# 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. ```epsil 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` | ```epsil 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.