I’ve already written a fair amount on these topics, and I don’t propose to blog that as I go. If you’d like some background, you might want to look at the following notes of mine:

- Calculating Functional Programs
- Origami Programming
- Design Patterns as Higher-Order Datatype-Generic Programs

Of course, many others have also written on these topics too. Some articles that have particularly inspired me are:

- Richard Bird’s Marktoberdorf notes An Introduction to the Theory of Lists and Lectures on Constructive Functional Programming (which I’m in the process of making electronically available)
- Roland Backhouse’s Exploration of the Bird-Meertens Formalism
- Grant Malcolm’s PhD thesis Algebraic Datatypes and Program Transformation (sadly not online, as far as I know; but his SCP paper is a good approximation)
- Maarten Fokkinga’s and Erik Meijer’s Program Calculation Properties of Continuous Algebras, and (with Ross Paterson) the bananas paper Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire
- Phil Wadler’s papers Theorems for Free! and Monads for Functional Programming
- Richard Bird and Oege de Moor’s book Algebra of Programming
- The AFP notes on Generic Programming, by Roland Backhouse, Patrik Jansson, Johan Jeuring, and Lambert Meertens
- Roland Backhouse and Paul Hoogendijk’s notes on Generic Properties of Datatypes
- Ralf Hinze and Johan Jeuring’s notes on the Practice and Theory and the Applications of Generic Haskell

(I’m sure there are many others too, which I’ve forgotten to mention.)

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Jeremy, I’m very interested in the topic, and your blog it’s a really good and clear source of information. Currently i’m reading “Calculating functional programs”, from the link at the top. I’m stuck with some properties which I cannot understand. The docs says “See Exercise 1.7.5 for the proofs” (for example). I found the exercise, but not the answer, so I want to ask you if the doc is from a book or if can I get the complete text in another way.

Thanks

I’m afraid that what I meant by that comment was that Ex 1.7.5 requires you to complete the proof – it doesn’t give the proof. Sorry! Where are you stuck?

Oh, I see, sorry for the misundestanding. When I wrote my problem explanation, I figured it out. Thanks for your help!. I’ll try to finish this lectures as fast I can, so I’ll able to follow your posts in time.

Thanks again,

Hugo.