I'm not going to summarize classic equational reasoning (with it's deep connection to algebraic geometry and whatnot) here in a single HN post ;) I can point you to some classic works/authors in the field, though (and I'm sure some fellow HNers can provide some more): Gauss, Knuth, Bendix, Gröbner, Buchberger, Bachmaier, Euclid, Ganzinger, Davis, Putnam, Robinson, and Colmerauer for Prolog 2. There are also category theory papers relevant to reasoning about data structures, and of course Damas, Hindley, Miller for type theories. The way is the goal here.
>> I'm not going to summarize classic equational reasoning (with it's deep connection to algebraic geometry and whatnot) here in a single HN post ;)
Aw :(
Alright, I'll just chase down some of the references you say. I was going to check out Prolog 2 anyway, after browsing the wikipedia article on Colmerauer a few days ago and seeing a reference to his later work there.
To be a bit more concrete than the grandparent's name soup, I liked this handbook article about unification in theories: Franz Baader and Jörg Siekmann. Unification Theory. In D.M. Gabbay, C.J. Hogger, and J.A. Robinson, editors, Handbook of Logic in Artificial Intelligence and Logic Programming, pages 41-125. Oxford University Press, Oxford, UK, 1994.
