Archive for January, 2007

Bart Jacobs’ question (FP lunch 19/1/07)

Sunday, January 21st, 2007 by Thorsten

Recently, Bart Jacob’s asked me a question about containers: He is looking for a formula for the derivative of a quotient container. I sketched a possible answer (I haven’t yet checked the details) and used this opportunity to give a quick introduction to containers.

A container is given by a set of shapes and a family of position, giving rise to a functor
given by . It’s derivative as a functor is
. A quotient container is specified by additionally
giving a family of subgroups of the isomorphism group, it gives rise to a functor
where the equivalence relation is generated by for
. I believe that it’s derivative is given by extending the previous formula by additionally specifying
where iff is given by restricting an isomorphim with the property (by restricting I mean that ).

A question about observations

Friday, January 19th, 2007 by Graham

Suppose you are interested in the semantics of effects, such as state, input/output, non-determinism, exceptions, etc. Suppose further that you are interested in small-step operational semantics of effects. Is there a systematic way to determine what the “observations” should be in such semantics, i.e. the actions that label the transitions?