https://ych817.github.io/tags/agda/采石场Hugo 0.158.0 & FixIt v0.4.5zh-CNThu, 22 Oct 2026 16:12:16 +1300https://ych817.github.io/posts/2ceeee8/Thu, 22 Oct 2026 16:12:16 +1300https://ych817.github.io/posts/2ceeee8/<h2 class="heading-element" id="摘要-abstract"><span>摘要 Abstract</span> <a href="#%e6%91%98%e8%a6%81-abstract" class="heading-mark"> <svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg> </a> </h2><p>We present four constructions for standard equipment which can be generated for every inductive datatype: case analysis, structural recursion, no confusion, acyclicity. Our constructions follow a two-level approach— they require less work than the standard techniques which inspired them. Moreover, given a suitably heterogeneous notion of equality, they extend without difficulty to inductive families of datatypes. These constructions are vital components of the translation from dependently typed programs in pattern matching style to the equivalent programs expressed in terms of induction principles and as such play a crucial behind-the-scenes rˆole in Epigram.</p>