arXiv subjects

Rodolphe Lepigre

Publications and source records attributed to Rodolphe Lepigre.

5 recordsLinked to original sources

arXiv2019

PML 2 : Integrated Program Verification in ML

We present the PML 2 language, which provides a uniform environment for programming, and for proving properties of programs in an ML-like setting. The language is Curry-style and call-by-value, it provides a control operator (interpreted in terms of classical logic), it supports general recursion and a very general form of (implicit, non-coercive) subtyping. In the system, equational properties of programs are expressed using two new type formers, and they are proved by constructing terminating programs. Although proofs rely heavily on equational reasoning, equalities are exclusively managed by the type-checker. This means that the user only has to choose which equality to use, and not where to use it, as is usually done in mathematical proofs. In the system, writing proofs mostly amounts to applying lemmas (possibly recursive function calls), and to perform case analyses (pattern matchings).

cs.LO↗

arXiv2018

Unboxing Mutually Recursive Type Definitions in OCaml

In modern OCaml, single-argument datatype declarations (variants with a single constructor, records with a single field) can sometimes be `unboxed'. This means that their memory representation is the same as their single argument (omitting the variant or record constructor and an indirection), thus achieving better time and memory efficiency. However, in the case of generalized/guarded algebraic datatypes (GADTs), unboxing is not always possible due to a subtle assumption about the runtime representation of OCaml values. The current correctness check is incomplete, rejecting many valid definitions, in particular those involving mutually-recursive datatype declarations. In this paper, we explain the notion of separability as a semantic for the unboxing criterion, and propose a set of inference rules to check separability. From these inference rules, we derive a new implementation of the unboxing check that properly supports mutually-recursive definitions.

cs.PL↗

arXiv2018

Abstract Representation of Binders in OCaml using the Bindlib Library

The Bindlib library for OCaml provides a set of tools for the manipulation of data structures with variable binding. It is very well suited for the representation of abstract syntax trees, and has already been used for the implementation of half a dozen languages and proof assistants (including a new version of the logical framework Dedukti). Bindlib is optimised for fast substitution, and it supports variable renaming. Since the representation of binders is based on higher-order abstract syntax, variable capture cannot arise during substitution. As a consequence, variable names are not updated at substitution time. They can however be explicitly recomputed to avoid "visual capture" (i.e., distinct variables with the same apparent name) when a data structure is displayed.

cs.PL↗

arXiv2017

Practical Subtyping for System F with Sized (Co-)Induction

We present a rich type system with subtyping for an extension of System F. Our type constructors include sum and product types, universal and existential quantifiers, inductive and coinductive types. The latter two size annotations allowing the preservation of size invariants. For example it is possible to derive the termination of the quicksort by showing that partitioning a list does not increase its size. The system deals with complex programs involving mixed induction and coinduction, or even mixed (co-)induction and polymorphism (as for Scott-encoded datatypes). One of the key ideas is to completely separate the induction on sizes from the notion of recursive programs. We use the size change principle to check that the proof is well-founded, not that the program terminates. Termination is obtained by a strong normalization proof. Another key idea is the use symbolic witnesses to handle quantifiers of all sorts. To demonstrate the practicality of our system, we provide an implementation that accepts all the examples discussed in the paper and much more.

cs.LO↗

arXiv2016

A Classical Realizability Model for a Semantical Value Restriction

We present a new type system with support for proofs of programs in a call-by-value language with control operators. The proof mechanism relies on observational equivalence of (untyped) programs. It appears in two type constructors, which are used for specifying program properties and for encoding dependent products. The main challenge arises from the lack of expressiveness of dependent products due to the value restriction. To circumvent this limitation we relax the syntactic restriction and only require equivalence to a value. The consistency of the system is obtained semantically by constructing a classical realizability model in three layers (values, stacks and terms).

cs.LO↗