[Question]: How to correctly use the library for the construction of a BoundedLattice

[aleSuglia]

Hi @phadej,

I'm working with your library in order to define a bounded lattice. I've seen that everything should be constructed using joins and meets methods. I want to construct it from a set or a range of values. Please, can you give me an example?

I've tried to use the methods joins and meets in this way:

      let s = Data.Set.fromList [1,2,3,4,5]
      let a = L.joins s
      let b = L.meets s

I don't understand how to obtain a single bounded lattice using the defined methods. I've also tried to take the bottom and top element from a and b, but I obtain some errors. I think that I'm not correctly using the methods.

Thank you for your help.

Cheers, Alessandro

[phadej]

Sorry, I'm not really understand your question. Do you want to construct bounded ordered lattice of elements 1..5 ? i.e. a to be 1 and b = 5?

[aleSuglia]

I want to create, from the set of integers [1..5], a bounded ordered lattice which should have as top element 5 and as bottom element 1.

[phadej]

You can use Ordered newtype:

> Ordered 1 /\ Ordered 2 :: Ordered Int
Ordered {getOrdered = 1}

If you really need bounded lattice to 1 and 5, you'd need to create a new newtype:

newtype Int1to5 = I Int

instance JoinSemiLattice Int1to5 where
    I a \/ I b = I . getOrdered $ Ordered a \/ Ordered b

instance BoundedJoinSemiLattice Int1to5 where
    bottom = I 1

if you want to create lattices based on runtime sets (i.e. not known at the compile time, so you cannot create a newtype for each), then the situation is quite difficult (AFAIK possible though). I'm not sure if you really want to do that.

[aleSuglia]

I don't know why it's not possible to define a simple concept like a set of natural numbers from 1 to 5, following the natural ordering. In this lattice, the maximum element should be 5 and the minimum 1. Why is so difficult and strange to define it in your library?

Maybe I'm missing the point, sorry about that. I hope that you can provide to me more information because I've not understood how to use your example.

[phadej]

The problem of defining set of natural numbers from 1 to 5 is not a problem with this library. The question is more general: How to define type of natural numbers from 1 to 5? you can do

data Nat1to5 = N1 | N2 | N3 | N4 | N5

and write all required instances (including classes from this library) for it.

if you want a quotient type Int | \n -> 1 <= n && n <= 5, then it's not possible simply in Haskell (or any other mainstream language AFAIK).

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I'm not sure what you are trying to do. If you could write what you are trying to do in some other language (preferably statically typed), then I might be able to convert it to Haskell.