Yes, that's exactly what the objective of this book is! I am not using computation out of necessity, but rather because I think it provides leverage for understanding the concepts, and learning to (as you say) compose traditional models and build new ones.

As the book comes along, I am finding that many ideas that are hard to explain and understand mathematically can be very easy to express computationally, especially using discrete approximations to continuous distributions.

For example, I just posted a section on ABC

http://www.greenteapress.com/thinkbayes/html/thinkbayes008.h...

that (I think) really demonstrates the strength of this approach.

Of course, my premise only applies for people who are as comfortable with programming as with math, or more so.