Sequent Calculus and Notation – Par Part 1
Comments
dunham
cylinder714
Support for sequent calculus is built into Mark Tarver's Shen language; here's the relevant chapter in his Book of Shen: https://shenlanguage.org/TBoS/tbos_228.html
hoping1
Extensive and patiently-paced, with many examples, and therefore unfortunately pretty long lol
btilly
What is the upside down v supposed to be? Yeah, I know that it is "and". But it isn't specified, and I do little enough logic that I had to look it up.
hoping1
Fair, I think of this as advanced logic, and those concepts (and that notation) as prerequisite.
groby_b
Alas, not having had the time to fully read yet, but starting at the "Axiom rule" part, a strong feeling starts popping up that this is Lean, but with mathy symbols.
I don't know if the intuition will hold on further reading, but there was a strong "I've seen you in a different trench coat" feeling.
rck
Yup! Lean is based on a variant of the Calculus of Constructions, which is in turn based on strong connections between (intuitionistic) natural deduction and type theory. The connection is incredibly beautiful:
hoping1
Ah heck, I should have added a section on PTSs, maybe I still will or maybe that will be standalone later. It really is gorgeous stuff!!
There is a interactive web toy for sequent calculus proofs here: http://logitext.mit.edu/main
For natural deduction and other topics, Bob Atkey's interactive course is fun: https://personal.cis.strath.ac.uk/robert.atkey/cs208/index.h...