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This is not true. For example, The typeclassopedia contains all you need to know about functors and doesn't go into detail about the underlying Category Theory

by platz 7y ago

This is not true. For example, The typeclassopedia contains all you need to know about functors and doesn't go into detail about the underlying Category Theory.

tome 7y ago
Agreed. Having worked closely with them, I would say such Haskell luminaries as Simon PJ, Lennart Augustsson and Neil Mitchell have not "learned category theory" (and I don't think I'm being too offensive to them if I state that). In fact the only figure of highest repute in the community who puts much stock in category theory is Edward Kmett.
crimsonalucard 7y ago
excerpt from typeclassopedia: "The wise student will focus their attention on definitions and examples, without leaning too heavily on any particular metaphor. Intuition will come, in time, on its own." typeclassopedia admits that the intuition is missing. I would go on to argue that just going from the definition alone you would think that a functor is anything that is mappable and that fmap simply maps a function across a functor to produce a new functor. The intuition that cannot be grasped without some category theory is that fmap actually lifts a regular function of standard types into a function between functors. A functor is more than just fmaps.
- platz 7y ago
  you draw the wrong conclusion from that excerpt. It does not say "Intuition that cannot be grasped without some category theory". It is saying that you need to see many concrete examples to learning something abstract. This is how it works in all of education basically, and there's isn't an easy substitute. Learning "category theory" will not replace your need to see concrete examples to grok something inherently abstract. You'll have to go through the concrete examples anyway.
  - crimsonalucard 7y ago
    Those concrete examples aren't visible until you do category theory. That is what I'm saying. You are drawing the wrong conclusions. There is literally not enough information from the definition of the type class Functor and from examples of usages of that definition for a programmer to truly understand the concept of a functor. That is the conclusion I am deriving. It is not wrong. You are wrong. What's going on is you are deriving a conclusion convenient to your view point. Sure you can get by programming haskell without category theory just like you can program without knowing the notion of an algorithm. However in both cases you are worse off without the knowledge.

by platz 7y ago

This is not true. For example, The typeclassopedia contains all you need to know about functors and doesn't go into detail about the underlying Category Theory.

tome 7y ago

Agreed. Having worked closely with them, I would say such Haskell luminaries as Simon PJ, Lennart Augustsson and Neil Mitchell have not "learned category theory" (and I don't think I'm being too offensive to them if I state that). In fact the only figure of highest repute in the community who puts much stock in category theory is Edward Kmett.

crimsonalucard 7y ago

excerpt from typeclassopedia: "The wise student will focus their attention on definitions and examples, without leaning too heavily on any particular metaphor. Intuition will come, in time, on its own." typeclassopedia admits that the intuition is missing. I would go on to argue that just going from the definition alone you would think that a functor is anything that is mappable and that fmap simply maps a function across a functor to produce a new functor. The intuition that cannot be grasped without some category theory is that fmap actually lifts a regular function of standard types into a function between functors. A functor is more than just fmaps.

platz 7y ago
you draw the wrong conclusion from that excerpt. It does not say "Intuition that cannot be grasped without some category theory". It is saying that you need to see many concrete examples to learning something abstract. This is how it works in all of education basically, and there's isn't an easy substitute. Learning "category theory" will not replace your need to see concrete examples to grok something inherently abstract. You'll have to go through the concrete examples anyway.
- crimsonalucard 7y ago
  Those concrete examples aren't visible until you do category theory. That is what I'm saying. You are drawing the wrong conclusions. There is literally not enough information from the definition of the type class Functor and from examples of usages of that definition for a programmer to truly understand the concept of a functor. That is the conclusion I am deriving. It is not wrong. You are wrong. What's going on is you are deriving a conclusion convenient to your view point. Sure you can get by programming haskell without category theory just like you can program without knowing the notion of an algorithm. However in both cases you are worse off without the knowledge.