Haskell: Will the GHC optimize this?

Question

Can the GHC simplify id = (\(a, b) -> (a, b)).(\(a, b) -> (a, b))in id = \(a, b) -> (a, b)?

How about a more complicated case:

id (Just x) = Just x
id Nothing = Nothing

map f (Just x) = Just (f x)
map _ Nothing  = Nothing

Will the GHC simplify id . mapin map?

I tried using a simple beta reduction, but it seems that these conditions are not applicable due to unpleasant pattern matching.

So I'm curious how the GHC optimization methods handle this.

Answer 1

ghc, -ddump-simpl. ghc "" , . Core - , Haskell , .

-O2 -ddump-simpl, .

tupid1 :: (a, b) -> (a, b)
tupid1 = (\(a, b) -> (a, b))

tupid2 :: (a, b) -> (a, b)
tupid2 = (\(a, b) -> (a, b)) . (\(a, b) -> (a, b))

​​ tupid1 .

-- RHS size: {terms: 4, types: 7, coercions: 0}
tupid1 :: forall a_aqo b_aqp. (a_aqo, b_aqp) -> (a_aqo, b_aqp)
[GblId,
 Arity=1,
 Caf=NoCafRefs,
 Str=DmdType <S,1*U(U,U)>m,
 Unf=Unf{Src=InlineStable, TopLvl=True, Value=True, ConLike=True,
         WorkFree=True, Expandable=True,
         Guidance=ALWAYS_IF(arity=1,unsat_ok=True,boring_ok=True)
         Tmpl= \ (@ a_ayd)
                 (@ b_aye)
                 (ds_dIl [Occ=Once] :: (a_ayd, b_aye)) ->
                 ds_dIl}]
tupid1 = \ (@ a_ayd) (@ b_aye) (ds_dIl :: (a_ayd, b_aye)) -> ds_dIl

. tupid1 , a_ayd b_aye, a b . ds_dIl, (ds_dIl :: (a_ayd, b_aye)) .

: tupid2...

-- RHS size: {terms: 1, types: 0, coercions: 0}
tupid2 :: forall a_aqm b_aqn. (a_aqm, b_aqn) -> (a_aqm, b_aqn)
[GblId,
 Arity=1,
 Caf=NoCafRefs,
 Str=DmdType <S,1*U(U,U)>m,
 Unf=Unf{Src=InlineStable, TopLvl=True, Value=True, ConLike=True,
         WorkFree=True, Expandable=True,
         Guidance=ALWAYS_IF(arity=1,unsat_ok=True,boring_ok=True)
         Tmpl= \ (@ a_axZ) (@ b_ay0) (x_aIw [Occ=Once] :: (a_axZ, b_ay0)) ->
                 x_aIw}]
tupid2 = tupid1

... ghc tupid1! , .

---

Maybe

maybeid :: Maybe a -> Maybe a
maybeid (Just x) = Just x
maybeid Nothing = Nothing

-- RHS size: {terms: 3, types: 4, coercions: 0}
maybeid :: forall a_aqn. Maybe a_aqn -> Maybe a_aqn
[GblId,
 Arity=1,
 Caf=NoCafRefs,
 Str=DmdType <S,1*U>,
 Unf=Unf{Src=InlineStable, TopLvl=True, Value=True, ConLike=True,
         WorkFree=True, Expandable=True,
         Guidance=ALWAYS_IF(arity=1,unsat_ok=True,boring_ok=True)
         Tmpl= \ (@ a_aqI) (ds_dIq [Occ=Once] :: Maybe a_aqI) -> ds_dIq}]
maybeid = \ (@ a_aqI) (ds_dIq :: Maybe a_aqI) -> ds_dIq

map Maybe

maybemap :: (a -> b) -> Maybe a -> Maybe b
maybemap f (Just x) = Just (f x)
maybemap _ Nothing = Nothing

maybeid

maybeidmap :: (a -> b) -> Maybe a -> Maybe b
maybeidmap f = maybeid . maybemap f

ghc maybemap

-- RHS size: {terms: 1, types: 0, coercions: 0}
maybeidmap
  :: forall a_aqp b_aqq.
     (a_aqp -> b_aqq) -> Maybe a_aqp -> Maybe b_aqq
[GblId,
 Arity=2,
 Caf=NoCafRefs,
 Str=DmdType <L,1*C1(U)><S,1*U>,
 Unf=Unf{Src=InlineStable, TopLvl=True, Value=True, ConLike=True,
         WorkFree=True, Expandable=True,
         Guidance=ALWAYS_IF(arity=0,unsat_ok=True,boring_ok=True)
         Tmpl= maybemap}]
maybeidmap = maybemap

, id f.

maybemapid :: (a -> b) -> Maybe a -> Maybe b
maybemapid f = maybemap (id . f)

The composition with the identity function is deleted, and the whole function is simplified to maybemap

-- RHS size: {terms: 1, types: 0, coercions: 0}
maybemapid
  :: forall a_aqq b_aqr.
     (a_aqq -> b_aqr) -> Maybe a_aqq -> Maybe b_aqr
[GblId,
 Arity=2,
 Caf=NoCafRefs,
 Str=DmdType <L,1*C1(U)><S,1*U>,
 Unf=Unf{Src=InlineStable, TopLvl=True, Value=True, ConLike=True,
         WorkFree=True, Expandable=True,
         Guidance=ALWAYS_IF(arity=2,unsat_ok=True,boring_ok=False)
         Tmpl= \ (@ a_ar2)
                 (@ b_ar3)
                 (f_aqL [Occ=Once!] :: a_ar2 -> b_ar3)
                 (eta_B1 [Occ=Once!] :: Maybe a_ar2) ->
                 case eta_B1 of _ [Occ=Dead] {
                   Nothing -> GHC.Base.Nothing @ b_ar3;
                   Just x_aqJ [Occ=Once] -> GHC.Base.Just @ b_ar3 (f_aqL x_aqJ)
                 }}]
maybemapid = maybemap