Problem 46

Define functions to provide the logical binary functions and, or, nand, nor, xor, implies, and equivalent.

    -- True if and only if a and b are true
    and' : Bool -> Bool -> Bool

    -- True if either a or b are true
    or' : Bool -> Bool -> Bool

    -- True either a or b are false
    nand' : Bool -> Bool -> Bool

    -- True if and only if a and b are false
    nor' : Bool -> Bool -> Bool

    -- True if a or b is true, but not if both are true
    xor' : Bool -> Bool -> Bool

    -- True if a is false or b is true 
    implies : Bool -> Bool -> Bool

    -- True if both a and b are true, or both a and b ar false
    equivalent : Bool -> Bool -> Bool

Define a function to show a truth table for a logical expression.

truthTable : (Bool -> Bool -> Bool) -> List (Bool, Bool, Bool)

Unit Test

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


-- True if and only if a and b are true


and_ : Bool -> Bool -> Bool
and_ a b =
    -- your implementation here
    True



-- True if either a or b are true


or_ : Bool -> Bool -> Bool
or_ a b =
    -- your implementation here
    True



-- True either a or b are false


nand_ : Bool -> Bool -> Bool
nand_ a b =
    -- your implementation here
    True



-- True if and only if a and b are false


nor_ : Bool -> Bool -> Bool
nor_ a b =
    -- your implementation here
    True



-- True if a or b is true, but not if both are true


xor_ : Bool -> Bool -> Bool
xor_ a b =
    -- your implementation here
    True



-- True if a is false or b is true


implies : Bool -> Bool -> Bool
implies a b =
    -- your implementation here
    True



-- True if both a and b are true, or both a and b ar false


equivalent : Bool -> Bool -> Bool
equivalent a b =
    -- your implementation here
    True


truthTable : (Bool -> Bool -> Bool) -> List ( Bool, Bool, Bool )
truthTable f =
    -- your implementation goes here
    List.repeat 4 ( True, 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 and_
            == [ ( True, True, True )
               , ( True, False, False )
               , ( False, True, False )
               , ( False, False, False )
               ]
        , truthTable or_
            == [ ( True, True, True )
               , ( True, False, True )
               , ( False, True, True )
               , ( False, False, False )
               ]
        , truthTable nand_
            == [ ( True, True, False )
               , ( True, False, True )
               , ( False, True, True )
               , ( False, False, True )
               ]
        , truthTable nor_
            == [ ( True, True, False )
               , ( True, False, False )
               , ( False, True, False )
               , ( False, False, True )
               ]
        , truthTable xor_
            == [ ( True, True, False )
               , ( True, False, True )
               , ( False, True, True )
               , ( False, False, False )
               ]
        , truthTable implies
            == [ ( True, True, True )
               , ( True, False, False )
               , ( False, True, True )
               , ( False, False, True )
               ]
        , truthTable equivalent
            == [ ( True, True, True )
               , ( True, False, False )
               , ( False, True, False )
               , ( False, False, True )
               ]
        , truthTable (\a b -> (and_ a (or_ a b)))
            == [ ( True, True, True )
               , ( True, False, True )
               , ( False, True, False )
               , ( False, False, False )
               ]
        ]

Solutions

Solutions