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1answer
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Understanding the definition of Positivity Constraints in Coq

In Interactive Theorem Proving and Program Development the authors explain constraints on constructors of inductive types in Coq. For inductive type $T$, a constructor must have the form $t_1 \...
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1answer
324 views

Type Theory and Principia Mathematica Part IV “Relation Arithmetic”

As type theory is a principle focus of modern computer science, its origins are in Bertrand Russel's theory of types, Principia Mathematica is both the origin of and is expressed in the theory of ...
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Universal/existential quantification?

I'm struggling to understand the purpose of universal and existential quantification of types. I'm playing around with writing a toy language based on the calculus of constructions. I've been reading ...
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1answer
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What is the difference between ∀ and Π in the Calculus of Constructions?

As I've learned, the Calculus of Constructions has only two binders - $\lambda$ and $\Pi$. Morte, for example, has $\forall$ as a mere alias of $\Pi$. Yet, on the paper Self Types for Dependently ...