Questions tagged [agda]

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5
votes
0answers
126 views

An axiom for John Major's Equality

In the the standard library of Coq, there is the axiom: Axiom JMeq_eq : forall (A:Type) (x y:A), JMeq x y -> x = y. Why isn't it provable? Can it be reduced ...
4
votes
1answer
195 views

Can a term on normal form prove an illogical assertion?

Suppose we take a language such as Agda and disable the features that make it consistent; for example, universe polymorphism, structural recursion checks and similar. Suppose then that we take a term ...
7
votes
1answer
517 views

Is Church-pentation implementable in Agda?

Inspired by suggestion in this question, I've implemented predicative Church encoding of Peano arithmetic. Exponentiation works fine, unfortunately tetration requires the level of one of the arguments ...
1
vote
0answers
184 views

Is it possible to type Ackermann function with (stratified variant of) System F?

I was surprised to find no open-source implementation of Ackermann function in pure System F as an illustrative example. I finally managed to implement it myself in Haskell using Church encoding: <...
2
votes
1answer
99 views

Is there a formalization of normalization of impredicative system F?

In particular Agda seems not strong enough to prove that. Is the predicative Calculus of Inductive Constructions universes (Coq without Prop) sufficient? How about with the impredicative Prop?
8
votes
2answers
198 views

How can you build a coinductive memoization table for recursive functions over binary trees?

The StreamMemo library for Coq illustrates how to memoize a function f : nat -> A over the natural numbers. In particular when ...