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Updated Graphviz notebook
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flach committed Jan 24, 2017
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229 changes: 200 additions & 29 deletions graphviz_intro.swinb
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<div class="notebook">

<div class="nb-cell program" data-background="true">
<div class="nb-cell program" data-background="true" data-singleline="true">
:- use_rendering(graphviz).
:- include(graphviz_swish).

%%% Plotting terms as trees using Graphviz %%%

term_list_linear(false). % change to true for plotting lists linearly

term(Term,Dot) :-
gv_start,
Term =.. [Functor|Subterms],
gv_root(Functor,0),
term_list(Subterms,0),
gv_stop(Dot).

terml(Term,N) :-
var(Term),!,
gv_node(N,Term,_).
terml(Term,N) :-
term_list_linear(true),
list(Term),!,
gv_node(N,Term,N1),
term_list(Term,N1).
terml([],N) :- !,
gv_node(N,'$empty_list',_).
terml(Term,N):-
Term =.. [Functor|Subterms],
gv_node(N,Functor,N1),
term_list(Subterms,N1).

term_list([],_).
term_list([Term|Terms],N) :-
terml(Term,N),
term_list(Terms,N).

% testing
term1(Dot) :- term([a,b,b,a],Dot).
term2(Dot) :-
term(html(
head(title('Peter A. Flach')),
body([
img([align=right,src='logo.jpg']),
img([align=left,src='peter.jpg']),
h1('Peter Flach\'s homepage'),
h2('Research interests'),
ul([li('Learning from structured data'),
bla,
li(a([href='CV.pdf'],'Full CV'))]),
h2('Current activities'),
bla,
h2('Past activities'),
bla,
h2('Archives'),
bla,
hr,address(bla)
])
), Dot).

%%% Meta-interpreter plotting (part of) the SLD-tree using Graphviz %%%

sld(Goal,Dot) :-
sld(Goal,5,Dot). % default depth bound

sld(Goal,D,_) :-
gv_start,
gv_root((?-Goal),0),
prove_d(Goal,Goal,0,D),
fail. % failure-driven loop to get all solutions
sld(_,_,Dot) :-
gv_stop(Dot).

% meta-interpreter with complete resolvent and depth bound
prove_d(true,Goal,N,_) :- !,
gv_answer(N,Goal).
prove_d((A,B),Goal,N,D) :- !,
D&gt;0, D1 is D-1,
resolve(A,C),
conj_append(C,B,E),
gv_node(N,(:-E),N1),
prove_d(E,Goal,N1,D1).
prove_d(A,Goal,N,D) :-
D&gt;0, D1 is D-1,
resolve(A,B),
gv_node(N,(:-B),N1),
prove_d(B,Goal,N1,D1).

resolve(A,B):-
clause(A,B).

% testing
student_of(X,T) :- follows(X,C), teaches(T,C).
follows(paul,computer_science).
follows(paul,expert_systems).
follows(maria,ai_techniques).
teaches(adrian,expert_systems).
teaches(peter,ai_techniques).
teaches(peter,computer_science).

brother_of(paul,peter).
brother_of(peter,adrian).
brother_of(X,Y) :- brother_of(X,Z),brother_of(Z,Y).
brother_of(X,Y) :- brother_of(Y,X).

sld1(Dot) :- sld(student_of(_,peter),Dot).
sld2(Dot) :- sld(brother_of(paul,_),Dot).


%%% Utilities %%%
list([]).
list([_|T]) :- list(T).

conj_element(X,X) :- % single-element conjunction
X \= true,
X \= (_,_).
conj_element(X,(X,_)).
conj_element(X,(_,Ys)) :-
conj_element(X,Ys).

conj_append(true,Ys,Ys).
conj_append(X,Ys,(X,Ys)) :- % single-element conjunction
X \= true,
X \= (_,_).
conj_append((X,Xs),Ys,(X,Zs)) :-
conj_append(Xs,Ys,Zs).

writes([]) :- !.
writes([H|T]) :- !,writes(H),writes(T).
writes((A,B)) :- !,writes(A),my_assert(',\\n'),writes(B). % break up conjunctions
writes(:-A) :- !,my_assert(':-'),writes(A).
writes(?-A) :- !,my_assert('?-'),writes(A).
writes('$empty_list') :- !,my_assert('[]').
writes(A) :-
( atom(A) -&gt; my_assert(A)
; term_to_atom(A,B), my_assert(B)
). % catch-all

my_assert(A) :-
assertz('$my_assert'(A)).

get_dot(A) :-
get_dot('',A).

get_dot(In,Out) :-
( retract('$my_assert'(A)) -&gt; atom_concat(In,A,In1),get_dot(In1,Out)
; otherwise -&gt; Out=In
).


%%% Graphviz utilities %%%
gv_max_id(200). % max number of nodes in the graph

% open file and start new graph
gv_start :-
retractall('$my_assert'(_)),
writes(['digraph {']),
%writes(['graph [size="4,6"];']),
writes(['node [shape=plaintext, fontname=Courier, fontsize=12]']).

% next graph
gv_next :-
writes(['}']),
writes(['digraph {']),
writes(['node [shape=plaintext, fontname=Courier, fontsize=12]']).

% finish graph and close file
gv_stop(Dot) :-
writes(['}']),
get_dot(Dot).

% write the root of a tree and initialise node IDs
gv_root(L,N) :-
writes([N,' [label="',L,'"];']),
gv_init_ids(N).

% add a node with label L and parent N0
gv_node(N0,L,N) :-
gv_id(N),
writes([N,' [label="',L,'"];']),
writes([N0,' -&gt; ',N,';']).

% add a specially formatted leaf
gv_answer(N0,L) :-
gv_id(N),
writes([N,' [label="Answer:\\n',L,'", shape=ellipse, style=dotted, fontsize=10];']),
writes([N0,' -&gt; ',N,' [style=dotted, arrowhead=none];']).
%writes(['{rank=same;',N0,';',N,';}']).

% generate a new node ID
gv_id(N) :-
retract('$gv_id'(N0)),
gv_max_id(M),
N0 &lt; M, % don't generate infinite graphs
N is N0+1,
assert('$gv_id'(N)).

% initialise node IDs, next free ID is N+1
gv_init_ids(N) :-
retractall('$gv_id'(_)),
assert('$gv_id'(N)).
</div>

<div class="nb-cell markdown">
# Visualising terms and SLD trees with Graphviz
[Graphviz](http://www.graphviz.org/) is a collection of programs for visualising graphs. Here, we conveniently use it for visualising Prolog terms and SLD trees.

[`graphviz_swish.pl`](graphviz_swish.pl) defines the two main predicates `term/2` and `sld/2`. The query `?-term(+Term, -Dot)`, where `Term` is bound to a Prolog term, will return a variable `Dot`, which defines a tree in Graphviz format. For example, the query `?-term([a,b,b,a], Dot)` produces the following Graphviz input:
The code in the box above defines the two main predicates `term/2` and `sld/2`. The query `?-term(+Term, -Dot)`, where `Term` is bound to a Prolog term, will return a variable `Dot`, which defines a tree in Graphviz format. For example, the query `?-term([a,b,b,a], Dot)` produces the following Graphviz input:

Dot = '
digraph {
Expand All @@ -34,43 +229,23 @@
}
'

The command `?-term([a,b,b,a], Dot), X = dot(Dot).` then produces the following tree:
Adding `X = dot(Dot)` to the query then invokes the Graphviz renderer:
</div>

<div class="nb-cell query">
term([a,b,b,a], _Dot), X = dot(_Dot).
</div>

<div class="nb-cell markdown">
You can also try the following query:
</div>

<div class="nb-cell query">
term1(_Dot), X = dot(_Dot).
</div>

<div class="nb-cell markdown">
See [here](http://www.graphviz.org/pub/scm/graphviz2/doc/info/command.html) for more information about how to use Graphviz programs from the command line.

Similarly, the query `?-Goal sld Dot`, where Goal is bound to a Prolog goal, will produce an atom, which defines a tree in Graphviz format (notice that `sld/2` has been defined as an infix operator and can thus be used without brackets). For example, the query `?-student_of(S,peter) sld Dot` produces the following tree when run through `dot/1`:
</div>

<div class="nb-cell query">
sld(student_of(S,peter), _Dot), X = dot(_Dot).
Similarly, the query `?-sld(Goal,Dot)`, where Goal is bound to a Prolog goal, will produce an atom, which defines a tree in Graphviz format. For example, the query `?-sld(student_of(S,peter),Dot)` produces the following tree when rendered with Graphviz:
</div>

<div class="nb-cell query">
student_of(S,peter) sld _Dot, X = dot(_Dot).
</div>

<div class="nb-cell markdown">
The following query results in the same tree:
</div>

<div class="nb-cell query">
sld1(_Dot), X = dot(_Dot).
</div>

<div class="nb-cell markdown">
Now, try the example queries `?-term2` and `?-sld2` that have been pre-defined in [`graphviz_swish.pl`](graphviz_swish.pl).
</div>
Expand All @@ -83,8 +258,4 @@ term2(_Dot), X = dot(_Dot).
sld2(_Dot), X = dot(_Dot).
</div>

<div class="nb-cell markdown">
To use Graphviz in the SWISH notebook remember to use `use_rendering/1` and `include/1` predicates (see the top of the notebook for details).
</div>

</div>
31 changes: 4 additions & 27 deletions graphviz_swish.pl
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%%% Plotting terms as trees using Graphviz %%%

term_list_linear(false). % change to true for plotting lists linearly
:- dynamic write_to_file/1.
write_to_file(false). % write the dot structure to a file?

term(Term,Dot) :-
gv_start('term.dot'),
gv_start,
Term =.. [Functor|Subterms],
gv_root(Functor,0),
term_list(Subterms,0),
Expand Down Expand Up @@ -56,13 +54,11 @@

%%% Meta-interpreter plotting (part of) the SLD-tree using Graphviz %%%

%:-op(1100,fx,sld). % can write ?-sld Goal instead of ?-sld(Goal)

sld(Goal,Dot) :-
sld(Goal,5,Dot). % default depth bound

sld(Goal,D,_) :-
gv_start('sld.dot'),
gv_start,
gv_root((?-Goal),0),
prove_d(Goal,Goal,0,D),
fail. % failure-driven loop to get all solutions
Expand All @@ -84,10 +80,6 @@
gv_node(N,(:-B),N1),
prove_d(B,Goal,N1,D1).

resolve(A,true) :-
write_to_file(true),
predicate_property(A,built_in),!,
call(A).
resolve(A,B):-
clause(A,B).

Expand Down Expand Up @@ -151,12 +143,11 @@


%%% Graphviz utilities %%%
gv_max_id(1000). % max number of nodes in the graph
gv_max_id(200). % max number of nodes in the graph

% open file and start new graph
gv_start(FileName) :-
gv_start :-
retractall('$my_assert'(_)),
(write_to_file(true) -> tell(FileName); true),
writes(['digraph {']),
%writes(['graph [size="4,6"];']),
writes(['node [shape=plaintext, fontname=Courier, fontsize=12]']).
Expand All @@ -170,22 +161,8 @@
% finish graph and close file
gv_stop(Dot) :-
writes(['}']),
(write_to_file(true) -> told; true),
get_dot(Dot).

% start new subgraph
gv_cluster_start :-
( retract('$gv_cluster'(N)) -> N1 is N+1
; otherwise -> N1=0
),assert('$gv_cluster'(N1)),
writes(['subgraph cluster_',N1,' {']),
writes(['[style=filled, color=lightgrey];']),
writes(['node [style=filled,color=white];']).

% finish subgraph
gv_cluster_stop :-
writes(['}']).

% write the root of a tree and initialise node IDs
gv_root(L,N) :-
writes([N,' [label="',L,'"];']),
Expand Down

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