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Prior Year Forms and Instructions
The ITP conference series is concerned with all topics related to interactive theorem proving, ranging from theoretical foundations to implementation aspects and applications in program verification, security, and formalization of mathematics.
TPHOLs meetings took place every year from until The proceedings for ITP conference are published in the Springer series Lecture Notes in Computer Science LNCS , volume and will be freely accessible, as a courtesy of Springer, for registered attendees during the event in the following link: Call for Papers ITP welcomes submissions describing original research on all aspects of interactive theorem proving and its applications. Suggested topics include but are not limited to the following: All submissions must be original, unpublished, and not submitted concurrently for publication elsewhere.
Furthermore, submissions are expected to be accompanied by verifiable evidence of a suitable implementation, such as the source files of a formalization for the proof assistant used. Submissions should be no more than 16 pages in length and are to be submitted in PDF via EasyChair at the following address: The proceedings are to be published as a volume in the Lecture Notes in Computer Science series and will be available to participants at the conference. Authors of accepted papers are expected to present their paper at the conference and will be required to sign a copyright release forms.
In addition to regular papers, described above, there will be a rough diamond section. Rough diamond submissions are limited to 6 pages and may consist of an extended abstract. They will be refereed and be expected to present innovative and promising ideas, possibly in an early form and without supporting evidence.
Accepted diamonds will be published in the main proceedings and will be presented as short talks. Formatting instructions and the LNCS style files can be obtained at: After the conference the authors of selected papers will be invited to submit revised papers for a special issue of the Journal of Automated Reasoning. Important Dates Submission of title and abstracts: Monday, April 3, Submission of full papers: Monday, April 10, Author notification: Friday, June 2, Camera-ready papers: September , Main conference: The perimeter of decidability with sequent calculi on the inside Abstract: Sequent calculi are preeminently capable of controlling the shape of proofs in a logic.
Sometimes this allows decidability to be proved. However, formulating certain intensional logics as sequent calculi creates challenges. I will start with sequent calculi for implicational ticket entailment, and highlight some of the key ideas behind a well-behaved sequent calculus, which was partly inspired by structurally free logics. The decidability of implicational ticket entailment was an open problem for about 50 years.
The decidability proof of pure relevant implication Kripke can be and has been utilized differently than for implicational ticket entailment.
I will focus on adding modalities, lattice connectives and structural rules both in unrestricted and limited forms. Many of the resulting logics are not among the well-known normal modal logics. I will show that certain ways of adding modalities keep the logic decidable. Moreover, the Curry-Kripke method possibly, with some additions still can be used to prove their decidability.
These co datatypes are complemented by definitional principles for co recursive functions and reasoning principles for co induction. In contrast with other systems offering codatatypes, no additional axioms or logic extensions are necessary with our approach. An introduction to the Hipster system Abstract: Theory exploration is a technique for automatically discovering new interesting lemmas in a mathematical theory development using testing.
This work was originally motivated by attempts to provide a higher level of automation for proofs by induction. Automating inductive proofs is tricky, not least because they often need auxiliary lemmas which themselves need to be proved by induction.
We found that many such basic lemmas can be discovered automatically by theory exploration, and importantly, quickly enough for use in conjunction with an interactive theorem prover without boring the user.
Hipster consists of two main components: The conjectures are then passed on to the prover component which is implemented in Isabelle.
Hipster can be configured to use various Isabelle tactics, including combining it with Sledgehammer. Hipster discards any conjectures that are trivial to prove and outputs snippets of proof scripts for each interesting lemma it discovers. The user can then easily include these lemmas and their proofs into the Isabelle theory file by a mouse-click.
The Hipster project is ongoing and open source, with code available from GitHub: We happily invite those interested in Hipster to try it out and welcome contributions to further development. We discuss the progress in our project which aims to automate formalization by combining natural language processing with deep semantic understanding of mathematical expressions. We introduce the overall motivation and ideas behind this project, and then propose a context-based parsing approach that combines efficient statistical learning of deep parse trees with their semantic pruning by type checking and large-theory automated theorem proving.
We show that our learning method allows efficient use of large amount of contextual information, which in turn significantly boosts the precision of the statistical parsing and also makes it more efficient. This leads to a large improvement of our first results in parsing theorems from the Flyspeck corpus. We describe the metaprogramming language currently in use in Lean, a new open source theorem prover that is designed to bridge the gap between interactive use and automation.
Lean implements a version of the Calculus of Inductive Constructions. Its elaborator and unification algorithms are designed around the use of type classes, which support algebraic reasoning, programming abstractions, and other generally useful means of expression.
Lean also has parallel compilation and checking of proofs, and provides a server mode that supports a continuous compilation and rich user interaction in editing environments such as Emacs, Vim, and Visual Studio Code. Lean currently has a conditional term rewriter, and several components commonly found in state-of-the-art Satisfiability Modulo Theories SMT solvers such as forward chaining, congruence closure, handling of associative and commutative operators, and E-matching. All these components are available in the metaprogramming framework, and can be combined and customized by users.
In this talk, we provide a short introduction to the Lean theorem prover and its metaprogramming framework. We also describe how this framework extends Lean’s object language with an API to many of Lean’s internal structures and procedures, and provides ways of reflecting object-level expressions into the metalanguage. We provide evidence to show that our implementation is performant, and that it provides a convenient and flexible way of writing not only small-scale interactive tactics, but also more substantial kinds of automation.
We view this as important progress towards our overarching goal of bridging the gap between interactive and automated reasoning. Users who develop libraries for interactive use can now more easily develop special-purpose automation to go with them thereby encoding procedural heuristics and expertise alongside factual knowledge. At the same time, users who want to use Lean as a back end to assist in complex verification tasks now have flexible means of adapting Lean’s libraries and automation to their specific needs.
As a result, our metaprogramming language opens up new opportunities, allowing for more natural and intuitive forms of interactive reasoning, as well as for more flexible and reliable forms of automation. More information about Lean can be found at http: In the HTML version, all examples and exercises can be executed in the reader’s web browser.
ITP Accepted Papers.
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