# Set

```ruby
class MySet(*set) {

    method init {
        var elems = set
        set = Hash()
        elems.each { |e| self += e }
    }

    method +(elem) {
        set{elem} = elem
        self
    }

    method del(elem) {
        set.delete(elem)
    }

    method has(elem) {
        set.has_key(elem)
    }

    method ∪(MySet that) {
        MySet(set.values..., that.values...)
    }

    method ∩(MySet that) {
        MySet(set.keys.grep{ |k| k ∈ that } \
                    .map { |k| set{k} }...)
    }

    method ∖(MySet that) {
        MySet(set.keys.grep{|k| !(k ∈ that) } \
                    .map {|k| set{k} }...)
    }

    method ^(MySet that) {
        var d = ((self ∖ that) ∪ (that ∖ self))
        MySet(d.values...)
    }

    method count { set.len }

    method ≡(MySet that) {
        (self ∖ that -> count.is_zero) && (that ∖ self -> count.is_zero)
    }

    method values { set.values }

    method ⊆(MySet that) {
        that.set.keys.each { |k|
            k ∈ self || return false
        }
        return true
    }

    method to_s {
        "Set{" + set.values.map{|e| "#{e}"}.sort.join(', ') + "}"
    }
}

class Object {
    method ∈(MySet set) {
        set.has(self)
    }
}
```

Usage example:

```ruby
var x = MySet(1, 2, 3)
5..7 -> each { |i| x += i }

var y = MySet(1, 2, 4, x)

say "set x is: #{x}"
say "set y is: #{y}"

[1,2,3,4,x].each { |elem|
    say ("#{elem} is ", elem ∈ y ? '' : 'not', " in y")
}

var (w, z)
say ("union: ", x ∪ y)
say ("intersect: ", x ∩ y)
say ("z = x ∖ y = ", z = (x ∖ y) )
say ("y is ", x ⊆ y ? "" : "not ", "a subset of x")
say ("z is ", x ⊆ z ? "" : "not ", "a subset of x")
say ("z = (x ∪ y) ∖ (x ∩ y) = ", z = ((x ∪ y) ∖ (x ∩ y)))
say ("w = x ^ y = ", w = (x ^ y))
say ("w is ", w ≡ z ? "" : "not ", "equal to z")
say ("w is ", w ≡ x ? "" : "not ", "equal to x")
```

#### Output:

```
set x is: Set{1, 2, 3, 5, 6, 7}
set y is: Set{1, 2, 4, Set{1, 2, 3, 5, 6, 7}}
1 is  in y
2 is  in y
3 is not in y
4 is  in y
Set{1, 2, 3, 5, 6, 7} is  in y
union: Set{1, 2, 3, 4, 5, 6, 7, Set{1, 2, 3, 5, 6, 7}}
intersect: Set{1, 2}
z = x ∖ y = Set{3, 5, 6, 7}
y is not a subset of x
z is a subset of x
z = (x ∪ y) ∖ (x ∩ y) = Set{3, 4, 5, 6, 7, Set{1, 2, 3, 5, 6, 7}}
w = x ^ y = Set{3, 4, 5, 6, 7, Set{1, 2, 3, 5, 6, 7}}
w is equal to z
w is not equal to x
```


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