Problem 47

Create custom infix operators for the logical functions from Problem 46. Use the following operator tokens to replace the functions in Problem 46.

.& = and_
.| = or_
/& = nand_
/| = nor_
*| for xor_
.^ for implies
.= for equivalent

Precedence and associativity of custom operators can be set with the keywords infixl, infix, and infixr. See http://elm-lang.org/blog/announce/0.10#infix-operators.

Example

truthTable (\a b -> a .& ( a .| b)) == 
        [ (True, True, True)
        , (True, False, True)
        , (False, True, False)
        , (False, False, False)
        ]
        {--
        a=True  b=True  True
        a=True  b=False True
        a=False b=True  False
        a=False b=False False
        --}

Unit Test

import Html exposing (text)
import List exposing (map)


truthTable : (Bool -> Bool -> Bool) -> List (Bool, Bool, Bool)
truthTable f = 
    -- your implementation goes here
    List.repeat 4 (True, True, f True True)


main =
        text
            (if (test) then
                "Your implementation passed all tests."
             else
                "Your implementation failed at least one test."
            )


test : Bool
test =
        List.all ((==) True)
            [ truthTable (.&) ==
                [ (True, True, True)
                , (True, False, False)
                , (False, True, False)
                , (False, False, False)
                ]
            , truthTable (.|) == 
                [ (True, True, True)
                , (True, False, True)
                , (False, True, True)
                , (False, False, False)
                ]
            , truthTable (/&) == 
                [ (True, True, False)
                , (True, False, True)
                , (False, True, True)
                , (False, False, True)
                ]
            , truthTable (/|) == 
                [ (True, True, False)
                , (True, False, False)
                , (False, True, False)
                , (False, False, True)
                ]
            , truthTable (*|) == 
                [ (True, True, False)
                , (True, False, True)
                , (False, True, True)
                , (False, False, False)
                ]
            , truthTable (.^) == 
                [ (True, True, True)
                , (True, False, False)
                , (False, True, True)
                , (False, False, True)
                ]
            , truthTable (.=) == 
                [ (True, True, True)
                , (True, False, False)
                , (False, True, False)
                , (False, False, True)
                ]
            , truthTable (\a b -> ( a .& ( a .| b))) == 
                [ (True, True, True)
                , (True, False, True)
                , (False, True, False)
                , (False, False, False)
                ]
            ]

Solutions

Solutions