Proof nets and the call-by-value lambda-calculus
Copyright policy )Proof nets and the call-by-value lambda-calculus
This paper gives a detailed account of the relationship between (a variant of) the call-by-value lambda calculus and linear logic proof nets. The presentation is carefully tuned in order to realize a strong bisimulation between the two systems: every single rewriting step on the calculus maps to a single step on the nets, and viceversa. In this way, we obtain an algebraic reformulation of proof nets. Moreover, we provide a simple correctness criterion for our proof nets, which employ boxes in an unusual way.
In Proceedings LSFA 2012, arXiv:1303.7136
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], Linear logic, graphical syntaxes, Proof-theoretic aspects of linear logic and other substructural logics, proof nets, explicit substitutions, Proof-nets, linear logic, QA1-939, Combinatory logic and lambda calculus, Functional programming and lambda calculus, Computer Science - Programming Languages, Lambda-calculus with explicit substitutions, QA75.5-76.95, Logic in Computer Science (cs.LO), Electronic computers. Computer science, call-by-value \(\lambda\)-calculus, Curry-Howard isomorphism, Mathematics, correctness criteria, Programming Languages (cs.PL)
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], Linear logic, graphical syntaxes, Proof-theoretic aspects of linear logic and other substructural logics, proof nets, explicit substitutions, Proof-nets, linear logic, QA1-939, Combinatory logic and lambda calculus, Functional programming and lambda calculus, Computer Science - Programming Languages, Lambda-calculus with explicit substitutions, QA75.5-76.95, Logic in Computer Science (cs.LO), Electronic computers. Computer science, call-by-value \(\lambda\)-calculus, Curry-Howard isomorphism, Mathematics, correctness criteria, Programming Languages (cs.PL)
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