Static Type Analysis of Pattern Matching by Abstract Interpretation

Abstract

Abstract. Pattern matching is one of the most attractive features of functional programming languages. Recently, pattern matching has been applied to programming languages supporting the main current object oriented features. In this paper, we present a static type analysis based on the abstract interpretation framework aimed at proving the exhaustiveness of pattern matchings and the safety of type casts. The analysis is composed by two distinct abstract domains. The first domain collects information about dynamic typing, while the second one tracks the types that an object cannot be instance of. The analysis has been implemented and applied to all the Scala library. The experimental results underline that our approach scales up since it analyzes a method in 90 msec in average. In addition, the analysis is precise in practice as well, since we prove the exhaustiveness of 42% of pattern matchings and 27% of the type casts without any manual annotation on the code.

Static Analysis of String Values

“…We chose some string operators on which we focused our approach defining the concrete and the abstract semantics. Future work We are working on the implementation of our approach in Sample (Static Analyzer of Multiple Programming LanguagEs) [9]. We plan to apply our analysis to some case studies to study the precision of our analysis.…”

Satisfiability Modulo Recursive Programs

“…Previously, researchers have developed specialized analyses for checking such exhaustiveness properties [9,11]. Our system generates verification conditions for checking the exhaustiveness of all pattern-matching expressions, and then uses the same procedure to prove or disprove them as for the other verification conditions.…”

Generic Combination of Heap and Value Analyses in Abstract Interpretation

“…The most part of the theoretical ideas contained in this paper came from some practical experience the authors get with Sample [8,14,17,34], a generic static analyzer that combines different heap and value analyses. We are currently extending this analyzer with all the results of this paper, and to provide an interface to plug implementation of heap and numerical analyses to external users.…”