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- Bernardy, Jean-Philippe, 1978, et al.
(author)
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A Computational Interpretation of Parametricity
- 2012
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In: IEEE Symposium on Logic in Computer Science. 27th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), Dubrovnik, Croatia, June 25-28, 2012. - 1043-6871. - 9780769547695 ; , s. 135-144
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Conference paper (peer-reviewed)abstract
- 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 Pure Type Systems with a special parametricity rule (with computational content), and prove fundamental properties such as Church-Rosser's and strong normalization. All instances of the abstraction theorem can be both expressed and proved in the calculus itself. Moreover, one can apply parametricity to the parametricity rule: parametricity is itself parametric.
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- Bernardy, Jean-Philippe, 1978, et al.
(author)
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A Presheaf Model of Parametric Type Theory
- 2015
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In: Electronical Notes in Theoretical Computer Science. - : Elsevier BV. - 1571-0661. ; 319, s. 67-82
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Journal article (peer-reviewed)abstract
- We extend Martin-Löf's Logical Framework with special constructions and typing rules providing internalized parametricity. Compared to previous similar proposals, this version comes with a denotational semantics which is a refinement of the standard presheaf semantics of dependent type theory. Further, this presheaf semantics is a refinement of the one used to interpret nominal sets with restrictions. The present calculus is a candidate for the core of a proof assistant with internalized parametricity.
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- Bernardy, Jean-Philippe, 1978, et al.
(author)
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Towards a computational interpretation of parametricity
- 2011
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Journal article (other academic/artistic)abstract
- 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 Calculus of Constructions with a special parametricity rule (with computational content), and prove fundamental properties such as Church-Rosser's and strong normalization. The instances of the abstraction theorem can be both expressed and proved in the calculus itself.
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- Bernardy, Jean-Philippe, 1978, et al.
(author)
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Type-Theory in Color
- 2013
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In: 18th ACM SIGPLAN International Conference on Functional Programming, ICFP 2013; Boston, MA; United States; 25 September 2013 through 27 September 2013. - New York, NY, USA : ACM. - 9781450323260 ; , s. 61-71
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Conference paper (peer-reviewed)abstract
- Dependent-type theory is on the verge of becoming the standard way to formalise mathematics at the same time as displace traditional platforms for high-insurance programming. However, current implementations of type theory are still lacking, in the sense that obvious truths are simply impossible to prove, making type-theory awkward to use for many applications, both in formalisation or programming. In particular, notions of erasure are poorly supported. In this paper we propose to conservatively extend type-theory with colored terms, color erasure and color selection. The result is a more powerful type-theory: some definitions and proofs may be omitted as they become trivial; it becomes easier to program with precise types; and some parametricity results can be internalized.
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- Bernardy, Jean-Philippe, 1978, et al.
(author)
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Type-Theory In Color
- 2013
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In: SIGPLAN Notices (ACM Special Interest Group on Programming Languages). - : Association for Computing Machinery (ACM). - 0730-8566 .- 0362-1340 .- 1558-1160. ; 48:9, s. 61-71
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Journal article (peer-reviewed)abstract
- 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 formalization and programming. In particular, notions of erasure are poorly supported.In this paper we propose an extension of type-theory with colored terms, color erasure and interpretation of colored types as predicates. The result is a more powerful type-theory: some definitions and proofs may be omitted as they become trivial, it becomes easier to program with precise types, and some parametricity results can be internalized.
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- Cugnet-Anceau, Christine, et al.
(author)
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A controlled study of consumption of beta-glucan-enriched soups for 2 months by type 2 diabetic free-living subjects
- 2010
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In: British Journal of Nutrition. - 1475-2662. ; 103:3, s. 422-428
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Journal article (peer-reviewed)abstract
- Type 2 diabetes is associated with a higher cardiovascular risk and there has been a growing interest in using dietary intervention to improve lipid profile and glucose control. The present work aims at analysing the effects of the enrichment of a normal diet with beta-glucan (3-5 g/d) in free-living type 2 diabetic subjects for 2 months, using a palatable soup. This trial was a parallel, placebo-controlled, double-blinded randomised study performed in fifty-three type 2 diabetic subjects. During a 3-week run-in period, subjects daily consumed a ready meal control soup (without beta-glucan). For the following 8 weeks, Subjects were randomly assigned to consume daily either a control soup or a beta-glucan soup. Changes in lipid profile (total cholesterol (TC), HDL- and LDL-cholesterol (HDLc and LDLc), apo B and TAG) and in glucose control (HbA1c and fasting glucose) were measured. There was no significant alteration in lipid profile in the two groups (TC, HDLc. LDLc and apo B). TAG decreased significantly in the beta-glucan group compared with the control group (-0.12 (SD 0.38) v. 0.12 (SD 0.44)mmol/l, P=0.03). HbA1c and fasting glucose were not reduced in any group. A single daily ingestion of 3-5 g beta-glucan, as required by official dietary recommendations for 8 weeks did not change the lipid profile and HbA1c in type 2 diabetic subjects. To improve the metabolic profile of type 2 diabetic subjects in the long term, the quantity, the food vectors and the tolerability of P-glucan products may be re-evaluated.
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