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Advanced ComputationFrame tools

Open In Colab

This section of the documentation contains some more advanced ComputationFrame topics.

Set-like and graph-like operations on ComputationFrames

A CF is like a "graph of sets", where the elements of each set are either Refs (for variables) or Calls (for functions). As such, it supports both natural set-like operations applied node/edge-wise, and natural operations using the graph's connectivity:

  • union: given by cf_1 | cf_2, this takes the union of the two computation graphs (merging nodes/edges with the same names), and in case of a merge, the resulting set at the node is the union of the two sets of Refs or Calls.
  • intersection: given by cf_1 & cf_2, this takes the intersection of the two computation graphs (leaving only nodes/edges with the same name in both), and the set at each node is the intersection of the two corresponding sets.
  • .downstream(varnames): restrict the CF to computations that are downstream of the Refs in chosen variables
  • .upstream(varnames): dual to downstream

Consider the following example:

# for Google Colab
try:
    import google.colab
    !pip install git+https://github.com/amakelov/mandala
except:
    pass

from mandala.imports import *
storage = Storage()

@op
def inc(x): return x + 1

@op
def add(y, z): return y + z

@op
def square(w): return w ** 2

@op
def divmod_(u, v): return divmod(u, v)

with storage:
    xs = [inc(i) for i in range(5)]
    ys = [add(x, z=42) for x in xs] + [square(x) for x in range(5, 10)]
    zs = [divmod_(x, y) for x, y in zip(xs, ys[3:8])]

We have a "middle layer" in the computation that uses both add and square. We can get a shared view of the entire computation by taking the union of the expanded CFs for these two ops:

cf = (storage.cf(add) | storage.cf(square)).expand_all()
cf.draw(verbose=True)

svg

Selection

TODO