# A fully-abstract semantics of lambda-mu in the pi-calculus

@inproceedings{Bakel2014AFS, title={A fully-abstract semantics of lambda-mu in the pi-calculus}, author={Steffen van Bakel and Maria Grazia Vigliotti}, booktitle={CL\&C}, year={2014} }

We study the lambda-mu-calculus, extended with explicit substitution, and define a compositional output-based interpretation into a variant of the pi-calculus with pairing that preserves single-step explicit head reduction with respect to weak bisimilarity. We define four notions of weak equivalence for lambda-mu -- one based on weak reduction, two modelling weak head-reduction and weak explicit head reduction (all considering terms without weak head-normal form equivalent as well), and one…

## 5 Citations

### Fully Abstract Encodings of $\lambda$-Calculus in HOcore through Abstract Machines

- Computer Science, Mathematics
- 2022

This work presents fully abstract encodings of the call-by-name and call- by-value λ calculus into HOcore, a minimal higher-order process calculus with no name restriction, and considers several equivalences on the λ -calculus side that internalize into abstract machines in order to prove full abstraction of theencodings.

### Fully abstract encodings of λ-calculus in HOcore through abstract machines

- Computer Science, Mathematics2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2017

Two fully abstract encodings of the call-byname λ-calculus are presented into HOcore, a minimal higher-order process calculus with no name restriction, to prove full abstraction.

### Characterisation of Approximation and (Head) Normalisation for λμ using Strict Intersection Types

- MathematicsITRS
- 2016

A notion of approximants of lambda-mu-terms is defined, it is shown that it generates a semantics, and that for each typeable term there is an approximant that has the same type.

### A Strong Bisimulation for Control Operators by Means of Multiplicative and Exponential Reduction

- Computer ScienceArXiv
- 2021

This paper gives a translation of ΛM -terms into PPN which simulates the reduction relation of the authors' calculus via cut elimination of PPN, and establishes a precise correspondence between the relation ≃ and Laurent’s ≃σ -equivalence for λμ-terms.

### Strong Bisimulation for Control Operators

- Computer ScienceArXiv
- 2019

The purpose of this paper is to identify programs with control operators whose reduction semantics are in exact correspondence. This is achieved by introducing a relation $\simeq$, defined over a…

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