# 1 Talk page for "Comprehensive Comprehensions"

This is a discussion page for the paper Comprehensive Comprehensions.

If you are kind enough to read this paper, you may like to jot down any thoughts it triggers off, and see what others have written. This talk-page lets you do just that.

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Simonpj 08:42, 19 April 2007 (UTC) Note from Simon

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## 1.1 MichaelAdams 14:51, 19 June 2007 (UTC)

In theory these operators (order-by and group-by) should generalize to monads and once you do several other design options open up. These two operators could even be unified into a single operator.

Starting with sort-by, I think the monadic version is fairly obvious. Take something like the following code.

```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`

#### 1.1.1 Generalizing Order-by to Group-by

In fact after a few tweaks it turns out that order-by and group-by could operate under the exact same de-sugaring.

Suppose we let the type of foo be:

`foo :: (Functor n) => forall a. (a -> t) -> m a -> m (n a)`

Notice that I said "m (n a)" and not "m (m a)". The group-by de-sugaring that I'm going to show works for any Functor "n", and if we imagine "n" to be some type like the following then order-by is just a special case of group-by.

`type Ident a = a`

(It wouldn't actually be valid Haskell code to use a type synonym in that way though, but it conveys the idea.)

The de-sugaring to support this would take something like the following (inspired by arrow syntax).

```do a <- ma
b <- mb
c <- mc
foo args \$-< (a, b) -- group by (a, b) using (foo args)
g <- mg
return (a, b, c, d, e, f, g)```

It would produce:

```(ma >>= \a ->
mb >>= \b ->
mc >>= \c ->
return ((a, b), (a, b, c))) `foo` args >>= \result ->
let a = fmap (\(_, (a, _, _)) -> a) result
b = fmap (\(_, (_, b, _)) -> b) result
c = fmap (\(_, (_, _, c)) -> c) result in
md >>= \d ->
return (a, b, c, d)```

(Note that after the "foo", the types of "a", "b" and "c" have changed. Their types before "foo" get wrapped by "n" after "foo".)

#### 1.1.2 Even more generalization

Once we have done this, another possibility opens up. Notice that the first of each pair in "result" was never used except from within "foo". It doesn't do any work in the result. Now suppose we change the type of foo to:

`foo :: (Functor n) => forall a. m (t, a) -> m (n (u, a))`

Now "foo" can not only read existing bindings from "t", but it can also create new bindings with "u". (This hard wires the extraction function to always be "fst", but it simplifies the presentation a bit. The other form with a general extraction could still be used.)

The previous syntax could then be extended to something like:

```do a <- ma
b <- mb
c <- mc
(d, e, f) <-\$ foo args \$-< (a, b)
g <- mg
return (a, b, c, d, e, f, g)```

This would then de-sugar to:

```(ma >>= \a ->
mb >>= \b ->
mc >>= \c ->
return ((a, b), (a, b, c))) `foo` args >>= \result ->
let d = fmap (\((d, _, _), (_, _, _)) -> d) result
e = fmap (\((_, e, _), (_, _, _)) -> e) result
f = fmap (\((_, _, f), (_, _, _)) -> f) result
a = fmap (\((_, _, _), (a, _, _)) -> a) result
b = fmap (\((_, _, _), (_, b, _)) -> b) result
c = fmap (\((_, _, _), (_, _, c)) -> c) result in
mg >>= \g ->
return (a, b, c, d, e, f, g)```

#### 1.1.3 Conclusion

The above might have gone too far down the generalization road and put to many bells and whistles on the thing, so it may be worth trimming it down. I also haven't given any thought to what applications would need this. I just wanted to consider how far these operations