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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 {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

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A small interpreter for math operations.

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