Questions tagged [type-systems]

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Are the types that show monads are more powerful than continuations revealing something of fundamental importance?

In 1992 in the paper Imperative Functional Programming, Simon Peyton Jones and Philip Wadler write: So monads are more powerful than continuations, but only because of the types! It is not clear ...
hawkeye's user avatar
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10 votes
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Stratification of System Fω

I'm wondering if there's any update on this conjecture listed by Urzyczyn from years and years ago (I don't think that's its first appearance), which I'll restate below. System Fω can be stratified ...
ionchy's user avatar
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8 votes
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Denotational semantics of System $F_\omega$ with recursive types and general recursion

Is there a denotational semantics for System $F_\omega$ in literature that supports both recursive types and general recursion? I'm looking for a model of Ralf Hinze's variant of System $F_\omega$ [4]...
Yufei Cai's user avatar
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8 votes
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Decidability of equality between higher-kinded equirecursive types (or: between nonregular Böhm trees)

In §3 of Polytypic values possess polykinded types, Ralf Hinze described a calculus of types with higher-kinded recursive types. There is a fixed-point combinator $$\mu_\kappa : (\kappa \rightarrow \...
Yufei Cai's user avatar
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6 votes
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Programmatic higher inductive/inductive-inductive types with equalities between equalities

I can think of practical HITs in verified software that capture some form of alpha equivalence, context equivalence or the example which defines well-typed syntax of type theory from Signatures and ...
Ilk's user avatar
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5 votes
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258 views

Commonalities and differences between canonical structures and the implicit calculus

There is a paper on The Implicit Calculus as a generalization of type classes. Coq's canonical structures are also a generalization of type classes. The paper does not mention canonical structures ...
Jules's user avatar
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4 votes
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Finite intersection property of polymorphic type families

Let $\Phi$ be a type functor definable in polymorphic lambda calculus: $$ \alpha : * \vdash \Phi(\alpha) : * $$ $$ f : A \to B \vdash \mathsf{Map}^{A,B}_\Phi(f) : \Phi(A) \to \Phi(B)$$ Suppose further ...
Andrew Polonsky's user avatar
4 votes
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Non-objected oriented type theories that can express the $\nu Obj$ calculus

Odersky et al.'s $\nu Obj$ calculus [1] adds just enough dependent typeness on top of object oriented programming to express interfaces that define types (and consequently module systems and other ...
Geoffrey Irving's user avatar
4 votes
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198 views

Type-and-effect systems, stochasticism and effect squelching: how about quicksort?

There's a feature of Haskell's type system which bugs me: you can't implement a randomized sorting algorithm without the use of randomness spilling out into all of its callers. That seems undesirable....
Jonas Kölker's user avatar
3 votes
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Set:Set or Negative Inductives in a Total Language?

In total dependently typed languages, general recursion is forbidden, since this can allow for non-terimination. However, dependently typed language can still describe Turing-complete computations (...
Joey Eremondi's user avatar
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Is System-F with higher-kinded newtypes equivalent in computational power to System-F omega?

If we have System-F with higher-kinded types and newtypes, then we can express everything (I think) of System-F omega, except we have to manually (un)pack. For example: ...
Labbekak's user avatar
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Why use A-normal form in type systems and program verification systems?

In the literature of refinement type systems and program logics, I've observed that many authors choose to confine the programs under consideration to A-normal form. For context, A-normal form ...
yiyuan-cao's user avatar
2 votes
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75 views

Properties of the polymorphic type $\Pi t : * . ((t \to t) \to t) \to t$

In the context of pure type systems (say Calculus of Constructions) I am looking for references discussing the properties of the following polymorphic type: $\Pi t : * . ((t \to t) \to t) \to t$. What ...
Cristian Gratie's user avatar
1 vote
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Can this be formalized as a conversion rule for CoC?

Consider the Church encoding of booleans in CoC $$ Bool := \forall t : * . t \to t \to t \\ T := \lambda t : * . \lambda x : t . \lambda y : t . x \\ F := \lambda t : * . \lambda x: t . \lambda y : t ....
Cristian Gratie's user avatar
1 vote
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194 views

Is Kotlin's type system Turing complete?

Java's type system is Turing complete. For whatever reason, I was under the impression that Kotlin's type system (for concreteness, let's say the latest version of the language -- ...
Nathan BeDell's user avatar
1 vote
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64 views

Effect handlers, arrows and applicatives

After reading Lindley's paper on effect handlers for arrows and applicatives, I got the gist about dynamic and static flow and that it was added to the effect system and so on. However, I do not ...
Jesper Dahl's user avatar
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130 views

Has there been work on formal Semantics for linear algebra?

Could I get some references on formal semantics for a calculus on linear algebra that helps you study matrix or tensor based programming languages? I am looking for anything that encompasses linear or ...
ArtisanV's user avatar
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What does impredicativity mean in substructural and co-intuitionistic logics?

Predicative foundations puts restrictions on power sets and function sets. Entirely apart from the philosophy predicative theories are a lot easier to prove things about and this sounds interesting to ...
Molly Stewart-Gallus's user avatar
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A fundamental question about the proof by induction in session types

I have a question about proof by induction in the domain of session types. Let's assume we have the following lemma: $$ \text{Let}~ \Gamma \vdash P : T. ~~\text{If } P = \mu X. Q ~~\text{then}~~ \...
Coder's user avatar
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