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Diffstat (limited to 'content/zettel/3c3g5.md')
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diff --git a/content/zettel/3c3g5.md b/content/zettel/3c3g5.md new file mode 100644 index 0000000..33f3523 --- /dev/null +++ b/content/zettel/3c3g5.md @@ -0,0 +1,21 @@ ++++ +title = "Update function for operators" +author = "Yann Herklotz" +tags = [] +categories = [] +backlinks = ["3c3g4"] +forwardlinks = ["3c3g6"] +zettelid = "3c3g5" ++++ + +Updating an existing abstract tree with an operation, which has the +following syntax $i =$ `Iop` $p$ $\mathit{op}$ $\vec{r}$ $d$, can then +be implemented as follows, where `Eop` $\mathit{op}$ $\vec{r}$ is the +equivalent abstract expression used in the abstract language. This is +done by using the following update function. + +$$ \upsilon (f, i) \equiv f \# d \leftarrow (f \# d) \oplus_{p} ((\top,\texttt{Eop } \mathit{op}) \otimes_f (\texttt{fold} \otimes_l (f\ \#\#\\vec{r})\ (\top, []))) $$ + +This update function $\upsilon$ will update the correct node in the +abstract evaluation tree with the correct symbolic value, which is a +combination of the original symbolic value and the next. |