curry-howard

By Curry-Howard, the program is the proof, albeit usually not of an interesting proposition.

Only a subset is stated by Curry-Howard correspondence.

You're appleaing to the Curry-Howard correspondance, which is neat but is not used by many theorem provers.

As such it is in the same space as Curry-Howard based programming languages like Idris and Agda with dependent types.

Once you add the topology section to the Curry-Howard Isomorphism via homotopy type theory it all starts to merge anyway!

A fairly good summary, though more material on the Curry-Howard Isomorphism would have been nice.

The big-picture reason why ownership types and concurrency match so well is the Curry-Howard correspondence.

Also, its reliance on Curry-Howard for verification is limited and narrow-sighted, and its insistence on referential transparency everywhere is interesting yet misguided.

Very few (but definitely some!) go into computer science because they want to know about Turing Machines, or the Curry-Howard isomorphism, etc.

The core idea is not a CS one but instead in the free connection to logic provided by the Curry-Howard or BHK interpretations.

The Curry-Howard correspondence shows that all Turing-complete axiomatizations are mirrors of each other.

Surprised there's no mention of the Curry-Howard correspondence between proofs and programs.

Curry-Howard makes things easy to verify (in fact, makes them trivial, as the burden is on the developer -- the language "just" provides soundness and inference).

I think that other than the happy "coincidence" that is Curry-Howard, I see nothing in LC to suggest that it is the "right" way to model computation, and CH itself is just a form of verification (that requires programmers to prove their programs).