As we can see, for any
n, the actual output will be[n, n], not[n, -1]
While I have no problem with hand-waving a bit in a mathematical argument for popular consumption, "as we can see" is really begging the question. If we could simply see this, then we would really not need to proof by contradiction at all. I think this should be spelled out.
For example, the cardinality of
[0, 1, 2, 3, Infinity]is4, the same as its length.
Oops. There seems to be a miscount here.
| const R = require('ramda'); | |
| const permutations = (tokens, subperms = [[]]) => | |
| R.isEmpty(tokens) ? | |
| subperms : | |
| R.addIndex(R.chain)((token, idx) => permutations( | |
| R.remove(idx, 1, tokens), | |
| R.map(R.append(token), subperms) | |
| ), tokens); |
| // Based on a discussion with Michael Haufe: | |
| // https://groups.google.com/group/jsmentors/browse_thread/thread/d028fb0041f93a27 | |
| // Not really recommended for anything but the fun of knowing it can be done! | |
| var omega = function() { | |
| var queue = []; | |
| var valueOf = Function.prototype.valueOf; | |
| Function.prototype.valueOf = function() { | |
| queue.push(this); | |
| return 1; // not needed now, but could be used later to distinguish operators. |
| var compose = function compose(f) { | |
| var queue = f ? [f] : []; | |
| var fn = function fn(g) { | |
| if (arguments.length) { | |
| queue.push(g); | |
| return fn; | |
| } | |
| return function() { | |
| var args = Array.prototype.slice.call(arguments); | |
| queue.forEach(function(func) { |
| var R = require('./ramda'); | |
| // Discussion at https://github.com/ramda/ramda/issues/1258 | |
| var namedCurry = function(fn, argNames) { | |
| // TODO: what if fn.length != argNames.length? | |
| var f = R.curryN(fn.length, function() { | |
| return fn.apply(this, arguments); | |
| }); | |
| f['secret-sauce'] = { |
| <!DOCTYPE html> | |
| <html> | |
| <head> | |
| <meta charset="utf-8"/> | |
| <title>String#includes vs. String#indexOf vs. RegExp</title> | |
| <script src="https://cdnjs.cloudflare.com/ajax/libs/benchmark/1.0.0/benchmark.min.js"></script> | |
| <script src="./suite.js"></script> | |
| </head> | |
| <body> | |
| <h1>Open the console to view the results</h1> |
| // clean and pure: | |
| function cons(x, y) { | |
| return function(pick) { | |
| return pick(x, y); | |
| } | |
| } | |
| // does more stuff: | |
| function cons(x, y) { | |
| var fn = function(pick) { |
| Function.prototype.compose = function(g) { | |
| var fn = this; | |
| return function() { | |
| return fn.call(this, g.apply(this, arguments)); | |
| }; | |
| }; | |
| Function.prototype.pipe = function(g) { | |
| var fn = this; | |
| return function() { |
| var first = (function() { | |
| var chainNames = ["then", "andThen", "next"]; | |
| var endChainNames = ["finally", "andFinally", "last"]; | |
| var chain = function(fn) { | |
| var f1 = function(g) { | |
| var func = function() {return g.call(this, fn.apply(this, arguments));}; | |
| chain(func); | |
| return func; | |
| }; | |
| var f2 = function(g) { |
| (function() { | |
| var split = {}, intervalData, | |
| timeComponent = { | |
| seconds: function (split) {return split.seconds * 6;}, | |
| minutes: function (split) {return (split.minutes + (split.seconds / 60)) * 6;}, | |
| hours: function (split) {return (split.hours % 12 * 30 ) + split.minutes / 2;} | |
| }; | |
| var SVG = (function() { | |
| var SVG = function(config) { |