SUMMARY We present the design and implementation of a compiler from OCaml bytecode to JavaScript. The compiler first translates the bytecode into a static single‐assignment intermediate representation on which optimizations are performed, before generating JavaScript. We believe that taking bytecode as an input instead of a high‐level language is a sensible choice. Virtual machines provide a very stable API. Such a compiler is thus easy to maintain. It is also convenient to use, and it can just be added to an existing installation of the development tools. Already‐compiled libraries can be used directly, with no need to reinstall anything. Finally, some virtual machines are the target of several languages. A bytecode to JavaScript compiler would make it possible to retarget all these languages to Web browsers at once. Copyright © 2013 John Wiley & Sons, Ltd.

The evolution of Web sites towards very dynamic applications makes it necessary to reconsider current Web programming technologies. We believe that Web development would benefit greatly from more abstract paradigms and that a more semantical approach would result in huge gains in expressiveness. In particular, functional programming provides a really elegant solution to some important Web interaction problems, but few frameworks take advantage of it.

We present a notion of η-long β-normal term for the typed lambda calculus with sums and prove, using Grothendieck logical relations, that every term is equivalent to one in normal form. Based on this development we give the first type-directed partial evaluator that constructs %able to construct normal forms of terms in this calculus.

Tarski asked whether the arithmetic identities taught in high school are complete for showing all arithmetic equations valid for the natural numbers. The answer to this question for the language of arithmetic expressions using a constant for the number one and the operations of product and exponentiation is affirmative, and the complete equational theory also characterises isomorphism in the typed lambda calculus, where the constant for one and the operations of product and exponentiation respectively correspond to the unit type and the product and arrow type constructors. This paper studies isomorphisms in typed lambda calculi with empty and sum types from this viewpoint. We close an open problem by establishing that the theory of type isomorphisms in the presence of product, arrow, and sum types (with or without the unit type) is not finitely axiomatisable. Further, we observe that for type theories with arrow, empty and sum types the correspondence between isomorphism and arithmetic equality generally breaks down, but that it still holds in some particular cases including that of type isomorphism with the empty type and equality with zero.