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Naming Things and Finding Cothings

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The only category theory lesson you will ever need.

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Naming Things and Finding Cothings

  1. 1. The Eyjafjallajökull1,2 Lecture Paul Phillips Delivered @scala.world September 21 2015 1. ˈeɪjaˌfjatlaˌjœːkʏtl ̥ 2. Sure, that helped.
  2. 2. the origins of scala.world jon pretty's thirst for vengeance
  3. 3. the origins of scala.world jon pretty's thirst for vengeance April 2014
  4. 4. the origins of scala.world jon pretty's thirst for vengeance April 2014
  5. 5. the origins of scala.world jon pretty's thirst for vengeance April 2014 September 2015
  6. 6. the origins of scala.world jon pretty's thirst for vengeance April 2014 September 2015
  7. 7. Topic? My last scala commit Mar 12, 2014 What have I learned since?
  8. 8. That's it. Won't fill an hour.
  9. 9. • What to call Typesafe • What Scala could learn from Rust and Go • Suffuse: the reactive filesystem • Realization: inebriated audience = opportunity Topic?
  10. 10. - Richard Hamming You and Your Research "If you do not work on an important problem, it is unlikely you’ll do important work."
  11. 11. Naming Things and Finding Cothings The Eyjafjallajökull Lecture Topic!
  12. 12. Part 0: Core Search
  13. 13. A is A Aristotle's Law of Identity
  14. 14. A is A Aristotle's Law of Identity A IS COCOA Phillips's Categorical Corollary
  15. 15. COCOON = ON COCONUT = NUT COCOUNSELLED = BOUGHT Ongoing research
  16. 16. Part I: Naming Things
  17. 17. arity, boxity, fixity, totality, purity... complexity, generality, modularity, portability... productivity, security, simplicity, stability... finality, mutability, opacity, polarity... atomicity, locality, mobility, volatility... BUT WHAT ABOUT... OVERUSED -ITIES
  18. 18. atrocity calamity obscenity... depravity criminality complicity... profanity perplexity debility... inanity hilarity indignity temerity... duplicity culpability impunity... futility hostility enmity... UNDERUSED -ITIES
  19. 19. liberty, equality, fraternity... intercity, intracity, supercity... validity, probability, advisability... FUNCTIONAL FIXEDNESS POP QUIZ
  20. 20. CLARIFICTION It's just a monoid in the category of endofunctors, what's the problem? CODIFICTION Follow consensus, as long as you were doing that anyway. EDIFICTION Mansplaining FORTIFICTION More tests UNIFICTION M[Any] SIMPLIFICTION go
  21. 21. REIFICTION scala.reflect VERIFICTION We have tests, we don't need types. RAMIFICTION Y2K RATIFICTION SIP-18 BEAUTIFICTION gofmt DEMYSTIFICTION A bialgebra is a monoid in the category of coalgebras. Equivalently, it is a comonoid in the category of algebras. Equivalently, it is a monoid in the category of comonoids in Vect Equivalently, a comonoid in the category of monoids in Vect
  22. 22. DIVERSIFICTION We play both kinds of music, Country and Western! GRATIFICTION That wonderful feeling you don't have after pouring your life into software IDENTIFICTION Biometrics INDEMNIFICTION AIG JUSTIFICTION Unbelieber NOTIFICTION Read receipt
  23. 23. DIVERSIFICTION We play both kinds of music, Country and Western! GRATIFICTION That wonderful feeling you don't have after pouring your life into software IDENTIFICTION Biometrics INDEMNIFICTION AIG JUSTIFICTION Unbelieber NOTIFICTION Read receipt
  24. 24. Part II: Finding Cothings "Every algebraic structure in a category has a co-version with all morphisms reversed"
  25. 25. THE FORMAL THEORY OF TANNAKA DUALITY in 105 pages
  26. 26. THE FORMAL THEORY OF TANNAKA DUALITY in 105 pages coevaluation coproduct cofiltered cofibrant codomain coalgebra cokernel coequalizer cohomology comonoid cosplit coclosed cocone coaction corestriction comodule cocontinuous cotensor cocomplete cocompletion comonad comultiplication cocommutative cospan coend coassociative coalgebroid colimit
  27. 27. In the same 105 pages
  28. 28. In the same 105 pages combine composite contain complicated common converse coherence convenience colloquium correspond compose concatenation corollary consist concrete content condition convolution constraint continuous component cosmoi compatible could convention conservative coefficient corps commutative conical considerable compare contravariant consequence companion combinatorial conclusion conceptual computation collectively coincide cosmos compute concern counit construct context course complete
  29. 29. Too many cothings are virtually unknown!
  30. 30. MEDIAN COMEDIAN
  31. 31. ACHES COACHES
  32. 32. BRA COBRA
  33. 33. AXES COAXES
  34. 34. DING CODING
  35. 35. L.A. COLA
  36. 36. LANDER COLANDER
  37. 37. MA COMA
  38. 38. MET COMET
  39. 39. MIC COMIC
  40. 40. PIER COPIER
  41. 41. ME COME
  42. 42. 65518
  43. 43. FFEE COFFEE 65518
  44. 44. PIOUS COPIOUS
  45. 45. VET COVET
  46. 46. STING COSTING
  47. 47. (Bool, T, T) => T
  48. 48. IF COIF (Bool, T, T) => T
  49. 49. UNTIES COUNTIES
  50. 50. WARD COWARD
  51. 51. UGH COUGH
  52. 52. UP COUP
  53. 53. DICES CODICES
  54. 54. JONES COJONES
  55. 55. Q COQ
  56. 56. ARSE COARSE

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