8 research outputs found
Characterization of strong normalizability for a sequent lambda calculus with co-control
We study strong normalization in a lambda calculus of proof-terms
with co-control for the intuitionistic sequent calculus. In this sequent
lambda calculus, the management of formulas on the left hand
side of typing judgements is “dual" to the management of formulas
on the right hand side of the typing judgements in Parigot’s lambdamu
calculus - that is why our system has first-class “co-control".
The characterization of strong normalization is by means of intersection
types, and is obtained by analyzing the relationship with
another sequent lambda calculus, without co-control, for which a
characterization of strong normalizability has been obtained before.
The comparison of the two formulations of the sequent calculus,
with or without co-control, is of independent interest. Finally, since
it is known how to obtain bidirectional natural deduction systems
isomorphic to these sequent calculi, characterizations are obtained
of the strongly normalizing proof-terms of such natural deduction
systems.The authors would like to thank the anonymous
referees for their valuable comments and helpful suggestions.
This work was partly supported by FCT—Fundação para a Ciência
e a Tecnologia, within the project UID-MAT-00013/2013; by
COST Action CA15123 - The European research network on types
for programming and verification (EUTypes) via STSM; and by the
Ministry of Education, Science and Technological Development,
Serbia, under the projects ON174026 and III44006.info:eu-repo/semantics/publishedVersio
Glueability of Resource Proof-Structures: Inverting the Taylor Expansion
A Multiplicative-Exponential Linear Logic (MELL) proof-structure can be expanded into a set of resource proof-structures: its Taylor expansion. We introduce a new criterion characterizing those sets of resource proof-structures that are part of the Taylor expansion of some MELL proof-structure, through a rewriting system acting both on resource and MELL proof-structures
Advances in Proof-Theoretic Semantics
Logic; Mathematical Logic and Foundations; Mathematical Logic and Formal Language