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##### PI.R2 - 2011

Project-Team Pi.r2

Application Domains
Partnerships and Cooperations
Dissemination
Bibliography

## Section: Partnerships and Cooperations

### International Initiatives

#### INRIA Associate Teams

##### SEMACODE
• Title: Proof theory and functional programming languages

• INRIA principal investigator: Alexis SAURIN

• International Partner:

• Institution: University of Oregon (United States)

• Laboratory: Computer and Information Science Department

• Researcher: Zena ARIOLA

• International Partner:

• Institution: University of Novi Sad

• Laboratory: Faculty of Engineering

• Researcher: Silvia GHILEZAN

• Duration: 2011 - 2013

• Cross-fertilization between logic and programming languages theory is at the root of many striking developments in programming concepts as well as tools for formal analysis of programs. Our associated team project aims at gathering senior and young researchers from both sites in order to put a joint research effort on the following research themes:formalizing particular evaluation strategies of functional languages based logical techniques coming from sequent calculi. More specifically, we shall be interested in incorporating control operator directly in call-by-need and in developing a uniform framework for call-by-value and call-by-name calculi with delimited controlinvestigating (delimited) control operators, in particular to unveil the logical interpretation of delimited control (that is its logical counter-part with respect to Curry-Howard correspondence), and developing; connections between delimited control and stream calculi;developing the logical content of realistic abstract machines and associated formal analysis tools for realistic abstract machines building on Curien-Herbelin lambda-bar calculi. The project will gather PiR2 expertise in proof theory and in the logical foundations of functional programming languages, the expertise of the oregonian group on call-by-need evaluation and delimited control as well as respective crucial inputs of Gaboardi and Ghilezan on stream calculi, delimited control, semantics and type theory. The project will in particular allow to have the INRIA and American students and post-docs involved in the project (7 out of 13 people involved) to travel between both sites and to organize joint workshops (one such workshop is planned in June 2011).

#### Visits of International Scientists

Olivier Danvy (University of Aarhus) visited $\pi {r}^{2}$ and PPS for one month and gave a talk on call-by-need abstract machines.

Beta Ziliani (MPI, Sarbrucken) visited $\pi {r}^{2}$ and PPS for a week in november and gave a talk on ad-hoc proof automation.

Danko Ilik visited $\pi {r}^{2}$ and PPS for one week and gave a talk on normalization by evaluation for delimited control.

Silvia Ghilezan (University of Novi Sad) visited $\pi {r}^{2}$ and PPS for one week and worked with Alexis Saurin and Hugo Herbelin on the classification of several calculi of delimited control.

Zerna Ariola (University of Oregon) visited $\pi {r}^{2}$ for one week and worked with Alexis Saurin and Hugo Herbelin on the definition of abstract amchines for classical call-by-need.

Keiko Nakata (University of Tallin) visited $\pi {r}^{2}$ and worked with Hugo Herbelin on recursive definitions and control operators in call-by-need $\lambda$-calculus.

Gyesik Lee visited $\pi {r}^{2}$ for one week and worked with Hugo Herbelin on the formal representation of binders in Coq and on representing primitive recursive arithmetic in Coq.

##### Internship

Paul Downen and Luke Maurer (University of Oregon) spent two months in the team during the summer, working with Alexis Saurin and Hugo Herbelin. Paul Downen studied calculi for multi-prompt, the derivation of abstract machines as well as infinitary $\lambda$-calculi. Luke Maurer studied Coq and did some formalization in Coq and studied Zeilberger's polarized approach to delimited control as well as connections with $\Lambda \mu$-calculus.

#### Visits abroad of members of the team

Matthieu Sozeau visited Ana Bove in Gothenburg for a week in January and gave a talk on Equations and dependent pattern-matching. They worked on a joint paper on tools and methods for recursion in type theory.

Matthieu Sozeau visited Alexandar Nanvesky at IMDEA Madrid from 19th to 23rd october and gave a talk on Type Classes and unification. They worked on the unification algorithm of Coq.

Guillaume Munch-Maccagnoni visited the Programming, Logic, and Semantics Group at the University of Cambridge from March to June. He is grateful to the Fondation Sciences Mathematiques de Paris which provided the funding.

Pierre-Louis Curien visited the University of Tsinghua in Beijing for three months, from March to May (funded by the Professor Group Chair of the Software School of this university). He was hosted by Gu Ming and Jean-Pierre- Jouannaud.