Questions tagged [agda]

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8
votes
2answers
223 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 ...
7
votes
1answer
552 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 ...
6
votes
0answers
153 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 ...
5
votes
1answer
254 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 ...
4
votes
1answer
170 views

Small kernel (i.e. proof-verifier) for Agda?

Proof-assistants usually include a lot of machinery that assists in the creation of proofs. The creation process may be unsound without risking the soundness of the proof-assistant if the alleged ...
3
votes
1answer
74 views

Formalization of dependent record types/kinds in MLTT or variant thereof?

Has anyone formalized Pollack's Dependently Typed Records in Type Theory ? Agda would be preferred, but anyone close to MLTT would work. Weaker versions would be fine too, i.e. what Luo dubs '...
2
votes
1answer
106 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?
1
vote
0answers
223 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: <...