[Feb 17th.] Talking Points - CH5 & CH6

[JonathanLorimer]

This should be a forum for points that we want to discuss in our meeting on Feb 17, the material we will be covering is:

• Chapter 5 - Products and Coproducts
• Chapter 6 - Simple Algebraic Data Types

[chiroptical]

Chapter 5: Products and Coproducts

• Universal Construction
  • pattern: Consider a shape constructed from objects and morphisms, look for all occurrences in a category
  • recall: A pattern which yields a lot of examples
  • precision: Reducing your recall by refining your pattern
• Initial Objects
  • In Haskell, absurd :: Void -> a
• Terminal Objects
  • In Haskell, unit :: a -> ()
• Duality
  • For any category, there is a dual category with all of the morphisms flipped
  • The dual category is prefaced with co-
  • The initial object in a category becomes the final object in the co-category (and vice-versa)
• Isomorphisms, define functions a -> b and b -> a
• Cartesian Products and factorizer's i.e. (&&&)
  • Projection functions, i.e. fst :: (a, b) -> a and snd
  • Can consider patterns such as r :: c -> a and s :: c -> b to produce large recall
  • rank
  • Factorization
• Coproducts e.g. Either
  • Opposite of projection is injection
• Asymmetry

[chiroptical]

Chapter 6: Simple Algebraic Data Types

• Product leads to Product Types e.g. (,)
  • empty is (), similar to 1 for multiplication
• Coproducts lead to Sum Types, e.g. Either
  • empty is Void, similar to 0 for addition
• The Algebra of Types
• The Curry-Howard Isomorphism

[chiroptical]

I skipped the videos because they are a bit too long. I might choose to watch some after our discussion.

[chiroptical]

I think this is really useful. I think it highlights our common issue when trying to avoid observability.

[JonathanLorimer]

This is awesome Barry. I am just finishing up CH6 right now. I have my notes in a subdirectory under my name. I will submit a pull request tonight or tomorrow with them.

[chiroptical]

Closing this as we are done with the week.