Beloch, named after Margherita Piazzola Beloch, is a declarative language for origami, built on the Huzita-Justin axioms, that compiles source models into folded states, crease patterns, and step-by-step folding diagrams.

Status: the evaluator implements all seven Huzita-Justin axioms over an exact real-algebraic number kernel and emits FOLD. See decisions/ for the architecture, spec/SPECIFICATION.md for the language, and notes/ for the design journal. More at beloch.toph.so.

Quick example

paper square
--d1 = through .a .c
--d2 = through .b .d
.center = cross --d1 --d2
@map .a onto .center

Two diagonals, a named crossing, one fold — @ actually folds .a onto .center (a bare map would just mark the crease) along the crease axiom 2 derives. That program produces a FOLD file, which renders into this — crease pattern and folded state, named constructions overlaid:

crease pattern	folded

More programs, from simple midline folds to Messer's cube-root-of-two construction (axiom 7), are in examples/.

Development

The evaluator core is OCaml; tooling lives at the edges in TypeScript (see decision 0001). A Nix flake provides the OCaml toolchain (dune, menhir, sedlex, ocaml-lsp, …):

direnv allow          # or: nix develop
dune build
dune exec beloch -- --version

Layout

lib/          evaluator core (OCaml library)
bin/          the `beloch` CLI
spec/         human-readable language specification (grows per increment)
decisions/    architecture decision records (ADRs)
notes/        dated design journal
examples/     .bel programs, tagged works / aspirational / anti
paper/        the eventual write-up (arXiv / JOSS / OSME)
antipatterns.md  dead ends and rejected approaches
bibliography.md  annotated sources