String Diagrams for Ring-and-Rope Puzzles

This repository contains a formalisation of string diagrams used to solve ring-and rope puzzles.

Tested with Agda 2.6.0.1 (might be fragile due to the use of rewrite pragmas)

Structure

StrictNat.agda a version of the natural numbers strictified by some additional rewrite rules.
Diags.agda contains the definition of the diagrams.
Arity.agda contains short cuts for operations with greater arity.
Identities.agda other identities derived from the diagram laws.
Sliding.agda contains sliding laws.
Bracket.agda formalises brackets over n strings.
BraidingNaturality.agda proves the naturality of the braiding.
InverseBraiding.agda constructs the inverse of the (lax) braiding.

RingOnString.agda formalises the solution of freeing a ring from a loop of string.
2x2Block.agda formalises the puzzle (but not yet the solution) of a more complex puzzle.