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What and Who
Title:Proof-relevant logical relations
Speaker:Martin Hofmann
coming from:Ludwig-Maximilians-Universitaet Muenchen
Speakers Bio:
Event Type:SWS Colloquium
Visibility:SWS, RG1
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Level:AG Audience
Language:English
Date, Time and Location
Date:Monday, 13 May 2013
Time:14:00
Duration:90 Minutes
Location:Saarbr├╝cken
Building:E1 5
Room:029
Abstract
We introduce a novel variant of logical relations that maps types not merely to partial equivalence relations on values, as is

commonly done, but rather to a proof-relevant generalisation thereof, namely setoids.

A setoid is like a category all of whose morphisms are isomorphisms (a groupoid) with the exception that no
equations between these morphisms are required to hold.

The objects of a setoid establish that values inhabit semantic types, whilst its morphisms are understood as evidence
for semantic equivalence.

The transition to proof-relevance solves two well-known problems caused by the use of existential quantification over future
worlds in traditional Kripke logical relations: failure of admissibility, and spurious functional dependencies.

We illustrate the novel format with two applications: a direct-style validation of Pitts and Stark's equivalences for ``new'' and a
denotational semantics for a region-based effect system that supports type abstraction in the sense that only externally visible
effects need to be tracked; non-observable internal modifications, such as the reorganisation of a search tree or lazy initialisation,
can count as `pure' or `read only'. This `fictional purity' allows clients of a module soundly to validate more effect-based program
equivalences than would be possible with traditional effect systems.

This is joint work with Nick Benton and Vivek Nigam

Contact
Name(s):Claudia Richter
Phone:9303 9103
EMail:--email address not disclosed on the web
Video Broadcast
Video Broadcast:YesTo Location:Kaiserslautern
To Building:G26To Room:112
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Created:Claudia Richter/MPI-SWS, 05/06/2013 09:34 AM Last modified:Uwe Brahm/MPII/DE, 11/24/2016 04:14 PM
  • Claudia Richter, 05/06/2013 01:15 PM
  • Claudia Richter, 05/06/2013 09:49 AM -- Created document.