Braces-Brackets-Parentheses-combinator

The title of this article is not correct because of technical limitations. The correct title is actually {}[]()combinator.

BinaryDict

Designed by	User:namotanu
Appeared in	2026
Computational class	Turing-complete
Reference implementation	Unimplemented

{}[]()combinator is an esoteric programming language created by User:namotanu in 2026. It is a minimalist bracket-based string rewriting system that directly mirrors the mechanics of SKI combinator calculus using three distinct pairs of brackets: parentheses `()`, square brackets `[]`, and curly braces `{}`.

Syntax

A program in {}[]()combinator consists of sequences of elements enclosed in three types of brackets, along with arbitrary symbols or quoted string payloads (represented here using quote marks e.g., `「...」`).

Term Rewriting Rules

The semantics of the language are defined by three basic reduction rules acting on bracketed structures:

1. I-Combinator / Application (Parentheses)

Parentheses `()` handle function application and act as the identity element I combinator, where ($Ix=x$):

( <x...> y... )  ==>  <x... y...>

2. K-Combinator / Erasure (Square Brackets)

Square brackets `[]` discard intermediate terms, functioning similarly to the K combinator ($Kxy\to x$):

[<x...> y z...]  ==>  <x... z...>

3. S-Combinator / Duplication & Substitution (Curly Braces)

Curly braces `{}` duplicate and distribute arguments across payloaded targets, operating like the S combinator ($Sxyz\to xz(yz)$):

{<x...> 「y...」 z w...}  ==>  <x... z 「y... z」 w...>

Computational Completeness

Because the reduction rules directly map to the primitive operations of the SKI combinator calculus.