Naming Things and Finding Cothings

•

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Paul Phillips

The only category theory lesson you will ever need.

Tecnologia

The
Eyjafjallajökull1,2
Lecture
Paul Phillips
Delivered @scala.world
September 21 2015
1. ˈeɪjaˌfjatlaˌjœːkʏtl ̥
2. Sure, that helped.

the origins of scala.world
jon pretty's thirst for vengeance

the origins of scala.world
jon pretty's thirst for vengeance
April 2014

the origins of scala.world
jon pretty's thirst for vengeance
April 2014 September 2015

Topic?
My last scala commit
Mar 12, 2014
What have I learned since?

• What to call Typesafe
• What Scala could learn from Rust and Go
• Suffuse: the reactive ﬁlesystem
• Realization: inebriated audience = opportunity
Topic?

- Richard Hamming
You and Your Research
"If you do not work on an important problem,
it is unlikely you’ll do important work."

Naming Things and
Finding Cothings
The Eyjafjallajökull Lecture
Topic!

A is A
Aristotle's Law of Identity
A IS COCOA
Phillips's Categorical Corollary

COCOON = ON
COCONUT = NUT
COCOUNSELLED = BOUGHT
Ongoing research

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

atrocity calamity obscenity...
depravity criminality complicity...
profanity perplexity debility...
inanity hilarity indignity temerity...
duplicity culpability impunity...
futility hostility enmity...
UNDERUSED -ITIES

liberty, equality, fraternity...
intercity, intracity, supercity...
validity, probability, advisability...
FUNCTIONAL FIXEDNESS
POP QUIZ

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

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

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

Part II:
Finding Cothings
"Every algebraic structure in a category
has a co-version with all morphisms reversed"

THE FORMAL THEORY OF TANNAKA DUALITY
in 105 pages

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

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

Too many cothings
are virtually unknown!

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Naming Things and Finding Cothings

1. The Eyjafjallajökull1,2 Lecture Paul Phillips Delivered @scala.world September 21 2015 1. ˈeɪjaˌfjatlaˌjœːkʏtl ̥ 2. Sure, that helped.

2. the origins of scala.world jon pretty's thirst for vengeance

3. the origins of scala.world jon pretty's thirst for vengeance April 2014

4. the origins of scala.world jon pretty's thirst for vengeance April 2014

5. the origins of scala.world jon pretty's thirst for vengeance April 2014 September 2015

6. the origins of scala.world jon pretty's thirst for vengeance April 2014 September 2015

7. Topic? My last scala commit Mar 12, 2014 What have I learned since?

9. That's it. Won't fill an hour.

10. • What to call Typesafe • What Scala could learn from Rust and Go • Suffuse: the reactive ﬁlesystem • Realization: inebriated audience = opportunity Topic?

11. - Richard Hamming You and Your Research "If you do not work on an important problem, it is unlikely you’ll do important work."

12.

13.

14.

15. Naming Things and Finding Cothings The Eyjafjallajökull Lecture Topic!

16. Part 0: Core Search

17. A is A Aristotle's Law of Identity

18. A is A Aristotle's Law of Identity A IS COCOA Phillips's Categorical Corollary

19. COCOON = ON COCONUT = NUT COCOUNSELLED = BOUGHT Ongoing research

20. Part I: Naming Things

21. 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

22. atrocity calamity obscenity... depravity criminality complicity... profanity perplexity debility... inanity hilarity indignity temerity... duplicity culpability impunity... futility hostility enmity... UNDERUSED -ITIES

23. liberty, equality, fraternity... intercity, intracity, supercity... validity, probability, advisability... FUNCTIONAL FIXEDNESS POP QUIZ

24. 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

25. 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

26. 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

27. 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

28. Part II: Finding Cothings "Every algebraic structure in a category has a co-version with all morphisms reversed"

29. THE FORMAL THEORY OF TANNAKA DUALITY in 105 pages

30. 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

31. In the same 105 pages

32. 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

33. Too many cothings are virtually unknown!

34.

35. MEDIAN COMEDIAN

36.

37. ACHES COACHES

38.

39. BRA COBRA

40.

41. AXES COAXES

42.

43. DING CODING

44.