# Tagged Questions

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### Interaction-based approximation for HP-complete λ-theory?

We are looking for a proof or counter-examples for the following hypothesis.
Two combinators $M$ and $N$ are solvable and equivalent in the HP-complete sensible $\lambda$-theory iff either
$$
\exists ...

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### Hypothesis: interaction-based model for λKβη

We are looking for a proof or counter-examples to the following
Hypothesis. In interaction calculus $\langle \varnothing\ |\ \Gamma(M, x) \cup \Gamma(N, x)\rangle \downarrow \langle \varnothing\ |\ ...

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### Is it possible to implement η-reduction in interaction nets?

There are several ways to encode λ-terms in interaction nets; for instance, using the original optimal algorithm by Lamping, or compiling λ-calculus into interaction combinators. However, all the ...

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### Optimal Reduction in Interaction Calculus

We work in interaction calculus.
Let $\Sigma = \{\lambda, \psi, \delta, \epsilon\}$, $\text{Ar}(\lambda) = \text{Ar}(\psi) = \text{Ar}(\delta) = 2$, and $\text{Ar}(\epsilon) = 0$.
For any $\alpha ...

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### Turing-complete primitive interaction systems

Let us call primitive an interaction system with the signature
$\Sigma = \{(\rho, 0), (\xi, n)\}, \quad n \geq 2;$
and the only rule being of the form
$\rho \bowtie \xi[\rho, \xi(a_1, \dots , a_n), ...