Decrypting Local Type Inference

Statically typed languages verify programs at compile-time. As a result many programming mistakes are detected at an early stage of development. A programmer does not have to specify types for every single term manually, however. Many programming languages can reconstruct a termâ s type using type inference algorithms. While helpful, programmers often find it hard to comprehend the choice of typing decisions that led to the derived type for a term. A particularly serious consequence is that the reporting of type errors yields cryptic messages and misleading program locations. In this thesis we propose a novel approach to explaining type checking decisions by exploring fragments of type derivation trees. Our approach applies to programming languages that use local type inference: typing decisions are made locally and the type information is only propagated between the adjacent AST nodes. We design an algorithm that backtracks through the nodes of type derivation trees in order to discover the typing decisions that introduce the types for the first time during the type inference process. Our algorithm has two properties: - it is type-driven, meaning that we only visit the nodes and their respective typing decisions if they participated in the inference of a type. - it is autonomous, meaning that it does not require any user-input in its operation. These properties allow us to identify the complete and precise set of locations defining the source of a type; previous work mostly focussed on heuristics or used approximations for locating the cause of an error. Our algorithm is not tied to a particular implementation of a type checker: our type derivation trees can be reconstructed from a pre-existing type checker without modifying its internal logic or affecting its regular compilation times. It therefore readily applies to existing programs: we can not only provide improved feedback for them, we also expose limitations of local type inference algorithms and their implementations, without artificially limiting the language features. We implement our type debugging algorithm on top of Scalaâ s type checker. Our analysis applies to a range of erroneous scenarios. It provides better error locations than the standard type error reporter of the Scala compiler. This type debugging analysis is just a starting point from which many interesting and useful applications around type debugging can be built: - we implement an interactive type debugger that guides the users through the decisions of local type inference for erroneous and error-free programs alike. - with precise and minimal source code locations we can also offer surgical-level code modifications that fix for example the limitations of local type inference. - we open the door for programmatically defined, application-specific error feedback or corrections. To the best of our knowledge this thesis is the first to address the problem of type errors for programming languages that use local type infere