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ICFP 2019
Sun 18 - Fri 23 August 2019 Berlin, Germany
Sun 18 Aug 2019 11:16 - 11:43 at Reindeer - Orthogonal Bases Chair(s): Gabriele Keller

Vectors in numerical computation, i.e., arrays of numbers, often represent continuous functions. We would like to reflect this with types. One apparent obstacle is that spaces of functions are typically infinite-dimensional, while the code must run in finite time and memory. We argue that this can be overcome: even in an infinite-dimensional space, the vectors can in practice be stored in finite memory. However, dual vectors (corresponding essentially to distributions) require infinite data structure. The distinction is usually lost in the finite dimensional case, since dual vectors are often simply represented as vectors (by implicitly choosing a scalar product establishing the correspondence). However, we shall see that an explicit type-level distinction between functions and distributions makes sense and allows directly expressing useful concepts such as the Dirac distribution, which are problematic in the standard finite-resolution picture. The example implementation uses a very simple local basis that corresponds to a Haar Wavelet transform.

Sun 18 Aug

10:50 - 12:10: FHPNC - Orthogonal Bases at Reindeer
Chair(s): Gabriele KellerUtrecht University
FHPNC-2019-papers10:50 - 11:16
Bastian KöpckeUniversity of Münster, Michel SteuwerUniversity of Glasgow, Sergei Gorlatch
Link to publication DOI Pre-print File Attached
FHPNC-2019-papers11:16 - 11:43
Olivier Verdier, Justus SagemüllerWestern Norway University of Applied Sciences
Link to publication Pre-print
FHPNC-2019-papers11:43 - 12:10
Wojciech Michal PawlakUniversity of Copenhagen, Denmark, Martin ElsmanUniversity of Copenhagen, Denmark, Cosmin OanceaUniversity of Copenhagen, Denmark
Link to publication