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Last active Feb 16, 2020
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GraphViz category in python
plus = GraphCat.block("+", ["a","b"], ["c"])
I = GraphCat.idd()
p1 = plus
p2 = p1 @ (p1 * p1)
p3 = p1 @ (p2 * p2)
p4 = p1 @ (p3 * p3)
d =
d.format = "png"
import random
import graphviz
class GraphCat():
GC = GraphCat
def __init__(self,res): # just hold the graphviz processor function
self.res = res
def fresh(n): # makes random numbers for fresh node labels
return list([str(random.randint(0,1e9)) for i in range(n)])
def idd(): # identity morhism. 1 input 1 output.
def res(g):
#nodes = GC.fresh(n)
node = GC.fresh(1)[0]
#for node in nodes:
g.node(node, shape="point")
return [node], [node]
return GraphCat(res)
def compose(g, f): # compose morphisms. Makes graphviz edges between node labels generated by g and f
f = f.res
g = g.res
def res(G):
a, b = f(G)
b1, c = g(G)
assert(len(b) == len(b1))
return a, c
return GraphCat(res)
def par(f, g): #monoidal product. Puts f and g in parallel
f = f.res
g = g.res
def res(G):
a, b = f(G)
c, d = g(G)
return a + c, b + d
return GraphCat(res)
def dump(): # dump deletes this edge with an empty circle
def res(G):
node = GC.fresh(1)[0]
G.node(node, shape="point", fillcolor="white")
return [node], []
return GraphCat(res)
def dup(): # duplicate this edge
def res(G):
node = GC.fresh(1)[0]
G.node(node, shape="point", fillcolor="green")
return [node], [node, node]
return GraphCat(res)
def converse(f): # turn input to output of this combinator
f = f.res
def res(G):
a, b = f(G)
return b, a
return GraphCat(res)
def named_simple(name): # a simple labeled 1 input 1 output object
def res(G):
node = GC.fresh(1)[0]
return [node], [node]
return GraphCat(res)
def block(name, inputs, outputs): # an object with labelled ports
inputs_label = [f"<{inp}> {inp}" for inp in inputs]
outputs_label = [f"<{outp}> {outp}" for outp in outputs]
#return # use graphviz to build block with label and n ports
def res(G):
node = GC.fresh(1)[0]
inputs1 = [f"{node}:{inp}" for inp in inputs]
outputs1 = [f"{node}:{outp}" for outp in outputs]
grphstring = "{ {" + " | ".join(inputs_label) + "} | " + name + " | {" + "|".join(outputs_label) + "} }"
G.node(node,grphstring, shape="record")
return inputs1, outputs1
return GC(res)
def fst(): # project out first par of tuple. semnatically equal to (id * dump)
return GraphCat.block("fst", ["a","b"], ["a1"])
def snd(): # dump * id
return GraphCat.block("fst", ["a","b"], ["b1"])
def run(self): # will run the object on a fresh graphviz object
dot = graphviz.Digraph()
return dot
def __matmul__(self, rhs): # matrix multiplication is a natural analog of composition
return GC.compose(self, rhs)
def __mul__(self, rhs): # monoidal product
return GC.par(self, rhs)
def __add__(self,rhs): # hmm. What should addition be? Join?
def const(label): # inject a constant in. A labelled node with 1 outport and no input
def res(G):
node = GraphCat.fresh(1)[0]
G.node(node, str(label))
return [], [node]
return GC(res)
def cup():
def res(G):
nodes = GraphCat.fresh(2)
for node in nodes:
G.node(node, shape="point")
return [], nodes
return GraphCat(res)
def cap():
return GraphCat.converse(GraphCat.cup())
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