As Little As Possible

FizzBuzz, in lambda calculus, in JavaScript.

Transcript

1. As Little As Possible Edinburgh JS: June 2014
2. John Sutherland Python & JavaScript at FanDuel @sneeu on the Internet
3. FanDuel We’re hiring!
4. As Little As Possible Edinburgh JS: June 2014
7. λx.x
8. function (x) { return x; }
9. (λx.x) y
10. (function (x) { return x; })(y);
11. (λx.x) s ! (x)[x:=s] = s
13. FizzBuzz • Print the numbers 1–100; • Replace numbers divisible by 3 with “Fizz”; • Replace numbers divisible by 5 with “Buzz”; • Replace numbers divisible by both 3 & 5 with “FizzBuzz”.
14. FizzBuzz • 1, 2, Fizz, 4, Buzz, Fizz, 7, 8, Fizz, Buzz, 11, Fizz, 13, 14, FizzBuzz, 16, 17, Fizz, 19, Buzz, Fizz …
15. FizzBuzz var fizzbuzz = function () { var i, s; for (i = 1; i <= 100; i++) { s = ''; if (i % 3 === 0) s += 'Fizz'; if (i % 5 === 0) s += 'Buzz'; if (s === '') s += i; console.log(s); } };
16. True & False var TRUE = function (l, r) { return l; }; var FALSE = function (l, r) { return r; }; var IF = function (f, e1, e2) { return f(e1, e2)(); };
17. Lists • The empty list; • Prepend to a list; • Get the head of a list; • Get the tail of a list; • Check if it’s the empty list.
18. Lists var EMPTY_LIST = function (selector) { return selector(undefined, undefined, TRUE); }; var PREPEND = function (h, t) { return function (selector) { return selector(h, t, FALSE); }; }; var IS_EMPTY = function (list) { return list(function (h, t, e) { return e; }); };
19. Lists var HEAD = function (list) { return list(function (h, t) { return h; }); }; var TAIL = function (list) { return list(function (h, t) { return t; }); };
20. Logic var AND = function (a, b) { return IF( a, function () { return b; }, function () { return FALSE; } ); }; var OR = function (a, b) { return IF( a, function () { return TRUE; }, function () { return b; } ); };
21. Numbers var ZERO = EMPTY_LIST; var ONE = PREPEND(EMPTY_LIST, ZERO); var TWO = PREPEND(EMPTY_LIST, ONE); var INC = function (n) { return PREPEND(EMPTY_LIST, n); }; var DEC = function (n) { return TAIL(n); }; var IS_ZERO = function (n) { return IS_EMPTY(n); };
22. Addition var ADD = function (a, b) { return IF( IS_ZERO(b), function () { return a; }, function () { return ADD(INC(a), DEC(b)); } ); };
23. Addition var ADD = function (a, b) { return IF( IS_ZERO(b), function () { return a; }, function () { return ADD(INC(a), DEC(b)); } ); };
24. Y–combinator var Y = function (f) { return (function (x) { return f(function (y) { return (x(x))(y); }); })(function (x) { return f(function (y) { return (x(x))(y); }); }); };
25. Addition var ADD = Y(function (g) { return function (n) { return function (m) { return IF( IS_ZERO(m), function () { return n; }, function () { return g(INC(n))(DEC(m)); } ); }; }; });
26. Subtraction var SUB = Y(function (g) { return function (n) { return function (m) { return IF( IS_ZERO(m), function () { return n; }, function () { return g(DEC(n))(DEC(m)); } ); }; }; });
27. < var LESS_THAN = Y(function (g) { return function (m) { return function (n) { return IF( AND(IS_ZERO(m), IS_ZERO(n)), function () { return FALSE; }, function () { return IF( IS_ZERO(m), function () { return TRUE; }, function () { return IF( IS_ZERO(n), function () { return FALSE; }, function () { return g(DEC(m))(DEC(n)); } ); } ); } ); }; }; });
28. REM var REM = Y(function (g) { return function (n) { return function (d) { return IF( LESS_THAN(n)(d), function () { return n; }, function () { return REM(SUB(n)(d))(d); } ); }; }; });
29. Fizz & Buzz & FizzBuzz var FIZZ = function (n) { return IF( IS_EQUAL(REM(n)(THREE))(ZERO), function () { return TRUE; }, function () { return FALSE; } ); };
30. 1–100 var ONE_TO_ONE_HUNDRED = PREPEND( ONE, PREPEND( TWO, PREPEND( THREE, PREPEND( FOUR, PREPEND( FIVE, PREPEND( SIX, PREPEND( SEVEN, PREPEND( EIGHT, PREPEND( NINE, PREPEND( ADD(MUL(TEN)(ONE))(ZERO), PREPEND( ADD(MUL(TEN)(ONE))(ONE), PREPEND( ADD(MUL(TEN)(ONE))(TWO), PREPEND( ADD(MUL(TEN)(ONE))(THREE), PREPEND( …
31. FizzBuzz MAP( function (n) { return IF( FIZZBUZZ(n), function () { console.log('FizzBuzz'); }, function () { return IF( FIZZ(n), function () { console.log('Fizz'); }, function () { return IF( BUZZ(n), function () { console.log('Buzz'); }, function () { console.log(TO_NUMBER(n)); } ); } ); } ); } )(ONE_TO_ONE_HUNDRED);
32. More • Steve Losh–List Out of Lambda • Tom Stuart–Programming with Nothing • Greg Michaelson–Functional Programming Through Lambda Calculus • Jim Wierich–Adventures in Functional Programming
33. The Whole Thing • Wrote a compiler an hour ago. • It’s broken—maybe after James’ talk. • 37KLOC.