How is this used to solve real problems?
What are real problems?
AliceInWonderland said:"Alice" = "Peach""Peach" = "Alice"I knew it.
Don't try to deny it later.
I've posited this idea but no one believes me.
How is this used to solve real problems?
What are real problems?
I meant something you can puts your hands on. Like a rocket to the moon math. Or simple Newtonian physics. Does this math in your thread lead to a useful tool? Or is it a foundation for proofs of some kind? Just curious how you would use this math you are speaking of.
How is this used to solve real problems?
What are real problems?
I meant something you can puts your hands on. Like a rocket to the moon math. Or simple Newtonian physics. Does this math in your thread lead to a useful tool? Or is it a foundation for proofs of some kind? Just curious how you would use this math you are speaking of.
The most practical application of category theory is in software engineering where it is used to formulate optimal code via design patterns and in the proving of correct code.
In this thread, while the code may not be optimal given I am trying to keep it beginner friendly, we are formulating design patterns and as the thread continues I hope to start showing how CT leads to correct code.
The mathematical model that is Newtonian Mechanics can be formulated and explored via the Category of Smooth Manifolds.
How is this used to solve real problems?
What are real problems?
I meant something you can puts your hands on. Like a rocket to the moon math. Or simple Newtonian physics. Does this math in your thread lead to a useful tool? Or is it a foundation for proofs of some kind? Just curious how you would use this math you are speaking of.
The most practical application of category theory is in software engineering where it is used to formulate optimal code via design patterns and in the proving of correct code.
In this thread, while the code may not be optimal given I am trying to keep it beginner friendly, we are formulating design patterns and as the thread continues I hope to start showing how CT leads to correct code.
The mathematical model that is Newtonian Mechanics can be formulated and explored via the Category of Smooth Manifolds.
Do you have any references on this? I would like to understand better how this is used.
Omari said:Do you have any references on this? I would like to understand better how this is used.
Sources for program correctness and the relationship between CT and Computation:
Correctness (Ocaml Programming) (This lecture series taught me most of what I know about functional programming and also introduced me to Proving Correctness, the link is specifically about the latter).
Curry-Howard Correspondence (OCaml Programming) (From the same lecture series, explain Programs = Proofs)
The Curry-Howard Isomorphism for Dummies (A gentle overview of the correspondence)
Curry-Howard-Lambek Correspondence (Programs = Proofs = Categories Haskell wiki)
Types and Functions (From Category Theory for Programmers, this link specifically is a very gentle introduction to the relationship between type theory in programming and composability in CT)
Functional Completeness of Cartesian Categories (Lambeks paper about the correspondence)
Curry-Howard-lambek Correspondence (technical introduction)
Category Theory and Diagrammatic Reasoning (Technical)
Notions of Computation and Monads (Technical, pay attention to section titled A Categorical Semantics of Computation)
Physics, Topology, Logic, and Computation (Technical, goes in proof relationship between CT, Logic, and Computation and touches upon CT relationship with mathematics and physics)
From Design Patterns to Category Theory (Lecture series on designing software via CT)
Category Theory for Programmers (I already linked a section from this book, but in general its a design patterns book from a CT perspective)
I am not well versed in CT use in physics, I just know that it is used especially in those areas formalized in differential geometry and algebra. I assume its a tool in research programs for theoretical and mathematical physics. Again, a good place to start looking is results around the Category of Smooth Manifolds
last edit on
1/13/2023 4:06:27 AM
