Static typing can guide programmers if feedback is immediate. Therefore, all major IDEs incrementalize type checking in some way. However, prior approaches to incremental type checking are often specialized and hard to transfer to new type systems. In this paper, we propose a systematic approach for deriving incremental type checkers from textbook-style type system specifications. Our approach is based on compiling inference rules to Datalog, a carefully limited logic programming language for which incremental solvers exist. The key contribution of this paper is to discover an encoding of the infinite typing relation as a finite Datalog relation in a way that yields efficient incremental updates. We implemented the compiler as part of a type system DSL and show that it supports simple types, some local type inference, operator overloading, universal types, and iso-recursive types.

Exploration of language specifications helps to discover errors and inconsistencies early during the development of a programming language. We propose exploration of language specifications via application of existing automated first-order theorem provers (ATPs). To this end, we translate language specifications and exploration tasks to first-order logic, which many ATPs accept as input. However, there are several different strategies for compiling a language specification to first-order logic, and even small variations in the translation may have a large impact on the time it takes ATPs to find proofs. In this paper, we first present a systematic empirical study on how to best compile language specifications to first-order logic such that existing ATPs can solve typical exploration tasks efficiently. We have developed a compiler product line that implements 36 different compilation strategies and used it to feed language specifications to 4 existing first-order theorem provers. As benchmarks, we developed language specifications for typed SQL and for a Questionnaire Language (QL), with 50 exploration goals each. Our study empirically confirms that the choice of a compilation strategy greatly influences prover performance in general and shows which strategies are advantageous for prover performance. Second, we extend our empirical study with 4 domain-specific strategies for axiom selection and find that axiom selection does not influence prover performance in our benchmark specifications.

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A structural diffing algorithm compares two pieces of treeshaped data and computes their difference. Existing structural diffing algorithms either produce concise patches or ensure type safety, but never both. We present a new structural diffing algorithm called truediff that achieves both properties by treating subtrees as mutable, yet linearly typed resources. Mutation is required to derive concise patches that only mention changed nodes, but, in contrast to prior work, truediff guarantees all intermediate trees are well-typed. We formalize type safety, prove truediff has linear run time, and evaluate its performance and the conciseness of the derived patches empirically for real-world Python documents. While truediff ensures type safety, the size of its patches is on par with Gumtree, a popular untyped diffing implementation. Regardless, truediff outperforms Gumtree and a typed diffing implementation by an order of magnitude.CCS Concepts: • Software and its engineering → Software notations and tools.

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