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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

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

  2. Linear- is CP (more or less)

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

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

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

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

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

  8. Wadler CP & Session T ypes 2012

  9. Wadler CP & Session T ypes 2012 process

  10. Wadler CP & Session T ypes 2012 process channels

  11. Wadler CP & Session T ypes 2012 process channels session protocols

  12. Caires and A Session-typed Store Pfenning 2010

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

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

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

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

  17. 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

  18. 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

  19. A Session-typed Customer

  20. A Session-typed Customer buy output choice of quote or

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

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

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

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

  25. 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

  26. 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

  27. Session-T yped Processes processes = linear proofs

  28. Session-T yped Processes processes = linear proofs

  29. Session-T yped Processes processes = linear proofs

  30. Session-T yped Processes processes = linear proofs

  31. Session-T yped Processes processes = linear proofs

  32. Session-T yped Processes processes = linear proofs

  33. Session-T yped Processes processes = linear proofs

  34. Session-T yped Processes processes = linear proofs

  35. Session-T yped Processes processes = linear proofs

  36. Session-T yped Processes processes = linear proofs

  37. Caires and -DILL Pfenning 2010

  38. Caires and -DILL Pfenning 2010 input

  39. Caires and -DILL Pfenning 2010 process input

  40. Caires and -DILL Pfenning 2010 process output input

  41. (STLC) -DILL

  42. non- (STLC) linear -DILL linear

  43. non- (STLC) linear -DILL linear- linear (DILL)

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

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

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

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

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

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

  50. Parigot 1992

  51. Parigot 1992 multiple inputs

  52. Parigot 1992 multiple inputs multiple outputs

  53. Parigot 1992

  54. Parigot 1992

  55. Parigot 1992

  56. Parigot 1992

  57. Parigot 1992

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

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

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

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

  62. linear- vs CP

  63. linear- vs CP input

  64. linear- vs CP input output

  65. linear- vs CP input output

  66. linear- vs CP input output

  67. dualizing linear-

  68. dualizing linear-

  69. dualizing linear-

  70. dualizing linear- output input

  71. dualizing linear- output input input output

  72. dualizing linear- output input input output

  73. negation: switching input and output output input

  74. negation: switching input and output output input input output

  75. negation: switching input and output output input input output

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

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

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

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

  80. shifts: switching input and output output input

  81. shifts: switching input and output output input polarized logic

  82. CP : a polarized CP output input

  83. CP : a polarized CP Pfenning and Griffith 2015 output input

  84. CP : a polarized CP

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

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

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

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

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

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

  91. CP is CP (more or less)

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

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

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

  95. CP

  96. linear- CP

  97. CP linear- CP

  98. CP linear- CP

  99. T h a n k s ! CP linear- CP

  100. 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.

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