Logic Programming

Given at #HNLondon on Nov 22, 2012

Transcript

1. Logic Programming Peteris Erins
2. p_e @
3. Logic
4. Logic Formal models of human reasoning
5. Logic is expressive
6. ∀m ∃n ∀a ∀b (n ≥ m) ∧ [(a = 1) ∨ (b = 1) ∨ (ab ≠ n)] ?
7. ∀m ∃n ∀a ∀b (n ≥ m) ∧ [(a = 1) ∨ (b = 1) ∨ (ab ≠ n)] There are infinitely many primes ≡
8. Prolog (1972)
9. Relations are relationships between stuff
10. human(you) less_than(2, 3) prefix(‘ban’, ‘banana’) even(X) relation name upper case for variables lower case for constants
11. add(2, 3, 5) sorted([3, 1, 2], [1, 2, 3]) Functions are easily turned into relations add(2, 3) = 5
12. Horn clauses
13. Horn clauses If four legs and has a tail, then a dog many “if”s one “then”
14. Horn clauses If four legs and has a tail, then a dog D is a dog if has four legs, has a tail
15. Horn clauses If four legs and has a tail, then a dog D is a dog if has four legs, has a tail dog(D) if legs(D, 4) & has_tail(D)
16. Horn clauses If four legs and has a tail, then a dog D is a dog if has four legs, has a tail dog(D) if legs(D, 4) & has_tail(D) dog(D) :- legs(D, 4), has_tail(D). “if” “and”
17. Prolog, how does it work?
18. even(2). even(4). even(6). Prolog, how does it work? 1. Write facts prolog, 2 is even prolog, 4 is even prolog, 6 is even
19. even(2). even(4). even(6). Prolog, how does it work? 1. Write facts 2. Ask a question with a variable ?- even(X). prolog, 2 is even prolog, 4 is even prolog, 6 is even prolog, can you find an even X?
20. even(2). even(4). even(6). Prolog, how does it work? 1. Write facts 2. Ask a question with a variable ?- even(X). 3. Prolog solves for the variable prolog, 2 is even prolog, 4 is even prolog, 6 is even prolog, can you find an even X? X = 2 ; X = 4 ; X = 6.
21. Example Meta compiler? NLP grammar parser? Bayesian expert system?
22. Example Meta compiler NLP grammar parser Bayesian expert system Todo list
23. Todo list % source code file % [= fact/relation database] % interactive console for queries code repl
24. Todo list code repl todo(Item) homework laundry dishes talk the relation we want to construct
25. Todo list todo(homework). todo(laundry). todo(dishes). todo(talk). code repl todo(Item) homework laundry dishes talk the construction
26. Todo list todo(homework). todo(laundry). todo(dishes). todo(talk). ?- todo(X). X = homework ; X = laundry ; X = dishes ; X = talk. code repl todo(Item) homework laundry dishes talk testing
27. Todo list just_before(laundry, homework). just_before(dishes, laundry). ?- just_before(X, homework). X = laundry. code repl just_before just_before Before After laundry homework dishes laundry
28. Todo list cannot_do(X) :- just_before(Y, X), todo(Y). ?- cannot_do(X). X = homework ; X = laundry. code repl cannot_do(Item) homework laundry
29. Todo list code repl before before Before After laundry homework dishes laundry dishes homework just_before just_before Before After laundry homework dishes laundry
30. Todo list before(X, Y) :- just_before(X, Y). before(X, Y) :- just_before(X, T), before(T, Y). ?- before(X, homework). X = laundry ; X = dishes. code repl before before Before After laundry homework dishes laundry dishes homework
31. Todo list tag(homework, work). tag(laundry, home). tag(dishes, home). tag(talk, work). ?- tag(dishes, T). T = home. ?- tag(X, work). X = homework ; X = talk. code repl tag tag Task Tag homework work laundry home dishes home talk work
32. Todo list agenda_tagged(Tag, Agenda) :- findall(X, tag(X, Tag) , Need_Doing), findall(X, cannot_do(X), Cant_Do), subtract(Need_Doing, Cant_Do, Agenda). ?- agenda_tagged(home,Y). Y = [dishes]. ?- agenda_tagged(work,Y). Y = [talk]. code repl agenda_tagged agenda_tagged Tag Agenda home [dishes] work [talk]
33. How to think about logic programming?
34. How to think about logic programming? 1. functional = imperative – mutable state logic = functional – manual search
35. How to think about logic programming? 1. functional = imperative – mutable state logic = functional – manual search 2. combining database and program
36. How to think about logic programming? 1. functional = imperative – mutable state logic = functional – manual search 2. combining database and program 3. an implementation of mathematical logic
37. How to think about logic programming? 1. functional = imperative – mutable state logic = functional – manual search 2. combining database and program 3. an implementation of mathematical logic not really
38. Here’s the catch: io flow scoping numerics
39. Logic in the wild
40. IBM Watson
41. Wolfram Mathematica
42. Datomic
43. Type systems
44. /** * Type class witnessing that `A` is less than or equal to `B`. * * @author Miles Sabin */ trait LTEq[A <: Nat, B <: Nat] object LTEq { import Nat._0 type <=[A <: Nat, B <: Nat] = LTEq[A, B] implicit def ltEq1 = new <=[_0, _0] {} implicit def ltEq2[B <: Nat] = new <=[_0, Succ[B]] {} implicit def ltEq3[A <: Nat, B <: Nat](implicit lt : A <= B) = new <=[Succ[A], Succ[B]] {} } Scala shapeless library Try finding the logic
45. p_e @ Thank you! github.com/Pet3ris/talk-logic-programming Peteris Erins thanks to reviewers: @DARowlands @Sedols @Springcoil Panagiotis Charalampopolous special thanks: @swannodette @zoltanvarju @richlitt