I'm attempting to axiomatize a proof-irrelevant disjunction proposition with type elimination in Agda using the universe of proof-irrelevant propositi ...

I'm writing an implementation for a non-deterministic finite state automaton (NFA) which has the goal to accurately convey information about the state ...

If I have these definitions The type of twice is infered to (a -> a) -> a -> a and swap is infered to (a,b) -> (b,a). If I write swap ...

I'm writing Agda code as I read the HoTT book. I'm stuck on Lemma 2.3.9: Type-checking with Adga Emacs Mode gives me the following error: Questi ...

By subtyping, here I mean implicit coercion between types, not sig. In programming languages, sum types have associated data and it matters which var ...

I am trying to understand the apparent paradox of the logical framework of theorem provers like Coq not including LEM yet also being able to construct ...

According the Rustonomicon, &mut T is invariant over T. How can the following code compile when &mut (str, str) is not a subtype of &mut ( ...

I'm new to Haskell, so please forgive if this question is dumb. Imagine that we have two data structures bound to the names x and y. x is mutable. ...

What is the difference between IO (a) and IO a in Haskell? For instance: IO (String) vs IO String IO (Int) vs IO Int Most books I've seen wrap a t ...

I am a bit confused about the name Intersection Types in Typescript. In set theory, intersection would imply that only properties that are common to ...

Can I prove "coinductive principles" about coinductive type? For example, the pseudo code of the coinductive principle for the stream type would look ...

Here are a few simple functions: f1 :: () -> () f1 () = () f2 :: a -> a f2 a = a f3 :: a -> (a, a) f3 a = (a, a) f4 :: (a, b) -> a f4 ...

Consider the type of a function from a's to pairs of b's and c's, a -> (b, c). (I'll use Haskell notation for types and functions, but this isn't a ...

Here I mean axiom as what we can define with the Axiom keyword in Coq Gallina, not with such command-line argument passing to Coq. I know some axioms ...

. Answers to this question are eligible for a +200 reputation bounty. J ...

I'm trying to wrap my head around this blog post about the ConstraintKinds extension. There was a post in the comment section which I totally did not ...

This is a follow-up question of Lean pass type as parameter I tried jmc's suggestion, which seemed to work, but then I got stuck at another point. Th ...

I am trying to do some category theory in Lean. However, I am not yet very fluent in type theory, and the following does not really seem to work: I ...

Are there high-level API/environments/libraries for testing the effectiveness of a particular approach (e.g. heuristic algorithm) for generating const ...

I am pretty new to type inference and was wondering if there are any good extensions or papers out there for HM that allows allowing more than one err ...