Applicative donotation
This is a proposal to add support to GHC for desugaring donotation into Applicative expressions where possible.
It's described in some detail in the paper: Desugaring Haskell’s donotation Into Applicative Operations (ICFP'16).
An implementation was merged for GHC8: https://github.com/ghc/ghc/commit/8ecf6d8f7dfee9e5b1844cd196f83f00f3b6b879.
See also RecursiveDo
Tickets
See the ApplicativeDo label.
Summary
ApplicativeDo
is a language extension enabled in the usual way via
{# LANGUAGE ApplicativeDo #}
When ApplicativeDo
is turned on, GHC will use a different method for desugaring do
notation, which attempts to use the Applicative
operator <*>
as far as possible, along with fmap
and join
.
ApplicativeDo
makes it possible to use do
notation for types that are Applicative
but not Monad
. (See examples below).
For a type that is a Monad
, ApplicativeDo
implements the same semantics as the standard do
notation desugaring, provided <*>
= ap
for this type.
ApplicativeDo
respects RebindableSyntax
: it will pick up whatever <*>
, fmap
, and join
are in scope when RebindableSyntax
is on.
Motivation

Some Monads have the property that Applicative bind is more efficient than Monad bind. Sometimes this is really important, such as when the Applicative bind is concurrent whereas the Monad bind is sequential (c.f. Haxl). For these monads we would like the donotation to desugar to Applicative bind where possible, to take advantage of the improved behaviour but without forcing the user to explicitly choose.

Applicative syntax can be a bit obscure and hard to write. Donotation is more natural, so we would like to be able to write Applicative composition in donotation where possible. For example:
(\x y z > x*y + y*z + z*x) <$> expr1 <*> expr2 <*> expr3
vs.
do x < expr1; y < expr2; z < expr3; return (x*y + y*z + z*x)
Example 1
do
x < a
y < b
return (f x y)
This translates to
(\x y > f x y) <$> a <*> b
Here we noticed that the statements x < a
and y < b
are independent, so we can make an Applicative
expression. Note that the desugared version uses the operators <$>
and <*>
, so its inferred type will mention Applicative
only rather than Monad
. Therefore this do
block will work for a type that is Applicative
but not Monad
.
Example 2
If the final statement does not have a return
, then we need to use join
:
do
x < a
y < b
f x y
Translates to
join ((\x y > f x y) <$> a <*> b)
Since join
is a Monad
operation, this expression requires Monad
.
Example 3
do
x1 < A
x2 < B
x3 < C x1
x4 < D x2
return (x1,x2,x3,x4)
Here we can do A
and B
together, and C
and D
together. We could do it like this:
do
(x1,x2) < (,) <$> A <*> B
(\x3 x4 > (x1,x2,x3,x4)) <$> C x1 <*> D x2
But it is slightly more elegant like this:
join ((\x1 x2 > (\x3 x4 > (x1,x2,x3,x4)) <$> C x1 <*> D x2)) <$> A <*> B)
because we avoid the intermediate tuple.
Example 4
do
x < A
y < B x
z < C
return (f x y z)
Now we have a dependency: y
depends on x
, but there is still an opportunity to use Applicative
since z
does not depend on x
or y
. In this case we end up with:
(\(x,y) z > f x y z) <$> (do x < A; y < B x; return (x,y)) <*> C
Note that we had to introduce a tuple to return both the values of x
and y
from the inner do
expression
It's important that we keep the original ordering. For example, we don't want this:
do
(x,z) < (,) <$> A <*> C
y < B x
return (f x y z)
because this has a different semantics from the standard 'do' desugaring; a Monad
that cares about ordering will expose the difference.
Another wrong result would be:
do
x < A
(\y z > f x y z) <$> B x <*> C
Because this version has less parallelism than the first result, in which A
and B
could be performed at the same time as C
.
Example 5
In general, ApplicativeDo
might have to build a complicated nested Applicative
expression.
do
x1 < a
x2 < b
x3 < c x1
x4 < d
return (x2,x3,x4)
Here we can do a/b/d
in parallel, but c
depends on x1
, which makes things a bit tricky: remember that we have to retain the semantics of standard do
desugaring, so we can't move the call to c
after the call to d
.
This translates to
(\(x2,x3) x4 > (x2, x3, x4))
<$> join ((\x1 x2 > do
x3 < c x1
return (x2,x3))
<$> a
<*> b)
<*> d)
We can write this expression in a simpler way using 
for applicative composition (like parallel composition) and ;
for monadic composition (like sequential composition): ((a  b) ; c)  d
.
Note that this isn't the only good way to translate this expression, this is also possible: (a ; (b  c))  d
. It's not possible to know which is better. ApplicativeDo
makes a besteffort attempt to use parallel composition where possible while retaining the semantics of the standard 'do' desugaring.
Syntax & spec
There's a toy implementation which includes the syntax, desugaring, transformation and some examples here: https://github.com/simonmar/ado/blob/52ba028cad68af578bcdfb3f1c5b905f5b9c5617/adosim.hs
Syntax:
expr ::= ...  do {stmt_1; ..; stmt_n} expr  ...
stmt ::= pat < expr
 (arg_1  ...  arg_n)  applicative composition, n>=1
 ...  other kinds of statement (e.g. let)
arg ::= pat < expr
 {stmt_1; ..; stmt_n} {var_1..var_n}
Desugaring for do stmts
:
dsDo {} expr = expr
dsDo {pat < rhs; stmts} expr =
rhs >>= \pat > dsDo stmts expr
dsDo {(arg_1  ...  arg_n)} (return expr) =
(\argpat (arg_1) .. argpat(arg_n) > expr)
<$> argexpr(arg_1)
<*> ...
<*> argexpr(arg_n)
dsDo {(arg_1  ...  arg_n); stmts} expr =
join (\argpat (arg_1) .. argpat(arg_n) > dsDo stmts expr)
<$> argexpr(arg_1)
<*> ...
<*> argexpr(arg_n)
where
argpat (pat < expr) = pat
argpat ({stmt_1; ..; stmt_n} {var_1..var_n}) = (var_1, .., var_n)
argexpr (pat < expr) = expr
argexpr ({stmt_1; ..; stmt_n} {var_1..var_n}) =
dsDo {stmt_1; ..; stmt_n; return (var_1, ..., var_n)}
Transformation
ado {} tail = tail
ado {pat < expr} {return expr'} = (mkArg(pat < expr)); return expr'
ado {one} tail = one : tail
ado stmts tail
 n == 1 = ado before (ado after tail) where (before,after) = split(stmts_1)
 n > 1 = (mkArg(stmts_1)  ...  mkArg(stmts_n)); tail
where
{stmts_1 .. stmts_n} = segments(stmts)
segments(stmts) =
 divide stmts into segments with no interdependencies
mkArg({pat < expr}) = (pat < expr)
mkArg({stmt_1; ...; stmt_n}) =
{stmt_1; ...; stmt_n} {vars(stmt_1) u .. u vars(stmt_n)}
split({stmt_1; ..; stmt_n) =
({stmt_1; ..; stmt_i}, {stmt_i+1; ..; stmt_n})
 1 <= i <= n
 i is a good place to insert a bind
Differences from the actual implementation

The final expr in a "do" is a LastStmt, instead of being carried around separately.

there is no stripping of "return" during desugaring, it is handled earlier in the renamer instead.

arg has an optional "return", for the same reason as (2)
(2) and (3) are so that we can typecheck the syntax without having to desugar it first.
The syntax and desugaring rules are:
expr ::= ...  do {stmt_1; ..; stmt_n}  ...
stmt ::= expr  last stmt in a "do" must be this
 pat < expr
 (arg_1  ...  arg_n)
 join (arg_1  ...  arg_n)
 ...
arg ::= pat < expr
 {stmt_1..stmt_n} {var_1..var_n} maybe_return
maybe_return ::= return  ()
dsDo {expr} = expr
dsDo {pat < rhs; stmts} =
rhs >>= \pat > dsDo stmts
dsDo {(arg_1  ...  arg_n); stmts} =
(\argpat (arg_1) .. argpat(arg_n) > dsDo stmts)
<$> argexpr(arg_1)
<*> ...
<*> argexpr(arg_n)
dsDo {join (arg_1  ...  arg_n); stmts} =
join (\argpat (arg_1) .. argpat(arg_n) > dsDo stmts)
<$> argexpr(arg_1)
<*> ...
<*> argexpr(arg_n)
where
argpat (pat < expr) = pat
argpat ({stmt_1..stmt_n} {var_1..var_n} _) = (var_1, .., var_n)
argexpr (pat < expr) = expr
argexpr ({stmt_1..stmt_n} {var_1..var_n} ()) =
dsDo {stmt_1; ..; stmt_n; (var_1, ..., var_n)}
argexpr ({stmt_1..stmt_n} {var_1..var_n} return) =
dsDo {stmt_1; ..; stmt_n; return (var_1, ..., var_n)}
Note that there's no matching on "return" during desugaring, the "return" has already been removed.
Related proposals
Implementation
The implementation is tricky, because we want to do a transformation that affects type checking (and renaming, because we might be using RebindableSyntax
), but we still want type errors in terms of the original source code. Therefore we calculate everything necessary to do the transformation during renaming, but leave enough information behind to reconstruct the original source code for the purposes of error messages.
See comments in https://phabricator.haskell.org/D729 for more details.
Tricky case
do { x < A
; y < B
; z < C x
; return (z+y) }
Then we could do A ; (B  C)
or (A  B) ; C
.
 If
tA + (max( tB, tC )) < max( tA, tB ) + tC
, then first is best, otherwise second.
If A is smaller than B and C, first is best. If C is smaller than A and B then second is best.