clean up set section

msg/COS_ListPre.js

@@ -149,8 +149,8 @@ for (var i=0; i<8; i++) {
 
 
 cos.add("define pair | list 2");
-cos.add("define first | ? lst | head $lst");
-cos.add("define second | ? lst | head | tail $lst");
+cos.add("define first | ? x:list | head $x:list");
+cos.add("define second | ? x:list | head | tail $x:list");
 
 
 var examples = cos.prand(10,3);

msg/COS_NewType.scm

@@ -187,7 +187,7 @@
  (set! (contents) (remove-element (x) (get! (contents))))))
  ((= (msg) =)
  (lambda ((c container))
- (set= (self inventory) (c inventory))))
+ (set:= (self inventory) (c inventory))))
  0))))));
 
 # Can pass anything to container function to create an object
@@ -198,9 +198,9 @@
 (pocket add 77);
 (pocket add 88);
 (pocket add 99);
-(set= (pocket inventory) (vector 77 88 99));
+(set:= (pocket inventory) (vector 77 88 99));
 (pocket remove 88);
-(set= (pocket inventory) (vector 77 99));
+(set:= (pocket inventory) (vector 77 99));
 
 (define pocket2 (container new));
 (pocket2 add 77);

msg/COS_Set.js

@@ -0,0 +1,78 @@
+#!/usr/bin/env node
+
+const cos = require('./cosmic');
+
+cos.seed(42);
+cos.add('intro element');
+cos.add('define element | ? x | ? y:list | not | = $undefined | list:find $y:list $x');
+
+for (let i=0; i<5; i++) {
+ const hset = new Map();
+ const lst = [];
+ for (let j=0; j<6; j++) {
+ const x = cos.irand(10);
+ if (!hset.has(x)) {
+ hset.set(x, 1);
+ lst.push(x);
+ }
+ }
+ for (let j=0; j<3; j++) {
+ const mem = lst[cos.irand(lst.length)];
+ cos.add(`element ${mem} | ${cos.vector(lst)}`);
+ }
+}
+
+for (let i=0; i<5; i++) {
+ const hset = new Map();
+ const lst = [];
+ for (let j=0; j<6; j++) {
+ const x = cos.irand(10);
+ if (!hset.has(x)) {
+ hset.set(x, 1);
+ lst.push(x);
+ }
+ }
+ const mem = lst.shift();
+ cos.add(`not | element ${mem} | ${cos.vector(lst)}`);
+}
+
+cos.doc('Set some rules for set equality.');
+
+cos.add(`define set:<= | ? x | ? y |
+ if (= 0 | list-length $x) $true |
+ and (element (head $x) $y) |
+ set:<= (tail $x) $y`);
+
+cos.add(`define set:= | ? x | ? y |
+ and (set:<= $x $y) (set:<= $y $x)`);
+
+cos.add(`set:= (vector 1 5 9) (vector 5 1 9)`);
+cos.add(`set:= (vector 1 5 9) (vector 9 1 5)`);
+cos.add(`not | set:= (vector 1 5 9) (vector 1 5)`)
+
+cos.doc(`let's go leave ourselves wide open to Russell's paradox
+ by using characteristic functions since it doesn't really matter
+ within the bounds of this message`);
+
+cos.add(`element 5 | all | ? x | = 15 | + $x 10`);
+cos.add(`element 3 | all | ? x | = (* $x 3) (+ $x 6)`);
+
+cos.add(`define set:0 | vector`);
+cos.add(`element 0 $set:int:+`);
+cos.add(`forall | ? x | => (element $x $set:int:+) (element (+ $x 1) $set:int:+)`);
+
+for (let i=1; i<10; i++) {
+ cos.add(`element ${i} $set:int:+`);
+}
+
+cos.add(`define set:true:false | vector $true $false`);
+cos.add(`element $true $set:true:false`);
+cos.add(`element $false $set:true:false`);
+
+cos.add(`define set:even | all | ? x | exists | ? y |
+ and (element $y $set:int:+) (= $x | * 2 $y)`);
+
+for (let i=0; i<=6; i++) {
+ cos.add(`element ${i} $set:int:+`)
+ cos.add(`${(i % 2 === 0) ? '' : 'not | '}element ${i} $set:even`);
+}

msg/COS_Set.md

@@ -0,0 +1 @@
+# MATH introduce sets and set membership

msg/cosmic.js

@@ -168,5 +168,11 @@ CosWrite.prototype.listExpression = function(lst) {
  return this.stringify(this.listVerbose(lst, true));
 }
 
+CosWrite.prototype.vector = function(lst,wrap) {
+ const result = "vector " + lst.map(x => String(x)).join(" ");
+ if (wrap) { return `(${result})`; }
+ return result;
+}
+
 
 module.exports = new CosWrite();

src/cosmicos/Evaluate.hx

@@ -280,7 +280,7 @@ class Evaluate {
  vocab.check("set!",28);
  vocab.check("get!",29);
  vocab.check("all",30);
- vocab.check("natural-set",31);
+ vocab.check("set:int:+",31);
  vocab.check("undefined",32);
  vocab.check("!",33);
  vocab.check("div",34);
@@ -364,7 +364,7 @@ class Evaluate {
  function(x) {
  return Math.sqrt(x);
  });
- mem.add(vocab.get("natural-set"), 
+ mem.add(vocab.get("set:int:+"), 
  mem.get(vocab.get("all"))(function (x) { return x>=0; }));
  mem.add(vocab.get("div"), function(x:Dynamic){ 
  return function(y:Dynamic) : Dynamic { 

variant/iconic/vocab.json

@@ -391,6 +391,14 @@
  {
  "title": "exists",
  "text": "∃"
+ },
+ {
+ "title": "element",
+ "alias": "list:in"
+ },
+ {
+ "title": "set",
+ "text": "Ψ"
  }
  ]
 }