6.2.8. Monad comprehensions¶

MonadComprehensions
¶ Since: 7.2.1 Enable list comprehension syntax for arbitrary monads.
Monad comprehensions generalise the list comprehension notation, including parallel comprehensions (Parallel List Comprehensions) and transform comprehensions (Generalised (SQLlike) List Comprehensions) to work for any monad.
Monad comprehensions support:
Bindings:
[ x + y  x < Just 1, y < Just 2 ]
Bindings are translated with the
(>>=)
andreturn
functions to the usual donotation:do x < Just 1 y < Just 2 return (x+y)
Guards:
[ x  x < [1..10], x <= 5 ]
Guards are translated with the
guard
function, which requires aMonadPlus
instance:do x < [1..10] guard (x <= 5) return x
Transform statements (as with
TransformListComp
):[ x+y  x < [1..10], y < [1..x], then take 2 ]
This translates to:
do (x,y) < take 2 (do x < [1..10] y < [1..x] return (x,y)) return (x+y)
Group statements (as with
TransformListComp
):[ x  x < [1,1,2,2,3], then group by x using GHC.Exts.groupWith ] [ x  x < [1,1,2,2,3], then group using myGroup ]
Parallel statements (as with
ParallelListComp
):[ (x+y)  x < [1..10]  y < [11..20] ]
Parallel statements are translated using the
mzip
function, which requires aMonadZip
instance defined in Control.Monad.Zip:do (x,y) < mzip (do x < [1..10] return x) (do y < [11..20] return y) return (x+y)
All these features are enabled by default if the MonadComprehensions
extension is enabled. The types and more detailed examples on how to use
comprehensions are explained in the previous chapters
Generalised (SQLlike) List Comprehensions and
Parallel List Comprehensions. In general you just have to replace
the type [a]
with the type Monad m => m a
for monad
comprehensions.
Note
Even though most of these examples are using the list monad, monad
comprehensions work for any monad. The base
package offers all
necessary instances for lists, which make MonadComprehensions
backward compatible to builtin, transform and parallel list
comprehensions.
More formally, the desugaring is as follows. We write D[ e  Q]
to
mean the desugaring of the monad comprehension [ e  Q]
:
Expressions: e
Declarations: d
Lists of qualifiers: Q,R,S
 Basic forms
D[ e  ] = return e
D[ e  p < e, Q ] = e >>= \p > D[ e  Q ]
D[ e  e, Q ] = guard e >> \p > D[ e  Q ]
D[ e  let d, Q ] = let d in D[ e  Q ]
 Parallel comprehensions (iterate for multiple parallel branches)
D[ e  (Q  R), S ] = mzip D[ Qv  Q ] D[ Rv  R ] >>= \(Qv,Rv) > D[ e  S ]
 Transform comprehensions
D[ e  Q then f, R ] = f D[ Qv  Q ] >>= \Qv > D[ e  R ]
D[ e  Q then f by b, R ] = f (\Qv > b) D[ Qv  Q ] >>= \Qv > D[ e  R ]
D[ e  Q then group using f, R ] = f D[ Qv  Q ] >>= \ys >
case (fmap selQv1 ys, ..., fmap selQvn ys) of
Qv > D[ e  R ]
D[ e  Q then group by b using f, R ] = f (\Qv > b) D[ Qv  Q ] >>= \ys >
case (fmap selQv1 ys, ..., fmap selQvn ys) of
Qv > D[ e  R ]
where Qv is the tuple of variables bound by Q (and used subsequently)
selQvi is a selector mapping Qv to the ith component of Qv
Operator Standard binding Expected type

return GHC.Base t1 > m t2
(>>=) GHC.Base m1 t1 > (t2 > m2 t3) > m3 t3
(>>) GHC.Base m1 t1 > m2 t2 > m3 t3
guard Control.Monad t1 > m t2
fmap GHC.Base forall a b. (a>b) > n a > n b
mzip Control.Monad.Zip forall a b. m a > m b > m (a,b)
The comprehension should typecheck when its desugaring would typecheck,
except that (as discussed in Generalised (SQLlike) List Comprehensions) in the
“then f
” and “then group using f
” clauses, when the “by b
” qualifier
is omitted, argument f
should have a polymorphic type. In particular, “then
Data.List.sort
” and “then group using Data.List.group
” are
insufficiently polymorphic.
Monad comprehensions support rebindable syntax
(Rebindable syntax and the implicit Prelude import). Without rebindable syntax, the operators
from the “standard binding” module are used; with rebindable syntax, the
operators are looked up in the current lexical scope. For example,
parallel comprehensions will be typechecked and desugared using whatever
“mzip
” is in scope.
The rebindable operators must have the “Expected type” given in the table above. These types are surprisingly general. For example, you can use a bind operator with the type
(>>=) :: T x y a > (a > T y z b) > T x z b
In the case of transform comprehensions, notice that the groups are
parameterised over some arbitrary type n
(provided it has an
fmap
, as well as the comprehension being over an arbitrary monad.