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Questions tagged [proof-assistants]

Applications that allow to create formal proofs. They assist the user by finding partial and checking complete proofs. General questions about proof assistants can also be asked on the Proof Assistants Stack Exchange site.

Applications that allow to create formal proofs. They assist the user by finding partial and checking complete proofs. General questions about proof assistants can also be asked on the Proof Assistants Stack Exchange site.

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Learning Automated Theorem Proving

I am learning Automated Theorem Proving / SMT solvers / Proof Assistants by myself and post a series of questions about the process, starting here. Note that these topics are not easily digested without a background in (mathematical) logics. If you…
Guy Coder
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Recursive definitions over an inductive type with nested components

Consider an inductive type which has some recursive occurrences in a nested, but strictly positive location. For example, trees with finite branching with nodes using a generic list data structure to store the children. Inductive LTree : Set := Node…
Gilles 'SO- stop being evil'
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How hard would it be to state P vs. NP in a proof assistant?

GJ Woeginger lists 116 invalid proofs of P vs. NP problem. Scott Aaronson published "Eight Signs A Claimed P≠NP Proof Is Wrong" to reduce hype each time someone attempts to settle P vs. NP. Some researchers even refuse to proof-read papers settling…
Isinlor
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Types of Automated Theorem Provers

I am learning Automated Theorem Proving / SMT solvers / Proof Assistants by myself and post a series of questions about the process, starting here. Which are the relevant automated theorem provers? I found A Review of Theorem Provers Is this still…
Guy Coder
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Why is unification so important to inference engines?

I am learning Automated Theorem Proving / SMT solvers / Proof Assistants by myself and post a series of questions about the process, starting here. I keep reading about the Unification Algorithm. What is it and why is so important to Inference…
Guy Coder
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Has Anyone Actually Created a System that Writes Computer Programs from specification?

Has anyone ever actually written a system (software or detailed explanation on paper with simple examples) that generates computer programs? I input $Prime(x) \wedge x<10$ and it creates a program that lists the prime numbers less than 10. …
Charlie
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Why do some inference engines need human assistance while others don't?

I am learning Automated Theorem Proving / SMT solvers / Proof Assistants by myself and post a series of questions about the process, starting here. Why is it that automated theorem provers, i.e. ACL2, and SMT solvers do not need human assistance…
Guy Coder
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Is there a repository for the hierarchy of proofs?

I am self-learning proof assistants and decided to start on some basic proofs and work my way up. Since proofs are based on other proofs and so form a hierarchy, is there a repository of the hierarchy of proofs? I know I can pick a particular…
Guy Coder
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The "CPS" approach has done great harm to performance in SML/NJ; reasoning desired

In a comment to Learning F#: What books using other programming languages can be translated to F# to learn functional concepts? Makarius stated: Note that the "CPS" approach has done great harm to performance in SML/NJ. Its physical evaluation…
Guy Coder
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Is Agda sound as a proof system?

I was browsing Agda's stdlib source code, since I was trying to get into it seriously and therefore wanted to know more. I was amazed at that Agda is way more developed than I thought and it's significantly much closer to Haskell than Coq. However,…
Jason Hu
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Theorem Proofs in Coq

Background I am learning assistance, Coq, on my own. So far, I have completed reading Yves Bertot's Coq in a Hurry. Now, my goal is to prove some basic results concerning the natural numbers, culminating with the so-called division algorithm.…
user11942
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What are the implications of Homotopy Type Theory?

I've recently come across the topic of homotopy type theory and I'm interested to learn more. I have a very limited background in type theory. Can anyone tell me, in functional programming terms or through practical examples, how exactly is HoTT…
thoughtpolice
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Is Coq synthetic or analytic?

In CMU's HoTT course, lecture 1, which can be found here: https://scs.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=0945cc7f-48b7-4803-81af-e7193a3f461d At 33:52, Harper was giving parallel comparison between synthetic theories and analytic ones,…
Jason Hu
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Can a type system serve as a proof assistant for foreign functions?

Given that: A language with very expressive type systems (e.g. Idris) can also have escape mechanisms like foreign function interfaces/unsafePerformIO. There are proof assistants that can be used to prove some properties of a program written in a…
dukereg
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Looking for a book that derives and constructs a model checking application

I am teaching myself program verification and am currently learning proof assistants. I have the book Handbook of Practical Logic and Automated Reasoning which gives the proofs necessary for the understanding of such a system, but more importantly…
Guy Coder
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