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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: Semantics & Type TheoryResearch Papers at Ile de France II (IDF II)
Chair(s): Arthur Azevedo de AmorimCarnegie Mellon University, USA
15:35 - 15:56
Talk
Taylor Subsumes Scott, Berry, Kahn and PlotkinDistinguished Paper
Research Papers
Davide BarbarossaUniversité Paris 13, Giulio ManzonettoUniversité Paris 13
Link to publication DOI Media Attached File Attached
15:56 - 16:18
Talk
Reduction Monads and Their Signatures
Research Papers
Benedikt AhrensUniversity of Birmingham, United Kingdom, André HirschowitzUniversité Côte d'Azur, Ambroise LafontInria, France, Marco MaggesiUniversità di Firenze
Link to publication DOI Media Attached
16:18 - 16:40
Talk
Coq Coq Correct! Verification of Type Checking and Erasure for Coq, in Coq
Research Papers
Matthieu SozeauInria, Simon BoulierInria, Yannick ForsterSaarland University, Nicolas TabareauInria, Théo WinterhalterInria — LS2N
Link to publication DOI Media Attached File Attached