We propose a way to unify two approaches of non-cloning in quantum lambda-calculi: logical and algebraic linearities. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms ...

In this paper we present two flavors of a quantum extension to the lambda calculus. The first one, λρ,follows the approach of classical control/quantum data, where the quantum data is represented by density matrices. We ...

The logic of proofs is a refinement of modal logic introduced by Artemov in 1995 in which the modality ◻A is revisited as ⟦t⟧A where t is an expression that bears witness to the validity of A. It enjoys arithmetical soundness ...

We propose a way to unify two approaches of non-cloning in quantum lambda-calculi. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as algebraic-linear functions. We ...

Lambda-S is an extension to first-order lambda calculus unifying two approaches of non-cloning in quantum lambda-calculi. One is to forbid duplication of variables, while the other is to consider all lambda-terms as algebraic ...

We describe a type system for the linear-algebraic λ-calculus. The type system accounts for the linear-algebraic aspects of this extension of λ-calculus: it is able to statically describe the linear combinations of terms ...

We lift the theory of optimal reduction to a decomposition of the lambda calculus known as the Linear Substitution Calculus (LSC). LSC decomposes β-reduction into finer steps that manipulate substitutions in two distinctive ...

We present a call-by-need strategy for computing strong normal forms of open terms (reduction is admitted inside the body of abstractions and substitutions, and the terms may contain free variables), which guarantees that ...