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Register a new userParametric Compositional Data Types
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Publication date
2012
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Informatics Engineering
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English
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In previous work we have illustrated the benefits that compositional data types (CDTs) offer for implementing languages and in general for dealing with abstract syntax trees (ASTs). Based on Swierstras data types a la carte, CDTs are implemented as a Haskell library that enables the definition of recursive data types and functions on them in a modular and extendable fashion. Although CDTs provide a powerful tool for analysing and manipulating ASTs, they lack a convenient representation of variable binders. In this paper we remedy this deficiency by combining the framework of CDTs with Chlipalas parametric higher-order abstract syntax (PHOAS). We show how a generalisation from functors to difunctors enables us to capture PHOAS while still maintaining the features of the original implementation of CDTs, in particular its modularity. Unlike previous approaches, we avoid so-called exotic terms without resorting to abstract types: this is crucial when we want to perform transformations on CDTs that inspect the recursively computed CDTs, e.g. constant folding.
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We address the problem of proving the satisfiability of Constrained Horn Clauses (CHCs) with Algebraic Data Types (ADTs), such as lists and trees. We propose a new technique for transforming CHCs with ADTs into CHCs where predicates are defined over basic types, such as integers and booleans, only. Thus, our technique avoids the explicit use of inductive proof rules during satisfiability proofs. The main extension over previous techniques for ADT removal is a new transformation rule, called differential replacement, which allows us to introduce auxiliary predicates corresponding to the lemmas that are often needed when making inductive proofs. We present an algorithm that uses the new rule, together with the traditional folding/unfolding transformation rules, for the automatic removal of ADTs. We prove that if the set of the transformed clauses is satisfiable, then so is the set of the original clauses. By an experimental evaluation, we show that the use of the differential replacement rule significantly improves the effectiveness of ADT removal, and we show that our transformation-based approach is competitive with respect to a well-established technique that extends the CVC4 solver with induction.
We consider the verification of lock-free data structures that manually manage their memory with the help of a safe memory reclamation (SMR) algorithm. Our first contribution is a type system that checks whether a program properly manages its memory. If the type check succeeds, it is safe to ignore the SMR algorithm and consider the program under garbage collection. Intuitively, our types track the protection of pointers as guaranteed by the SMR algorithm. There are two design decisions. The type system does not track any shape information, which makes it extremely lightweight. Instead, we rely on invariant annotations that postulate a protection by the SMR. To this end, we introduce angels, ghost variables with an angelic semantics. Moreover, the SMR algorithm is not hard-coded but a parameter of the type system definition. To achieve this, we rely on a recent specification language for SMR algorithms. Our second contribution is to automate the type inference and the invariant check. For the type inference, we show a quadratic-time algorithm. For the invariant check, we give a source-to-source translation that links our programs to off-the-shelf verification tools. It compiles away the angelic semantics. This allows us to infer appropriate annotations automatically in a guess-and-check manner. To demonstrate the effectiveness of our type-based verification approach, we check linearizability for various list and set implementations from the literature with both hazard pointers and epoch-based memory reclamation. For many of the examples, this is the first time they are verified automatically. For the ones where there is a competitor, we obtain a speed-up of up to two orders of magnitude.
Global session types prevent participants from waiting for never coming messages. Some interactions take place just for the purpose of informing receivers that some message will never arrive or the session is terminated. By decomposing a big global type into several light global types, one can avoid such kind of redundant interactions. Lightening global types gives us cleaner global types, which keep all necessary communications. This work proposes a framework which allows to easily decompose global types into light global types, preserving the interaction sequences of the original ones but for redundant interactions.
Session types are a rich type discipline, based on linear types, that lifts the sort of safety claims that come with type systems to communications. However, web-based applications and microservices are often written in a mix of languages, with type disciplines in a spectrum between static and dynamic typing. Gradual session types address this mixed setting by providing a framework which grants seamless transition between statically typed handling of sessions and any required degree of dynamic typing. We propose Gradual GV as a gradually typed extension of the functional session type system GV. Following a standard framework of gradual typing, Gradual GV consists of an external language, which relaxes the type system of GV using dynamic types, and an internal language with casts, for which operational semantics is given, and a cast-insertion translation from the former to the latter. We demonstrate type and communication safety as well as blame safety, thus extending previous results to functional languages with session-based communication. The interplay of linearity and dynamic types requires a novel approach to specifying the dynamics of the language.
Constraint Handling Rules (CHR) are a committed-choice declarative language which has been designed for writing constraint solvers. A CHR program consists of multi-headed guarded rules which allow one to rewrite constraints into simpler ones until a solved form is reached. CHR has received a considerable attention, both from the practical and from the theoretical side. Nevertheless, due the use of multi-headed clauses, there are several aspects of the CHR semantics which have not been clarified yet. In particular, no compositional semantics for CHR has been defined so far. In this paper we introduce a fix-point semantics which characterizes the input/output behavior of a CHR program and which is and-compositional, that is, which allows to retrieve the semantics of a conjunctive query from the semantics of its components. Such a semantics can be used as a basis to define incremental and modular analysis and verification tools.
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