TerpreT: A Probabilistic Programming Language for Program Induction

We study machine learning formulations of inductive program synthesis; that is, given input-output examples, we would like to synthesize source code that maps inputs to corresponding outputs. Our aims in this work are to develop new machine learning approaches to the problem based on neural networks and graphical models, and to understand the capabilities of machine learning techniques relative to traditional alternatives, such as those based on constraint solving from the programming languages community. Our key contribution is the proposal of TerpreT, a domain-specific language for expressing program synthesis problems. TerpreT is similar to a probabilistic programming language: a model is composed of a specification of a program representation (declarations of random variables) and an interpreter that describes how programs map inputs to outputs (a model connecting unknowns to observations). The inference task is to observe a set of input-output examples and infer the underlying program. TerpreT has two main benefits. First, it enables rapid exploration of a range of domains, program representations, and interpreter models. Second, it separates the model specification from the inference algorithm, allowing proper like-to-like comparisons between different approaches to inference. From a single TerpreT specification we can automatically perform inference using four different back-ends that include machine learning and program synthesis approaches. These are based on gradient descent (thus each specification can be seen as a differentiable interpreter), linear program (LP) relaxations for graphical models, discrete satisfiability solving, and the Sketch program synthesis system. We illustrate the value of TerpreT by developing several interpreter models and performing an extensive empirical comparison between alternative inference algorithms on a variety of program models. Our key, and perhaps surprising, empirical finding is that constraint solvers dominate the gradient descent and LP-based formulations. We conclude with some suggestions on how the machine learning community can make progress on program synthesis.