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I describe the mechanisation in HOL of some basic λ-calculus theory, using the axioms proposed by Gordon and Melham . ... Using these as a foundation, I mechanised the proofs from Chapters 2 and 3 of Hankin  (equational theory and reduction theory), followed by most of Chapter 11 of Barendregt  (residuals, finiteness ... The mechanisation features the use of the Gordon-Melham axioms for α-equivalent terms, and demonstrates those axioms' effectiveness and utility. ...doi:10.1145/976571.976577 dblp:conf/icfp/Norrish03 fatcat:y4nugdgk5ff4tahj6homx7ti4u
The issues in mechanising pen-and-paper proofs are discussed; in particular, those difficulties arising from the sources' use of the Barendregt Variable Convention. ... The proofs are taken from standard sources (books by Hankin and Barendregt), and cover: equational theory, reduction theory, residuals, finiteness of developments, and the standardisation theorem. ... , both for discussions about standardisation and adequacy, and for the excellent working conditions at his recent "Binding Challenges" workshop. ...doi:10.1007/s10990-006-8745-7 fatcat:u5jw53nhljcj5cd4tpkmmrclpu