TY - GEN

T1 - Species, profunctors and taylor expansion weighted by SMCC

T2 - 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018

AU - Tsukada, Takeshi

AU - Asada, Kazuyuki

AU - Ong, C. H.Luke

N1 - Funding Information:
Œe authors would like to thank Marcelo Fiore for insightful discussions. Œis work was supported by JSPS KAKENHI 15H05706, 16K16004 and 18K11156, and EPSRC grant EP/M023974/1.
Publisher Copyright:
© 2018 ACM.

PY - 2018/7/9

Y1 - 2018/7/9

N2 - Motivated by a tight connection between Joyal's combinatorial species and quantitative models of linear logic, this paper introduces weighted generalised species (or weighted profunctors), where weights are morphisms of a given symmetric monoidal closed category (SMCC). For each SMCC W, we show that the category of W-weighted profunctors is a Lafont category, a categorical model of linear logic with exponential. As a model of programming languages, the construction of this paper gives a unified framework that induces adequate models of nondeterministic, probabilistic, algebraic and quantum programming languages by an appropriate choice of the weight SMCC.

AB - Motivated by a tight connection between Joyal's combinatorial species and quantitative models of linear logic, this paper introduces weighted generalised species (or weighted profunctors), where weights are morphisms of a given symmetric monoidal closed category (SMCC). For each SMCC W, we show that the category of W-weighted profunctors is a Lafont category, a categorical model of linear logic with exponential. As a model of programming languages, the construction of this paper gives a unified framework that induces adequate models of nondeterministic, probabilistic, algebraic and quantum programming languages by an appropriate choice of the weight SMCC.

KW - Generalised species

KW - Quantitative model

KW - Quantum computation

KW - Rigid resource calculus

KW - Weighted species

UR - http://www.scopus.com/inward/record.url?scp=85051109371&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051109371&partnerID=8YFLogxK

U2 - 10.1145/3209108.3209157

DO - 10.1145/3209108.3209157

M3 - Conference contribution

AN - SCOPUS:85051109371

T3 - Proceedings - Symposium on Logic in Computer Science

SP - 889

EP - 898

BT - Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 9 July 2018 through 12 July 2018

ER -