# Traced Premonoidal Categories

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 37, Issue: 4, page 273-299
- ISSN: 0988-3754

## Access Full Article

top## Abstract

top## How to cite

topBenton, Nick, and Hyland, Martin. "Traced Premonoidal Categories." RAIRO - Theoretical Informatics and Applications 37.4 (2010): 273-299. <http://eudml.org/doc/92724>.

@article{Benton2010,

abstract = {
Motivated by some examples from functional programming, we propose a
generalization of the notion of trace to symmetric premonoidal
categories and of Conway operators to Freyd categories. We show that
in a Freyd category, these notions are equivalent, generalizing a
well-known theorem relating traces and Conway operators in Cartesian
categories.
},

author = {Benton, Nick, Hyland, Martin},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Traces; fixed point operators; premonoidal categories; recursion; monads.; Freyd category; Conway operators in Cartesian categories},

language = {eng},

month = {3},

number = {4},

pages = {273-299},

publisher = {EDP Sciences},

title = {Traced Premonoidal Categories},

url = {http://eudml.org/doc/92724},

volume = {37},

year = {2010},

}

TY - JOUR

AU - Benton, Nick

AU - Hyland, Martin

TI - Traced Premonoidal Categories

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 37

IS - 4

SP - 273

EP - 299

AB -
Motivated by some examples from functional programming, we propose a
generalization of the notion of trace to symmetric premonoidal
categories and of Conway operators to Freyd categories. We show that
in a Freyd category, these notions are equivalent, generalizing a
well-known theorem relating traces and Conway operators in Cartesian
categories.

LA - eng

KW - Traces; fixed point operators; premonoidal categories; recursion; monads.; Freyd category; Conway operators in Cartesian categories

UR - http://eudml.org/doc/92724

ER -

## References

top- R.S. Bird, Using circular programs to eliminate multiple traversals of data. Acta Informatica21 (1984) 239-250. Zbl0551.68017
- P. Bjesse, K. Claessen, M. Sheeran and S. Singh, Lava: Hardware design in Haskell, in International Conference on Functional Programming (1998).
- S.L. Bloom and Z. Ésik, Axiomatizing schemes and their behaviors. J. Comput. Syst. Sci.31 (1985) 375-393. Zbl0613.68013
- S.L. Bloom and Z. Ésik, Iteration Theories. EATCS Monographs on Theoretical Computer Science, Springer-Verlag (1993). Zbl0773.03033
- V.E. Cazanescu and Gh. Stefanescu, A general result on abstract flowchart schemes with applications to the study of accessibility, reduction and minimization. Theor. Comput. Sci.99 (1992) 1-63 . Zbl0770.68037
- K. Claessen and D. Sands, Observable sharing for functional circuit description, in Asian Computing Science Conference (1999).
- J.H. Conway, Regular Algebra and Finite Machines. Chapman Hall (1971). Zbl0231.94041
- R.L. Crole and A.M. Pitts, New foundations for fixpoint computations: FIX-hyperdoctrines and the FIX-logic. Inf. Comput.98 (1992) 171-210. Zbl0763.03031
- L. Erkök, Value Recursion in Monadic Computations. Ph.D. thesis, Oregon Graduate Institute, OHSU (October 2002). Zbl1011.68017
- L. Erkök, J. Launchbury and A. Moran, Semantics of value recursion for monadic input/output. RAIRO Theoret. Informatics Appl.36 (2002) 155-180. Zbl1011.68017
- Z. Ésik, Axiomatizing iteration categories. Acta Cybernet.14 (1999). Zbl0959.68059
- Z. Ésik, Group axioms for iteration. Inf. Comput.148 (1999) 131-180 Zbl0924.68143
- D.P. Friedman and A. Sabry, Recursion is a computational effect. Technical Report 546, Computer Science Department, Indiana University (December 2000).
- C. Fuhrmann, A. Bucalo and A. Simpson, An equational notion of lifting monad. Theor. Comput. Sci.294 (2003) 31-60 . Zbl1022.18003
- J.-Y. Girard, Towards a geometry of interaction, in Categories in Computer Science and Logic, edited by J.W. Gray and A. Scedrov. Contemp. Math.92 (1989) 69-108.
- M. Hasegawa, Models of Sharing Graphs (A Categorical Semantics of Let and Letrec). Distinguished Dissertations in Computer Science, Springer-Verlag (1999).
- M. Hasegawa, The uniformity principle on traced monoidal categories, edited by R. Blute and P. Selinger. Elsevier, Electronic Notes in Theor. Comput. Sci. (2003). Zbl1270.18019
- J. Hughes, Generalising monads to arrows. Sci. Comput. Program.37 (2000) 67-112 . Zbl0954.68034
- M. Hyland and A.J. Power, Symmetric monoidal sketches, in Proc. of the 2nd Conference on Principles and Practice of declarative Programming (2000) 280-288. Zbl1271.68185
- A. Jeffrey, Premondoidal categories and a graphical view of programs. (June 1998). URIhttp://www.cogs.susx.ac.uk/users/alanje/premon/
- A. Joyal, R. Street and D. Verity, Traced monoidal categories. Math. Proc. Cambridge Philoso. Soc.119 (1996). Zbl0845.18005
- J. Launchbury and L. Erkök, Recursive monadic bindings, in International Conference on Functional Programming (2000). Zbl1321.68151
- J. Launchbury, J.R. Lewis and B. Cook, On embedding a microarchitectural design language within Haskell. International Conference on Functional Programming (1999).
- J. Launchbury and S.L. Peyton Jones, State in Haskell. Lisp and Symbolic Computation8 (1995) 293-341.
- E. Moggi, Notions of computation and monads. Inf. Comput.93 (1991) 55-92. Zbl0723.68073
- E. Moggi and A. Sabry, An abstract monadic semantics for value recursion, in Proc. of the 2003 Workshop on Fixed Points in Computer Science (April 2003). Zbl1089.68029
- P.S. Mulry, Strong monads, algebras and fixed points, in Applications of Categories in Computer Science, edited by M.P. Fourman, P.T. Johnstone and A.M. Pitts. LMS Lecture Notes177 (1992) 202-216. Zbl0797.18005
- R. Paterson, A new notation for arrows, in Proc. of the International Conference on Functional Programming. ACM Press (September 2001). Zbl1323.68147
- R. Paterson, Arrows and computation, in The Fun of Programming, edited by J. Gibbons and O. de Moor. Palgrave (2003) 201-222.
- A.J. Power and E.P. Robinson, Premonoidal categories and notions of computation. Math. Struct. Comput. Sci.7 (1997) 453-468. Zbl0897.18002
- A.J. Power and H. Thielecke, Closed Freyd and $\kappa $-categories. International Conference on Automata, Languages and Programming (1999). Zbl0938.03026
- A.K. Simpson and G.D. Plotkin, Complete axioms for categorical fixed-point operators, in Proc. of 15th Annual Symposium on Logic in Computer Science. IEEE Computer Society (2000).
- P. Wadler, The essence of functional programming, in Proc. of the 19th Symposium on Principles of Programming Languages. ACM (1992).

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.