Mercurial > hg > Papers > 2015 > atton-lola
changeset 11:079a9829d204
Add monad-laws
author | Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp> |
---|---|
date | Sun, 19 Apr 2015 12:28:46 +0900 |
parents | e1f4ace7c818 |
children | d62cfdf464fe |
files | cfopm.pdf cfopm.tex |
diffstat | 2 files changed, 9 insertions(+), 3 deletions(-) [+] |
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--- a/cfopm.tex Sun Apr 19 12:16:14 2015 +0900 +++ b/cfopm.tex Sun Apr 19 12:28:46 2015 +0900 @@ -144,7 +144,13 @@ Abstractions has many arguments notated by abstraction took a argument, and returns a abstraction that argument numbers has decreased(Currying). Abstractions can be extended using Monad. -Monad is $ triple (T, \eta, \mu) $ satisfies laws(Figure) % TODO :commutative diagram +Monad is $ triple (T, \eta, \mu) $ satisfies laws. + +\begin{itemize} + \item association law : $ {\mu}_{A} \circ {\mu}_{T A} = {\mu}_{A} \circ T {\mu}_{A} $ + \item unity law : $ {\mu}_{A} \circ \eta_{T A} = \mu_{A} \circ T \eta_{A} = id_{T A} $ +\end{itemize} + Various meta computations represents by definition of triple. Monad has another description Kleisli Triple $ (T, \eta, \_^{*}) $. @@ -369,8 +375,8 @@ % (used to reserve space for the reference number labels box) \nocite{agda, opac-b1092711, BarrM:cattcs, Girard:1989:PT:64805, JonesDuponcheel93} -\bibliographystyle{jplain} -\bibliography{reference} +\bibliographystyle{IEEEtran} +\bibliography{IEEEabrv,reference}