Abstract
Interactive theorem provers (ITPs) are software tools that allow human users to write and verify formal proofs. In recent years, an emerging research area in ITPs is proof mining, which consists of identifying interesting proof patterns that can be used to guide the interactive proof process in ITPs. In previous studies, some data mining techniques, such as frequent pattern mining, have been used to analyze proofs to find frequent proof steps. Though useful, such models ignore the facts that not all proof steps are equally important. To address this issue, this paper proposes a novel proof mining approach based on finding not only frequent patterns but also high utility patterns to find proof steps of high importance (utility). A proof process learning approach is proposed based on high utility itemset mining (HUIM) for the PVS (Prototype Verification System) proof assistant. Proofs in PVS theories are first abstracted to a computer-processable corpus, where each line represents a proof sequence and proof commands in proof sequences are associated with utilities representing their weightage (importance). HUIM techniques are then applied on the corpus to discover frequent proof steps/high utility patterns and their relationships with each other. Experimental results suggest that combining frequent pattern mining techniques, such as sequential pattern mining and high utility itemset mining, with proof assistants, such as PVS, is useful to learn and guide the proof development process.
Highlights
Theorem proving is a famous approach in formal methods that is used for the analysis of hardware and software systems, especially safety critical systems
The main reason to select the proofs in [32], [33] is that we are extending the formalization framework to cover the stochastic [5] and hybrid [8] behavior of Reo connectors. We believe that this proof learning approach will enable us to comprehend the proof process for stochastic and hybrid connectors and can be considered far more effective in providing the necessary guidance to attain the proofs of such connectors
To make the proof process simpler and for providing proof guidance, high utility itemset mining (HUIM)-based learning approach is adopted in this work to find the frequent proof steps/patterns and their relationship in Prototype verification system (PVS) theories
Summary
Theorem proving is a famous approach in formal methods that is used for the analysis of hardware and software systems, especially safety critical systems. If the corpus has 20 PPS, we need to calculate the utilities of 220 − 1 possible PSS This is very hard to achieve with the naive approach as the size of the search space (that indicates the total number of possible PSS) is very large even if there are few proofs in the corpus. Some fast algorithms are designed in recent years that can avoid the scanning of all possible itemsets in the search space and can find all high utility patterns Some of these algorithms that we used in this work to mine PVS proofs are described
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