Theoretical Computer Science
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Call-by-name call-by-value, call-by-need and the linear lambda calculus
Theoretical Computer Science - Special issue on mathematical foundations of programming semantics
The optimal implementation of functional programming languages
The optimal implementation of functional programming languages
Strong Normalization of Explicit Substitutions via Cut Elimination in Proof Nets
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Extending the explicit substitution paradigm
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Deduction Graphs with Universal Quantification
Electronic Notes in Theoretical Computer Science (ENTCS)
A sequent calculus with implicit term representation
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
From deduction graphs to proof nets: boxes and sharing in the graphical presentation of deductions
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
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In this paper, we introduce the formalism of deduction graphs as a generalisation of both Gentzen–Prawitz style natural deduction and Fitch style flag deduction. The advantage of this formalism is that, as with flag deductions (but not natural deduction), subproofs can be shared, but the linearisation used in flag deductions is avoided. Our deduction graphs have both nodes and boxes, which are collections of nodes that also form a node themselves. This is reminiscent of the bigraphs of Milner, where the link graph describes the nodes and edges and the place graph describes the nesting of nodes. We give a precise definition of deduction graphs, together with some illustrative examples. Furthermore, we analyse their computational behaviour by studying the process of cut-elimination and by defining translations from deduction graphs to simply typed lambda terms. From a slight variation of this translation, we conclude that the process of cut-elimination is strongly normalising. The translation to simple type theory removes quite a lot of structure, so we also propose a translation to a context calculus with lets that faithfully captures the structure of deduction graphs. The proof nets of linear logic also offer a graph-like presentation of natural deduction, and we point out some similarities between the two formalisms.