Step by Step solution about How to resolve the algorithm Ternary logic step by step in the Haskell programming language

Haskell Code Overview

The provided Haskell code demonstrates various logical operations using a three-valued logic system where truth values are represented as False, Maybe, or True.

Trit Data Type

The code defines a custom data type Trit with three possible values: False, Maybe, and True.

Logical Operations

• not: Negation. Returns True if the input is False, False if the input is True, and Maybe otherwise.
• &&: Conjunction (AND). Returns False if either input is False, Maybe if both inputs are Maybe, and True otherwise.
• ||: Disjunction (OR). Returns True if either input is True, Maybe if both inputs are Maybe, and False otherwise.
• =->: Implication. Returns False if the first input is True and the second is False, Maybe if the first input is Maybe, and True otherwise.
• ==: Equality. Returns True if both inputs are equal, False if they are both different, and Maybe otherwise.

Table Generation

The code generates truth tables for each of the logical operations by combining possible values for the inputs. It uses the inputs1 and inputs2 lists to generate input combinations for unary and binary operations, respectively.

Truth Table Formatting

The table function formats the truth tables as strings. It adds a header row with column labels and pads the values to align them.

Main Function

The main function applies the table function to each logical operation and prints the resulting truth tables.

Sample Input and Output

The provided inputs1 and inputs2 lists represent sample inputs for the truth tables. The output will be a set of truth tables for each logical operation, with the following format:

And so on for the other logical operations.

import Prelude hiding (Bool(..), not, (&&), (||), (==))

main = mapM_ (putStrLn . unlines . map unwords)
    [ table "not"     $ unary not
    , table "and"     $ binary (&&)
    , table "or"      $ binary (||)
    , table "implies" $ binary (=->)
    , table "equals"  $ binary (==)
    ]

data Trit = False | Maybe | True deriving (Show)

False `nand` _     = True
_     `nand` False = True
True  `nand` True  = False
_     `nand` _     = Maybe

not a = nand a a

a && b = not $ a `nand` b

a || b = not a `nand` not b

a =-> b = a `nand` not b

a == b = (a && b) || (not a && not b)

inputs1 = [True, Maybe, False]
inputs2 = [(a,b) | a <- inputs1, b <- inputs1]

unary f = map (\a -> [a, f a]) inputs1
binary f = map (\(a,b) -> [a, b, f a b]) inputs2

table name xs = map (map pad) . (header :) $ map (map show) xs
    where header = map (:[]) (take ((length $ head xs) - 1) ['A'..]) ++ [name]

pad s = s ++ replicate (5 - length s) ' '