Section: New Results

Static analysis

Participant : Sergueï Lenglet.

Static analysis for control operators

Control operators allow programs to have access and manipulate their execution context. Abortive control operators, such as call/cc in Scheme or SML, capture the entire execution context (also called continuation), while delimited-control operators, such as shift and reset captures only a part of the continuation (delimited by reset). We want to prove properties (like equivalences between terms or termination) for languages with these operators, using static analysis.

In [9] , [16] , we study the behavioral theory of a language with delimited control. More precisely, we define environmental bisimilarities for the delimited-control operators shift and reset. We consider two different notions of contextual equivalence: one that does not require the presence of a top-level control delimiter when executing tested terms, and another one, fully compatible with the original CPS semantics of shift and reset, that does. For each of them, we develop sound and complete environmental bisimilarities, and we discuss up-to techniques.

In [8] , we present new proofs of termination of evaluation in reduction semantics (i.e., a small-step operational semantics with explicit representation of evaluation contexts) for System F with control operators. We introduce a modified version of Girard's proof method based on reducibility candidates, where the reducibility predicates are defined on values and on evaluation contexts as prescribed by the reduction semantics format. We address both abortive control operators (callcc) and delimited-control operators (shift and reset) for which we introduce novel polymorphic type systems, and we consider both the call-by-value and call-by-name evaluation strategies.

Polymorphism and higher-order functions for XML

In [11] , we define a calculus with higher-order polymorphic functions, recursive types with arrow and product type constructors and set-theoretic type connectives (union, intersection, and negation). We study the explicitly-typed version of the calculus in which type instantiation is driven by explicit instantiation annotations. In particular, we define an explicitly-typed $\lambda$-calculus with intersection types and an efficient evaluation model for it. In a companion paper  [21] , we define a local type inference system that allows the programmer to omit explicit instantiation annotations, and a type reconstruction system that allows the programmer to omit explicit type annotations. The work presented in the two articles provides the theoretical foundations and technical machinery needed to design and implement higher-order polymorphic functional languages for semi-structured data.