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Mechanising Hankin and Barendregt using the Gordon-Melham axioms

Michael Norrish
2003 Proceedings of the 2003 workshop on Mechanized reasoning about languages with variable binding - MERLIN '03  
I describe the mechanisation in HOL of some basic λ-calculus theory, using the axioms proposed by Gordon and Melham [4].  ...  Using these as a foundation, I mechanised the proofs from Chapters 2 and 3 of Hankin [5] (equational theory and reduction theory), followed by most of Chapter 11 of Barendregt [2] (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

Mechanising λ-calculus using a classical first order theory of terms with permutations

Michael Norrish
2006 Higher-Order and Symbolic Computation  
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