Gradual Certified Programming in Coq

Expressive static typing disciplines are a powerful way to achieve high-quality software. However, the adoption cost of such techniques should not be under-estimated. Just like gradual typing allows for a smooth transition from dynamically-typed to statically-typed programs, it seems desirable to support a gradual path to certified programming. We explore gradual certified programming in Coq, providing the possibility to postpone the proofs of selected properties, and to check "at runtime" whether the properties actually hold. Casts can be integrated with the implicit coercion mechanism of Coq to support implicit cast insertion a la gradual typing. Additionally, when extracting Coq functions to mainstream languages, our encoding of casts supports lifting assumed properties into runtime checks. Much to our surprise, it is not necessary to extend Coq in any way to support gradual certified programming. A simple mix of type classes and axioms makes it possible to bring gradual certified programming to Coq in a straightforward manner.Comment: DLS'15 final version, Proceedings of the ACM Dynamic Languages Symposium (DLS 2015

Ambiguity in multicriteria quality decisions.

Quality is becoming an issue of increasing strategic importance in business. The aim of this paper is to analyze quality from a decision-making perspective. Quality decisions are characterized by their ambiguity while their evaluation uses a multicriteria viewpoint. Fuzzy decision theory provides a conceptual framework to model decisions with these features. It enables the decision maker to add his/her own experience and any other type of information to that obtained from hard figures. This theory is applied to a set of quality decision alternatives which are evaluated using different criteria such as their impact on fixed costs, cost of quality, leadtime and flexibility. The approach provided in this paper can be extended to other quality decisions.Quality decision-making; Quality dimensions; Fuzzy multicriteria decision making;

A Reasonably Gradual Type Theory

Gradualizing the Calculus of Inductive Constructions (CIC) involves dealing with subtle tensions between normalization, graduality, and conservativity with respect to CIC. Recently, GCIC has been proposed as a parametrized gradual type theory that admits three variants, each sacrificing one of these properties. For devising a gradual proof assistant based on CIC, normalization and conservativity with respect to CIC are key, but the tension with graduality needs to be addressed. Additionally, several challenges remain: (1) The presence of two wildcard terms at any type-the error and unknown terms-enables trivial proofs of any theorem, jeopardizing the use of a gradual type theory in a proof assistant; (2) Supporting general indexed inductive families, most prominently equality, is an open problem; (3) Theoretical accounts of gradual typing and graduality so far do not support handling type mismatches detected during reduction; (4) Precision and graduality are external notions not amenable to reasoning within a gradual type theory. All these issues manifest primally in CastCIC, the cast calculus used to define GCIC. In this work, we present an extension of CastCIC called GRIP. GRIP is a reasonably gradual type theory that addresses the issues above, featuring internal precision and general exception handling. GRIP features an impure (gradual) sort of types inhabited by errors and unknown terms, and a pure (non-gradual) sort of strict propositions for consistent reasoning about gradual terms. Internal precision supports reasoning about graduality within GRIP itself, for instance to characterize gradual exception-handling terms, and supports gradual subset types. We develop the metatheory of GRIP using a model formalized in Coq, and provide a prototype implementation of GRIP in Agda.Comment: 27pages + 2pages bibliograph

Ambiguity in multicriteria quality decisions

Quality is becoming an issue of increasing strategic importance in business. The aim of this paper is to analyze quality from a decision-making perspective. Quality decisions are characterized by their ambiguity while their evaluation uses a multicriteria viewpoint. Fuzzy decision theory provides a conceptual framework to model decisions with these features. It enables the decision maker to add his/her own experience and any other type of information to that obtained from hard figures. This theory is applied to a set of quality decision alternatives which are evaluated using different criteria such as their impact on fixed costs, cost of quality, leadtime and flexibility. The approach provided in this paper can be extended to other quality decisions

A bisimulation between DPLL(T) and a proof-search strategy for the focused sequent calculus

International audienceWe describe how the Davis-Putnam-Logemann-Loveland proced- ure DPLL is bisimilar to the goal-directed proof-search mechanism described by a standard but carefully chosen sequent calculus. We thus relate a procedure described as a transition system on states to the gradual completion of incomplete proof-trees. For this we use a focused sequent calculus for polarised clas- sical logic, for which we allow analytic cuts. The focusing mech- anisms, together with an appropriate management of polarities, then allows the bisimulation to hold: The class of sequent calculus proofs that are the images of the DPLL runs finishing on UNSAT, is identified with a simple criterion involving polarities. We actually provide those results for a version DPLL(T ) of the procedure that is parameterised by a background theory T for which we can decide whether conjunctions of literals are con- sistent. This procedure is used for Satisfiability Modulo Theor- ies (SMT) generalising propositional SAT. For this, we extend the standard focused sequent calculus for propositional logic in the same way DPLL(T ) extends DPLL: with the ability to call the de- cision procedure for T . DPLL(T ) is implemented as a plugin for P SYCHE, a proof- search engine for this sequent calculus, to provide a sequent- calculus based SMT-solver