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The speculative ambition of replacing the old theory of program approximation based on syntactic continuity with the theory of resource consumption based on Taylor expansion and originating from the differential λ-calculus is nowadays at hand. Using this resource sensitive theory, we provide simple proofs of important results in λ-calculus that are usually demonstrated by exploiting Scott’s continuity, Berry’s stability or Kahn and Plotkin’s sequentiality theory. A paradigmatic example is given by the Perpendicular Lines Lemma for the Böhm tree semantics, which is proved here simply by induction, but relying on the main properties of resource approximants: strong normalization, confluence and linearity.

Slides Talk (ManzonettoTalk.pdf)1.46MiB

Fri 24 Jan
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15:35 - 16:40: Research Papers - Semantics & Type Theory at Ile de France II (IDF II)
Chair(s): Arthur Azevedo de AmorimCarnegie Mellon University, USA
POPL-2020-Research-Papers15:35 - 15:56
Davide BarbarossaUniversité Paris 13, Giulio ManzonettoUniversité Paris 13
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POPL-2020-Research-Papers15:56 - 16:18
Benedikt AhrensUniversity of Birmingham, United Kingdom, André HirschowitzUniversité Côte d'Azur, Ambroise LafontInria, France, Marco MaggesiUniversità di Firenze
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POPL-2020-Research-Papers16:18 - 16:40
Matthieu SozeauInria, Simon BoulierInria, Yannick ForsterSaarland University, Nicolas TabareauInria, Théo WinterhalterInria — LS2N
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