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>I initially thought "why do we need another one of these", like rolling your eyes at another programming language or JS framework. There's even another large-s

>I initially thought "why do we need another one of these", like rolling your eyes at another programming language or JS framework. There's even another large-scale research project already underway at Cambridge [3]. I had a complete opposite reaction to yours. I feel like automatic proving languages are very quirky and stem from the creators not really knowing much about programming. At my university a bunch of professors who really liked Prolog made a formal proving language and guess what syntax it had? Yeah... terrible stuff. Personally it's been a few years since I started thinking about this matter, but one of my personal objectives in live is to create a decently simple and intuitive (for both mathematicians and programmers) environment for formally proving their theorems

rscho 4y ago
Are you implying that giving prolog-like syntax to a language suggests ignorance about programming? Why would that be terrible? IMO, syntax is really not the main attraction, neither is it the main problem to solve when writing a theorem prover. Prolog has the advantage of a regular syntax, just like lisp. Instead of wanting to make your miracle-own-thing, it would be far better to contribute to something like Idris. It's brilliant and in dire need of libraries.
- HidyBush 4y ago
  Who are automatic theorem provers aimed at? Computer scientists with an interest in maths or mathematicians with an interest in CS? If you are a mathematician starting off with something like Coq is a nightmare. Nobody learns OCamel in college, math majors usually learn R, Python and maybe Java or C. Making formal proving simple and intuitive is the first step to have it heavily adopted. It should look as close as possible to writing a proof in pure first order logic.
  - rscho 4y ago
    IMO, you overstate the issue of syntax. As a hobbyist in both programming and math, Coq's syntax has never been the reason I failed to complete a proof. But perhaps I'm just too dumb and my difficulties lie elsewhere, so that's just my 2c. I think there's room for a spectrum of theorem provers made for academic pure mathematicians, industry programmers and everything in between. Those should perhaps not have identical syntax, neither should they have the same goals. To support my point, here's an example of an exotic theorem prover: https://github.com/webyrd/mediKanren https://github.com/webyrd/mediKanren It is aimed at medical researchers, and computes proofs about the medical literature, no less! This is a very different system and audience than which you are thinking about, but it's still a theorem prover.
- mhh__ 4y ago
  It's not really the syntax but rather that until very recently theorem provers have been quite niche even in formal disciplines, so the tooling isn't quite there. In an analogy with traditional programming I'd say we have goto but we are yet to have structured loops. Enormously powerful but still hard to apply to either real mathematics or real problem.
practal 4y ago
We share this objective! I am sharing my thoughts on that here: https://practal.com https://practal.com

rscho 4y ago

Are you implying that giving prolog-like syntax to a language suggests ignorance about programming? Why would that be terrible? IMO, syntax is really not the main attraction, neither is it the main problem to solve when writing a theorem prover. Prolog has the advantage of a regular syntax, just like lisp. Instead of wanting to make your miracle-own-thing, it would be far better to contribute to something like Idris. It's brilliant and in dire need of libraries.

HidyBush 4y ago
Who are automatic theorem provers aimed at? Computer scientists with an interest in maths or mathematicians with an interest in CS? If you are a mathematician starting off with something like Coq is a nightmare. Nobody learns OCamel in college, math majors usually learn R, Python and maybe Java or C. Making formal proving simple and intuitive is the first step to have it heavily adopted. It should look as close as possible to writing a proof in pure first order logic.
- rscho 4y ago
  IMO, you overstate the issue of syntax. As a hobbyist in both programming and math, Coq's syntax has never been the reason I failed to complete a proof. But perhaps I'm just too dumb and my difficulties lie elsewhere, so that's just my 2c. I think there's room for a spectrum of theorem provers made for academic pure mathematicians, industry programmers and everything in between. Those should perhaps not have identical syntax, neither should they have the same goals. To support my point, here's an example of an exotic theorem prover: https://github.com/webyrd/mediKanren https://github.com/webyrd/mediKanren It is aimed at medical researchers, and computes proofs about the medical literature, no less! This is a very different system and audience than which you are thinking about, but it's still a theorem prover.
mhh__ 4y ago
It's not really the syntax but rather that until very recently theorem provers have been quite niche even in formal disciplines, so the tooling isn't quite there. In an analogy with traditional programming I'd say we have goto but we are yet to have structured loops. Enormously powerful but still hard to apply to either real mathematics or real problem.

practal 4y ago

We share this objective! I am sharing my thoughts on that here: https://practal.com https://practal.com