# Monad comprehensions

After a long absence, monad comprehensions are back, thanks to George Giorgidze and his colleagues. With `{-# LANGUAGE MonadComprehensions #-}`

the comprehension `[f x | x <- xs, x>4 ]`

is interpreted in an arbitrary monad, rather than being restricted to lists. Not only that, it also generalises nicely for parallel/zip and SQL-like comprehensions. The aforementioned generalisations can be turned on by enabling the `MonadComprehensions`

extension in conjunction with the `ParallelListComp`

and `TransformListComp`

extensions.

Rebindable syntax is fully supported for standard monad comprehensions with generators and filters. We also plan to allow rebinding of the parallel/zip and SQL-like monad comprehension notations.

For further details and usage examples, see the paper "Bringing back monad comprehensions" http://db.inf.uni-tuebingen.de/staticfiles/publications/haskell2011.pdf at the 2011 Haskell Symposium.

See ticket #4370 (closed).

## Translation rules

```
Variables : x and y
Expressions : e, f and g
Patterns : w
Qualifiers : p, q and r
```

The main translation rule for monad comprehensions.

`[e | q ] = [| q |] >>= (return . (\q_v -> e))`

`(.)_v`

rules. Note that `_v`

is a postfix rule application.

```
(w <- e)_v = w
(let w = d)_v = w
(g)_v = ()
(p , q)_v = (p_v,q_v)
(p | v)_v = (p_v,q_v)
(q, then f)_v = q_v
(q, then f by e)_v = q_v
(q, then group by e using f)_v = q_v
(q, then group using f)_v = q_v
```

`[|.|]`

rules.

```
[| w <- e |] = e
[| let w = d |] = return d
[| g |] = guard g
[| p, q |] = ([| p |] >>= (return . (\p_v -> [| q |] >>= (return . (\q_v -> (p_v,q_v)))))) >>= id
[| p | q |] = mzip [| p |] [| q |]
[| q, then f |] = f [| q |]
[| q, then f by e |] = f (\q_v -> e) [| q |]
[| q, then group by e using f |] = (f (\q_v -> e) [| q |]) >>= (return . (unzip q_v))
[| q, then group using f |] = (f [| q |]) >>= (return . (unzip q_v))
```

`unzip (.)`

rules. Note that `unzip`

is a desugaring rule (i.e., not a function to be included in the generated code).

```
unzip () = id
unzip x = id
unzip (w1,w2) = \e -> ((unzip w1) (e >>= (return .(\(x,y) -> x))), (unzip w2) (e >>= (return . (\(x,y) -> y))))
```

### Examples

Some translation examples using the do notation to avoid things like pattern matching failures are:

```
[x+y | x <- Just 1, y <- Just 2 ]
-- translates to:
do x <- Just 1
y <- Just 2
return (x+y)
```

Transform statements:

```
[x | x <- [1..], then take 10 ]
-- translates to:
take 10 (do
x <- [1..]
return x)
```

Grouping statements (note the change of types):

```
[(x :: [Int]) | x <- [1,2,1,2], then group by x ] :: [[Int]]
-- translates to:
do x <- mgroupWith (\x -> x) [1,2,1,2]
return x
```

Parallel statements:

```
[x+y | x <- [1,2,3]
| y <- [4,5,6] ]
-- translates to:
do (x,y) <- mzip [1,2,3] [4,5,6]
return (x+y)
```

Note that the actual implementation is **not** using the `do`

-Notation, it's only used here to give a basic overview about how the translation works.

## Implementation details

Monad comprehensions had to change the `StmtLR`

data type in the `GHC/Hs/Expr.lhs`

file in order to be able to lookup and store all functions required to desugare monad comprehensions correctly (e.g. `return`

, `(>>=)`

, `guard`

etc). Renaming is done in `rename/RnExpr.lhs`

and typechecking in `typecheck/TcMatches.lhs`

. The main desugaring is done in `deSugar/DsListComp.lhs`

. If you want to start hacking on monad comprehensions I'd look at those files first.

Some things you might want to be aware of:

[todo]