Name
Abstract | ||
|---|---|---|
If a monad $T$ is monoidal, then operations on a set $X$ can be lifted canonically to operations on $TX$. In this paper we study structural properties under which $T$ preserves equations between those operations. It has already been shown that any monoidal monad preserves linear equations; affine monads preserve drop equations (where some variable appears only on one side, such as $x\cdot y = y$) and relevant monads preserve dup equations (where some variable is duplicated, such as $x \cdot x = x$). We start the paper by showing a converse: if the monad at hand preserves a drop equation, then it must be affine. From this, we show that the problem whether a given (drop) equation is preserved is undecidable. A converse for relevance turns out to be more subtle: preservation of certain dup equations implies a weaker notion which we call $n$-relevance. Finally, we identify the subclass of equations such that their preservation is equivalent to relevance. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.4230/LIPIcs.MFCS.2020.77 | MFCS |
DocType | Citations | PageRank |
Conference | 0 | 0.34 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Parlant Louis | 1 | 0 | 0.34 |
| Jurriaan Rot | 2 | 104 | 18.53 |
| Silva Alexandra | 3 | 0 | 0.34 |
| Westerbaan Bas | 4 | 0 | 0.34 |