TANGLE is an experimental, Turing-complete, topologically inspired programming language where programs are represented as tangles — isotopy classes of braided strands in 3D space.
Programs are braids; equivalence is isotopy; crossings define operations.
The type system separates matchable braid words (Word[n]) from extensional
tangle morphisms (Tangle[A,B]), with implicit coercion between them.
See Formal Semantics for the full
denotational model.
Caveat: This is an experimental research language. The compiler is early-stage and the formal semantics are still being refined. Turing completeness is established via recursive definitions and pattern matching, not via a traditional proof.
| Path | Proves |
|---|---|
|
Core grammar exists and is specified in EBNF |
|
Formal denotational semantics are documented |
|
Idris2 ABI definitions for type-level guarantees |
|
Rust implementation of the compiler pipeline |
|
Zig FFI layer per hyperpolymath ABI/FFI standard |
|
Conformance test suite for language behaviour |
|
Worked examples demonstrating language features |
| Technology / Pattern | Role in Tangle | Also Used In |
|---|---|---|
Idris2 ABI + Zig FFI standard |
|
gossamer, burble, ephapax, hypatia, verisimdb, typed-wasm — universal pattern across the estate |
Rust compiler pipeline |
|
ephapax (17-crate Rust workspace), panic-attack (Rust analysis engine), k9-rs, a2ml-rs |
Formal semantics + topological domain |
|
KnotTheory.jl (Julia knot invariant library), KRLAdapter.jl (KRL bridging), typed-wasm (structured braid-type analogues), standards (spec-first documentation pattern) |