Constructive logics: Part I: a tutorial on proof systems and typed &lgr;-calculi
Theoretical Computer Science
Handbook of logic in computer science (vol. 2)
Intersection and union types: syntax and semantics
Information and Computation
Basic proof theory
Basic simple type theory
Permutability of proofs in intuitionistic sequent calculi
Theoretical Computer Science - Special issue: Gentzen
Terminiation of permutative conversions in intuitionistic Gentzen calculi
Theoretical Computer Science - Special issue: Gentzen
A Lambda-Calculus Structure Isomorphic to Gentzen-Style Sequent Calculus Structure
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Combinatory Reduction Systems with Explicit Substitution that Preserve Strong Nomalisation
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Characterizing strong normalization in a language with control operators
PPDP '04 Proceedings of the 6th ACM SIGPLAN international conference on Principles and practice of declarative programming
Strong Normalisation of Cut-Elimination in Classical Logic
Fundamenta Informaticae - Typed Lambda Calculi and Applications (TLCA'99)
Computation with classical sequents
Mathematical Structures in Computer Science
A cut-free sequent calculus for pure type systems verifying the structural rules of Gentzen/Kleene
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
Characterising strongly normalising intuitionistic sequent terms
TYPES'07 Proceedings of the 2007 international conference on Types for proofs and programs
Classical call-by-need and duality
TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
The language X: circuits, computations and classical logic
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Strong Normalisation of Cut-Elimination in Classical Logic
Fundamenta Informaticae - Typed Lambda Calculi and Applications (TLCA'99)
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It is well known that there is an isomorphism between natural deduction derivations and typed lambda terms. Moreover, normalising these terms corresponds to eliminating cuts in the equivalent sequent calculus derivations. Several papers have been written on this topic. The correspondence between sequent calculus derivations and natural deduction derivations is, however, not a one-one map, which causes some syntactic technicalities. The correspondence is best explained by two extensionally equivalent type assignment systems for untyped lambda terms, one corresponding to natural deduction (λN) and the other to sequent calculus (λL). These two systems constitute different grammars for generating the same (type assignment relation for untyped) lambda terms. The second grammar is ambiguous, but the first one is not. This fact explains the many-one correspondence mentioned above. Moreover, the second type assignment system has a ‘cut-free’ fragment (λLcf). This fragment generates exactly the typeable lambda terms in normal form. The cut elimination theorem becomes a simple consequence of the fact that typed lambda terms possess a normal form.