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(-) [+]
line wrap: on
line diff
Binary file cfopm.pdf has changed
--- 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}