Naming Conventions

Epsil follows the naming convention already used throughout MathJSON and the Compute Engine's library: capitalized identifiers denote library or engine operators, lowercase identifiers denote user-defined variables and functions.

Sin(x)
Simplify(2 + 3x^3)
Map([1, 2, 3], x |-> x^2)

Sin, Simplify, and Map are library operators; x is an ordinary user symbol.

Glyph Aliases

A few mathematical glyphs are input aliases for library symbols, canonicalized at the lexer — every position (expression, parameter, binding, match pattern) treats the glyph exactly like its ASCII spelling, and serialization emits the canonical name:

Glyph	Symbol
`π`	`Pi`
`∞`	`Infinity`
`ⅈ`	`ImaginaryUnit`
`ⅇ`	`ExponentialE`
`∅`	`EmptySet`
`⧝`	`ComplexInfinity`
`ℝ`	`RealNumbers`
`ℤ`	`Integers`
`ℚ`	`RationalNumbers`
`ℕ`	`NonNegativeIntegers`
`ℂ`	`ComplexNumbers`

3.1 ∈ ℝ
// ➔ True

Note the doublestruck ⅈ/ⅇ (U+2148/U+2147), not the ordinary letters: i and e remain plain user symbols. To name a raw symbol that happens to be a glyph, use the verbatim form (`π`).

This is a convention with no enforced semantics — nothing in the parser or the engine requires a capitalized name to be an operator or a lowercase name to be a variable. A user can declare a lowercase function or a capitalized variable; it will work exactly the same way. The convention exists so that, by scanning a program, it's usually obvious at a glance which names come from the library and which are the author's own.

Because the convention isn't enforced, a name collision — a user symbol that happens to share a capitalized library name, or vice versa — isn't a parse error. It resolves the same way any other symbol lookup does: by scope, not by case. A local declaration shadows an outer one (including a library operator) for the rest of that scope, exactly as it would for any other symbol.

Glyph Aliases​

Glyph Aliases