Semantical Analysis of Higher-Order Abstract Syntax
نویسنده
چکیده
It is the aim of this paper to advocate the use of functor categories as a semantic foundation of higher-order abstract syntax (HOAS). By way of example, we will show how functor categories can be used for at least the following applications: relating first-order and higher-order abstract syntax (proofs of adequacy) without using reduction rules, justifying induction principles and other axioms assumed in conjunction with HOAS, suggesting new logical principles to reason about HOAS, making precise the relationship between proofs involving HOAS and properties of first-order syntax (what exactly does this or that HOAS proof prove?)
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