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Computation, Proof, Machine by Marion Roman, Pierre Guillot, Gilles Dowek

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Chapter Nine Intuitionistic Type Theory

IT WOULD NOT BE UNTIL THE EARLY 1970S that the axiomatic method would be challenged. Then, surprisingly enough, it was called into question simultaneously and independently in several branches of mathematics and computer science. Few of the main players in this episode in the history of mathematics were aware that they were pursuing the same aim, within logic as researchers pushed forward the work of their predecessors on constructivity, within computer science, and within “real-world” mathematics. This chapter will focus on logic.

Intuitionistic Type Theory

In the late sixties, many breakthroughs sparked a revival of interest in constructivity. On one hand, the algorithmic interpretation of proofs was ...

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