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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.

42
votes
6answers
8k views

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 ...
15
votes
3answers
3k views

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. ...
1
vote
2answers
130 views

What to prove and how to prove it

In learning about proof theory, I am interested to know how to go about "proving properties of a program". I don't exactly see yet what needs to be proven, nor how to prove it, which leads to this ...
19
votes
1answer
948 views

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 ...
16
votes
2answers
357 views

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,...
9
votes
2answers
1k views

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, ...
20
votes
2answers
2k views

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 ...
4
votes
1answer
135 views

What does it mean if we disable K-rule in Agda?

TL;DR: Can I say, "K-rule in Agda enables people to match $ \forall a.a \equiv a $ with $ refl $"? In https://agda.readthedocs.io/en/v2.5.4.1/language/without-k.html#without-k, K-rule is introduced ...
6
votes
2answers
284 views

Can we prove that $1 + 2 + \dots + n = \frac{n(n+1)}{2}$ using a computer program?

Chapter 7 of The Haskell Road to Logic Math and Programming discusses induction and recursion. Haskell is strongly typed and we can define the natural numbers ...