Conditional Independence by Typing

A central goal of probabilistic programming languages (PPLs) is to separate modelling from inference. However, this goal is hard to achieve in practice. Users are often forced to re-write their models to improve efficiency of inference or meet restrictions imposed by the PPL. Conditional independence (CI) relationships among parameters are a crucial aspect of probabilistic models that capture a qualitative summary of the specified model and can facilitate more efficient inference. We present an information flow type system for probabilistic programming that captures conditional independence (CI) relationships and show that, for a well-typed program in our system, the distribution it implements is guaranteed to have certain CI-relationships. Further, by using type inference, we can statically deduce which CI-properties are present in a specified model. As a practical application, we consider the problem of how to perform inference on models with mixed discrete and continuous parameters. Inference on such models is challenging in many existing PPLs, but can be improved through a workaround, where the discrete parameters are used implicitly , at the expense of manual model re-writing. We present a source-to-source semantics-preserving transformation, which uses our CI-type system to automate this workaround by eliminating the discrete parameters from a probabilistic program. The resulting program can be seen as a hybrid inference algorithm on the original program, where continuous parameters can be drawn using efficient gradient-based inference methods, while the discrete parameters are inferred using variable elimination. We implement our CI-type system and its example application in SlicStan: a compositional variant of Stan. 1

Language-Independent Type Inference of the Instances from Multilingual Wikipedia

Extracting knowledge from Wikipedia has attracted much attention in recent ten years. One of the most valuable kinds of knowledge is type information, which refers to the axioms stating that an instance is of a certain type. Current approaches for inferring the types of instances from Wikipedia mainly rely on some language-specific rules. Since these rules cannot catch the semantic associations between instances and classes (i.e. candidate types), it may lead to mistakes and omissions in the process of type inference. The authors propose a new approach leveraging attributes to perform language-independent type inference of the instances from Wikipedia. The proposed approach is applied to the whole English and Chinese Wikipedia, which results in the first version of MulType (Multilingual Type Information), a knowledge base describing the types of instances from multilingual Wikipedia. Experimental results show that not only the proposed approach outperforms the state-of-the-art comparison methods, but also MulType contains lots of new and high-quality type information.

SimTyper: sound type inference for Ruby using type equality prediction

Many researchers have explored type inference for dynamic languages. However, traditional type inference computes most general types which, for complex type systems—which are often needed to type dynamic languages—can be verbose, complex, and difficult to understand. In this paper, we introduce SimTyper, a Ruby type inference system that aims to infer usable types—specifically, nominal and generic types—that match the types programmers write. SimTyper builds on InferDL, a recent Ruby type inference system that soundly combines standard type inference with heuristics. The key novelty of SimTyper is type equality prediction , a new, machine learning-based technique that predicts when method arguments or returns are likely to have the same type. SimTyper finds pairs of positions that are predicted to have the same type yet one has a verbose, overly general solution and the other has a usable solution. It then guesses the two types are equal, keeping the guess if it is consistent with the rest of the program, and discarding it if not. In this way, types inferred by SimTyper are guaranteed to be sound. To perform type equality prediction, we introduce the deep similarity (DeepSim) neural network. DeepSim is a novel machine learning classifier that follows the Siamese network architecture and uses CodeBERT, a pre-trained model, to embed source tokens into vectors that capture tokens and their contexts. DeepSim is trained on 100,000 pairs labeled with type similarity information extracted from 371 Ruby programs with manually documented, but not checked, types. We evaluated SimTyper on eight Ruby programs and found that, compared to standard type inference, SimTyper finds 69% more types that match programmer-written type information. Moreover, DeepSim can predict rare types that appear neither in the Ruby standard library nor in the training data. Our results show that type equality prediction can help type inference systems effectively produce more usable types.

Relational nullable types with Boolean unification

We present a simple, practical, and expressive relational nullable type system. A relational nullable type system captures whether an expression may evaluate to null based on its type, but also based on the type of other related expressions. The type system extends the Hindley-Milner type system with Boolean constraints, supports parametric polymorphism, and preserves principal types modulo Boolean equivalence. We show how to support full Hindley-Milner style type inference with an extension of Algorithm W. We conduct a preliminary study of open source projects showing that there is a need for relational nullable type systems across a wide range of programming languages. The most important findings from the study are: (i) programmers use programming patterns where the nullability of one expression depends on the nullability of other related expressions, (ii) such invariants are commonly enforced with run-time exceptions, and (iii) reasoning about these programming patterns requires not only knowledge of when an expression may evaluate to null, but also when it may evaluate to a non-null value. We incorporate these observations in the design of the proposed relational nullable type system.

An existential crisis resolved: type inference for first-class existential types

Despite the great success of inferring and programming with universal types, their dual—existential types—are much harder to work with. Existential types are useful in building abstract types, working with indexed types, and providing first-class support for refinement types. This paper, set in the context of Haskell, presents a bidirectional type-inference algorithm that infers where to introduce and eliminate existentials without any annotations in terms, along with an explicitly typed, type-safe core language usable as a compilation target. This approach is backward compatible. The key ingredient is to use strong existentials, which support (lazily) projecting out the encapsulated data, not weak existentials accessible only by pattern-matching.

Bidirectional Typing

Bidirectional typing combines two modes of typing: type checking, which checks that a program satisfies a known type, and type synthesis, which determines a type from the program. Using checking enables bidirectional typing to support features for which inference is undecidable; using synthesis enables bidirectional typing to avoid the large annotation burden of explicitly typed languages. In addition, bidirectional typing improves error locality. We highlight the design principles that underlie bidirectional type systems, survey the development of bidirectional typing from the prehistoric period before Pierce and Turner’s local type inference to the present day, and provide guidance for future investigations.