Multi-Set Manipulator/String

This is a string-based version of Multi-Set Manipulator/Subset, as there are programming difficulties for using lists.

This attempts to make Multi-Set Manipulator a pure set-based language. All sets in Set Manipulator are multi-sets, although they can occasionally be treated as normal sets.

Set-manipulational instructions

A∩B A with all items not in B removed; Intersection
A∪B A appended with B; Union
«I  Make the I set's items exclusive.
AΔB (A-B)∪(B-A)
A\B A with all B items removed
"ABC" Define a set
I The set that results from 1 line of input; all expressions are outputted by default.
← Initializement; for all of the undefined variables it searches for where that variable is in the program and then evaluates that variable's expression first. The initialized value will be returned.
= Equivalency symbol
¶ Separate lines
∴ expression∴action; conditional statement

Set-comparison instructions

∈ ELEMENT OF
∉ NOT AN ELEMENT OF
⊂ STRICT SUBSET OF
⊆ SUBSET OF OR EQUAL TO

Built-in sets

Z Is the set a positive integer? "\x01\x02\x03\x04\x05\x06..."
P Prime number set; "\x02\x03\x05\x07\x0B\x0D..."
∅ Null set; ""
U Universal set; "\x00\x01...\xFE\xFF"

Proof as a programming language

Primality checker

I∈P

Unary Adder

I∪I

Exchange "Good" and "Bad"

"GoodBad"\I

Output with the same length as the code

A←"aaaa"¶A∪A

Create output twice the length as the code

It is impossible... here is an approximate one.

A←"aaaa"¶A∪A∪A∪A∪A∪A∪A∪A∪A∪A∪A∪A∪A∪A∪A∪A∪A∪A

Shortest code to produce infinite output

A←"H"∪A

Is it double speak?

A←I=A\«A

Code page

  _0_1_2_3_4_5_6_7_8_9_A_B_C_D_E_F
0_ ∩ ∪ « Δ \ " ← = ¶ ∈ ∉ ⊂ ⊆ ∅ Z P
1_ A I U E ∴