Lanugage of Thought (LOT) models in Python.
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LOTlib is a Python 2 library for implementing "language of thought" models. A LOTlib model specifies a set of primitives and captures learning as inference over compositions of those primitives in order to express complex concepts. LOTlib permits lambda expressions, meaning that learners can come up with abstractions over compositions and define new primitives. Frequently, models use sampling in order to determine likely compositional hypotheses given some observed data.

There are several sampling methods provided, including tree-regeneration Metropolis-Hastings (from the "rational rules" model of Goodman et al. 2008), and variants that include tempering, annealing, tempered transitions, and other search algorithms.

The best way to use this library is to read and modify the examples.

LOTlib also provides support for MPI through a wrapper for mpi4py (LOTlib.MPI), allowing sampling algorithms to run in parallel on a simple computer or cluster.


  • numpy
  • scipy
  • cachetools (for memoization)
  • mpi4py (for running on MPI)

The following are used by some LOTlib components:

  • matplotlib (for plotting)
  • graphviz (for DOT images of trees)
  • pyswip (for Prolog example)


Put this library somewhere - e.g. ~/Libraries/LOTlib/

Set the PYTHONPATH environment variable to point to LOTlib/:

$ export PYTHONPATH=$PYTHONPATH:~/Libraries/LOTlib

You can put this into your .bashrc file to make it loaded automatically when you open a terminal. On ubuntu and most linux, this is:

$ echo 'export PYTHONPATH=\$PYTHONPATH:~/Libraries/LOTlib' >> ~/.bashrc

And you should be ready to use the library via:

import LOTlib


A tutorial can be found in the "Documentation" folder above.

A good starting place is the FOL folder, which contains a simple example to generate first-order logical expressions. These have simple boolean functions as well as lambda expressions.

More examples are provided in the "Examples" folder. These include: simple symbolic regression, the recursive number learning model, a quantifier learning model. The "tests" folder may also be useful, as this runs some simple models to check for, e.g., correct sampling and inference.


LOTlib contains experimental GPU code in C under LOTlib.GrammarInference. This takes a set of behavioral data (see LOTlib.GrammarInference.Demo.ExportToGPU for the format) and doing inference over the production probabilities on a finite approximation to the fully PCFG hypothesis space.


This software may be cited as:

        author={Steven T. Piantadosi},
        title={{LOTlib: Learning and Inference in the Language of Thought}},
        howpublished={available from}