInt
+
+We want foo to get arity 2 even though the eta-expander will leave it
+unchanged, in the expectation that it'll be inlined. But occasionally it
+isn't, because foo is blacklisted (used in a rule).
+
+Similarly, see the ok_note check in exprEtaExpandArity. So
+ f = __inline_me (\x -> e)
+won't be eta-expanded.
+
+And in any case it seems more robust to have exprArity be a bit more intelligent.
+But note that (\x y z -> f x y z)
+should have arity 3, regardless of f's arity.
+
+\begin{code}
+exprArity :: CoreExpr -> Arity
+exprArity e = go e
+ where
+ go (Var v) = idArity v
+ go (Lam x e) | isId x = go e + 1
+ | otherwise = go e
+ go (Note n e) = go e
+ go (App e (Type t)) = go e
+ go (App f a) | exprIsCheap a = (go f - 1) `max` 0
+ -- NB: exprIsCheap a!
+ -- f (fac x) does not have arity 2,
+ -- even if f has arity 3!
+ -- NB: `max 0`! (\x y -> f x) has arity 2, even if f is
+ -- unknown, hence arity 0
+ go _ = 0
+\end{code}
%************************************************************************
%* *
\begin{code}
cheapEqExpr :: Expr b -> Expr b -> Bool
-cheapEqExpr (Var v1) (Var v2) = v1==v2
-cheapEqExpr (Con con1 args1) (Con con2 args2)
- = con1 == con2 &&
- and (zipWithEqual "cheapEqExpr" cheapEqExpr args1 args2)
+cheapEqExpr (Var v1) (Var v2) = v1==v2
+cheapEqExpr (Lit lit1) (Lit lit2) = lit1 == lit2
+cheapEqExpr (Type t1) (Type t2) = t1 `eqType` t2
cheapEqExpr (App f1 a1) (App f2 a2)
= f1 `cheapEqExpr` f2 && a1 `cheapEqExpr` a2
-cheapEqExpr (Type t1) (Type t2) = t1 == t2
-
cheapEqExpr _ _ = False
+
+exprIsBig :: Expr b -> Bool
+-- Returns True of expressions that are too big to be compared by cheapEqExpr
+exprIsBig (Lit _) = False
+exprIsBig (Var v) = False
+exprIsBig (Type t) = False
+exprIsBig (App f a) = exprIsBig f || exprIsBig a
+exprIsBig other = True
\end{code}
\begin{code}
eqExpr :: CoreExpr -> CoreExpr -> Bool
-- Works ok at more general type, but only needed at CoreExpr
+ -- Used in rule matching, so when we find a type we use
+ -- eqTcType, which doesn't look through newtypes
+ -- [And it doesn't risk falling into a black hole either.]
eqExpr e1 e2
= eq emptyVarEnv e1 e2
where
Just v1' -> v1' == v2
Nothing -> v1 == v2
- eq env (Con c1 es1) (Con c2 es2) = c1 == c2 && eq_list env es1 es2
+ eq env (Lit lit1) (Lit lit2) = lit1 == lit2
eq env (App f1 a1) (App f2 a2) = eq env f1 f2 && eq env a1 a2
eq env (Lam v1 e1) (Lam v2 e2) = eq (extendVarEnv env v1 v2) e1 e2
eq env (Let (NonRec v1 r1) e1)
(Let (NonRec v2 r2) e2) = eq env r1 r2 && eq (extendVarEnv env v1 v2) e1 e2
eq env (Let (Rec ps1) e1)
- (Let (Rec ps2) e2) = length ps1 == length ps2 &&
+ (Let (Rec ps2) e2) = equalLength ps1 ps2 &&
and (zipWith eq_rhs ps1 ps2) &&
eq env' e1 e2
where
eq_rhs (_,r1) (_,r2) = eq env' r1 r2
eq env (Case e1 v1 a1)
(Case e2 v2 a2) = eq env e1 e2 &&
- length a1 == length a2 &&
+ equalLength a1 a2 &&
and (zipWith (eq_alt env') a1 a2)
where
env' = extendVarEnv env v1 v2
eq env (Note n1 e1) (Note n2 e2) = eq_note env n1 n2 && eq env e1 e2
- eq env (Type t1) (Type t2) = t1 == t2
+ eq env (Type t1) (Type t2) = t1 `eqType` t2
eq env e1 e2 = False
eq_list env [] [] = True
eq (extendVarEnvList env (vs1 `zip` vs2)) r1 r2
eq_note env (SCC cc1) (SCC cc2) = cc1 == cc2
- eq_note env (Coerce f1 t1) (Coerce f2 t2) = f1==f2 && t1==t2
+ eq_note env (Coerce t1 f1) (Coerce t2 f2) = t1 `eqType` t2 && f1 `eqType` f2
eq_note env InlineCall InlineCall = True
eq_note env other1 other2 = False
\end{code}
+
+%************************************************************************
+%* *
+\subsection{The size of an expression}
+%* *
+%************************************************************************
+
+\begin{code}
+coreBindsSize :: [CoreBind] -> Int
+coreBindsSize bs = foldr ((+) . bindSize) 0 bs
+
+exprSize :: CoreExpr -> Int
+ -- A measure of the size of the expressions
+ -- It also forces the expression pretty drastically as a side effect
+exprSize (Var v) = v `seq` 1
+exprSize (Lit lit) = lit `seq` 1
+exprSize (App f a) = exprSize f + exprSize a
+exprSize (Lam b e) = varSize b + exprSize e
+exprSize (Let b e) = bindSize b + exprSize e
+exprSize (Case e b as) = exprSize e + varSize b + foldr ((+) . altSize) 0 as
+exprSize (Note n e) = noteSize n + exprSize e
+exprSize (Type t) = seqType t `seq` 1
+
+noteSize (SCC cc) = cc `seq` 1
+noteSize (Coerce t1 t2) = seqType t1 `seq` seqType t2 `seq` 1
+noteSize InlineCall = 1
+noteSize InlineMe = 1
+
+varSize :: Var -> Int
+varSize b | isTyVar b = 1
+ | otherwise = seqType (idType b) `seq`
+ megaSeqIdInfo (idInfo b) `seq`
+ 1
+
+varsSize = foldr ((+) . varSize) 0
+
+bindSize (NonRec b e) = varSize b + exprSize e
+bindSize (Rec prs) = foldr ((+) . pairSize) 0 prs
+
+pairSize (b,e) = varSize b + exprSize e
+
+altSize (c,bs,e) = c `seq` varsSize bs + exprSize e
+\end{code}
+
+
+%************************************************************************
+%* *
+\subsection{Hashing}
+%* *
+%************************************************************************
+
+\begin{code}
+hashExpr :: CoreExpr -> Int
+hashExpr e | hash < 0 = 77 -- Just in case we hit -maxInt
+ | otherwise = hash
+ where
+ hash = abs (hash_expr e) -- Negative numbers kill UniqFM
+
+hash_expr (Note _ e) = hash_expr e
+hash_expr (Let (NonRec b r) e) = hashId b
+hash_expr (Let (Rec ((b,r):_)) e) = hashId b
+hash_expr (Case _ b _) = hashId b
+hash_expr (App f e) = hash_expr f * fast_hash_expr e
+hash_expr (Var v) = hashId v
+hash_expr (Lit lit) = hashLiteral lit
+hash_expr (Lam b _) = hashId b
+hash_expr (Type t) = trace "hash_expr: type" 1 -- Shouldn't happen
+
+fast_hash_expr (Var v) = hashId v
+fast_hash_expr (Lit lit) = hashLiteral lit
+fast_hash_expr (App f (Type _)) = fast_hash_expr f
+fast_hash_expr (App f a) = fast_hash_expr a
+fast_hash_expr (Lam b _) = hashId b
+fast_hash_expr other = 1
+
+hashId :: Id -> Int
+hashId id = hashName (idName id)
+\end{code}