It is proved that the equality of interpretations in Pcoh characterizes the operational indistinguishability of programs in PCF with a random primitive, the first result of full abstraction for a semantics of probabilistic PCF.Expand

A semantic account of the execution time (i.e. the number of cut elimination steps leading to the normal form) of an untyped MELL net and proves that a net is head-normalizable if and only if its exhaustive interpretation (a suitable restriction of its interpretation) is not empty.Expand

This paper proposes a denotational semantics for a quantum lambda calculus with recursion and an infinite data type, using constructions from quantitative semantics of linear logic.Expand

A probabilistic version of PCF, a well-known simply typed universal functional language, is presented and an adequacy and an equational full abstraction theorem are proved showing that equality in the model coincides with a natural notion of observational equivalence.Expand

The generalization of the category Rel of sets and relations to an arbitrary continuous semiring R is considered, producing a cpo-enriched category which is a semantics of LL, and its (co)Kleisli category is an adequate model of an extension of PCF, parametrized by R.Expand

We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpo-enriched cartesian closed category. This category gives a denotational… Expand

This work defines parallel reduction in resource calculus and applies the technique by Tait and Martin-Lof to achieve confluence, and slightly generalizes a technique by Takahashi to obtain a standardization result.Expand

The conservation theorem for differential nets – the graph-theoretical syntax of the differential extension of Linear Logic (Ehrhard and Regnier's DiLL) is proved, which turns the quest for strong normalisation into one for non-erasing weak normalisation (WN), and indeed this result is used to prove SN of simply typed DiLL.Expand

This paper proves that a denotational semantics interpreting programs by power series with non negative real coefficients is adequate for a probabilistic extension of the untyped $\lambda$-calculus: the probability that a term reduces to ahead normal form is equal to its denotation computed on a suitable set of values.Expand

The paper contains the first complete proof of strong normalization (SN) for full second order linear logic (LL) by showing how standardization for sps allows to prove SN of LL, using as usual Girard's reducibility candidates.Expand