Uppaal is a tool suite for automatic verification of safety and bounded liveness properties of real-time systems modeled as networks of timed automata. It includes: a graphical interface that supports graphical and textual representations of networks of timed automata, and automatic transformation from graphical representations to textual format, a compiler that transforms a certain class of linear hybrid systems to networks of timed automata, and a model-checker which is implemented based on constraint-solving techniques. Uppaal also supports diagnostic model-checking providing diagnostic information in case verification of a particular real-time systems fails.

UPPAAL: a Tool Suite for Automatic Verification of Real Time Systems

Handbook of logic in computer science.

https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.70.9621&rep=rep1&type=pdf

UPPAAL—a tool suite for automatic verification of real-time systems

A Combinatory Logic

The mismatch between the operational semantics of the lambda calculus and the actual behavior of implementations is a major obstacle for compiler writers. They cannot explain the behavior of their evaluator in terms of source level syntax, and they cannot easily compare distinct implementations of different lazy strategies. In this paper we derive an equational characterization of call-by-need and prove it correct with respect to the original lambda calculus. The theory is a strictly smaller theory than the lambda calculus. Immediate applications of the theory concern the correctness proofs of a number of implementation strategies, e.g., the call-by-need continuation passing transformation and the realization of sharing via assignments.

/pdf/a-call-by-need-lambda-calculus-44qdmt1cvy.pdf

A call-by-need lambda calculus

Explicit substitutions were proposed by Abadi, Cardelli, Curien, Hardin and Levy to internalise substitutions into $\lambda$-calculus and to propose a mechanism for computing on substitutions. $\lambda\upsilon$ is another view of the same concept which aims to explain the process of substitution and to decompose it in small steps. $\lambda\upsilon$ is simple and preserves strong normalisation. Apparently that important property cannot stay with another important one, namely confluence on open terms. The spirit of $\lambda\upsilon$ is closely related to another calculus of explicit substitutions proposed by de Bruijn and called $C\lambda\xi\phi$. In this paper, we introduce $\lambda\upsilon$, we present $C\lambda\xi\phi$ in the same framework as $\lambda\upsilon$ and we compare both calculi. Moreover, we prove properties of $\lambda\upsilon$; namely $\lambda\upsilon$ correctly implements $\beta$ reduction, $\lambda\upsilon$ is confluent on closed terms, i.e., on terms of classical $\lambda$-calculus and on all terms that are derived from those terms, and finally $\lambda\upsilon$ preserves strong normalization of $\beta$-reduction.

https://hal.inria.fr/inria-00074197/document

λν, a calculus of explicit substitutions which preserves strong normalisation

We present the λσ w a -calculus, a formal synthesis of the concepts of sharing and explicit substitution for weak reduction. We show how λσ w a , can be used as a foundation of implementations of functional programming languages by modeling the essential ingredients of such implementations, namely weak reduction strategies, recursion, space leaks, recursive data structures, and parallel evaluation. We use λσ w a , to give a unified model of several computational aspects. First, we give a precise account of the major reduction strategies used in functional programming and the consequences of choosing λ-graph-reduction vs. environment-based evaluation. Second, we show how to add constructors and explicit recursion to give a precise account of recursive functions and data structures even with respect to space complexity. Third, we formalize the notion of space leaks in λσ w a and use this to define a space leak free calculus; this suggests optimisations for call-by-need reduction that prevent space leaking and enables us to prove that the “trimming” performed by the STG machine does not leak space. In summary we give a formal account of several implementation techniques used by state of the art implementations of functional programming languages.

/pdf/modeling-sharing-and-recursion-for-weak-reduction-strategies-330spmkabi.pdf

Modeling Sharing and Recursion for Weak Reduction Strategies Using Explicit Substitution

We present the lambda sigma^a_w calculus, a formal synthesis of the concepts of sharing and explicit substitution for weak reduction. We show how lambda sigma^a_w can be used as a foundation of implementations of functional programming languages by modelling the essential ingredients of such implementations, namely weak reduction strategies, recursion, space leaks, recursive data structures, and parallel evaluation, in a uniform way. First, we give a precise account of the major reduction strategies used in functional programming and the consequences of choosing lambda-graph-reduction vs. environment-based evaluation. Second, we show how to add constructors and explicit recursion to give a precise account of recursive functions and data structures even with respect to space complexity. Third, we formalize the notion of space leaks in lambda sigma^a_w and use this to define a space leak free calculus; this suggests optimisations for call-by-need reduction that prevent space leaking and enables us to prove that the "trimming" performed by the STG machine does not leak space. In summary we give a formal account of several implementation techniques used by state of the art implementations of functional programming languages. Keywords. Implementation of functional programming, lambda calculus, weak reduction, explicit substitution, sharing, recursion, space leaks.

/pdf/modeling-sharing-and-recursion-for-weak-reduction-strategies-1cy8krmle7.pdf

Zine-El-Abidine Benaissa

Papers

λν, a calculus of explicit substitutions which preserves strong normalisation

Modeling Sharing and Recursion for Weak Reduction Strategies Using Explicit Substitution

Modeling, Sharing, and Recursion for Weak Reduction Strategies using Explicit Substitution