# Questions tagged [dependent-types]

An overlapping feature of type theory and type systems.

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### Dependent types vs refinement types

Could somebody explain the difference between dependent types and refinement types? As I understand it, a refinement type contains all values of a type fulfilling a predicate. Is there a feature of ...
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### What makes type inference for dependent types undecidable?

I have seen it mentioned that dependent type systems are not inferable, but are checkable. I was wondering if there is a simple explanation of why that is so, and whether or not there is there a limit ...
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### What can Idris not do by giving up Turing completeness?

I know that Idris has dependent types but isn't turing complete. What can it not do by giving up Turing completeness, and is this related to having dependent types? I guess this is quite a specific ...
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### What are the strongest known type systems for which inference is decidable?

It's well known that Hindley–Milner type inference (the simply-typed $\lambda$-calculus with polymorphism) has decidable type inference: you can reconstruct principle types for any programs without ...
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### Difference between Dependent type , refinement type and Hoare Logic

I know little dependent type theory. From wikipedia : A dependent type is a type whose definition depends on a value. And from my Type theory course i recall that a dependent type is : Family ...
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### if (λ x . x x) has a type, then is the type system inconsistent?

If a type system can assign a type to λ x . x x, or to the non-terminating (λx . x x) (λ x . x x), then is that system ...
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### How to understand equivalence of indexes of a family of types that are not definitionally equal

So I've been reading things about HoTT and trying to get solid on the foundations before getting too much further into the book. I am confused by a certain point; maybe I just haven't read far enough ...
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### Rules for consistency with mutual inductive families?

I'm trying to use a proof assistant to define a type and a relation that are mutually dependent on each other: ...
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