David Farrell dajfarrell at gmail.com
Fri Sep 25 18:34:33 UTC 2015

```Hello Roman,

Thanks for your feedback. These are good questions and I realize that
not enough documentation on the concept or usage of polymaps is
provided, so my next step will be to expand the Haddock documentation to
include a detailed explanation of the concept and how to use the
Relation data type and the Storage typeclass.

As far as what a polymap actually is, the example I've used to describe
to concept to a couple of people is as follows. I'll briefly explain a
couple of concepts first.

A unidirectional map--or just map for short--is a data structure holding
a number of keys of some type and an identical number of values of some
other type, forming a bijection between the keys and values. The data
structure stores the keys and values in such a way so as to allow values
to be looked up by their corresponding keys; in other words, each key
maps to the corresponding value. To illustrate this mapping:

A==>B

A bidirectional map is similar to a map with the difference that each
value also maps back to its corresponding key, allowing two-way
(bidirectional) mapping between the keys and values. In the case of a
bimap, it may be more useful to refer to both the keys and values as a
set of keys on one of the sides of the bimap. To illustrate this mapping:

A<=>B

Or to illustrate more consistently for the illustration following this one:

A---B

A 3-sided map builds on these concepts, applying them to three sides as
opposed to two (left and right), creating a relational mapping between
three different sets of keys where each side maps to every other side.
To illustrate this mapping:

A---B
|  /
| /
|/
C

Similarly, a 4-sided map is illustrated as:

A---B
|\ /|
| X |
|/ \|
C---D

A polymap essentially generalizes these previous examples as an n-sided
map, allowing values to looked up by any of their of corresponding keys
on one of the sides of the polymap.

I hope this clears things up somewhat with respect to what a polymap is.
I'll be adding Haddock explaining all of this as well as Storage and
Relation and the definitions in Data.PolyMap.Nat as soon as I get the
chance.

Apologies for my awful ASCII illustrations.

On 25/09/2015 07:42, Roman Cheplyaka wrote:
>
> Hi David,
>
> As someone who is not familiar with the concept of polygonal maps, I
> find this package severely underdocumented.
>
> What is a polymap? Why would I want to use one? What is storage and how
> should I choose it?
>
> The example clears it up a bit, but it could also use more prose. And
> perhaps there could be a more motivated example (showing how polymap
> solves an actual problem).
>
> On 09/24/2015 09:53 PM, David Farrell wrote:
>> I'm excited to announce the first release of a package I've been working
>> on over the last week called polymap, a library providing type-safe
>> polygonal maps whose sides are defined by a kindlist of types zipped
>> with a storage type for each side. I've tried to match the interface
>> exposed by the containers package as closely as possible. For example:
>>
>> import Data.Set (Set)
>> import Data.PolyMap.Nat (first, second, third)
>> import qualified Data.PolyMap as PM
>>
>> mEmpty :: PM.PolyMap '[ '(String, Set), '(Int, Set) ]
>> mEmpty = PM.empty
>>
>> mOne :: PM.SimplePolyMap '[String, Int] Set
>> mOne = PM.singleton ("one", length "one")
>>
>> main = do
>>      print mEmpty                              -- empty PolyMap
>>      print mOne                                -- PolyMap with one Relation
>>      print mTwo                                -- PolyMapwith two Relations
>>      print (PM.member first "one" mTwo)        -- True
>>      print (PM.notMember first "asdf" mTwo)    -- True
>>      --print (PM.notMember second "asdf" mTwo) -- will not typecheck
>>      --print (PM.notMember third "asdf" mTwo)  -- will not typecheck
>>      print (PM.lookup first "two" mTwo)        -- second Relation of PolyMap
>>    where mTwo = PM.insert ("two", length "two") mOne
>>
>> This is a short usage example of most of the functions currently written
>> for polymap. There's still a long way to go both in terms of exposed
>> functions and in terms of efficiency and such, but I felt it prudent to
>> make a public release of my work so far as I feel it's reached a stage
>> where it could be beneficial to others. Note that GHC 7.10 (base >=4.8,
>> GHC extensions) is required.
>>
>> Git Repository:
>> https://github.com/shockkolate/hs-polymap
>>
>> Issue Tracker:
>> https://github.com/shockkolate/hs-polymap
>>
>> Hackage:
>>
>> code is released into the public domain for the benefit of others.
>>
>> I'd love to hear any feedback/suggestions/improvements/anything you want
>> to say about polymap over the mailing list (which may be more suited to
>> the haskell-cafe mailing list; I don't know) or in #haskell on Freenode
>> (I'm usually in there as Shockk).
>>
>> N.B. Version 0.1.0.0 of the package will not build due to the use of a
>> function in containers that has been submitted as a pull request but
>> does not exist yet/at all.
>> _______________________________________________