Add inductive invariants example

Signed-off-by: Claire Xenia Wolf <claire@clairexen.net>

docs/examples/indinv/example.py

@@ -0,0 +1,96 @@
+from collections import defaultdict
+import inspect
+
+N = 32
+f = lambda x: (2*x-1) ^ (x&7)
+
+table = [f(i) & (N-1) for i in range(N)]
+rtable = [table.count(i) for i in range(N)]
+
+def getPath(v):
+    if table[v] is None:
+        return [v]
+    bak = table[v]
+    table[v] = None
+    r = [v] + getPath(bak)
+    table[v] = bak
+    return r
+
+def getPaths():
+    visited = set()
+    paths = list()
+    for i in range(N):
+        if rtable[i] == 0:
+            paths.append(getPath(i))
+    for path in paths:
+        for i in path:
+            visited.add(i)
+    for i in range(N):
+        if i not in visited:
+            paths.append(getPath(i))
+            for j in paths[-1]:
+                visited.add(j)
+    return paths
+
+pathsByLidx = defaultdict(set)
+loopsByIdx = dict()
+loopsByLidx = dict()
+
+for path in getPaths():
+    i = path.index(path[-1])+1
+    head, loop, lidx = tuple(path[:i]), tuple(path[i:]), max(path[i:])
+    pathsByLidx[lidx].add((head, loop))
+
+print()
+print("The %d-bit function f(x) produces %d loops:" % (N.bit_length()-1, len(pathsByLidx)))
+print("  ", inspect.getsource(f).strip())
+
+for lidx, paths in pathsByLidx.items():
+    loop = None
+    for path in paths:
+        for i in path[0] + path[1]:
+            loopsByIdx[i] = lidx
+        if loop is None or path[1][0] > loop[0]:
+            loop = path[1]
+
+    loopsByLidx[lidx] = loop
+    
+    print()
+    print("%d-Element Loop:" % len(loop))
+    print("  ", " ->- ".join(["%2d" % i for i in loop + (loop[0],)]))
+
+    lines = []
+    lastPath = []
+    for path in sorted([tuple(reversed(p[0])) for p in paths]):
+        line = ""
+        for i in range(len(path)):
+            if i < len(lastPath) and lastPath[i] == path[i]:
+                line += " %s   " % (" " if i == 0 else "|  ")
+            else:
+                line += " %s %2d" % (" " if i == 0 else "`<-" if len(lastPath) else "-<-", path[i])
+                lastPath = []
+        lastPath = path
+        lines.append(line)
+
+    for i in range(len(lines)-1, -1, -1):
+        line, nextline = list(lines[i]), "" if i == len(lines)-1 else lines[i+1]
+        if len(nextline) < len(line): nextline = nextline.ljust(len(line))
+
+        for k in range(len(line)):
+            if line[k] == "|" and nextline[k] in " -":
+                line[k] = " "
+
+        lines[i] = "".join(line)
+
+    print("%d Lead-Ins:" % len(lines))
+    for line in lines:
+        print(line)
+
+print()
+print("Loop Membership:")
+for lidx in pathsByLidx:
+    print("%18s |" % (loopsByLidx[lidx],), end="")
+    for i in range(N):
+        print("*" if loopsByIdx[i] == lidx else ".", end="")
+    print("|")
+print()