You are familiar with equations about real numbers from algebra. For example, you know that, for all real numbers x, y and z,
We can also write equations about lists. Here are a few that are true for all lists x and y.
| 2:[ ] | = | [2] |
| x:[ ] | = | [x] |
| [3, 4, 5] | = | 3:[4, 5] |
| tail([3, 4, 5]) | = | [4, 5] |
| tail(x:y) | = | y |
| head([3, 4, 5]) | = | 3 |
| head(x:y) | = | x |
Suppose that length(x) is the length of list x. Here are some equations about length.
| length([2,4,6]) | = | 3 |
| length([ ]) | = | 0 |
| length(x:y) | = | length(y) + 1 |