* dds: A Home-made Toolkit for Discrete Dynamical Systems in Racket
This is a toolkit for playing with various discrete dynamical systems
in [[https://racket-lang.org/][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:

  - [[file:generic.rkt][generic.rkt]]: The generic interface for a discrete dynamical
    system, with functions for constructing state graphs.
  - [[file:utils.rkt][utils.rkt]]: Misc utilities.
  - [[file:functions.rkt][functions.rkt]]: Definitions for working with functions: tabulating,
    constructing from tables, generating random functions, etc.
  - [[file:networks.rkt][networks.rkt]]: Implements network-based models, which generalise
    Boolean networks, threshold Boolean automata networks, multivalued
    networks, etc.
  - [[file:rs.rkt][rs.rkt]]: Implements reaction systems, a variant of set rewriting.

The toolkit is designed with Emacs [[https://orgmode.org/][Org-mode]] interoperability in mind.
The file [[file:example/example.org][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 Fix =ob-racket= to work with Typed Racket
Currently, the =ob-racket= backend for running Racket code blocks in
Org-mode assumes the code is written in =#lang racket=, which breaks
the output for tables for example.  This makes the typed version of
=dds= essentially useless with tables.

*** TODO Fix [[file:example/example.org][example.org]]
I changed quite a number of things while converting =dds= to Typed
Racket, which should break a lot of things in [[file:example/example.org][example.org]].

*** TODO Think about splitting the library into lib and doc
*** TODO Implement string rewriting
*** TODO Implement [[https://en.wikipedia.org/wiki/P_system][P systems]]
*** TODO Consider splitting =dds/utils= into a separate package
*** TODO Implement a shorter syntax for defining Boolean functions
    Right now, this is how one defines the Boolean function:

    #+BEGIN_SRC racket :results output silent
(define (update-go st)
  (auto-hash-ref/:
   st
   (or (and (not :Go) :new-x) (and :Go :old-x))))
    #+END_SRC

    It would be nice and probably not too difficult to implement
    a macro allowing for a syntax like the following one:
    #+BEGIN_SRC racket :results output silent
(define-pbf my-pbf (or (and (not :Go) :new-x) (and :Go :old-x)))
    #+END_SRC

*** TODO Submit =update-graph= to =stchang=
*** TODO Implement =monotone?=
    =monotone?= would verify whether a given Boolean function is
    monotone according to the definition in the book /Boolean
    Functions: Theory, Algorithms, and Applications/ by Crama
    and Hammer.

*** TODO Consider optimizing the algorithms in =networks= and =dynamics=
*** TODO Implement the BN \to 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 [[https://docs.racket-lang.org/racklog/index.html][Racklog]]