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I've heard of nuPRL, it seems to be also based on type theory, with special emphasis on constructivity. It's basically the same as Coq, foundationally. At a sum

I've heard of nuPRL, it seems to be also based on type theory, with special emphasis on constructivity. It's basically the same as Coq, foundationally. At a summer school Bob Constable once said that he would refuse to fly in a plane with software which had been verified formally using classical logic, instead of constructive logic... Well, I wouldn't mind an intuitionistic verification, but I'd definitely take even "just" a classical one.

mbrodersen 4y ago
No it is actually quite different. nuPRL starts with an untyped programming language and you then prove that an untyped expression has a certain behaviour. The behaviour is called a Type but it is fundamentally a very different idea from Martin Loff type theory (IMHO). They do say that it is MLTT, and in principle they are right, but MLTT is as powerful as set theory so that is true of anything mathematically. LEAN for example supports non-constructive mathematics. But it is still based on a type theory. Anyways … YouTube has a great talk about the ideas: https://www.youtube.com/watch?v=LE0SSLizYUI https://www.youtube.com/watch?v=LE0SSLizYUI