my reading list

It would be interesting to keep a reading list, logging what I have read.

Category:
        Basic_Category_Theory_for_Computer_Scientists_-_B._Pierce

        Categories for the working mathematician
        A Gentle Introduction to Category Theory —
                the calculational approach — Maarten M. Fokkinga
                Better read Topoi before read this.  A little bit hard as a tutorial,
                but his calculation approach is unique and clear.

        Computational Category Theory - D.E.Rydeheard
                Implementation Category in ML.

        Conceptual_Mathematics_-_A_First_Introduction_to_Categories

        Topoi - the categorial analysis of logic. Robert GoldBlatt. (Great book )
                     Best introduction book. From this book, I begin to understand why category was invented.

Pointfree, Program algebra
        an introduction to the Bird Meertens formalism
        Law and Order in Algorithmics. Maarten M. Fokkinga (Great)

Math:
        Linear Algebra . Jim Hefferon. (Great)

Haskell:
        Arrow and compuation. Ross Paterson

(2009 Nov 12)
Motivation : combinator completeness
        The Church-Turing Thesis
                http://plato.stanford.edu/entries/church-turing/
        Combinatory logic
                http://plato.stanford.edu/entries/logic-combinatory/
                It's quite long, but at least, there is an algorithm to convert from lambda to point-free.

        http://plato.stanford.edu/entries/recursive-functions/
               This means : with

• zero(x) = 0, 
• inc(x) = x+1, 
• Prj(i, x1,x2,x3...) = xi , and function composition:
•  ƒ(x₁,…,x_n) = g(h₁(x₁,…,x _n), … , h_m(x₁,…,x _n))

       we can build a whole class of functions, which is supposed to all Turn-machine calculable.

Thus point-free is complete.

Automatic Theorem Prover : Prover9, ACL2,
Logic for application : Anil Nerode

REST:
http://www.ics.uci.edu/~fielding/pubs/dissertation/fielding_dissertation.pdf

To read:
        Designing and Using Combinators: The Essence of Functional Programming
                http://www.cs.chalmers.se/~rjmh/Combinators/
        Algebra, abstract algebra, universal algebra, topological algebra, algebras
        constructive mathematics
        intuition mathematics