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What's a good introduction to contracts? I'd like to know how a basic contract system works and which extensions are there? What's the relation between contracts and assert?

Provided that to you, a "good introduction" is something with a lambda-calculus extension and a reduction semantics, the 2002 paper by Findler and Felleisen[1] is a good read.

1. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.11....

Thanks, that is exactly what I meant :)

I also found this one quite interesting: http://www.cs.brown.edu/~arjun/public/poly-contracts.pdf

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