On Coinduction and Quantum Lambda Calculi

Applicative Bisimulation and Quantum $\lambda$-Calculi (Long Version)

Applicative bisimulation is a coinductive technique to check program equivalence in higherorder functional languages. It is known to be sound— and sometimes complete — with respect to context equivalence. In this paper we show that applicative bisimulation also works when the underlying language of programs takes the form of a linear λ-calculus extended with features such as probabilistic binar...

On Probabilistic Applicative Bisimulation and Call-by-Value $\lambda$-Calculi (Long Version)

Probabilistic applicative bisimulation is a recently introduced coinductive methodology for program equivalence in a probabilistic, higher-order, setting. In this paper, the technique is generalized to a typed, call-by-value, lambda-calculus. Surprisingly, the obtained relation coincides with context equivalence, contrary to what happens when call-by-name evaluation is considered. Even more sur...

Coinductive Techniques on a Linear Quantum λ-Calculus

Probabilistic Applicative Bisimulation and Call-by-Value λ-Calculi (Long Version)

Probabilistic applicative bisimulation is a recently introduced coinductive methodology for program equivalence in a probabilistic, higher-order, setting. In this paper, the technique is generalized to a typed, call-by-value, lambda-calculus. Surprisingly, the obtained relation coincides with context equivalence, contrary to what happens when call-by-name evaluation is considered. Even more sur...

Two Extensions of System F with (co)iteration and Primitive (co)recursion Principles

This paper presents two extensions of the second order polymorphic lambda calculus F with inductive and coinductive types including not only (co)iteration but primitive (co)recursion and inversion principles. The systems are proven to be safe, can be seen as extensions of Hagino’s categorical lambda calculus and are also related with the systems of higher-order iterators of [1]. 1991 Mathematic...