How to resolve the algorithm Ternary logic step by step in the Ada programming language
How to resolve the algorithm Ternary logic step by step in the Ada programming language
Table of Contents
Problem Statement
In logic, a three-valued logic (also trivalent, ternary, or trinary logic, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value.
This is contrasted with the more commonly known bivalent logics (such as classical sentential or boolean logic) which provide only for true and false.
Conceptual form and basic ideas were initially created by Łukasiewicz, Lewis and Sulski.
These were then re-formulated by Grigore Moisil in an axiomatic algebraic form, and also extended to n-valued logics in 1945.
Note: Setun (Сетунь) was a balanced ternary computer developed in 1958 at Moscow State University. The device was built under the lead of Sergei Sobolev and Nikolay Brusentsov. It was the only modern ternary computer, using three-valued ternary logic
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Step by Step solution about How to resolve the algorithm Ternary logic step by step in the Ada programming language
Source code in the ada programming language
package Logic is
type Ternary is (True, Unknown, False);
-- logic functions
function "and"(Left, Right: Ternary) return Ternary;
function "or"(Left, Right: Ternary) return Ternary;
function "not"(T: Ternary) return Ternary;
function Equivalent(Left, Right: Ternary) return Ternary;
function Implies(Condition, Conclusion: Ternary) return Ternary;
-- conversion functions
function To_Bool(X: Ternary) return Boolean;
function To_Ternary(B: Boolean) return Ternary;
function Image(Value: Ternary) return Character;
end Logic;
package body Logic is
-- type Ternary is (True, Unknown, False);
function Image(Value: Ternary) return Character is
begin
case Value is
when True => return 'T';
when False => return 'F';
when Unknown => return '?';
end case;
end Image;
function "and"(Left, Right: Ternary) return Ternary is
begin
return Ternary'max(Left, Right);
end "and";
function "or"(Left, Right: Ternary) return Ternary is
begin
return Ternary'min(Left, Right);
end "or";
function "not"(T: Ternary) return Ternary is
begin
case T is
when False => return True;
when Unknown => return Unknown;
when True => return False;
end case;
end "not";
function To_Bool(X: Ternary) return Boolean is
begin
case X is
when True => return True;
when False => return False;
when Unknown => raise Constraint_Error;
end case;
end To_Bool;
function To_Ternary(B: Boolean) return Ternary is
begin
if B then
return True;
else
return False;
end if;
end To_Ternary;
function Equivalent(Left, Right: Ternary) return Ternary is
begin
return To_Ternary(To_Bool(Left) = To_Bool(Right));
exception
when Constraint_Error => return Unknown;
end Equivalent;
function Implies(Condition, Conclusion: Ternary) return Ternary is
begin
return (not Condition) or Conclusion;
end Implies;
end Logic;
with Ada.Text_IO, Logic;
procedure Test_Tri_Logic is
use Logic;
type F2 is access function(Left, Right: Ternary) return Ternary;
type F1 is access function(Trit: Ternary) return Ternary;
procedure Truth_Table(F: F1; Name: String) is
begin
Ada.Text_IO.Put_Line("X | " & Name & "(X)");
for T in Ternary loop
Ada.Text_IO.Put_Line(Image(T) & " | " & Image(F(T)));
end loop;
end Truth_Table;
procedure Truth_Table(F: F2; Name: String) is
begin
Ada.Text_IO.New_Line;
Ada.Text_IO.Put_Line("X | Y | " & Name & "(X,Y)");
for X in Ternary loop
for Y in Ternary loop
Ada.Text_IO.Put_Line(Image(X) & " | " & Image(Y) & " | " & Image(F(X,Y)));
end loop;
end loop;
end Truth_Table;
begin
Truth_Table(F => "not"'Access, Name => "Not");
Truth_Table(F => "and"'Access, Name => "And");
Truth_Table(F => "or"'Access, Name => "Or");
Truth_Table(F => Equivalent'Access, Name => "Eq");
Truth_Table(F => Implies'Access, Name => "Implies");
end Test_Tri_Logic;
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