Y-Combinator in PHP

This talk is about Y-Combinator and implementation in PHP

Article associated to this talk

https://blog.darkwood.fr/article/y-combinator-en-php

Video associated to this talk

https://www.youtube.com/watch?v=QSS_ZcO8Q1g

Transcript

1. Y-Combinator @matyo91 25-04-2023 In PHP
2. ⾠ I’m not an expert ⾠ I will speak with my own words @matyo91 @matyo91 25-04-2023
3. Objectives : Go back up to theoretical concepts that solve an issue How I discovered Y-Combinator and why I do need them ? Why Y-Combinator ? Introduction to Lambda Calculus Exemples of basic Lambda Calculus and equivalent in PHP Y-Combinator in PHP (for me and others github repositories) Plan @matyo91 25-04-2023 @matyo91
4. How I discovered Y-Combinator ? @matyo91 25-04-2023 Why I need them ?
5. In PHP https://github.com/darkwood-fr/flow In PHP https://github.com/phpflo/phpflo 25-04-2023 Flow Based Railway Flow Based MulByTwo MinusThree AddOne @matyo91
6. Why Y-Combinator ? @matyo91 25-04-2023 What does it solve ?
7. Do recursion in a language that do not have any recursion mechanism at all “ @matyo91 25-04-2023
8. Recursive Iterative @matyo91 @matyo91 25-04-2023
9. Pipe @matyo91 @matyo91 25-04-2023
10. A Y-combinator is a "functional" (a function that operates on other functions) that enables recursion, when you can't refer to the function from within itself. In computer-science theory, it generalises recursion, abstracting its implementation, and thereby separating it from the actual work of the function in question. This is applicable in languages that support Lambda-Calculus functions Y-Combinator @matyo91 25-04-2023 @matyo91
11. Lambda Calculus @matyo91 25-04-2023
12. Alonzo Church ( 1903 - 1995 ) Inventor of Lambda Calculus @matyo91 @matyo91 25-04-2023
13. Church Turing @matyo91 @matyo91 25-04-2023
14. λ x . x + 1 ( λ x . x + 1 ) ( 5 ) = 5 + 1 = 6 @matyo91 @matyo91 25-04-2023 X X + 1
15. λ x . λ y . x+y 
 
 ( λ x . λ y . x+y ) ( 5 , 6 ) = 5 + 6 = 11 @matyo91 @matyo91 25-04-2023 X X + Y Y
16. There are variables. We got a way to build functions. We can apply functions to each others by providing elements of the language itself. All derivatives of lambda calculus language is something defined in terms of this definition. Lambda Calculus @matyo91 25-04-2023 @matyo91
17. True ? False ? @matyo91 @matyo91 25-04-2023
18. @matyo91 @matyo91 25-04-2023
19. True = λ x . λ y . x False = λ x . λ y . y @matyo91 @matyo91 25-04-2023 X X Y True X Y Y False
20. True = λ x . λ y . x @matyo91 @matyo91 25-04-2023 False = λ x . λ y . y
21. Not ? @matyo91 @matyo91 25-04-2023
22. @matyo91 @matyo91 25-04-2023
23. Not = λ b . b False True @matyo91 @matyo91 25-04-2023 b False True b Not
24. Not = ( λ b . b False True ) ( True ) = True False True = ( λ x . λ y . x ) ( False True ) = False @matyo91 @matyo91 25-04-2023
25. @matyo91 @matyo91 25-04-2023 Not = λ b . b False True
26. Y-Combinator @matyo91 25-04-2023
27. Y ( f ) = f ( Y ( f ) ) = f ( f ( Y ( f ) ) ) = f ( f ( f ( f ( ... ) ) ) ) @matyo91 @matyo91 25-04-2023
28. Fac (n) = if n == 1 then 1 else n * Fac (n - 1) 
 Fac (3) = 3 * Fac (2) = 3 * 2 * Fac (1) = 3 * 2 * 1 = 6 @matyo91 @matyo91 25-04-2023 YCombinator in Lambda Calculus
29. Fac = Y ( ? ) @matyo91 @matyo91 25-04-2023 YCombinator in Lambda Calculus
30. Fac = Y ( ? ) = Y ( λ f . λ n . ? ) = Y ( λ f . λ n . max( n , 1 ) * Fac ( n - 1 ) ) @matyo91 @matyo91 25-04-2023 YCombinator in Lambda Calculus
31. Loop = ? @matyo91 @matyo91 25-04-2023 YCombinator in Lambda Calculus
32. Loop = Loop @matyo91 @matyo91 25-04-2023 YCombinator in Lambda Calculus
33. Loop = ( λ x . x . x ) ( λ x . x . x ) @matyo91 @matyo91 25-04-2023 YCombinator in Lambda Calculus
34. Loop = ( λ x . x . x ) ( λ x . x . x ) @matyo91 @matyo91 25-04-2023 YCombinator in Lambda Calculus
35. Loop = ( λ x . x . x ) ( λ x . x . x ) Loop = ( λ x . ( λ x . x . x ) . ( λ x . x . x ) ) @matyo91 @matyo91 25-04-2023 YCombinator in Lambda Calculus
36. Loop = ( λ x . x . x ) ( λ x . x . x ) Loop = ( λ x . ( λ x . x . x ) . ( λ x . x . x ) ) Loop = ( λ x . x . x ) ( λ x . x . x ) @matyo91 @matyo91 25-04-2023 YCombinator in Lambda Calculus
37. Loop = Y ( ? ) @matyo91 @matyo91 25-04-2023 YCombinator in Lambda Calculus
38. Loop = Y ( λ x . x . x ) = ( λ x . x . x ) ( Y ( λ x . x . x ) ) = ( λ x . x . x ) ( λ x . x . x ) ( Y ( λ x . x . x ) ) @matyo91 @matyo91 25-04-2023 YCombinator in Lambda Calculus
39. Y ( f ) = λ f ( λ x . f ( x x ) ) ( λ x . f ( x x ) ) @matyo91 @matyo91 25-04-2023 YCombinator in Lambda Calculus
40. https://github.com/darkwood-fr/flow @matyo91 @matyo91 25-04-2023 YCombinator in PHP
41. https://github.com/loophp/combinator @matyo91 @matyo91 25-04-2023
42. https://github.com/igorw/lambda-php @matyo91 @matyo91 25-04-2023
43. In Real Life @matyo91 25-04-2023 @matyo91
44. Hello! I Am Mathieu Ledru You can contact me at @matyo91 25-04-2023 @matyo91 Thanks! Any questions?