perm.py: remove broken hack for excluding transitive edges

Graphviz includes the tred program for computing transitive reduction
so use this to post process the complete graph instead.  This means
that graphs containing edges that drop more than one perm that are not
implied by transitivity are displayed correctly.

Author: ronorton

archdoc/misc/perms/Makefile

@@ -2,7 +2,7 @@
 all: perms.svg
 
 perms.dot: perms.py
-	./perms.py > $@
+	./perms.py | tred > $@
 
 %.svg : %.dot
 	dot -Tsvg -o $@ $<

archdoc/misc/perms/perms.py

@@ -134,28 +134,26 @@ def comb_to_str(c):
     return '_'.join(cs) or "0"
 
 # Now we output a graph representation of the useful combinations in dot format.
-# To make it pretty we add edges for the subset partial order, excluding edges
-# implied by transitivity.
+# To make it pretty we add edges for the subset partial order.
 
 print("digraph {")
 
 # Output the names of nodes in the graph
 for x in useful_combinations:
     print(comb_to_str(x))
 
-# Output the edges for the subset relation. To exclude transitive edges
-# we stick to pairs of combinations that differ in size by one. This
-# doesn't work for all graphs but seems to be OK for us.
+# Output the edges for the subset relation. This results in many redundant edges
+# but fortunately graphviz provides `tred` for computing the transitive
+# reduction.
 for x in useful_combinations:
     for y in useful_combinations:
-        if len(x) + 1 == len(y):
-            xs = set(x)
-            ys = set(y)
-            if xs.issubset(ys):
-                # find the permission in ys not in xs to use as label
-                diff = (ys - xs).pop()
-                x_str=comb_to_str(x)
-                y_str=comb_to_str(y)
-                print(f"{y_str} -> {x_str} [label=\"{diff}\", fontsize=10]")
+        xs = set(x)
+        ys = set(y)
+        if xs < ys:
+            # find the permissions in ys not in xs to use as label
+            diff = ys - xs
+            x_str=comb_to_str(x)
+            y_str=comb_to_str(y)
+            print(f"{y_str} -> {x_str} [label=\"{comb_to_str(diff)}\", fontsize=10]")
 
 print("}")