[PPT] - The Challenge of Typed Expressiveness in Concurrency Jorge A. Prez PowerPoint Presentation

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The Challenge of Typed Expressiveness in Concurrency

Jorge A. Pérez

University of Groningen & CWI, Amsterdam Open Problems in Concurrency Theory Vienna, June 27, 2017

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This Talk, In One Slide

My view on the need for mature foundations for communication, distribution, and types

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Based on a FORTE 2016 paper

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The Future (According to Gartner)

Communication and distribution at a (very) large-scale:

2018: 6 billion connected ‘things’ requesting support
2020: Autonomous agents part of 5% of all transactions
2020: Smart agents facilitate 40% of mobile interactions

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The Present: Languages Promoted by Industry

Facebook’s Flow (gradual types for JavaScript)
Google’s Go (concurrency, message-passing communication)
Mozilla’s Rust (affine references/ownership types)
Erlang (actor-based concurrency)

The Future (According to Gartner)

Communication and distribution at a (very) large-scale:

2018: 6 billion connected ‘things’ requesting support
2020: Autonomous agents part of 5% of all transactions
2020: Smart agents facilitate 40% of mobile interactions

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Communication & Types: Here to Stay!

The Present: Languages Promoted by Industry

Facebook’s Flow (gradual types for JavaScript)
Google’s Go (concurrency, message-passing communication)
Mozilla’s Rust (affine references/ownership types)
Erlang (actor-based concurrency)

The Future (According to Gartner)

Communication and distribution at a (very) large-scale:

2018: 6 billion connected ‘things’ requesting support
2020: Autonomous agents part of 5% of all transactions
2020: Smart agents facilitate 40% of mobile interactions

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We Need Foundations. But Which Ones?

Much research on models of concurrency and communication.

Petri Nets, graph transformation & rewriting techniques,

declarative formalisms, process calculi, etc Process calculi already support communication and types:

Simple formalization of message-passing concurrency
Basis for type systems for concurrent programs

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 5 / 30

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We Need Foundations. But Which Ones?

Much research on models of concurrency and communication.

Petri Nets, graph transformation & rewriting techniques,

declarative formalisms, process calculi, etc Process calculi already support communication and types:

Simple formalization of message-passing concurrency
Basis for type systems for concurrent programs

Challenges

Many different foundations for types and communication

→ No single notion of correctness, but many!

How to transfer their analysis techniques into practice?
How to relate the tools derived from the different foundations?

→ A “Chomsky hierarchy” of [typed] concurrent languages?

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 5 / 30

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This Talk: A Plea for Typed Expressiveness

We need rigorous comparisons between well-established

(but distinct) typed process frameworks

New bridges between different typed models
Understand complementarities of their analysis techniques
Clear practical significance, given reality and trends in IT

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 6 / 30

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This Talk: A Plea for Typed Expressiveness

We need rigorous comparisons between well-established

(but distinct) typed process frameworks

New bridges between different typed models
Understand complementarities of their analysis techniques
Clear practical significance, given reality and trends in IT

My Claim: Maturity via Expressiveness

We may build upon approaches to relative expressiveness,

as studied in concurrency theory

Fruitful in the untyped setting, they should elucidate

connections in a typed setting

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 6 / 30

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Outline

Expressiveness in Concurrency Towards Relative Expressiveness for Behavioral Types Future Directions Concluding Remarks (and Shameless Publicity)

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 7 / 30

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Untyped Expressiveness: Key Ideas

Many efforts on assessing the expressivity of process calculi. Typical questions:

What is the nature of a process construct?
Can we transfer reasoning techniques across languages?

Main technical device: Language encodings

Translate a source language LS into a target language LT

satisfying certain encodability criteria

Criteria represent abstract indicators of an encoding’s quality;

they can be syntactic or semantic

No agreement on “good encodings”...

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 8 / 30

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Untyped Expressiveness: Outcomes

Encodability results:

A positive encodability result

→ All behaviors expressible in LS can also be expressed in LT

A negative encodability result

→ There are behaviors expressible in LS but not in LT Combinations of results may indicate expressiveness gaps.

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 9 / 30

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Sucesses of Untyped Expressiveness

Encodability results have clarified our understanding on interaction and communication as abstracted by process calculi.

Formally relate different computational models
Encoding the λ-calculus in the π-calculus [cf. Milner]
(Un)decidability of termination/convergence in CCS [cf. Busi et al]
Assess the expressive power of process languages
The interplay of choice and (a)synchronous communication, and

its influence on the π-calculus [cf. Palamidessi, Honda, Boudol]

Transfer proof techniques between different calculi
Encoding of process mobility into name mobility: key to the

behavioral theory of higher-order process calculi [cf. Sangiorgi]

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 10 / 30

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Outline

Expressiveness in Concurrency Towards Relative Expressiveness for Behavioral Types Future Directions Concluding Remarks (and Shameless Publicity)

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 11 / 30

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Type Systems for Concurrency

The development of process languages with type-based techniques has received much attention Type systems have revealed a rich landscape of concurrent models with disciplined communication

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 12 / 30

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Behavioral Type Systems

In contrast to usual data types, behavioral types represent

causality, alternatives, repetition.

A behavioral type for a communication channel defines
its resource-usage policy
the series of actions realized through that channel along time
Often defined on top of process calculi. General verification

techniques that may be tailored to different actual languages

A notable class of behavioral types: session types

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 13 / 30

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Behavioral Types: An Incomplete Timeline

1990 2017

Sortings for the π-calculus

[Milner]

1991

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Behavioral Types: An Incomplete Timeline

1990 2017

Sortings for the π-calculus

[Milner]

1991

Type & Effect System for CML

[Nielson & Nielson]

1993

Types for Dyadic Interaction

[Honda]

1993

A Typed Interaction-based Language

[Takeuchi et al.]

1994

Linear Types for π

[Kobayashi et al.]

1996

Types for Deadlock-freedom in π

[Kobayashi]

1997

Binary Session Types

[Honda et al.]

1998

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Behavioral Types: An Incomplete Timeline

1990 2017

Sortings for the π-calculus

[Milner]

1991

Type & Effect System for CML

[Nielson & Nielson]

1993

Types for Dyadic Interaction

[Honda]

1993

A Typed Interaction-based Language

[Takeuchi et al.]

1994

Linear Types for π

[Kobayashi et al.]

1996

Types for Deadlock-freedom in π

[Kobayashi]

1997

Binary Session Types

[Honda et al.]

1998

Types for Non-Uniform Objects

[Ravara & Vasconcelos]

2000

Generic Process Types

[Igarashi & Kobayashi]

2001

Spatial-behavioral Types

[Caires]

2008

Multiparty Session Types

[Honda et al.]

2008

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Behavioral Types: An Incomplete Timeline

1990 2017

Sortings for the π-calculus

[Milner]

1991

Type & Effect System for CML

[Nielson & Nielson]

1993

Types for Dyadic Interaction

[Honda]

1993

A Typed Interaction-based Language

[Takeuchi et al.]

1994

Linear Types for π

[Kobayashi et al.]

1996

Types for Deadlock-freedom in π

[Kobayashi]

1997

Binary Session Types

[Honda et al.]

1998

Types for Non-Uniform Objects

[Ravara & Vasconcelos]

2000

Generic Process Types

[Igarashi & Kobayashi]

2001

Spatial-behavioral Types

[Caires]

2008

Multiparty Session Types

[Honda et al.]

2008

Conversation Types

[Caires & Vieira]

2009

Parameterized Multiparty Session Types

[Yoshida et al.]

2010

Linear Session Types, Revisited

[Giunti & Vasconcelos]

2010

Session Types as Linear Logic

[Caires & Pfenning]

2010

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Behavioral Types: An Incomplete Timeline

1990 2017

Sortings for the π-calculus

[Milner]

1991

Type & Effect System for CML

[Nielson & Nielson]

1993

Types for Dyadic Interaction

[Honda]

1993

A Typed Interaction-based Language

[Takeuchi et al.]

1994

Linear Types for π

[Kobayashi et al.]

1996

Types for Deadlock-freedom in π

[Kobayashi]

1997

Binary Session Types

[Honda et al.]

1998

Types for Non-Uniform Objects

[Ravara & Vasconcelos]

2000

Generic Process Types

[Igarashi & Kobayashi]

2001

Spatial-behavioral Types

[Caires]

2008

Multiparty Session Types

[Honda et al.]

2008

Conversation Types

[Caires & Vieira]

2009

Parameterized Multiparty Session Types

[Yoshida et al.]

2010

Linear Session Types, Revisited

[Giunti & Vasconcelos]

2010

Session Types as Linear Logic

[Caires & Pfenning]

2010

Dynamic Multirole Session Types

[Deniélou & Yoshida]

2011

Choreographic Programming

[Carbone & Montesi]

2013

Behavioral Separation Types

[Caires & Seco]

2013

Context-free Session Types

[Thiemann & Vasconcelos]

2016

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Challenges on Typed Expressiveness

Given the jungle of typed process models, the need for establishing formal relations becomes pressing Research would benefit from efforts aimed at:

1. Relating different typed models
2. Assessing the expressivity of behaviorally typed languages
3. Transferring techniques between different typed formalisms

These are challenging issues!

As different type systems rely on unrelated concepts, discrepancies on typability arise easily Hence, objective comparisons are hard to establish

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 15 / 30

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A Brief Overview of Related Efforts

Existing Works

1. Connections Between Linear Types and Session Types
2. Connections Between Session Types and Automata
3. Other Approaches (e.g., Types and Declarative Models)

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 16 / 30

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A Brief Overview of Related Efforts (1/3)

Connections Between Linear Types and Session Types

Kobayashi observed that linear types can represent session

types, using a continuation-passing style translation1

Dardha et al. formalized and extended this observation2
Carbone et al. used this encoding to formally relate progress

in session π-calculus to lock-freedom in the linear π-calculus3

The encoding has had significant impact—cf. Scalas et al.’s

integration of binary sessions into Scala4

1“Type systems for concurrent programs” in Formal Methods at the Crossroads, 2003. 2“Session types revisited”, in PPDP 2012. 3“Progress as compositional lock-freedom’,’ in COORDINATION 2014. 4“A Linear Decomposition of Multiparty Sessions for Safe Distributed Programming”, in

ECOOP 2017.

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 17 / 30

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A Brief Overview of Related Efforts (2/3)

Connections Between Session Types and Automata

Villard showed that a subclass of communicating finite state

machines (CFSMs) characterizes binary session types5

Deniélou and Yoshida extended this characterization to

multiparty session types, inhering safety / liveness from CFSMs.6 Later they gave a sound and complete characterization of multiparty session types as CFSMs7

Lange et al. developed techniques to synthesize global

graphs from CFSMs, covering more global protocols8

5“Heaps and Hops”. Ph.D. thesis, 2011. 6“Multiparty session types meet communicating automata”, in ESOP 2012. 7“Multiparty compatibility in communicating automata: characterisation and synthesis”, in

ICALP 2013.

8“From communicating machines to graphical choreographies”, in POPL 2015.

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 18 / 30

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A Brief Overview of Related Efforts (3/3)

Other Approaches

Hüttel has given type systems for the ψ-calculus that

generalize different type systems for the π-calculus9

López et al. encoded binary sessions into a declarative

process calculus, enabling the transfer of LTL reasoning10

Padovani has related labeled choice operators in session

types with intersection and union types11

Orchard and Yoshida encoded PCF with an effect type system

into a session π-calculus; a reverse encoding enables a new implementation of sessions into Haskell12

9“Typed ψ-calculi”, in CONCUR 2011. 10“Towards a unified framework for declarative structured communications”, in PLACES 2009. 11“Session types = intersection types + union types”, in ITRS 2010. 12“Effects as sessions, sessions as effects”, in POPL 2016.

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 19 / 30

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Outline

Expressiveness in Concurrency Towards Relative Expressiveness for Behavioral Types Future Directions Concluding Remarks (and Shameless Publicity)

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 20 / 30

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Future Directions

Although existing works offer insightful relations between different frameworks of behavioral types, they are isolated. Since each work uses different techniques to relate typed models, further research is needed to integrate their results.

Promising Research Directions

1. Expressiveness Without Processes
2. Typed Encodability Criteria
3. A Logic Yardstick for Typed Expressiveness

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 21 / 30

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Expressiveness Without Processes

While process approaches are convenient in theory, the analysis

f practical multiparty communications uses mostly types

Very rich type theories, increasingly closer to process languages Recent works explore relative expressiveness for types, exploiting process techniques to define their their semantics:

Demangeon and Yoshida contrasted different classes of

multiparty session types by comparing trace denotations13

Cruz-Filipe and Montesi have studied the relative expressivity
f choreographies (multiparty session types)14

13“On the expressiveness of multiparty sessions”, in FSTTCS 2015. 14“Choreographies, Computationally”, in arXiv (1510.03271).

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 22 / 30

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Typed Encodability Criteria

Clarifying how existing frameworks for (untyped) relative expressiveness can account for behavioral types Understand how types induce encodability results and to relate different behavioral types in source/target languages Kouzapas et al. (ESOP’16) define a notion of typed encoding that extends Gorla’s framework with session types. Both processes and types need to be translated.15

15“On the relative expressiveness of higher- order session processes”, in ESOP 2016.

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 23 / 30

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CHoCO: Yardstick for Typed Expressiveness

What should be a fair yardstick to compare behavioral types? Curry-Howard correspondences for concurrency (CHoCO) define a fundamental model of behavioral types, which naturally identifies type preserving and deadlock-free process models:16 CONCURRENCY LOGIC Session types ⇐

⇒

Propositions π-calculus processes ⇐

⇒

Proofs Process communication ⇐

⇒

Proof reduction

16Caires and Pfenning: “Session types as intuitionistic linear propositions”. In CONCUR

2010.

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 24 / 30

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CHoCO: Yardstick for Typed Expressiveness

Some recent steps:

EXPRESS/SOS’15

Dardha and P . compare two classes of deadlock-free, session processes: one results from CHoCO; the other mixes Dardha et al.’s encoding and Kobayashi’s usage types17

FORTE’16

Caires and P . define the first logical explanation of multiparty sessions, using binary session types / CHoCO 18

ESOP’17

Caires and P . extend CHoCO with logical modalities for non-deterministic behavior. It supports a typed encoding of the λ-calculus with threads, sessions, and exceptions19

17“Comparing deadlock-free session typed processes”, in EXPRESS/SOS 2015. 18“Multiparty session types within a canonical binary theory, and beyond”, in FORTE 2016. 19“Linearity, Control Effects, and Behavioral Types”, in ESOP 2017.

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 25 / 30

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Curry-Howard for Concurrency

Polymorphism (2013) Proof-Carrying Code (2011) Objects (2015) Logical Relations (2012) Dependent Types (2011) Multiparty Protocols (2016) Monitors & Blame (2016) Co-recursion (2014) Conversation Types Multiparty STs Choreographic Programming Linear Types w. Usages Linear/Affine Types Generic Process Types Non Determinism (2017)

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Outline

Expressiveness in Concurrency Towards Relative Expressiveness for Behavioral Types Future Directions Concluding Remarks (and Shameless Publicity)

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 27 / 30

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Wrapping Up

We need mature models of concurrency and distribution!

Significant progresses on formal specification and analysis

techniques for concurrent processes

Our understanding is scattered around in valuable, yet

isolated, models and frameworks Maturity from systematic comparisons of known techniques:

We can draw inspiration from approaches and techniques

developed for untyped concurrent models

Curry-Howard for concurrency (CHoCO) should be a yardstick

in comparisons

A community-wide effort needed to clarify relationships and

enable tool interoperability

Jorge A. Pérez The Challenge of Typed Expressiveness in Concurrency 28 / 30

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RADICAL 2017

A Workshop on Recent Advances in Concurrency and Logic

Co-located with CONCUR 2017 (Monday, September 4)
Deadline (3-page talk proposals): 30 June 2017 (this Friday!)
Invited speakers: Luís Caires & Luke Ong

Topics of interest include:

design, verification, synthesis for concurrent systems
strategic reasoning for distributed and multi-agent systems
analysis and validation of concurrent and distributed programs

https://sites.google.com/site/radicalconcur/

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