Overview

Haydi (Haystack diver) is a framework for generating discrete structures. It provides a way to define a structure from basic building blocks (e.g. Cartesian product, mappings) and then enumerate all elements, all non-isomorphic elements, or generate random elements.

• Pure Python implementation (Python 2.7+, PyPy supported)
• MIT license
• Sequential or distributed computation (via dask/distributed)

Example of usage

• Let us define directed graphs on two vertices (represented as a set of edges):

  >>> import haydi as hd
  >>> nodes = hd.USet(2, "n")  # A two-element set with (unlabeled) elements {n0, n1}
  >>> graphs = hd.Subsets(nodes * nodes)  # Subsets of a cartesian product
  

• Now we can iterate all elements:

  >>> list(graphs.iterate())
  [{}, {(n0, n0)}, {(n0, n0), (n0, n1)}, {(n0, n0), (n0, n1), (n1, n0)}, {(n0,
  # ... 3 lines removed ...
  n1)}, {(n1, n0)}, {(n1, n0), (n1, n1)}, {(n1, n1)}]
  

• or iterate all non-isomorphic ones:

  >>> list(graphs.cnfs())  # cnfs = canonical forms
  [{}, {(n0, n0)}, {(n0, n0), (n1, n1)}, {(n0, n0), (n0, n1)}, {(n0, n0), (n0,
  n1), (n1, n1)}, {(n0, n0), (n0, n1), (n1, n0)}, {(n0, n0), (n0, n1), (n1, n0),
  (n1, n1)}, {(n0, n0), (n1, n0)}, {(n0, n1)}, {(n0, n1), (n1, n0)}]
  

• or generate random instances:

  >>> list(graphs.generate(3))
  [{(n1, n0)}, {(n1, n1), (n0, n0)}, {(n0, n1), (n1, n0)}]
  

• Haydi supports standard operations like map, filter and reduce:

  >>> op = graphs.map(lambda g: len(g)).reduce(lambda x, y: x + y)
  # Just a demonstration pipeline; nothing usefull
  >>> op.run()
  

• We can run it transparently as a distributed application:

  >>> from haydi import DistributedContext
  # We are now assuming that dask/distributed is running at hostname:1234
  >>> context = DistributedContext("hostname", 1234)
  >>> op.run(ctx=context)