Em

A small language for math operations.

Sample working program

Source

set := {1, 2, 3, 4}
set ⊆ ℝ
1 ∈ set
5 ∈ set

Result (line by line)

{1, 3, 2, 4}
⊤
⊤
⊥

Sets

Operations

Operation	Syntax	Return value	Supported
Create material set	set := {1, 5}	Set	✅
Create virtual set	set := {x | x ∈ ℝ}	Set	✅
Union	{1, 2} ∪ {3}	Set	✅
Intersection	{1, 2} ∩ {2}	Set	✅
Difference	{1, 2} - {2}	Set	❌
Symmetric difference	{1, 2} ∆ {2}	Set	❌
Cartesian product	{1} × {2}	Set	❌
Equality	{1} = {1}	Boolean	✅
Not equality	{1, 3} ≠ {4}	Boolean	✅
Element of	13 ∈ {1, 13}	Boolean	✅
Not element of	17 ∉ {1, 13}	Boolean	❌
Subset	{1} ⊆ {1, 2}	Boolean	✅
Not subset	{3} ⊄ {1, 3}	Boolean	✅
Superset	{1, 2} ⊇ {1}	Boolean	❌
Not superset	{3, 4} ⊅ {2}	Boolean	❌
Strict subset	{1} ⊂ {1, 2}	Boolean	❌
Strict superset	{1, 7} ⊃ {7}	Boolean	❌
Cardinality	|{1, 2, 3}|	Number	❌

Symbols

Symbol	Token	Value
Empty set	∅	{}
Real numbers set	ℝ	{x | -∞ < x <∞}

Functions

Operations

Operation	Syntax	Return value	Supported
Create function	h(x, y) = {x, y} ∪ {0, 9}	Function	✅
Call function	h(2, {4})	Any	✅

Symbols

Symbol	Token	Return value	Side effects
Print to standard input	print	Number	Prints provided value