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Reynolds' abstraction theorem shows how a typing judgement in System F can be translated into a relational statement (in second order predicate logic) about inhabitants of the type. We (in second order predicate logic) about inhabitants of the type. We obtain a similar result for a single lambda calculus (a pure type system), in which terms, types and their… (More)

- Jean-Philippe Bernardy, Patrik Jansson, Ross Paterson
- J. Funct. Program.
- 2012

- Jean-Philippe Bernardy, Marc Lasson
- FOSSACS
- 2011

We describe a systematic method to build a logic from any programming language described as a Pure Type System (PTS). The formulas of this logic express properties about programs. We define a parametricity theory about programs and a realizability theory for the logic. The logic is expressive enough to internalize both theories. Thanks to the PTS setting,… (More)

This paper is concerned with testing properties of polymor-phic functions. The problem is that testing can only be performed on specific monomorphic instances, whereas parametrically polymorphic functions are expected to work for any type. We present a schema for constructing a monomorphic instance for a polymorphic property, such that correctness of that… (More)

- Jean-Philippe Bernardy, Guilhem Moulin
- 2012 27th Annual IEEE Symposium on Logic in…
- 2012

Reynolds' abstraction theorem has recently been extended to lambda-calculi with dependent types. In this paper, we show how this theorem can be internalized. More precisely, we describe an extension of the Pure Type Systems with a special parametricity rule (with computational content), and prove fundamental properties such as Church-Rosser's and strong… (More)

Earlier studies have introduced a list of high-level evaluation criteria to assess how well a language supports generic programming. Since each language that meets all criteria is considered generic, those criteria are not fine-grained enough to differentiate between languages for generic programming. We refine these criteria into a taxonomy that captures… (More)

- Jean-Philippe Bernardy, Guilhem Moulin
- ICFP
- 2013

Dependent type-theory aims to become the standard way to formalize mathematics at the same time as displacing traditional platforms for high-assurance programming. However, current implementations of type theory are still lacking, in the sense that some obvious truths require explicit proofs, making type-theory awkward to use for many applications, both in… (More)

- Jean-Philippe Bernardy, Patrik Jansson, Marcin Zalewski, Sibylle Schupp
- J. Funct. Program.
- 2010

Earlier studies have introduced a list of high-level evaluation criteria to assess how well a language supports generic programming. Languages that meet all criteria include Haskell, because of its type classes, and C++ with the concept feature. We refine these criteria into a taxonomy that captures com-monalities and differences between type classes in… (More)

- Jean-Philippe Bernardy
- Haskell
- 2009

Structured documents are commonly edited using a free-form editor. Even though every string is an acceptable input, it makes sense to maintain a structured representation of the edited document. The structured representation has a number of uses: structural navigation (and optional structural editing), structure highlighting, etc. The construction of the… (More)