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# Comprehensive comprehensions

As part of his final year work at Cambridge, Max Bolingbroke worked on implementing the "Comprehensive Comprehensions" described in a paper available here in GHC. A patch with the complete functionality described here was integrated into GHCs HEAD branch on the 20th December 2007.

## Ordering Syntax

The paper uses a syntax based around the new keywords "order" and "by". For example:

[ (name, salary) | (name, dept, salary) <- employees , salary > 70 , order by salary ]

It has been noted that introducing a new keyword may not be desirable, especially given the fact that you can use "order" to achieve things which aren't really ordering:

[ (the dept, sum salary) | (name, dept, salary) <- employees , order by salary , order by salary < 50 using takeWhile , order using take 5 ]

For those reasons, Max's implementation was initially based around the syntax proposed in section 6.1 of the paper:

[ (the dept, sum salary) | (name, dept, salary) <- employees , then sortWith by salary , then takeWhile by salary < 50 , then take 5 ]

This reuses the "then" keyword and is probably less confusing. However, no final decision has been made on the optimal syntax: in particular it might be better to write:

[ (the dept, sum salary) | (name, dept, salary) <- employees , then sortWith using salary , then takeWhile using salary < 50 , then take 5 ]

Suggestions?

## Grouping Syntax

Some of the same concerns about keyword introduction apply here, but ordering is being implemented first so not much thought has been given to syntax improvements. The main suggestion from the paper is:

[ (the dept, sum salary) | (name, dept, salary) <- employees , group by dept ]

We could equally well substitute "using" for the "by" if desired:

[ (the dept, sum salary) | (name, dept, salary) <- employees , group using dept ]

Or we could even do an implicit call to "the" on the grouped-by variables:

[ (the_dept, namesalary) | (name, dept, salary) <- employees , the_dept <- group by dept where (name,salary) -> namesalary ]

We would be interested in hearing peoples thoughts on these issues.

SPJ, after looking at the issues above, has decided that Max's implementation should at least initially be based on syntax like this:

then group by dept using groupWith then group by dept -- The function groupWith is implicit here then group using runs 3 -- The runs function has type [a] -> [[a]] rather than the (a -> t) -> [a] -> [[a]] type required if you used "by"

## Bracketing Syntax

Due to the generality added to comprehensions by the paper, it now makes sense to allow bracketing of qualifiers. An example from the paper is:

xs = [1,2] ys = [3,4] zs = [5,6] p1 = [ (x,y,z) | ( x <- xs | y <- ys ) , z <- zs ] p2 = [ (x,y,z) | x <- xs | ( y <- ys , z <- zs ) ]

This results in:

p1 = [(1,3,5), (1,3,6), (2,4,5), (2,4,6)] p2 = [(1,3,5), (2,3,6)]

Unfortunately, there is a practical problem with using brackets in this way: doing so causes a reduce/reduce conflict in the grammar. Consider this expression:

[foo | (i, e) <- ies]

When the parser reaches the bracket after "e" it is valid to either reduce "(i, e)" to a pair of qualifiers (i.e. i and e are treated as guard expressions), OR to reduce it to the tuple expression (i, e) which will be later converted to a pattern. There are a number of alternative ways we could solve this:

- Disallow bracketing of qualifiers altogether!
- This keeps the concrete syntax simple and should cover all common use cases
- It does reduce the composability of the qualifier syntax rather drastically however

- Keep bracketing in this manner but use type information to resolve the ambiguity
- I will need to change the parser to consider qualifiers as expressions so that we can parse without any reduce/reduce conflicts
- We can then always use type information to determine which reading is correct, because guards are always boolean, and so can be distinguished from tuples as required
- Might have negative implications on the readability of some error messages :(
- If the parser finds it hard to understand this syntax, you can argue that any human reader would too and hence we should look for something less ambiguous

- Introduce new syntax to allow this idiom to be expressed unambiguously. Some examples of what we could use are below:

-- 1) A new keyword [ foo | x <- e, nest { y <- ys, z <- zs }, x > y + 3 ] -- 2) Trying to suggest pulling things out of a sublist -- without having to mention binders [ foo | x <- e, <- [ .. | y <- ys, z <- zs ], x > y + 3 ] -- 3) New kind of brackets [ foo | x <- e, (| y <- ys, z <- zs |), x < y + 3 ] -- 4) Variation on 2), slightly more concise [ foo | x <- e, <- [ y <- ys, z <- zs ], x > y + 3 ] -- 5) Another variation on 2), moving the ".." into -- the pattern rather than the comprehension body [ foo | x <- e, .. <- [ y <- ys, z <- zs ], x > y + 3 ]

This functionality was implemented and working, but owing to the syntactic difficulties support was dropped.

## Extending To Arbitrary Monads

On the paper talk page, Michael Adams has outlined how the new idioms could be extended to arbitrary monads. It looks very nice theoretically, but before we consider actually implementing this we need to know if anyone has a use case for the syntax. To demonstrate the kind of thing that this would make possible, consider the following example from Michael:

do a <- ma ... b <- mb c <- mc sort by (b, c) using foo d <- md ... return (a, b, c, d)

It would de-sugar to:

((do a <- ma ... b <- mb c <- mc return ((b, c), (a, b, c)) ) `foo` fst) >>= \result -> do let (a, _, _) = result (_, b, _) = result (_, _, c) = result d <- md ... return (a, b, c, d)

Where we have:

foo :: forall a. (a -> t) -> m a -> m a

## Extensions

Some other possible ways we could add to Max's implementation given the need:

- Add associativity back in
- Add desugaring support for parallel arrays as well as lists: every other part of the compiler should already handle these seamlessly