Results 1 
2 of
2
CutElimination and a PermutationFree Sequent Calculus for Intuitionistic Logic
, 1998
"... We describe a sequent calculus, based on work of Herbelin, of which the cutfree derivations are in 11 correspondence with the normal natural deduction proofs of intuitionistic logic. We present a simple proof of Herbelin's strong cutelimination theorem for the calculus, using the recursive ..."
Abstract

Cited by 41 (6 self)
 Add to MetaCart
We describe a sequent calculus, based on work of Herbelin, of which the cutfree derivations are in 11 correspondence with the normal natural deduction proofs of intuitionistic logic. We present a simple proof of Herbelin's strong cutelimination theorem for the calculus, using the recursive path ordering theorem of Dershowitz.
MachineAssisted MetaTheory of SequentStyle Calculi in Coq
"... . A formalisation of the implicational fragments of two sequent calculi and a sequentstyle presentation of natural deduction in Coq is presented. The systems presented are all typed lambda calculi. Based on this formalisation, some general comments on the feasibility of performing metatheoretic pro ..."
Abstract
 Add to MetaCart
(Show Context)
. A formalisation of the implicational fragments of two sequent calculi and a sequentstyle presentation of natural deduction in Coq is presented. The systems presented are all typed lambda calculi. Based on this formalisation, some general comments on the feasibility of performing metatheoretic proofs about typed lambda calculi in a proof assistant based on higherorder type theory are made. Conclusions about the suitability of Coq for this work, as well as some indications as to the future use of completely formal developments in metatheoretic reasoning, are drawn. 1 Introduction Research into the properties of logics (metatheory) is a rich and diverse field. Despite the tools available for implementing object logics in Logical Frameworks [HP91, HP93] that have been developed over the last twenty years, little has been done in the area of machine assistance for metatheory. Investigations of the properties of calculi [Coq93, Hue94, Alt93] and typechecking Pure Type Systems [vBJM...