The Theory of Contexts for First Order and Higher Order Abstract Syntax

We present two case studies in formal reasoning about untyped i-calculus in Coq, using both first-order and higher-order abstract syntax. In the first case, we prove the equivalence of three definitions of a-equivalence; in the second, we focus on properties of substitution. In both cases, we deal with contexts, which are rendered by means of higher-order terms (functions) in the metalanguage. These are successfully handled by using the Theory of Contexts.

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