74,933 research outputs found
Hipster: Integrating Theory Exploration in a Proof Assistant
This paper describes Hipster, a system integrating theory exploration with
the proof assistant Isabelle/HOL. Theory exploration is a technique for
automatically discovering new interesting lemmas in a given theory development.
Hipster can be used in two main modes. The first is exploratory mode, used for
automatically generating basic lemmas about a given set of datatypes and
functions in a new theory development. The second is proof mode, used in a
particular proof attempt, trying to discover the missing lemmas which would
allow the current goal to be proved. Hipster's proof mode complements and
boosts existing proof automation techniques that rely on automatically
selecting existing lemmas, by inventing new lemmas that need induction to be
proved. We show example uses of both modes
The use of data-mining for the automatic formation of tactics
This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques
Quantifying pervasive authentication: the case of the Hancke-Kuhn protocol
As mobile devices pervade physical space, the familiar authentication
patterns are becoming insufficient: besides entity authentication, many
applications require, e.g., location authentication. Many interesting protocols
have been proposed and implemented to provide such strengthened forms of
authentication, but there are very few proofs that such protocols satisfy the
required security properties. The logical formalisms, devised for reasoning
about security protocols on standard computer networks, turn out to be
difficult to adapt for reasoning about hybrid protocols, used in pervasive and
heterogenous networks.
We refine the Dolev-Yao-style algebraic method for protocol analysis by a
probabilistic model of guessing, needed to analyze protocols that mix weak
cryptography with physical properties of nonstandard communication channels.
Applying this model, we provide a precise security proof for a proximity
authentication protocol, due to Hancke and Kuhn, that uses a subtle form of
probabilistic reasoning to achieve its goals.Comment: 31 pages, 2 figures; short version of this paper appeared in the
Proceedings of MFPS 201
Learning to Prove Theorems via Interacting with Proof Assistants
Humans prove theorems by relying on substantial high-level reasoning and
problem-specific insights. Proof assistants offer a formalism that resembles
human mathematical reasoning, representing theorems in higher-order logic and
proofs as high-level tactics. However, human experts have to construct proofs
manually by entering tactics into the proof assistant. In this paper, we study
the problem of using machine learning to automate the interaction with proof
assistants. We construct CoqGym, a large-scale dataset and learning environment
containing 71K human-written proofs from 123 projects developed with the Coq
proof assistant. We develop ASTactic, a deep learning-based model that
generates tactics as programs in the form of abstract syntax trees (ASTs).
Experiments show that ASTactic trained on CoqGym can generate effective tactics
and can be used to prove new theorems not previously provable by automated
methods. Code is available at https://github.com/princeton-vl/CoqGym.Comment: Accepted to ICML 201
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