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Jónathan Heras

Publications and source records attributed to Jónathan Heras.

28 records · Page 2Linked to original sources
arXiv2014

Proof Pattern Search in Coq/SSReflect

ML4PG is an extension of the Proof General interface, allowing the user to invoke machine-learning algorithms and find proof similarities in Coq/SSReect libraries. In this paper, we present three new improvements to ML4PG. First, a new method of "recurrent clustering" is introduced to collect statistical features from Coq terms. Now the user can receive suggestions about similar definitions, types and lemma statements, in addition to proof strategies. Second, Coq proofs are split into patches to capture proof strategies that could arise at different stages of a proof. Finally, we improve ML4PG's output introducing an automaton-shape representation for proof patterns.

cs.LO↗
arXiv2013

Exploiting Parallelism in Coalgebraic Logic Programming

We present a parallel implementation of Coalgebraic Logic Programming (CoALP) in the programming language Go. CoALP was initially introduced to reflect coalgebraic semantics of logic programming, with coalgebraic derivation algorithm featuring both corecursion and parallelism. Here, we discuss how the coalgebraic semantics influenced our parallel implementation of logic programming.

cs.PL↗
arXiv2013

Proof-Pattern Recognition and Lemma Discovery in ACL2

We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already seen examples. This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it.

cs.LO↗
arXiv2013

Machine Learning in Proof General: Interfacing Interfaces

We present ML4PG - a machine learning extension for Proof General. It allows users to gather proof statistics related to shapes of goals, sequences of applied tactics, and proof tree structures from the libraries of interactive higher-order proofs written in Coq and SSReflect. The gathered data is clustered using the state-of-the-art machine learning algorithms available in MATLAB and Weka. ML4PG provides automated interfacing between Proof General and MATLAB/Weka. The results of clustering are used by ML4PG to provide proof hints in the process of interactive proof development.

cs.AI↗
arXiv2013

A certified reduction strategy for homological image processing

The analysis of digital images using homological procedures is an outstanding topic in the area of Computational Algebraic Topology. In this paper, we describe a certified reduction strategy to deal with digital images, but preserving their homological properties. We stress both the advantages of our approach (mainly, the formalisation of the mathematics allowing us to verify the correctness of algorithms) and some limitations (related to the performance of the running systems inside proof assistants). The drawbacks are overcome using techniques that provide an integration of computation and deduction. Our driving application is a problem in bioinformatics, where the accuracy and reliability of computations are specially requested.

cs.LO↗
arXiv2013

ML4PG in Computer Algebra verification

ML4PG is a machine-learning extension that provides statistical proof hints during the process of Coq/SSReflect proof development. In this paper, we use ML4PG to find proof patterns in the CoqEAL library -- a library that was devised to verify the correctness of Computer Algebra algorithms. In particular, we use ML4PG to help us in the formalisation of an efficient algorithm to compute the inverse of triangular matrices.

cs.LO↗
arXiv2013

Verifying a platform for digital imaging: a multi-tool strategy

Fiji is a Java platform widely used by biologists and other experimental scientists to process digital images. In particular, in our research - made together with a biologists team; we use Fiji in some pre-processing steps before undertaking a homological digital processing of images. In a previous work, we have formalised the correctness of the programs which use homological techniques to analyse digital images. However, the verification of Fiji's pre-processing step was missed. In this paper, we present a multi-tool approach filling this gap, based on the combination of Why/Krakatoa, Coq and ACL2.

cs.SE↗
arXiv2012

Computing Persistent Homology within Coq/SSReflect

Persistent homology is one of the most active branches of Computational Algebraic Topology with applications in several contexts such as optical character recognition or analysis of point cloud data. In this paper, we report on the formal development of certified programs to compute persistent Betti numbers, an instrumental tool of persistent homology, using the Coq proof assistant together with the SSReflect extension. To this aim it has been necessary to formalize the underlying mathematical theory of these algorithms. This is another example showing that interactive theorem provers have reached a point where they are mature enough to tackle the formalization of nontrivial mathematical theories.

cs.LO↗
arXiv2012

Verifying an algorithm computing Discrete Vector Fields for digital imaging

In this paper, we present a formalization of an algorithm to construct admissible discrete vector fields in the Coq theorem prover taking advantage of the SSReflect library. Discrete vector fields are a tool which has been welcomed in the homological analysis of digital images since it provides a procedure to reduce the amount of information but preserving the homological properties. In particular, thanks to discrete vector fields, we are able to compute, inside Coq, homological properties of biomedical images which otherwise are out of the reach of this system.

cs.AI↗