Difference between revisions of "99 questions/Solutions/46"
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<haskell> |
<haskell> |
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− | -- |
+ | -- NOT negates a single Boolean argument |
not' :: Bool -> Bool |
not' :: Bool -> Bool |
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not' True = False |
not' True = False |
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not' False = True |
not' False = True |
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+ | -- Type signature for remaining logic functions |
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⚫ | |||
and',or',nor',nand',xor',impl',equ' :: Bool -> Bool -> Bool |
and',or',nor',nand',xor',impl',equ' :: Bool -> Bool -> Bool |
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+ | |||
⚫ | |||
and' True True = True |
and' True True = True |
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and' _ _ = False |
and' _ _ = False |
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− | -- True if a or b or both are True |
+ | -- OR is True if a or b or both are True |
or' False False = False |
or' False False = False |
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or' _ _ = True |
or' _ _ = True |
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− | -- |
+ | -- NOR is the negation of 'or' |
nor' a b = not' $ or' a b |
nor' a b = not' $ or' a b |
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− | -- |
+ | -- NAND is the negation of 'and' |
nand' a b = not' $ and' a b |
nand' a b = not' $ and' a b |
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− | -- True if either a or b is |
+ | -- XOR is True if either a or b is True, but not if both are True |
xor' True False = True |
xor' True False = True |
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xor' False True = True |
xor' False True = True |
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xor' _ _ = False |
xor' _ _ = False |
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− | -- True if a implies b, equivalent to (not a) or (b) |
+ | -- IMPL is True if a implies b, equivalent to (not a) or (b) |
impl' a b = (not' a) `or'` b |
impl' a b = (not' a) `or'` b |
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− | -- True if a and b are equal |
+ | -- EQU is True if a and b are equal |
equ' True True = True |
equ' True True = True |
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equ' False False = True |
equ' False False = True |
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</haskell> |
</haskell> |
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− | The |
+ | The above implementations build each logic function from scratch; they could be shortened using Haskell's builtin equivalents: |
<haskell> |
<haskell> |
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</haskell> |
</haskell> |
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− | Some could be reduced even further |
+ | Some could be reduced even further using [[Pointfree]] style: |
<haskell> |
<haskell> |
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</haskell> |
</haskell> |
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− | + | The only remaining task is to generate the truth table; most of the complexity here comes from the string conversion and IO. The approach used here accepts a Boolean function <tt>(Bool -> Bool -> Bool)</tt>, then calls that function with all four combinations of two Boolean values, and converts the resulting values into a list of space-separated strings. Finally, the strings are printed out by mapping <hask>putStrLn</hask> across the list of strings: |
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<haskell> |
<haskell> |
Revision as of 04:07, 18 July 2010
(**) Define predicates and/2, or/2, nand/2, nor/2, xor/2, impl/2 and equ/2 (for logical equivalence) which succeed or fail according to the result of their respective operations; e.g. and(A,B) will succeed, if and only if both A and B succeed.
A logical expression in two variables can then be written as in the following example: and(or(A,B),nand(A,B)).
Now, write a predicate table/3 which prints the truth table of a given logical expression in two variables.
The first step in this problem is to define the Boolean predicates:
-- NOT negates a single Boolean argument
not' :: Bool -> Bool
not' True = False
not' False = True
-- Type signature for remaining logic functions
and',or',nor',nand',xor',impl',equ' :: Bool -> Bool -> Bool
-- AND is True if both a and b are True
and' True True = True
and' _ _ = False
-- OR is True if a or b or both are True
or' False False = False
or' _ _ = True
-- NOR is the negation of 'or'
nor' a b = not' $ or' a b
-- NAND is the negation of 'and'
nand' a b = not' $ and' a b
-- XOR is True if either a or b is True, but not if both are True
xor' True False = True
xor' False True = True
xor' _ _ = False
-- IMPL is True if a implies b, equivalent to (not a) or (b)
impl' a b = (not' a) `or'` b
-- EQU is True if a and b are equal
equ' True True = True
equ' False False = True
equ' _ _ = False
The above implementations build each logic function from scratch; they could be shortened using Haskell's builtin equivalents:
and' a b = a && b
or' a b = a || b
nand' a b = not (and' a b)
nor' a b = not (or' a b)
xor' a b = and' (or' a b) (nand' a b)
impl' a b = or' (not a) b
equ' a b = a == b
Some could be reduced even further using Pointfree style:
and' = (&&)
or' = (||)
equ' = (==)
The only remaining task is to generate the truth table; most of the complexity here comes from the string conversion and IO. The approach used here accepts a Boolean function (Bool -> Bool -> Bool), then calls that function with all four combinations of two Boolean values, and converts the resulting values into a list of space-separated strings. Finally, the strings are printed out by mapping putStrLn
across the list of strings:
table :: (Bool -> Bool -> Bool) -> IO ()
table f = mapM_ putStrLn [show a ++ " " ++ show b ++ " " ++ show (f a b)
| a <- [True, False], b <- [True, False]]
The table function in Lisp supposedly uses Lisp's symbol handling to substitute variables on the fly in the expression. I chose passing a binary function instead because parsing an expression would be more verbose in haskell than it is in Lisp. Template Haskell could also be used :)