2025-05-30: Liang-Ting Chen (Institute of Information Science, Academia Sinica, Taiwan)

Fri, 23 May 2025 16:32:13 +0000

Liang-Ting Chen (Institute of Information Science, Academia Sinica, Taiwan)

A formal treatment of bidirectional typing

Abstract

In this talks, we consider a general and formal theory of bidirectional typing for simply typed languages: for every signature that specifies a mode-correct bidirectionally typed language, there exists a proof-relevant type synthesiser which, given an input abstract syntax tree, constructs a typing derivation if any, gives its refutation if not, or reports that the input does not have enough type annotations.
Sufficient conditions for deriving a type synthesiser such as soundness, completeness, and mode-correctness are established for all signatures. We propose a preprocessing step, which helps the user to deal with missing type annotations. The entire theory is implemented in Agda, serving as a verified generator of proof-relevant type synthesisers as a by-product.

2025-05-30 14:00:00 UTC
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