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- 1. Introduction to Laws
- 2. About @nkpart Scalaz Functional JavaRuby/Scala/Haskell/Objective-C FunctionalKitMogeneration Kit Various ruby gems
- 3. Why Laws?They are the footnote in everymonad tutorial.Too hard at the beginning.Programming isn’t even Mathsanyway.
- 4. Laws are theNew/Old HotnessYou are already programming withLaws.Laws are fundamental tounderstanding most typeclasses.Programming *is* maths.
- 5. What are Laws Understanding LawsLegal Benefits Breaking Laws
- 6. What are Laws Common LawsLegal Benefits Breaking Laws
- 7. (7 + 5) + 3 = 7 + (5 + 3)
- 8. (a + b) + c = a + (b + c)
- 9. (a ⊗ b) ⊗ c = a ⊗ (b ⊗ c)
- 10. What are Laws?Laws are statements made aboutequivalence of expressions.Some Laws come from Maths Abstract Algebra
- 11. What are Laws?Integer addition obeys theAssociativity LawWherever we use IntegerAddition, we can use theproperties of the law to ouradvantage. 7 + 3 + 5 + 2 = 7 + (3 + 5) + 2For an implementor, the Law is aContract!
- 12. add :: Int -> Int -> Int
- 13. What are Laws?Laws are not checked by the typesystemLaws can be broken byimplementationsVerification is usually done byhand Alternatively, QuickCheck.
- 14. What are Laws?Statements of EquivalenceContracts for the ImplementorLaws are not checked by the typesystemOrigins in Maths. (Programming)
- 15. What are Laws Common LawsLegal Benefits Breaking Laws
- 16. Common LawsAbstract Algebra Associative Law Commutative Law IdentityTypeclasses and their Laws Monoid Functor
- 17. Associative Law(a ⊗ b) ⊗ c = a ⊗ (b ⊗ c) Satisfied by: +, *, concat Uses: Parallelism. String building (refactoring)
- 18. Associative Law [1,2,3,4,5,6] fold/each/inject1 + (2 + (3 + (4 + (5 + 6)))) apply the law!1 + (2 + ((3 + 4) + (5 + 6))))
- 19. Commutativity Lawa ⊗ b = b ⊗ a Satisfied by: +, *, but not concat! Uses: Parallelism (again!)
- 20. Commutative Law1 + (2 + ((3 + 4) + (5 + 6)))) apply the law!1 + (2 + ((5 + 6) + (3 + 4))))
- 21. Identity Lawa ⊗ Id = a = Id ⊗ a Satisfied by: +/0, */1, concat/ []
- 22. Typeclasses
- 23. Monoidclass Monoid a where mappend :: a -> a -> a mempty :: a
- 24. Monoidmappend satisfies theAssociative Lawmempty is the Identity for themappend operation.
- 25. class Monoid a where mappend :: a -> a -> a mempty :: a
- 26. MonoidCODE TIME
- 27. Functor
- 28. class Functor f where fmap :: (a -> b) -> f a -> f b
- 29. Functor Lawsfmap id x = id xfmap (g . h) = (fmap g) . (fmap h)where id a = a id a = a
- 30. Not a Functorinstance Functor [] where fmap f [] = [] fmap f (x:xs) = (f x):(f x):(fmap f xs)
- 31. Functor LawsFunctor is a structure with an`fmap` that does not affect thatstructure, just the valuesinside.To modify the structure you needa different typeclass. The lawsprevent it.
- 32. What are Laws Common LawsLegal Benefits Breaking Laws
- 33. Legal BenefitsMeaning to Multi-functionTypeclassesGreater understanding ofTypeclassesSubstitution of Expressions
- 34. Instancing Functor CODE TIME
- 35. Subsituting ExpressionsSome Haskell tooling can usethisHLintGHC Rewrite Rules
- 36. HLintCODE TIME
- 37. Rewrite Rules{-# RULES“map/map” forall f g xs.map f (map g xs) = map (f . g) xs#-}
- 38. What are Laws Common LawsLegal Benefits Breaking Laws
- 39. Breaking LawsLawless Typeclasses Pointed (Haskell [deprecated[ and Scalaz [never released]) Zero (Scalaz [never released])Real World Broken Instances Bijection (Twitter), ListT (Haskell Platform), Gen (from QuickCheck)
- 40. “Lawless Typeclasses”class Zero a where zero :: aclass Pointed f where return :: a -> f a
- 41. Broken Instances Broken typeclass instances exist Verification is hard. The Gen Monad: CODE TIME
- 42. Consequences ofIllegal Behaviour
- 43. Consequences ofIllegal Behaviour Bijection[Int, String]
- 44. Consequences ofIllegal Behaviour Specific code using a Bijection[Int, String] might be fine. What if I write a function that uses a Bijection[A,B]?
- 45. What are Laws Understanding LawsLegal Benefits Breaking Laws
- 46. Laws are GoodLaws have a huge impact on the waywe code (already). Refactoring, Algebraic LawsTaking advantage of laws is apowerful programming technique. Understanding typeclasses, writing new instancesWatch out for Law breakers!
- 47. Useful ResourcesHaskell Packages- Lens Typeclassopedia- Semigroupoids #scalaz- Pipes #haskell[.au] #bfpgScalaz
- 48. Thanks!

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