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Sergiu Ivanov b79bae9d67 example: Update the randomly generated network.
2020-03-22 21:03:20 +01:00

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#+TITLE: Examples of usage of =dds=
#+PROPERTY: header-args:racket :prologue "#lang racket\n(require graph (file \"~/Candies/prj/racket/dds/networks.rkt\") (file \"~/Candies/prj/racket/dds/utils.rkt\"))"
* Introduction
This document shows some examples of usage of the modules in =dds=
with Org-mode. It relies on [[https://github.com/hasu/emacs-ob-racket][emacs-ob-racket]].
The [[intro][following section]] describes how Org-mode can interact with
Racket, and how this interaction can be used for a fluid workflow
with =dds=. In particular, the code block =munch-sexp= is [[tabread][defined]]
in this section.
The subsequent sections show off some the functionalities of the
submodules of =dds=.
* Org-mode, Racket, and =dds= <<intro>>
** Importing a module from file
:PROPERTIES:
:header-args:racket: :prologue "#lang racket\n(require (file \"~/Candies/prj/racket/dds/networks.rkt\"))"
:END:
To require the modules from the files of =dds=, you can use the
following code (I only reset the prelude here because I set at the
top of this file):
#+BEGIN_SRC racket :results output :prologue ""
#lang racket
(require (file "~/Candies/prj/racket/dds/networks.rkt"))
(require (file "~/Candies/prj/racket/dds/utils.rkt"))
#+END_SRC
#+RESULTS:
Note that this code will not work with =:results value=. I think it
is because in this case the code is not really evaluated at top
level.
These initialisation lines can be put into the prologue of every
code block in a subtree by setting =:prologue= via
=:header-args:racket:= in the properties drawer. Check out the
properties drawer of this section for an example.
Alternatively, this property can be set via a =#+PROPERTY= line at
the top the file. For example, this file has such a line. Whenever
this property line changes, refresh the setup of the file by hitting
=C-c C-c= on the property line. This will update the prologue for
all racket code blocks.
Finally, you can also set =:prologue= (and other properties with
long values) in the following way:
#+HEADER: :prologue "#lang racket\n(require (file \"~/Candies/prj/racket/dds/networks.rkt\"))"
#+BEGIN_SRC racket :results output drawer
(st '((a . 1)))
#+END_SRC
#+RESULTS:
:RESULTS:
'#hash((a . 1))
:END:
** Output formats for results of evaluation of code blocks
[[https://orgmode.org/manual/Results-of-Evaluation.html#Results-of-Evaluation][This section]] of the Org manual describes various different formats
for presenting the results of code blocks. I find the following
three particularly useful as of [2020-02-22 Sat]: =output=, =list=,
and =table=.
The =output= result format is the simplest and the most natural
ones. It works as if the code block were inserted into a module
which would then be evaluated.
#+BEGIN_SRC racket :results output drawer
(println "This is the first line of output.")
(println (+ 1 2))
(println "This the third line of output.")
#+END_SRC
#+RESULTS:
:RESULTS:
"This is the first line of output."
3
"This the third line of output."
:END:
The =list= result format typesets the result of the last line in the
code block as a list:
#+BEGIN_SRC racket :results list
'(1 "hello" (and x y))
#+END_SRC
#+RESULTS:
- 1
- "hello"
- (and x y)
Note how nested lists are not recursively shown as nested Org-mode
lists.
For some reason, the =list= output format does not work with the
result drawer:
#+BEGIN_SRC racket :results list drawer
'(1 "hello" (and x y))
#+END_SRC
#+RESULTS:
:RESULTS:
- (1 "\"hello\"" (and x y))
:END:
Finally, the =table= result format typesets the output as a table:
#+BEGIN_SRC racket :results table drawer
'((a . #t) (b . #f))
#+END_SRC
#+RESULTS:
:RESULTS:
| a | #t |
| b | #f |
:END:
This is clearly very useful for printing states (and hash tables,
more generally):
#+BEGIN_SRC racket :results table drawer
(st '((a . 1) (b . #f) (c . "hello")))
#+END_SRC
#+RESULTS:
:RESULTS:
| a | 1 |
| b | #f |
| c | "hello" |
:END:
*** A note about printing update function forms
Automatic table typesetting may go in the way of readability for
hash tables whose values are lists, as the following example shows:
#+BEGIN_SRC racket :results table drawer
#hash((a . (and a b)) (b . (not b)))
#+END_SRC
#+RESULTS:
:RESULTS:
| a | and | a | b |
| b | not | b | |
:END:
To tackle this issue, [[../utils.rkt][=dds/utils=]] provides
=stringify-variable-mapping= (with the shortcut =sgfy=) which
converts all the values of a given variable mapping to strings:
#+BEGIN_SRC racket :results table drawer
(sgfy #hash((a . (and a b)) (b . (not b))))
#+END_SRC
#+RESULTS:
:RESULTS:
| a | "(and a b)" |
| b | "(not b)" |
:END:
** Reading Org-mode tables<<tabread>>
Org-mode allows supplying tables as arguments for code blocks.
#+NAME: test-table
| a | "(and a b)" |
| b | (or b (not a)) |
#+BEGIN_SRC elisp :var tab=test-table :results output drawer
tab
#+END_SRC
#+RESULTS:
:RESULTS:
:END:
((a (and a b)) (b (or b (not a))))
Unfortunately, the same trick does not work with Racket directly,
because Racket interprets the first elements in the parentheses as
function applications:
#+BEGIN_SRC racket :results output drawer :var tab=test-table
tab
#+END_SRC
#+RESULTS:
:RESULTS:
application: not a procedure;
expected a procedure that can be applied to arguments
given: "a"
arguments...:
"(and a b)"
context...:
"/tmp/babel-qkvrRR/org-babel-c4wuju.rkt": [running body]
temp37_0
for-loop
run-module-instance!125
perform-require!78
:END:
Fortunately, we can easily remedy this problem by creating a named
parameterised Elisp source block which will explicitly convert the
table to a string:
#+NAME: munch-sexp
#+BEGIN_SRC elisp :results output drawer :var sexp=test-table
(prin1 sexp)
#+END_SRC
#+RESULTS: munch-sexp
:RESULTS:
(("a" "(and a b)") ("b" "(or b (not a))"))
:END:
We can now correctly receive this table in a Racket source code
block by threading it through =munch-sexp=:
#+BEGIN_SRC racket :results output drawer :var tab=munch-sexp(sexp=test-table)
(println tab)
#+END_SRC
#+RESULTS:
:RESULTS:
"((\"a\" \"(and a b)\") (\"b\" \"(or b (not a))\"))"
:END:
[[../utils.rkt][=dds/utils=]] has several functions for parsing such strings, and
notably =read-org-variable-mapping=, with the shortcut =unorg=:
#+BEGIN_SRC racket :results output drawer :var tab=munch-sexp(sexp=test-table)
(unorg tab)
#+END_SRC
#+RESULTS:
:RESULTS:
'#hash((a . (and a b)) (b . (or b (not a))))
:END:
Of course, we can use =munch-sexp= to prepare any other table than
=test-table= for use with Racket:
#+NAME: another-test-table
| a | (not a) |
| b | (and a c) |
| c | (and a (not b)) |
#+BEGIN_SRC racket :results output drawer :var tab=munch-sexp(sexp=another-test-table)
(unorg tab)
#+END_SRC
#+RESULTS:
:RESULTS:
'#hash((a . (not a)) (b . (and a c)) (c . (and a (not b))))
:END:
** Inline graph visualisation with Graphviz
Some functions in =dds= build graphs:
#+BEGIN_SRC racket :results output drawer :var bf=munch-sexp(another-test-table)
(build-interaction-graph (unorg bf))
#+END_SRC
#+RESULTS:
:RESULTS:
#<unweighted-graph>
:END:
The =graph= library allows building a Graphviz description of the
constructed graph. (Note that you have to install the =graph=
library by running =raco pkg install graph= and require it. The
long property line at the top of this file defining the prologue for
racket source code blocks takes care of requiring =graph=.)
#+NAME: igraph
#+BEGIN_SRC racket :results output drawer :var bf=munch-sexp(another-test-table)
(display (graphviz (build-interaction-graph (unorg bf))))
#+END_SRC
#+RESULTS: igraph
:RESULTS:
digraph G {
node0 [label="c"];
node1 [label="b"];
node2 [label="a"];
subgraph U {
edge [dir=none];
node0 -> node1;
node2 -> node2;
}
subgraph D {
node2 -> node0;
node2 -> node1;
}
}
:END:
You can have an inline drawing of this graph by calling the previous
code block (=igraph=) via a noweb reference in Graphviz/DOT source
block:
#+BEGIN_SRC dot :file dots/exampleBQNp7Z.svg :results raw drawer :cmd sfdp :noweb yes
<<igraph()>>
#+END_SRC
#+RESULTS:
:RESULTS:
[[file:dots/exampleBQNp7Z.svg]]
:END:
Note that the =graph= library draws self-loops as undirected edges.
It also draws double-sided edges as undirected edges (e.g., in the
preceding graph, b depends on c and c depends on b).
* =dds/networks=
The [[../networks.rkt][=dds/networks=]] is a module for working with different network
models. A network is a set of variables which are updated according
to their corresponding update functions. The variables to be
updated at each step are given by the mode. This model can
generalise Boolean networks, TBANs, multivalued networks, etc.
** Boolean networks
Consider the following Boolean network:
#+NAME: simple-bn
| a | b |
| b | (and (not a) c) |
| c | (not c) |
Note that if you define the formula of a as 0, it will set a to 1,
because 0 is not #f. For example, =(if 0 1 2)= evaluates to 1, and
not to 2.
Here's the unsigned interaction graph of this network:
#+NAME: simple-bn-ig
#+BEGIN_SRC racket :results silent :var simple-bn=munch-sexp(simple-bn)
(dotit (build-interaction-graph (unorg simple-bn)))
#+END_SRC
#+BEGIN_SRC dot :file dots/examplejTo8XT.svg :results raw drawer :cmd sfdp :noweb yes
<<simple-bn-ig()>>
#+END_SRC
#+RESULTS:
:RESULTS:
[[file:dots/examplejTo8XT.svg]]
:END:
Here's the signed interaction graph of this network:
#+NAME: simple-bn-sig
#+BEGIN_SRC racket :results silent :var simple-bn=munch-sexp(simple-bn)
(dotit (build-boolean-signed-interaction-graph (unorg simple-bn)))
#+END_SRC
#+BEGIN_SRC dot :file dots/exampledpQygl.svg :results raw drawer :cmd sfdp :noweb yes
<<simple-bn-sig()>>
#+END_SRC
#+RESULTS:
:RESULTS:
[[file:dots/exampledpQygl.svg]]
:END:
For the interaction a \to b, note indeed that when c is #f, b is
always #f (positive interaction). On the other hand, when c is #t,
b becomes (not a) (negative interaction). Therefore, the influence
of a on b is neither activating nor inhibiting.
Here is the full state graph of this network under the asynchronous
dynamics:
#+NAME: simple-bn-sg
#+BEGIN_SRC racket :results silent :var simple-bn=munch-sexp(simple-bn)
(let* ([bn (nn (unorg simple-bn))]
[bn-asyn (make-asyn-dynamics bn)])
(dotit (ppsg (build-full-boolean-state-graph bn-asyn))))
#+END_SRC
#+BEGIN_SRC dot :file dots/examplem7LpTs.svg :results raw drawer :cmd sfdp :noweb yes
<<simple-bn-sg()>>
#+END_SRC
#+RESULTS:
:RESULTS:
[[file:dots/examplem7LpTs.svg]]
:END:
Alternatively, you may prefer a slighty more compact representation
of Boolean values as 0 and 1:
#+NAME: simple-bn-sg-bool
#+BEGIN_SRC racket :results silent :var simple-bn=munch-sexp(simple-bn)
(let* ([bn (nn (unorg simple-bn))]
[bn-asyn (make-asyn-dynamics bn)])
(dotit (ppsgb (build-full-boolean-state-graph bn-asyn))))
#+END_SRC
#+BEGIN_SRC dot :file dots/examplex1Irnk.svg :results raw drawer :cmd sfdp :noweb yes
<<simple-bn-sg-bool()>>
#+END_SRC
#+RESULTS:
:RESULTS:
[[file:dots/examplex1Irnk.svg]]
:END:
Consider the following state (appearing in the upper left corner of
the state graph):
#+NAME: some-state
| a | 0 |
| c | 1 |
| b | 1 |
These are the states which can be reached from it in at most 2
steps:
#+NAME: simple-bn-some-state
#+HEADER: :var simple-bn=munch-sexp(simple-bn)
#+HEADER: :var some-state=munch-sexp(some-state)
#+BEGIN_SRC racket :results silent
(let* ([bn (nn (unorg simple-bn))]
[bn-asyn (make-asyn-dynamics bn)]
[s0 (stb (unorg some-state))])
(dotit (ppsgb (dds-build-n-step-state-graph bn-asyn (set s0) 2))))
#+END_SRC
#+BEGIN_SRC dot :file dots/examplecHA6gL.svg :results raw drawer :cmd sfdp :noweb yes
<<simple-bn-some-state()>>
#+END_SRC
#+RESULTS:
:RESULTS:
[[file:dots/examplecHA6gL.svg]]
:END:
Here is the complete state graph with edges annotated with the
modality leading to the update.
#+NAME: simple-bn-sg-bool-ann
#+BEGIN_SRC racket :results silent :var simple-bn=munch-sexp(simple-bn)
(let* ([bn (nn (unorg simple-bn))]
[bn-asyn (make-asyn-dynamics bn)])
(dotit (ppsgb (build-full-boolean-state-graph-annotated bn-asyn))))
#+END_SRC
#+BEGIN_SRC dot :file dots/examplei4we6j.svg :results raw drawer :cmd sfdp :noweb yes
<<simple-bn-sg-bool-ann()>>
#+END_SRC
#+RESULTS:
:RESULTS:
[[file:dots/examplei4we6j.svg]]
:END:
For some networks, a single transition between two states may be
due to different modalities. Consider the following network:
#+NAME: bn2
| a | (not b) |
| b | b |
#+NAME: bn2-sgr
#+BEGIN_SRC racket :results silent :var input-bn=munch-sexp(bn2)
(let* ([bn (nn (unorg input-bn))]
[bn-asyn (make-asyn-dynamics bn)])
(dotit (ppsgb (build-full-boolean-state-graph-annotated bn-asyn))))
#+END_SRC
#+BEGIN_SRC dot :file dots/examplehsuRqc.svg :results raw drawer :cmd dot :noweb yes
<<bn2-sgr()>>
#+END_SRC
#+RESULTS:
:RESULTS:
[[file:dots/examplehsuRqc.svg]]
:END:
** Tabulating functions and networks
Here's how you can tabulate a function. The domain of x is {1, 2},
and the domain of y is {0, 2, 4}. The first column in the output
corresponds to x, the second to y, and the third corresponds to the
value of the function.
#+BEGIN_SRC racket :results table drawer
(tabulate (λ (x y) (+ x y)) '(1 2) '(0 2 4))
#+END_SRC
#+RESULTS:
:RESULTS:
| 1 | 0 | 1 |
| 1 | 2 | 3 |
| 1 | 4 | 5 |
| 2 | 0 | 2 |
| 2 | 2 | 4 |
| 2 | 4 | 6 |
:END:
Here's how you tabulate a Boolean function:
#+BEGIN_SRC racket :results table drawer
(tabulate/boolean (λ (x y) (and x y)))
#+END_SRC
#+RESULTS:
:RESULTS:
| #f | #f | #f |
| #f | #t | #f |
| #t | #f | #f |
| #t | #t | #t |
:END:
Here's how to tabulate the network =simple-bn=, defined at the top
of this section:
#+BEGIN_SRC racket :results table drawer :var in-bn=munch-sexp(simple-bn)
(tabulate-boolean-network (nn (unorg in-bn)))
#+END_SRC
#+RESULTS:
:RESULTS:
| a | b | c | f-a | f-b | f-c |
| #f | #f | #f | #f | #f | #t |
| #f | #f | #t | #f | #t | #f |
| #f | #t | #f | #t | #f | #t |
| #f | #t | #t | #t | #t | #f |
| #t | #f | #f | #f | #f | #t |
| #t | #f | #t | #f | #f | #f |
| #t | #t | #f | #t | #f | #t |
| #t | #t | #t | #t | #f | #f |
:END:
** Random functions and networks
To avoid having different results every time a code block in this
section is run, every code block seeds the random number generator
to 0.
=dds/networks= can generate random functions, given a domain for
each of its arguments and for the function itself. Consider the
following domains:
#+NAME: simple-domains
| a | (#f #t) |
| b | (1 2) |
| c | (cold hot) |
Here's a random function taking values in the codomain =(4 5 6)=:
#+BEGIN_SRC racket :results table drawer :var simple-domains=munch-sexp(simple-domains)
(random-seed 0)
(define rnd-func (random-function/state (unorg simple-domains) '(4 5 6)))
(tabulate-state rnd-func (unorg simple-domains))
#+END_SRC
#+RESULTS:
:RESULTS:
| a | b | c | f |
| #f | 1 | cold | 4 |
| #f | 1 | hot | 5 |
| #f | 2 | cold | 4 |
| #f | 2 | hot | 4 |
| #t | 1 | cold | 5 |
| #t | 1 | hot | 6 |
| #t | 2 | cold | 4 |
| #t | 2 | hot | 5 |
:END:
We can build an entire random network over these domains:
#+BEGIN_SRC racket :results table drawer :var simple-domains=munch-sexp(simple-domains)
(random-seed 0)
(define n (random-network (unorg simple-domains)))
(tabulate-network n (unorg simple-domains))
#+END_SRC
#+RESULTS:
:RESULTS:
| a | b | c | f-a | f-b | f-c |
| #f | 1 | cold | #f | 2 | hot |
| #f | 1 | hot | #f | 2 | cold |
| #f | 2 | cold | #t | 1 | cold |
| #f | 2 | hot | #t | 2 | hot |
| #t | 1 | cold | #f | 2 | cold |
| #t | 1 | hot | #t | 1 | cold |
| #t | 2 | cold | #f | 2 | hot |
| #t | 2 | hot | #t | 1 | cold |
:END:
* Reaction systems
:PROPERTIES:
:header-args:racket: :prologue "#lang racket\n(require graph (file \"~/Candies/prj/racket/dds/rs.rkt\") (file \"~/Candies/prj/racket/dds/utils.rkt\"))"
:END:
Consider the following reaction system:
#+NAME: rs1
| a | x t | y | z |
| b | x | q | z |
Here is how we read this reaction into Racket code:
#+BEGIN_SRC racket :results output drawer :var input-rs=munch-sexp(rs1)
(unorg-rs input-rs)
#+END_SRC
#+RESULTS:
:RESULTS:
(hash 'a (reaction (set 'x 't) (set 'y) (set 'z)) 'b (reaction (set 'x) (set 'q) (set 'z)))
:END:
Here is how we can put it back into an Org-mode table:
#+BEGIN_SRC racket :results table drawer :var input-rs=munch-sexp(rs1)
(org-rs (unorg-rs input-rs))
#+END_SRC
#+RESULTS:
:RESULTS:
| a | "t x" | "y" | "z" |
| b | "x" | "q" | "z" |
:END:
Here is how we can apply this reaction system to a state:
#+BEGIN_SRC racket :results output drawer :var input-rs=munch-sexp(rs1)
(let ([rs (unorg-rs input-rs)])
(apply-rs rs (set 'x 't)))
#+END_SRC
#+RESULTS:
:RESULTS:
(set 'z)
:END:
Let's see which reactions got applied:
#+BEGIN_SRC racket :results list :var input-rs=munch-sexp(rs1)
(let ([rs (unorg-rs input-rs)])
(list-enabled rs (set 'x 't)))
#+END_SRC
#+RESULTS:
- a
- b
You can also give a name to a list and read it with =munch-sexp=:
#+NAME: ctx1
- x y
- z
-
- t
#+BEGIN_SRC racket :results output drawer :var input-ctx=munch-sexp(ctx1)
(read-ctx input-ctx)
#+END_SRC
#+RESULTS:
:RESULTS:
(list (set 'x 'y) (set 'z) (set) (set 't))
:END:
Let's see what the evolution of =rs1= looks like with the context
sequence =ctx1=.
#+NAME: rs1-sgr
#+HEADER: :var input-rs=munch-sexp(rs1) :var input-ctx=munch-sexp(ctx1)
#+BEGIN_SRC racket :results output drawer
(dotit (ppsg (build-interactive-process-graph (unorg-rs input-rs) (read-ctx input-ctx))))
#+END_SRC
#+RESULTS: rs1-sgr
:RESULTS:
digraph G {
node0 [label="C:{}{t}\nD:{}"];
node1 [label="C:{z}{}{t}\nD:{z}"];
node2 [label="C:{t}\nD:{}"];
node3 [label="C:{x y}{z}{}{t}\nD:{}"];
node4 [label="C:\nD:{}"];
subgraph U {
edge [dir=none];
node4 -> node4 [label="{}"];
}
subgraph D {
node0 -> node2 [label="{}"];
node1 -> node0 [label="{}"];
node2 -> node4 [label="{}"];
node3 -> node1 [label="{b}"];
}
}
:END:
#+BEGIN_SRC dot :file dots/examplevvXFaI.svg :results raw drawer :cmd circo :noweb yes
<<rs1-sgr()>>
#+END_SRC
#+RESULTS:
:RESULTS:
[[file:dots/examplevvXFaI.svg]]
:END:
Note that we need to keep the full context sequence in the name of
each state to avoid merging states with the same result and
contexts, but which occur at different steps of the evolution.
The graphical presentation for interactive processes is arguably
less readable than just listing the contexts and the results
explicitly. Here is how you can do it.
#+NAME: rs1-ip
#+HEADER: :var input-rs=munch-sexp(rs1) :var input-ctx=munch-sexp(ctx1)
#+BEGIN_SRC racket :results table drawer
(build-interactive-process (unorg-rs input-rs) (read-ctx input-ctx))
#+END_SRC
#+RESULTS: rs1-ip
:RESULTS:
| (y x) | nil |
| (z) | (z) |
| nil | nil |
| (t) | nil |
| nil | nil |
:END:
The first column of this table shows the current context. The
second column shows the result of application of the reactions to
the previous state. The interactive process contains one more step
with respect to the context sequence. This is to show the effect
of the last context.
Note that empty sets are printed as =nil=.
* Local Variables :noexport:
# Local Variables:
# eval: (auto-fill-mode)
# ispell-local-dictionary: "en"
# org-link-file-path-type: relative
# End:
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