Refinements for Session-typed Concurrency · Refinements for Session-typed Concurrency Josh Acay & Frank Pfenning May 4, 2016 1

RefinementsforSession-typedConcurrency

JoshAcay&FrankPfenning

1May4,2016

Message-passingConcurrency

• Processesrepresentedasnodes• Channelsbetweenprocessesasedges• Eachchannelis“provided”byaspecificprocess(Pprovidesc,Qprovidesdetc.)

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Qd

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• Processescomputeinternally• Exchangemessagesalongchannels

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“aaa”

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“aaa”

end

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“aaa”

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• Processescanalsosendchannelstheyown

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4May4,2016

LinearSession-types

• Don’twanttosendintifexpectingstring• Don’ttrytoreceiveifotherprocessisnotsending

• Assigntypestoeachchannelfromprovider’sperspective

Pc:B

Qd:int⊃string∧A

Re:1

5May4,2016

LinearSession-types



Pc:B

Q3

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5May4,2016

LinearSession-types



Pc:B

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“aaa”

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LinearSession-types



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“aaa”end

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LinearSession-types



Pc:B

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“aaa”

d:A

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LinearSessionTypes

• Exampleinterfacespecification:

1 Terminate&{labi:Ai}i Externalchoice(receive)betweenlabi,continueasAi

A –o B ReceivechanneloftypeA,continueasBτ ⊃ B Receivevalueoftypeτ,continueasB⊕{labi:Ai}i Internalchoice(send)betweenlabi,continueasAi

A ⊗ B SendchanneloftypeA,continueasBτ ∧ B Sendvalueoftypeτ,continueasB

queue = &{enq: A –o queue, deq: ⊕{none: 1, some: A ⊗ queue}}

* where A is some predetermined type

6May4,2016

ImplementationofQueuesqueue = &{enq: A –o queue, deq: ⊕{none: 1, some: A ⊗ queue}}

empty : queueq ← empty = case q enq " x ← recv q ; e ← empty ; q ← elem x e deq " q.none ; close q

elem : A –o queue –o queueq ← elem x r = case q enq " y ← recv q ; r.enq ; send r y ; q ← elem x r deq " q.some ; send q x ; q ← r

7May4,2016

IntersectionsandUnions

• Allowsdescribingmoreinterestingbehavior• Intersectionoftwotypes:A⊓B– c:A⊓Bifchannelcoffersbothbehaviors

• Unionoftwotypes:A⊔B– c:A⊔Bifchannelcofferseitherbehavior

8May4,2016

RefinementTypes

• Whatifwewanttotrackmorepropertiesofqueues?Empty,non-empty,evenlength?

• Wecandefinetheminthebasesystem:

empty-queue = &{enq: A –o nonempty-queue, deq: ⊕{none: 1}}

nonempty-queue = &{enq: A –o nonempty-queue, deq: ⊕{some: A ⊗ queue}}

9May4,2016

RefinementTypes

• Butweneedintersectionsandunionstowriteinterestingprograms

queue A = empty-queue ⊔nonempty-queue

empty : empty-queue

elem : (A –o queue –o nonempty-queue)

concat : (empty-queue –o empty-queue –o empty-queue) ⊓ (queue –o nonempty-queue –o nonempty-queue) ⊓ (nonempty-queue –o queue –o nonempty-queue)

10May4,2016

DecidabilityofType-checking

• Algorithmicsystemthatiseasytotranslatetocode

• Provesoundandcompletewithrespecttotheoriginalsystem

• PartialimplementationinHaskell

11May4,2016

TypeSafety

• Progress– Deadlockfreedominconcurrentsetting– Atleastoneprocesscanmakeprogressiftheconfigurationiswell-typed

• Preservation[currentlyinprogress]– Sessionfidelityinconcurrentsetting– Processesobeysession-types

12May4,2016

Refinements for Session-typed Concurrency · Refinements for Session-typed Concurrency Josh Acay & Frank Pfenning May 4, 2016 1

Documents

Refinements for Session-typed Concurrency · Refinements for Session-typed Concurrency Josh Acay & Frank Pfenning May 4, 2016 1