Fwd: [Haskell-cafe] Newbie: generating a truth table

[Peter Berry]

Sigh, I seem to have done a reply to sender. Reposting to the list.

On 06/02/07, phiroc at free.fr <phiroc at free.fr> wrote:
> Hello,
>
> I would like to create a Haskell function that generates a truth table, for
> all Boolean values, say, using the following "and" function :
>
> and :: Bool -> Bool -> Bool
> and a b = a && b

A fairly old thread, but I had an interesting idea:

> combos :: (Enum a, Enum b) => a -> b -> (a -> b -> c) -> [(a, b, c)]
> combos min1 min2 op = [(x, y, x `op` y) | x <- [min1..],
>                                           y <- [min2..]]

Then:

*Main> combos False (&&)
[(False,False,False),(False,True,False),(True,False,False),(True,True,True)]

In the case of Bool and a few others, you can use a slightly nicer one:

> bCombos :: (Enum a, Bounded a, Enum b, Bounded b) =>
>             (a -> b -> c) -> [(a, b, c)]
> bCombos op = [(x, y, x `op` y) | x <- [minBound..maxBound],
>                                  y <- [minBound..maxBound]]

And:

*Main> bCombos (&&)
[(False,False,False),(False,True,False),(True,False,False),(True,True,True)]

The secret of these is of course in the Enum and Bounded type classes, which
define, respectively,
* enumFrom and enumFromTo (which have syntactic sugar in [foo..] and [foo..bar]
respectively), and
* minBound and maxBound.

You can do the same with any instance of these classes.

-- 
Peter Berry <pwberry at gmail.com>
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