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Questions tagged [applicative]

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2 votes
0 answers
109 views

Monads whose Kleisli arrows can be "applicativized"

Has anyone thought about what constraints a monad should satisfy in order for its arrows to be able to be "applicativized". That is, for what monads $M$ is it the case that there is an ...
Julian G.'s user avatar
4 votes
3 answers
375 views

Kleisli-like category for applicatives?

I am wondering if there is a good way to complete the following analogy: monad : Kleisli category :: applicative functor : ?? That is, a given monad T on a ...
Julian G.'s user avatar
-2 votes
1 answer
84 views

Forming ordered pairs using monads and doing without the Kuratowski encoding of ordered pairs

Suppose we have a set $S$ of constants of the Simply-Typed Lambda Calculus (STLC) various types, and the operation of union $\cup$ which takes two constants and forms their union. For example, $S$ ...
user65526's user avatar
  • 105
0 votes
1 answer
204 views

How to map random cardesian points in a 2d array

I was wondering if there is any algorithm, theoretical or already implemented, or if its even possible at all, where, given N random ...
BugShotGG's user avatar
  • 101
22 votes
3 answers
3k views

Is there a concept of something like co-applicative functors sitting between comonads and functors?

Any monad is also an applicative functor and any applicative functor is a functor. Also, any comonad is a functor. Is there a similar concept between comonads and functors, something like co-...
Petr's user avatar
  • 2,601
12 votes
2 answers
769 views

What are the relations between Alternative, MonadPlus(LeftCatch) and MonadPlus(LeftDistributive)?

Following up What’s an example of a Monad which is an Alternative but not a MonadPlus?: Assume $m$ is a monad. What are the relations betweem $m$ being an Alternative, a MonadPlusCatch and a ...
Petr's user avatar
  • 2,601