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System F is a well-known typed λ-calculus with polymorphic types, which provides a basis for polymorphic programming languages. We study an extension of F, called F <: (pronounced ef-sub) that combines parametric polymorphism with subtyping. The main focus of the paper is the equational theory of F <: , which is related to PER models and the notion of… (More)

We define a new cost model for the call-by-value lambda-calculus satisfying the invariance thesis. That is, under the proposed cost model, Turing machines and the call-by-value lambda-calculus can simulate each other within a polynomial time overhead. The model only relies on combinatorial properties of usual beta-reduction, without any reference to a… (More)

- Antonio Ruberti, Beniamino Accattoli, Stefano Guerrini, Simone Martini, Olivier Laurent
- 2011

We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In particular, weak call-by-value beta-reduction can be simulated by an orthogonal constructor term rewrite system in the same… (More)

In 1998 Asperti and Mairson proved that the cost of reducing a lambda-term using an optimal lambda-reducer (a la Lévy) cannot be bound by any elementary function in the number of shared-beta steps. We prove in this paper that an analogous result holds for Lamping's abstract algorithm. That is, there is no elementary function in the number of shared beta… (More)

We present natural deduction systems for fragments of intuitionistic linear logic obtained by dropping weakening and contractions also on !-preexed formulas. The systems are based on a two-dimensional generalization of the notion of sequent, which accounts for a clean formulation of the introduction/elimination rules of the modality. Moreover, the diierent… (More)