Extending LoweredDistributions

There are two different ways to extend the package: giving a distribution family its own exact lowering, and adding a new backend. The lowering type hierarchy itself — AbstractLowering, AbstractChainTrick, and the four concrete representations (ErlangChain, Coxian, PhaseType, CTMC) — is locked; every lowering is one of these four, so neither extension point adds a new representation type.

Giving a distribution an exact lowering

lower dispatches on the Distribution's type, with a moment-matched phase_type fit as the fallback (lower(d::Distribution) = phase_type(d) in src/lower.jl). A distribution with a known exact chain representation gets its own method, following lower(d::Gamma) and lower(d::Exponential):

LoweredDistributions.lower(d::MyDistribution) = ErlangChain(d; kwargs...)

This is ordinary Julia dispatch on your own type, so it needs no extension mechanism — add the method wherever MyDistribution is defined.

Adding a new backend

The four built-in backends (Catalyst, SciMLBase, AlgebraicPetri, JumpProcesses) each follow the same shape: 2. A stub function with no method, declared and exported in the core package — e.g. function ode_problem end in src/ode.jl — so it is part of the public API even before the backend package is loaded.

3. A package extension ext/LoweredDistributions<Backend>Ext.jl, gated on the backend as a weak dependency, adding the concrete method dispatching on AbstractLowering (or a narrower type, if the backend only applies to one branch of the hierarchy).

4. The extension builds on the internal numeric core every backend shares: _generator(m) (src/generator.jl) returns the full state-space generator Q and a default initial condition for ANY AbstractLowering uniformly, whether it came from a phase-type fit or a bare CTMC.

ext/LoweredDistributionsSciMLBaseExt.jl is the shortest of the four and the best template to start from — it wraps _generator's Q/u0 as an ODEProblem in about a dozen lines.

To add a fifth backend: 2. Add the target package as a [weakdeps] entry and register the extension in [extensions] in Project.toml.

3. Declare and export a stub function with a docstring in src/.

4. Write ext/LoweredDistributions<Backend>Ext.jl following the pattern above, building on _generator (or on PhaseType/CTMC directly, if the backend needs the phase-type view rather than the full generator).

5. Add a tutorial under docs/src/getting-started/tutorials/, mirroring the existing four backend tutorials, and register it in docs/pages.jl.

6. Check the new backend's output against the source distribution on the same delay every other backend tutorial uses.