We present two case studies in formal reasoning about untyped λ-calculus in Coq, using both first-order and higher-order abstract syntax. In the first case, we prove the equivalence of three definitions of α-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.

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

HONSELL, Furio;MICULAN, Marino;SCAGNETTO, Ivan
2001-01-01

Abstract

We present two case studies in formal reasoning about untyped λ-calculus in Coq, using both first-order and higher-order abstract syntax. In the first case, we prove the equivalence of three definitions of α-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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/737550
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