universe-0.4.0.4: Classes for types where we know all the values

Data.Universe.Helpers

Synopsis

# Documentation

This module is for functions that are useful for writing instances, but not necessarily for using them (and hence are not exported by the main module to avoid cluttering up the namespace).

universeDef :: (Bounded a, Enum a) => [a]Source

For many types, the `universe` should be `[minBound .. maxBound]`; `universeDef` makes it easy to make such types an instance of `Universe` via the snippet

``` instance Universe Foo where universe = universeDef
```

interleave :: [[a]] -> [a]Source

Fair n-way interleaving: given a finite number of (possibly infinite) lists, produce a single list such that whenever `v` has finite index in one of the input lists, `v` also has finite index in the output list. No list's elements occur more frequently (on average) than another's.

diagonal :: [[a]] -> [a]Source

Unfair n-way interleaving: given a possibly infinite number of (possibly infinite) lists, produce a single list such that whenever `v` has finite index in an input list at finite index, `v` also has finite index in the output list. Elements from lists at lower index occur more frequently, but not exponentially so.

(+++) :: [a] -> [a] -> [a]Source

Fair 2-way interleaving.

(+*+) :: [a] -> [b] -> [(a, b)]Source

Slightly unfair 2-way Cartesian product: given two (possibly infinite) lists, produce a single list such that whenever `v` and `w` have finite indices in the input lists, `(v,w)` has finite index in the output list. Lower indices occur as the `fst` part of the tuple more frequently, but not exponentially so.

choices :: [[a]] -> [[a]]Source

Slightly unfair n-way Cartesian product: given a finite number of (possibly infinite) lists, produce a single list such that whenever `vi` has finite index in list i for each i, `[v1, ..., vn]` has finite index in the output list.

unfairCartesianProduct :: [a] -> [b] -> [(a, b)]Source

Very unfair 2-way Cartesian product: same guarantee as the slightly unfair one, except that lower indices may occur as the `fst` part of the tuple exponentially more frequently. This mainly exists as a specification to test against.

unfairChoices :: [[a]] -> [[a]]Source

Very unfair n-way Cartesian product: same guarantee as the slightly unfair one, but not as good in the same sense that the very unfair 2-way product is worse than the slightly unfair 2-way product. Mainly for testing purposes.