Intersection types for unbind and rebind

We define a type system with intersection types for an extension of lambda-calculus with unbind and rebind operators. In this calculus, a term with free variables, representing open code, can be packed into an "unbound" term, and passed around as a value. In order to execute inside code, an unbound term should be explicitly rebound at the point where it is used. Unbinding and rebinding are hierarchical, that is, the term can contain arbitrarily nested unbound terms, whose inside code can only be executed after a sequence of rebinds has been applied. Correspondingly, types are decorated with levels, and a term has type decorated with k if it needs k rebinds in order to reduce to a value. With intersection types we model the fact that a term can be used differently in contexts providing different numbers of unbinds. In particular, top-level terms, that is, terms not requiring unbinds to reduce to values, should have a value type, that is, an intersection type where at least one element has level 0. With the proposed intersection type system we get soundness under the call-by-value strategy, an issue which was not resolved by previous type systems.Comment: In Proceedings ITRS 2010, arXiv:1101.410

Reconciling positional and nominal binding

We define an extension of the simply-typed lambda calculus where two different binding mechanisms, by position and by name, nicely coexist. In the former, as in standard lambda calculus, the matching between parameter and argument is done on a positional basis, hence alpha-equivalence holds, whereas in the latter it is done on a nominal basis. The two mechanisms also respectively correspond to static binding, where the existence and type compatibility of the argument are checked at compile-time, and dynamic binding, where they are checked at run-time.Comment: In Proceedings ITRS 2012, arXiv:1307.784

Constrained Polymorphic Types for a Calculus with Name Variables

We extend the simply-typed lambda-calculus with a mechanism for dynamic rebinding of code based on parametric nominal interfaces. That is, we introduce values which represent single fragments, or families of named fragments, of open code, where free variables are associated with names which do not obey alpha-equivalence. In this way, code fragments can be passed as function arguments and manipulated, through their nominal interface, by operators such as rebinding, overriding and renaming. Moreover, by using name variables, it is possible to write terms which are parametric in their nominal interface and/or in the way it is adapted, greatly enhancing expressivity. However, in order to prevent conflicts when instantiating name variables, the name-polymorphic types of such terms need to be equipped with simple {inequality} constraints. We show soundness of the type system

Computational Logic: Structure sharing and proof of program properties

Centre for Intelligent Systems and their ApplicationsThis thesis describes the results of two studies in computational logic. The first concerns a very efficient method of implementing resolution theorem provers. The second concerns a non-resolution program which automatically proves many theorems about LISP functions, using structural induction. In Part 1, a method of representing clauses, called 'structure sharing'is presented. In this representation, terms are instantiated by binding their variables on a stack, or in a dictionary, and derived clauses are represented in terms of their parents. This allows the structure representing a clause to be used in different contexts without renaming its variables or copying it in any way. The amount of space required for a clause is (2 + n) 36-bit words, where n is the number of components in the unifying substitution made for the resolution or factor. This is independant of the number of literals in the clause and the depth of function nesting. Several ways of making the unification algorithm more efficient are presented. These include a method od preprocessing the input terms so that the unifying substitution for derived terms can be discovered by a recursive look-up proceedure. Techniques for naturally mixing computation and deduction are presented. The structure sharing implementation of SL-resolution is described in detail. The relationship between structure sharing and programming language implementations is discussed. Part 1 concludes with the presentation of a programming language, based on predicate calculus, with structure sharing as the natural implementation. Part 2 of this thesis describes a program which automatically proves a wide variety of theorems about functions written in a subset of pre LISP. Features of this program include: The program is fully automatic, requiring no information from the user except the LISP definitions of the functions involved and the statement of the theorem to be proved. No inductive assertions are required for the user. The program uses structural induction when required, automatically generating its own induction formulas. All relationships in the theorem are expressed in terms of user defined LISP functions, rather than a secong logical language. The system employs no built-in information about any non-primitive function. All properties required of any function involved in a proof are derived and established automatically. The progeam is capable of generalizing some theorems in order to prove them; in doing so, it often generates interesting lemmas. The program can write new, recursive LISP functions automatically in attempting to generalize a theorem. Finally, the program is very fast by theorem proving standards, requiring around 10 seconds per proof

Programming language abstractions for mobile code

Scala is a general-purpose programming language developed at EPFL. It combines the most important concepts found in object-oriented and functional languages. Scala is a statically typed language; in particular it features an advanced type system and supports local type inference. Furthermore it integrates well with the Java and .net platforms: their libraries are accessible without glue code and the Scala compiler generates code for both execution environments. The Scala programming language has several features that make it desirable as a language for distributed application programming. In particular, it supports first-class functions which are useful in relation with the notions of distributed scope and code mobility. In that context, the missing support for run-time types is one important drawback of the Java run-time environment as a target platform. This thesis focuses on the realisation of a new concept combining essential notions from the functional and distributed programming and implying the extension of the notion of lexical scoping to the distributed context. In short, we claim that the notion of lambda abstraction provides an elegant way for dealing with the dynamic rebinding of local references in a distributed execution environment. The key ideas exposed in this research work have been implemented in our Scala compiler. This helped us to evaluate the used techniques, in particular their impact on the reliability and the performance of distributed programs. So far, most research works related to the present subject have focused on functional programming languages, in particular on the ML language family

Extending the lambda-calculus with unbind and rebind

We extend the simply typed lambda-calculus with unbind and rebind primitive constructs. That is, a value can be a fragment of open code, which in order to be used should be explicitly rebound. This mechanism nicely coexists with standard static binding. The motivation is to provide an unifying foundation for mechanisms of dynamic scoping, where the meaning of a name is determined at runtime, rebinding, such as dynamic updating of resources and exchange of mobile code, and delegation, where an alternative action is taken if a binding is missing. Depending on the application scenario, we consider two extensions which differ in the way type safety is guaranteed. The former relies on a combination of static and dynamic type checking. That is, rebind raises a dynamic error if for some variable there is no replacing term or it has the wrong type. In the latter, this error is prevented by a purely static type system, at the price of more sophisticated types