Linear- is CP (more or less) Jennifer Paykin and Steve - PowerPoint PPT Presentation

Linear- is CP (more or less) Jennifer Paykin and Steve Zdancewic University of Pennsylvania Wadlerfest April 11, 2016

Linear- is CP (more or less)

Linear- is CP (more or less) 1. What is CP?

-calculus Linear- is CP (more or less) 1. What is CP?

-calculus Linear- is CP (more or less) 1. What is CP? 2. What is linear- ?

-calculus -calculus Linear- is CP (more or less) 1. What is CP? 2. What is linear- ?

-calculus -calculus Linear- is CP (more or less) 1. What is CP? 2. What is linear- ? 3. Is linear- = CP?

Wadler CP & Session T ypes 2012

Wadler CP & Session T ypes 2012 process

Wadler CP & Session T ypes 2012 process channels

Wadler CP & Session T ypes 2012 process channels session protocols

Caires and A Session-typed Store Pfenning 2010

Caires and A Session-typed Store Pfenning 2010 input choice of buy quote or

Caires and A Session-typed Store Pfenning 2010 input choice of buy input product quote or

Caires and A Session-typed Store Pfenning 2010 input choice of buy input input credit product card quote or

Caires and A Session-typed Store Pfenning 2010 input choice of buy input input credit output choice: product card succeeds or fails quote or

Caires and A Session-typed Store Pfenning 2010 input choice of buy input input credit output choice: product card succeeds or fails quote or input product

Caires and A Session-typed Store Pfenning 2010 input choice of buy input input credit output choice: product card succeeds or fails quote or output cost, input then terminates product

A Session-typed Customer

A Session-typed Customer buy output choice of quote or

A Session-typed Customer buy output choice of output product quote or

A Session-typed Customer buy output choice of output output product credit card quote or

A Session-typed Customer buy output choice of output output input choice: product credit card succeeds or fails quote or

A Session-typed Customer buy output choice of output output input choice: product credit card succeeds or fails quote or output product

A Session-typed Customer buy output choice of output output input choice: product credit card succeeds or fails quote or input cost, output then continue product

A Session-typed Customer buy output choice of output output input choice: product credit card succeeds or fails quote or input cost, output then continue product

Session-T yped Processes processes = linear proofs

Session-T yped Processes processes = linear proofs

Session-T yped Processes processes = linear proofs

Session-T yped Processes processes = linear proofs

Session-T yped Processes processes = linear proofs

Session-T yped Processes processes = linear proofs

Session-T yped Processes processes = linear proofs

Session-T yped Processes processes = linear proofs

Session-T yped Processes processes = linear proofs

Session-T yped Processes processes = linear proofs

Caires and -DILL Pfenning 2010

Caires and -DILL Pfenning 2010 input

Caires and -DILL Pfenning 2010 process input

Caires and -DILL Pfenning 2010 process output input

(STLC) -DILL

non- (STLC) linear -DILL linear

non- (STLC) linear -DILL linear- linear (DILL)

non- (STLC) linear -DILL linear- linear (DILL) natural sequent deduction calculus

non- (STLC) linear -DILL linear- linear (DILL) natural sequent deduction calculus

Intuitionistic Logic non- (STLC) linear -DILL linear- linear (DILL) natural sequent deduction calculus

Classical Logic non- linear CP linear natural sequent deduction calculus

Classical Logic dual non- System L calculus linear CP linear natural sequent deduction calculus

Linear- is CP (more or less) 1. What is CP? 2. What is linear- ? 3. Is linear- = CP?

Parigot 1992

Parigot 1992 multiple inputs

Parigot 1992 multiple inputs multiple outputs

Parigot 1992

Parigot 1992

Parigot 1992

Parigot 1992

Parigot 1992

Classical Logic non- linear CP linear natural sequent deduction calculus

Classical Logic non- linear CP linear- linear natural sequent deduction calculus

Classical Logic non- linear ? CP linear- linear natural sequent deduction calculus

Linear- is CP (more or less) 1. What is CP? 2. What is linear- ? 3. Is linear- = CP?

linear- vs CP

linear- vs CP input

linear- vs CP input output

linear- vs CP input output

linear- vs CP input output

dualizing linear-

dualizing linear-

dualizing linear-

dualizing linear- output input

dualizing linear- output input input output

dualizing linear- output input input output

negation: switching input and output output input

negation: switching input and output output input input output

negation: switching input and output output input input output

shifts: switching input and output Mellies and Tabareau 2010 output input

shifts: switching input and output Mellies and Tabareau 2010 output input input output

shifts: switching input and output Mellies and Tabareau 2010 output input input input output output

shifts: switching input and output Mellies and Tabareau 2010 output input input input output output

shifts: switching input and output output input

shifts: switching input and output output input polarized logic

CP : a polarized CP output input

CP : a polarized CP Pfenning and Griffith 2015 output input

CP : a polarized CP

CP : a polarized CP input choice of buy switch quote or

CP : a polarized CP input choice of buy switch input quote or

CP : a polarized CP input choice of buy switch input input quote or

CP : a polarized CP input choice of buy switch switch input input output quote or

CP : a polarized CP input choice of buy switch switch input input output quote or input

CP : a polarized CP input choice of buy switch switch input input output quote or switch output input

CP is CP (more or less)

CP is CP (more or less) ● explicit input and output

CP is CP (more or less) ● explicit input and output ● fully dual types

CP is CP (more or less) ● explicit input and output ● fully dual types ● can always switch

CP

linear- CP

CP linear- CP

CP linear- CP

T h a n k s ! CP linear- CP

References ● Phil Wadler, Propositions are sessions, ICFP 2012. ● Luis Caires and Frank Pfenning, Session types as intuitionistic linear propositions, CONCUR 2010. ● Michel Parigot, Lambda-mu calculus: an algorithmic interpretation of classical natural deduction, Logic Programming and Automated Reasoning 1992. ● Paul-Andre Mellies and Nicolas Tabareau, Resource modalities in tensor logic, Annals of Pure and Applied Logic 2010. ● Frank Pfenning and Dennis Griffith, Polarized substructural session types, Foundations of Software Science and Computation Structures 2015.