A model-based QuickCheck test of ptrees (Patricia trees)
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A QuickCheck model-based test of ptrees (Patricia trees)

This is an example of building a model-based QuickCheck testsuite with OCaml's QCheck library.

It tests whether the Patricia tree implementation 'ptrees' agrees with a simple model (read: an abstract specification or semantics) of sets, represented as sorted lists. Interestingly it doesn't.

It turns out to be a problem due to signed integer comparison inherited from Okasaki and Gill's paper "Fast mergable integer maps" (ML'98).

For full details please see my paper draft "QuickChecking Patricia Trees".

To recreate the bug the directory 'ptrees' contains an old copy of the library. Note that 'ptrees' has since been split into separate libraries:

  • 'ptset' implementing integer sets and
  • 'ptmap' implementing maps with integer keys.


The Makefile includes two targets: old and new. To recreate the problem run make old and then ./qctest.byte This should illustrate the issue:

random seed: 413762386
law empty: 1 relevant cases (1 total)
law singleton test: 2500 relevant cases (2500 total)
law mem test: 2500 relevant cases (2500 total)
law add test: 2500 relevant cases (2500 total)
law remove test: 2500 relevant cases (2500 total)
law union test: 1776 relevant cases (1776 total)
  test `union test`
  failed on >= 1 cases:
  (Union (Singleton -4611686018427387904, Singleton 0), Add (1, Singleton -4611686018427387904)) (after 33 shrink steps)
law inter test: 2500 relevant cases (2500 total)
failure (1 tests failed, ran 7 tests)

To confirm that the issue has been fixed, run make new and ./qctest.byte again. This will instead test the newer (patched) 'ptset' submodule against the model.