From Fischer to Haworth

You will turn the pattern of a Fischer projection into the up and down groups of a Haworth ring. Then you will use the specific rotation to find the share of the α form.

The idea. In a D sugar, a group on the right of the Fischer projection points down in the ring, and a group on the left points up. The anomeric $\text{-}\text{OH}$ of an α anomer points down, and that of a β anomer points up. The specific rotation of a mixture is a weighted mean.

Your tasks.

1. Complete direction(side) so that it returns "down" for R and "up" for L.
2. Complete ring(pattern, anomer) so that it returns the directions of the $\text{-}\text{OH}$ groups on C-1, C-2, C-3 and C-4 of a D-pyranose.
3. Complete percent_alpha(rotation) so that it returns the percentage of the α form.