• dds: A Home-made Toolkit for Discrete Dynamical Systems in Racket
  • Roadmap
    • Write new functions for building the interaction graphs
    • Add variable domains to the network
    • Review build-interaction-graph
    • Start writing the docs properly with Scribble
    • Think about not using generics for the dynamics
    • Convert dds to Typed Racket
    • Split networks into general networks and threshold Boolean networks
    • Submit update-graph to stchang
    • Implement the BN → RS conversion
    • Implement the minimisation of TBF/SBF
    • Contribute to Racket
    • Test network inference with Racklog

dds: A Home-made Toolkit for Discrete Dynamical Systems in Racket

This is a toolkit for playing with various discrete dynamical systems in Racket. A discrete dynamical system is a system which evolves from a discrete state to some other discrete states (many or one). The systems are discrete in the sense that we can identify successive states with no other states in between. Equivalently, the phase state of the system is discrete (and is often called the state graph). These constraints imply the possibility of associating discrete, possibly branching timelines to any evolution of the system.

DISCLAIMER: I develop this toolkit as a support for my research on discrete dynamical systems. The primary objective for this framework is to fit my approach to these systems. Essentially, this framework should fit to the "shape of my mind", which is not necessarily the same as yours.

Currently, the toolkit includes the following files:

• generic.rkt: The generic interface for a discrete dynamical system, with functions for constructing state graphs.
• utils.rkt: Misc utility functions.
• networks.rkt: Implements network-based models, which generalise Boolean networks, threshold Boolean automata networks, multivalued networks, etc.
• rs.rkt: Implements reaction systems, a variant of set rewriting.

The toolkit is designed with Emacs Org-mode interoperability in mind. The file example/example.org explains the features available for interaction with Org-mode.

Roadmap

Here is my current roadmap for this toolkit, in order. The first element is what I am currently working on. The degree of certainty that I work on the subsequent items decreases with their position in the list.

TODO Write new functions for building the interaction graphs

1. variables-interact?
2. get-interaction-sign
3. build-interaction-graph

I currently have two different kinds of function for building interaction graphs: the syntactic interaction graphs and the interaction graphs as typically defined in the papers. These two kinds of graphs are not exactly the same. I have already started marking the split by renaming the original build-interaction-graph to build-syntactic-interaction-graph. The other functions are somewhat badly structured, somewhat badly written, and potentially somewhat wrong.

TODO Add variable domains to the network

I currently define a network as a mapping from variables to functions, but in fact I very often need the domains of the variables for very many operations.

I started this transformation a couple of days ago, and decided against it, because I thought that some networks may have unbounded domains. That's right, but stays hypothetical, while right now I need domains with my networks all the time.

TODO Review build-interaction-graph

Check that the definition of this function really follows the definition of the interaction graph. Pay attention to the existential vs. universal quantifiers.

TODO Start writing the docs properly with Scribble

Convert some of the comments to Scribble, in particular module-level comments introducing the modules and each of the sections.

Set up the infrastructure for extracting the in-source comments using this.

TODO Think about not using generics for the dynamics

Typed Racket can now type classes, and I can implement the idea from the module generics as a class. However, I got this advice on Racket Users group:

If you don't need to support arbitrary user implementations, you can avoid generics and classes altogether and use structs whose fields contain functions.

I will need to think about simpler implementations of the interface to dynamics, which should also be simpler to type.

TODO Convert dds to Typed Racket

This will necessarily lead to updates in the comments, which should be rewritten with Scribble.

I will do the conversion in the directory typed/, by incrementally translating existing modules, definition by definition.

The order I will convert the modules:

1. utils
2. functions
3. the module defining the interface to dynamics (currently generics)
4. networks
5. rs

TODO Split networks into general networks and threshold Boolean networks

TODO Submit update-graph to stchang

TODO Implement the BN → RS conversion

TODO Implement the minimisation of TBF/SBF

TODO Contribute to Racket

• Make sequence-filter allow multivalued sequences, provided the arity of the predicate is consistent with the arity of the sequence.
• Add a sequence->hash function that accepts a multivalued sequence of keys and values (exactly like what in-hash produces) and copies them into a hash table.

TODO Test network inference with Racklog