Questions tagged [automated-theorem-proving]

Machine-checked, machine-generated or machine-verified proofs

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2answers
189 views

Automated reasoning with real numbers

I have a large number of equivalences which look like: $(a \leq 0.54 \wedge b \geq 0.12) \vee (c \gt 0.98)$ $\Leftrightarrow$ $(x \leq 0.25) \vee (x \gt 0.91 \wedge y \geq 0.01)$ This is just an ...
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1answer
33 views

What were the shortcomings of Robinson's resolution procedure?

Paulson et alii. From LCF to Isabelle/HOL say: Resolution for first-order logic, complete in principle but frequently disappointing in practice. I think complete means they can proof any true ...
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1answer
43 views

Prove simple theorems in Haskell in automated way

I would like to prove in Haskell, whether in vanilla Haskell or using some libraries / tools, some simple theorems such as: ...
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3answers
51 views

Halting problem vs. automated theorem proving?

In the Theory of Computation tutorial offered by Complexity Tree (I just began the 2nd video), it talks about how the Halting problem was developed to show that mathematics could not be automated. ...
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1answer
70 views

on coq: Why is the proof complete after proving only for one induction when we have more than one variable?

So I'm learning coq. And I came across the proof for associativity in addition forall (a b c : nat) Appearntly when we do ...
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1answer
249 views

How to get an element from an existential proposition in Type theory proof assistant (Lean prover)

I am trying to implement set theory in type theory from scratch, just for self pedagogical purposes. Specifically, I'm using the Lean Prover, and defining the element-of relation from scratch using ...
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2answers
69 views

How the kernel works in a LCF theorem prover

I heard that there is some mechanism in LCF-based theorem provers that only allows some functions to create values of type theorem. I believe these are based on abstract data types. Could someone ...
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5answers
5k views

Do theorem provers demonstrate their own correctness?

I am not very well-versed in the world of theorem proving, much less automated theorem proving, so please correct me if anything I say or assume in my question is wrong. Basically my question is: are ...
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0answers
19 views

Review of Formal Verification and How to Apply it to Greenfield Project [duplicate]

Last year I looked heavily into Formal Verification, such as automated theorem proving, model checking, type systems, symbolic evaluation, and many others. I probably spent a few weeks or maybe months ...
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0answers
101 views

What's the problem of Learning Algorithms used for Automated Theorem Provers?

I've googled a lot but I haven't found an automated theorem prover/problem solver able to solve problems like a human. I am interested in a specific type of prover: the learning ones, like Support ...
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0answers
44 views

Is there a correspondence of steps between DPLL and sequent-calculus?

Is there a correspondence between the steps in using DPLL to find out that a formula in propositional logic is unsatisfiable and using sequent calculus to prove that its negation is valid? And given ...
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0answers
30 views

Superposition calculus: greater vs greater-or-equal

Bachmair and Ganzinger 1991, 'Rewrite-Based Equational Theorem Proving With Selection and Simplification', specifies the criterion for using an equation as, by some appropriate ordering, ...
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1answer
38 views

Superposition calculus: Elimination of redundant atoms

Bachmair and Ganzinger (1991), 'Rewrite-Based Equational Theorem Proving With Selection and Simplification', section 5.2, 'Simplification and Deletion Techniques', page 17, 'Elimination of redundant ...
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1answer
28 views

Bachmair and Ganzinger, ordering of equations

Bachmair and Ganzinger (1991), 'Rewrite-Based Equational Theorem Proving With Selection and Simplification', page 4, defines an order on equations. (This is an arcane piece of machinery but a critical ...
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1answer
168 views

Roadmap to formal verification

I would like to learn about different approaches to formal verification of software programs that goes beyond what Wikipedia has to offer. Ideally one would not only get an overview but also ...
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0answers
50 views

Unification algorithm that directly finds multiple substitutions?

Systems of formal logic generally have inference rules that require certain expressions to be syntactically the same in multiple steps. Typically two steps are involved, as for modus ponens, where ...
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0answers
68 views

Type theory based automated theorem prover?

I know that there exist type theory based proof-checker, and I know that there are logic/sequent-calculus based automated theorem provers. But I haven’t heard of a type-theory based automated theorem ...
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0answers
26 views

Why aren’t (type theory based) automated theorem provers efficient?

Note: my main experience with theorem provers is with Type theory based proof-assistant, rather than an actual automated theorem prover. It is obvious why naive automated theorem proving is ...
2
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1answer
52 views

Finding libraries of formalized mathematics

I want to formalize Interval Newton Methods in Isabelle. As a research, I have the curiosity of whether there is anything done in the field. For that, I need to know what mathematical contents have ...
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0answers
53 views

Are there any interesting terms in pure LF or $\lambda\Pi$?

In my searching, I've seen that if Church numerals are encoded in a dependently typed Lambda calculus, that we can't derive induction or that $0 \neq 1$. I know that LF and the dependently typed ...
3
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1answer
34 views

Has the concept of using a hand checked simple theorem prover to validate more complex theorem provers been explored before?

More specifically, has anyone used a chain of theorem provers to validate a highly evolved theorem prover, starting with a very simple hand checked prover such that each new theorem prover is used to ...
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0answers
17 views

Differentiate arguments in SPASS prover formula

I have a formula in FOL: $\forall x \exists y: B(x) \implies C(y)$ and in SPASS: forall([X], exists[Y], implies(B(X),C(Y))) I want to check the formula: $\exists x:...
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1answer
1k views

What kind of math problems can be solved by automated theorem provers?

Can I prove following statements with using available automated theorem provers? $(a+b)^2=a^2+b^2+2ab$. If $ 11 \mid 2a-3b$, then $ 11 \mid 7a-5b $. If $ ax^2+bx+c=0$, then $x=\frac{-b\pm\sqrt{b^2-...
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1answer
74 views

How to define function type in AGDA

The "function" type $\rightarrow$ is predefined in Agda. But how would one define it if it was not predefined? Specifically I am talking about $\rightarrow$ in: ...
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0answers
43 views

Modern presentation of Ackermann's “Solvable Cases?”

Ackermann's book "Solvable Cases of the Decision Problem" discusses decidable instances of first order logic, particularly monadic logic, and so called "equality formulas". However, the book is from ...
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1answer
69 views

Theorem Prover for complexity theoretic reductions

Can complexity theoretic reductions that lead to proofs of say NP completeness be formalized using an existing theorem prover such as Coq? If so, can you provide an outline of how to formalize a ...
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1answer
898 views

Monadic Second Order Logic for Dummies

I am programmer with a grip on automata, but not on logic. I read in papers that the two are very tightly related. Deterministic Finite Automata (DFA), Tree Automata and Visibly Pushdown Automata are ...
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1answer
74 views

Why do TPTP Performance plots look like this?

CASC is the premier Automated Theorem Prover competition performed annually at the Conference on Automated Deduction (CADE). The 2017 event has finished on the 9th of August this year. During this ...
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1answer
164 views

Procedure to automatically solve field theorems in a SMT solver

I'm working with the Welder proof assistant. Basically, this system uses basic inference rules to modify the goal one wants to proof. At a latter step, the modified goals are passed to a SMT solver to ...
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0answers
40 views

Sorts and constructors for modelling classes in a theorem prover

I have been working in the Welder theorem prover for some time now. But I'm confused in the way they handle data-types. I'm not familiar with the terminology of sorts and constructors. Here is how one ...
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1answer
241 views

What was the major breakthrough between Hoare-Floyd logic and Scott–Strachey semantics?

I'm reading through a commentary on Milner's "The use of machines to assist in rigorous proof" by Mike Gordon. In this paper, he explains how LCF was born from the ideas of denotational semantics by ...
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1answer
54 views

Verification condition in case of array theory

As far as i can understand the problem of checking safety property, can be reduce to solving for inductive invariants in VC's and there is following parts to it: Generate VC's from the program. Solve ...
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1answer
90 views

Formal specification; Logical formula

* Initial Question * I'm trying to write a logical formula consists of three Boolean variable C1, C2, C3. My program takes graph as input and checks properties about them. C1 represents presence of ...
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1answer
59 views

Is it possible to build short proofs of arbitrary folds over a huge list?

With the use of Merkle Trees, you can prove the presence of an element of a very big list, with an amount of information close to just logarithm of the size of the whole tree. Merkle proofs, thus, ...
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2answers
192 views

Why Church-encoded types aren't sufficient to express inductive proofs?

I've heard some claims that the calculus of constructions without inductive types isn't powerful enough to express proofs by induction. Is that correct? If so, why isn't the Church-encoding sufficient ...
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0answers
71 views

How to self-learn automated theorem proving? [duplicate]

Year 12 high school student here, but my ambition is set on Automated Theorem Proving. I wish to apply it to, of course, mathematics and computer science, and maybe if possible other applied subjects ...
6
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1answer
223 views

Framework or tools to generate theorem prover/solver/reasoner for new logic

I have new logic which has syntax and semantics in usual natural languages and I have to create theorem prover/solver/reasoner for this logic. Is there framework or tool set that can generate such ...
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1answer
64 views

How to reduce constrained proofs to 0-1 IP

Consider the following problem: Can $X$ be proven in fewer than $Y$ steps, from axioms $Z$, with finitely many transition rules $\tau$? This lies in $NP$, since if I supply a proof $M$, and ...
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1answer
270 views

How did 'Isabelle' (the theorem prover) get its name?

The title says it all, but I'm curious because it isn't obvious how a theorem prover came to be named 'Isabelle'. Was it named for a person? I couldn't find out by some Google searches.
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1answer
95 views

Why do presenttations of proof systems in logic and automated reasoning not include the algorithm that finds proofs?

Is is that a common way to present a proof system in the field of Logic and Automated Reasoning is to present a system of inference rules, without having to formally describe a particular algorithm or ...
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1answer
33 views

Derivation of implicational propositional axioms

Is there a way to subtract and add properties of axioms to generate new axioms? For example: {L} = {P S K} // natural deduction {P S K} = {P H K I} // natural deduction {S K} = {?} // constructive ...
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1answer
148 views

How can I check constraints on my state machine behaviour?

My background is fairly practical rather than theoretical, so this question may be a bit basic. I have a state machine with events, and events may optionally trigger action functions to be called as ...
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1answer
448 views

What happens to uninterpreted predicates in Ackermann's reduction?

I know the procedure to apply the Ackermann's reduction to a formula that doesn't involve uninterpreted predicates. But, how do we treat the uninterpreted boolean predicates? Nearly all the examples I ...
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1answer
451 views

What is the difference between superposition and paramodulation?

I am currently writing a paper about automated theorem proving in first-order logic. Equality is not uncommon for mathematical problems and almost every theorem prover like VAMPIRE or SPASS has a ...
5
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1answer
288 views

Proof Carrying LLVM?

I am intrigued by and understand the very basics of Proof Carrying Code (PCC) and I recognize that LLVM is a machine-independent intermediate language. LLVM is the intermediate form of many languages,...
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0answers
76 views

sets of axioms for LADR automated theorem provers

I am pretty new to ATP, but I'm really enjoying playing around with prover9. I have found a nice set of axioms for basic information-theoretic proofs here, I was wondering if there are some ...
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1answer
712 views

Why is automated theorem proving impossible?

As far I know, in general case there is no Turing machine which could get any theorem on its input and produce its proof on its output. Why is it so?
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1answer
358 views

Automated theorem proving with SAT

If you had a polynomial time algorithm for determining boolean satisfiability how would you prove/disprove a conjecture like the Reimann-Zeta hypothesis (or the Pythagorean theorem for that matter) ...
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1answer
1k views

Euclidean Algorithm in Coq

Question How do I write more intuitive proofs of the two following results in Coq? ...
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2answers
2k 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, ...