121 lines
5.5 KiB
Org Mode
121 lines
5.5 KiB
Org Mode
* dds: A Home-made Toolkit for Discrete Dynamical Systems in Racket
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This is a toolkit for playing with various discrete dynamical systems
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in [[https://racket-lang.org/][Racket]]. A discrete dynamical system is a system which evolves from
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a discrete state to some other discrete states (many or one). The
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systems are discrete in the sense that we can identify successive
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states with no other states in between. Equivalently, the phase state
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of the system is discrete (and is often called the state graph).
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These constraints imply the possibility of associating discrete,
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possibly branching timelines to any evolution of the system.
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*DISCLAIMER:* I develop this toolkit as a support for my research on
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discrete dynamical systems. The primary objective for this framework
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is to fit my approach to these systems. Essentially, this framework
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should fit to the "shape of my mind", which is not necessarily the
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same as yours.
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Currently, the toolkit includes the following files:
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- [[file:generic.rkt][generic.rkt]]: The generic interface for a discrete dynamical
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system, with functions for constructing state graphs.
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- [[file:utils.rkt][utils.rkt]]: Misc utilities.
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- [[file:functions.rkt][functions.rkt]]: Definitions for working with functions: tabulating,
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constructing from tables, generating random functions, etc.
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- [[file:networks.rkt][networks.rkt]]: Implements network-based models, which generalise
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Boolean networks, threshold Boolean automata networks, multivalued
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networks, etc.
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- [[file:rs.rkt][rs.rkt]]: Implements reaction systems, a variant of set rewriting.
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The toolkit is designed with Emacs [[https://orgmode.org/][Org-mode]] interoperability in mind.
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The file [[file:example/example.org][example/example.org]] explains the features available for
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interaction with Org-mode.
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** Roadmap
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Here is my current roadmap for this toolkit, in order. The first
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element is what I am currently working on. The degree of certainty
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that I work on the subsequent items decreases with their position
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in the list.
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*** TODO Convert =dds= to Typed Racket
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Rewriting =dds= with Typed Racket will be a major refactoring,
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consisting in the following 3 phases which will happen more or
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less in parallel:
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- define types, add type signatures, add types for functions
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I import from =graph=;
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- transfer the comments from the source files to Scribble
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documentation;
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- redefine the generic interface for dynamics, which is currently
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in =generics=.
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I plan to implement the new dynamics as a structure, from which
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all the concrete dynamics of the objects will inherit. This will
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hopefully work like interface inheritance. The current plan is to
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start converting =networks= to Typed Racket, then starting the new
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module =dynamics= to fill in the blanks progressively by moving
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over bits of code from =generics=. The goal is to have an empty
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=generics= module at the end.
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People on Racket Users suggested using structures with fields
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containing functions, but it does not seem to get me to my goal of
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having type-level methods/functions.
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The order in which I will convert the modules:
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1. =utils=,
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2. =functions=,
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3. =networks= and =dynamics= (currently =generics=) at the same
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time,
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4. =networks=,
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5. =rs=.
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I will convert the modules one by one by first creating a typed
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section (a submodule) and re-exporting its functions together with
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the untyped functions. I will then move the functions one by one
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from the untyped section to the typed section. When the untyped
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section is empty, I will convert the language of the entire module
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to Typed Racket and remove the submodule.
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*** TODO Remove the artifacts of conversion to Typed Racket
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Since I am converting =dds= to Typed Racket gradually, I need to
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leave a couple artifacts to ensure that older code compiles with
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newer code. These artifacts are marked with the keywords =TODO:=
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in the source.
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*** TODO Think about splitting the library into lib and doc
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*** TODO Implement a shorter syntax for defining Boolean functions
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Right now, this is how one defines the Boolean function:
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#+BEGIN_SRC racket :results output silent
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(define (update-go st)
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(auto-hash-ref/:
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st
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(or (and (not :Go) :new-x) (and :Go :old-x))))
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#+END_SRC
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It would be nice and probably not too difficult to implement
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a macro allowing for a syntax like the following one:
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#+BEGIN_SRC racket :results output silent
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(define-pbf my-pbf (or (and (not :Go) :new-x) (and :Go :old-x)))
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#+END_SRC
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*** TODO Implement =monotone?=
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=monotone?= would verify whether a given Boolean function is
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monotone according to the definition in the book /Boolean
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Functions: Theory, Algorithms, and Applications/ by Crama
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and Hammer.
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*** TODO Submit =update-graph= to =stchang=
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*** TODO Split =networks= into general networks and threshold Boolean networks
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*** TODO Consider optimizing the algorithms in =networks= and =dynamics=
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*** TODO Implement the BN \to RS conversion
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*** TODO Implement the minimisation of TBF/SBF
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*** TODO Contribute to Racket
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- Make sequence-filter allow multivalued sequences, provided the
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arity of the predicate is consistent with the arity of
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the sequence.
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- Add a sequence->hash function that accepts a multivalued
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sequence of keys and values (exactly like what in-hash produces)
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and copies them into a hash table.
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*** TODO Test network inference with [[https://docs.racket-lang.org/racklog/index.html][Racklog]]
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