While the use of XML is pervading all areas of IT, security challenges arise when XML files are used to transfer security data such as security policies. To tackle this issue, we have developed a lightweight secure XML validator and have chosen to base the development on the strongly typed functional language OCaml. The initial development took place as part of the LaFoSec Study which aimed at investigating the impact of using functional languages for security. We then turned the validator into an industrial application, which was successfully evaluated at EAL4+ level by independent assessors. In this paper, we explain the challenges involved in processing XML data in a critical context, we describe our choices in designing a secure XML validator, and we detail how we used features of functional languages to enforce security requirements.

We define a weak λ-calculus, λσ w , as a subsystem of the full λ-calculus with explicit substitutions λσ [uArr ] . We claim that λσ w could be the archetypal output language of functional compilers, just as the λ-calculus is their universal input language. Furthermore, λσ [uArr ] could be the adequate theory to establish the correctness of functional compilers. Here we illustrate these claims by proving the correctness of four simplified compilers and runtime systems modelled as abstract machines. The four machines we prove are the Krivine machine, the SECD, the FAM and the CAM. Thus, we give the first formal proofs of Cardelli's FAM and of its compiler.

Projet PARA

Categorical combinators [Curien 1986/1993; Hardin 1989; Yokouchi 1989] and more recently λσ-calculus [Abadi 1991; Hardin and Le´vy 1989], have been introduced to provide an explicit treatment of substitutions in the λ-calculus. We reintroduce here the ingredients of these calculi in a self-contained and stepwise way, with a special emphasis on confluence properties. The main new results of the paper with respect to Curien [1986/1993], Hardin [1989], Abadi [1991], and Hardin and Le´vy [1989] are the following: (1) We present a confluent weak calculus of substitutions, where no variable clashes can be feared; (2) We solve a conjecture raised in Abadi [1991]: λσ-calculus is not confluent (it is confluent on ground terms only). This unfortunate result is “repaired” by presenting a confluent version of λσ-calculus, named the λ Env -caldulus in Hardin and Le´vy [1989], called here the confluent λσ-calculus.

ασ-calculus is an extended λ-calculus where substitutions are handled explicitly. It is similar to, and inspired by, Categorical Combinatory logic (CCL). The strong normalization of σ, the subcalculus which computes substitutions, may be inferred from the strong normalization of the similar subsystem SUBST of CCL. We present here an independent proof of the termination of several substitution calculi, including σ and SUBST.

Higher-order unification is equational unification for /spl beta//spl eta/-conversion, but it is not first-order equational unification, as substitution has to avoid capture. In this paper higher-order unification is reduced to first-order equational unification in a suitable theory: the /spl lambda//spl sigma/-calculus of explicit substitutions.

In 1979, Klop (1980), answering a question raised by Mann in 1972, showed that the extension of λ-calculus with subjective pairing is not confluent. We refer to Klop (1980) and Barendregt (1981, revised 1984) for a perspective. The term presented by Klop to provide a counterexample is fairly simple, but the proof of non-confluence, although intuitively quite simple, involves some technical properties. Among others, a suitable standardization result on derivations in the extended system is needed in the proof. Klop's proof was revisited by Bunder (1985), who seemingly used less technical apparatus than Klop, starting with the same term as Klop. Although Bunder's proof does not explicitly use a standardization result, his proof proceeds internally with some rearrangements of derivations, so that it is fair to say that some standardization technique is present in Bunder (1985).