This simple program is using an edit as input, a button to trigger processing and a memo for output.
I used edit.text as s value and then reverse its value using for command and saved to rs variable.
We compared s and rs to determine that s is palindrom or not.
Here's the code
unit Unit1;
interface
uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls;
type
  TForm1 = class(TForm)
    Edit1: TEdit;
    Memo1: TMemo;
    Button1: TButton;
    procedure proses;
    procedure FormCreate(Sender: TObject);
    procedure Button1Click(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;
var
  Form1: TForm1;
implementation
{$R *.dfm}
procedure tform1.proses;
var s,rs:string;
  i:integer;
  palindrom:boolean;
begin
  memo1.Text:='';
  palindrom:=true;
  s:=edit1.Text;
  for i:=length(s) downto 1 do begin
    rs:=rs+s[i];
  end;
  for i:=1 to length(s) do begin
    if s[i]<>rs[i] then begin
      palindrom:=false;
      break;
    end;
  end;
  memo1.Lines.Append(s);
  memo1.Lines.Append(rs);
  if palindrom=true then
    memo1.Lines.Append('is palindrom')
      else
        memo1.Lines.Append('is not palindrom');
end;
procedure TForm1.FormCreate(Sender: TObject);
begin
  memo1.Text:='';
end;
procedure TForm1.Button1Click(Sender: TObject);
begin
  proses;
end;
end.

 
 

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