Questions tagged [dependent-types]

An overlapping feature of type theory and type systems.

9 questions with no upvoted or accepted answers
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Extensional constructs in minimal extensional type theory without eta equality

The extensional version of Intuitionistic Type Theory is usually formulated in a way that makes extensional concepts like functional extensionality derivable. In particular, equality reflection, ...
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Can we simulate any dependent datatype with `Eq`?

Consider the canonical homogeneous equality type: Eq : (A : Set) -> A -> A -> Set, with constructor ...
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49 views

Are there any interesting terms in pure LF or $\lambda\Pi$?

In my searching, I've seen that if Church numerals are encoded in a dependently typed Lambda calculus, that we can't derive induction or that $0 \neq 1$. I know that LF and the dependently typed ...
2
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Dependent types as regular expressions

Would be possible to encode dependent types as regular expressions? if so, ¿is there some work about? It's common to represent restrictions for elements in a traversable data structure with them, ...
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Test cases for subtyping with dependent types

I implemented a simple type system inside Agda and I'm trying to understand, how expressive it is. The system consists from a predicative hierarchy of universes in the style of Russell, natural ...
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DML , ML with restricted dependent types

Refering to this paper Dependent ML: An Approach to Practical Programming with Dependent Types Have defined datatype 'alist ( int ) Its not clear why they have used int as a parameter rather than a ...
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Representing inductive types

I implemented dependently typed lambda calculus in the spirit of this article: http://www.andres-loeh.de/LambdaPi/LambdaPi.pdf The calculus, works and I experimented with it and like it. However, I ...
0
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1answer
73 views

Is it possible to interpret some Martin-Löf types as abelian monoids in such a way that any abelian monoid can be represented as a type?

For instance, I can interpret the unit type as the trivial monoid with one element. Non-dependent pairs $A \times B$ can be interpreted as the direct sum $A ⊕ B$ when $A$ and $B$ can both be ...
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Type inference and Type checking

I understand that adding the annotations (dependent typing) may cause the type checking of the programming language to become undecidable. What about type inference ? Whether type checking and type ...