[Haskell-cafe] ANN: parameterized, indexed monads with a single "parameter" type variable

[Louis Pan]

Hi Haskell-Cafe,

I've been experimenting with indexed/parameterized monads with a single
"parameter" type variable.
The difference from my variation from Conor McBride's IMonad (which also
uses one "parameter") is that the "parameter" doesn't have postcondition
semanatics.

(FYI, a good intro to indexed monads is
https://stackoverflow.com/questions/28690448/what-is-indexed-monad)

Instead, in the instance of PApplicative, you have to specify the rule of
how to combine the "parameter" `t` and `u` into the final parameter `u`.

That way, I can create "parameterized" versions of Semigroup, Monoid, as
well as Applicative, Alternative, Monad.

It also allows for create different flavours of "parameterized" kinds for
ReaderT.

For example, I've created OverlappingWhichReader, DistinctWhichReader, and
ManyReader newtype wrappers around ReaderT.

OverlappingWhichReader and DistinctWhichReader can combine reader that read
`Which '[Int, Bool]` (polymorphic variant, analogous to 'Either Int Bool')
with another reader that reader `Which '[Bool, String]` into a reader that
can read `Which '[Int, Bool, String]`

ManyReader can combine reader that read `Many '[Int, Bool]`
(heterogenous record, analogous to tuple (Int, Bool)) with another reader
that reader `Many '[Bool, String]` into a reader that can read `Many '[Int,
Bool, String]`

See
https://github.com/louispan/parameterized/blob/master/src/Parameterized/Control/Monad/Trans/Reader.hs
https://github.com/louispan/parameterized/blob/master/test/Parameterized/Control/Monad/Trans/Reader/ReaderSpec.hs

-----

The single "parameter" still allows for the traditional changing state type
for StateT.
For example, I've created ChangingState newtype wrappers around StateT,
which changes the state parameter.

I've also created ManyState, which can combine StateT that modifies `Many
'[Int, Bool]` with another StateT that modifes `Many '[Bool, String]` into
a StateT that can modify `Many '[Int, Bool, String]`

See
https://github.com/louispan/parameterized/blob/master/src/Parameterized/Control/Monad/Trans/State/Strict.hs
https://github.com/louispan/parameterized/blob/master/test/Parameterized/Control/Monad/Trans/State/Strict/StateSpec.hs

---

I'd would appreciate if I could get any feedback on this approach.

Cheers,

Louis
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