118 research outputs found
Type Theory Unchained: Extending Agda with User-Defined Rewrite Rules
No full textDependently typed languages such as Coq and Agda can statically guarantee the correctness of our proofs and programs. To provide this guarantee, they restrict users to certain schemes a- such as strictly positive datatypes, complete case analysis, and well-founded induction a- that are known to be safe. However, these restrictions can be too strict, making programs and proofs harder to write than necessary. On a higher level, they also prevent us from imagining the different ways the language could be extended. In this paper I show how to extend a dependently typed language with user-defined higher-order non-linear rewrite rules. Rewrite rules are a form of equality reflection that is applied automatically by the typechecker. I have implemented rewrite rules as an extension to Agda, and I give six examples how to use them both to make proofs easier and to experiment with extensions of type theory. I also show how to make rewrite rules interact well with other features of Agda such as-equality, implicit arguments, data and record types, irrelevance, and universe level polymorphism. Thus rewrite rules break the chains on computation and put its power back into the hands of its rightful owner: Yours.Programming Language
Dependently Typed Languages in Statix
No full textStatic type systems can greatly enhance the quality of programs, but implementing a type checker that is both expressive and user-friendly is challenging and error-prone. The Statix meta-language (part of the Spoofax language workbench) aims to make this task easier by automatically deriving a type checker from a declarative specification of a type system. However, so far Statix has not been used to implement dependent types, which is a class of type systems which require evaluation of terms during type checking. In this paper, we present an implementation of a simple dependently typed language in Statix, and discuss how to extend it with several common features such as inductive data types, universes, and inference of implicit arguments. While we encountered some challenges in the implementation, our conclusion is that Statix is already usable as a tool for implementing dependent types
Freezing of gait in Parkinson’s disease is related to imbalanced stopping-related cortical activity
No full textSupplemental materials for preprint: The influence of doorway characteristics on freezing of gait
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