Klammerausdrücke is a German expression, we keep the German
expression also in the Russian and English versions. A direct English
translation is "bracket expression". `FORTRAN 0 ` was really not called
`FORTRAN 0`, it is just the very first version of Fortran.

The program is given here in Pascal, C and five variants of Fortran. The purpose of this is to show how Fortran has been developed from a cryptical, almost machine-dependent language, into a modern structured high-level programming language.

The final example shows the program in the new programming language F.

program tpk(input,output); (* Pascal program for Unix *) var i : integer; y : real; a : array [0..10] of real; function f (t : real) : real; begin f := sqrt(abs(t)) + 5*t*t*t end; begin for i := 0 to 10 do read(a[i]); for i := 10 downto 0 do begin y := f(a[i]); if y > 400 then writeln(i,' TOO LARGE') else writeln(i,y); end end.This program contains variables of the data types integer and floating-point numbers, and a vector of floating-point numbers. It also contains internal mathematical functions and a function written by the user, both forward and backward loops, a conditional statement and output of both floating-point numbers and characters.

Please note that exponentiation is not included in the Pascal language, therefore

# include <stdio.h> # include <math.h> /* Program TPK in ANSI C */ double f (double t); main() { int i; double y; double a[11]; for ( i = 0; i <= 10; ++i) scanf("%lf", &a[i]); for ( i = 10; i >= 0; i = i -1 ) { y = f(a[i]); if ( y > 400 ) {printf("%d",i); printf(" TOO LARGE\n");} else {printf("%d",i); printf("%lf",y); printf("\n");} } return 0; } /* Function */ double f (double t) { double temp; temp = sqrt(fabs(t)) + 5*pow(t,3); return temp; }The language C had the peculiar property that function calls were normally done in double precision, I have therefore written the whole program in double precision. This is not really necessary, because nowadays you can also use the single precision in most realizations. The exponentiation can be done here with the internal function

*The Fortran inventor John Backus in New Mexico, 1976*

DIMENSION A(11) READ A 2 DO 3,8,11 J=1,11 3 I=11-J Y=SQRT(ABS(A(I+1)))+5*A(I+1)**3 IF (400>=Y) 8,4 4 PRINT I,999. GOTO 2 8 PRINT I,Y 11 STOPPlease note the elegant treatment of the input of the vector A and that the symbol

C THE TPK ALGORITHM C FORTRAN I STYLE FUNF(T)=SQRTF(ABSF(T))+5.0*T**3 DIMENSION A(11) 1 FORMAT(6F12.4) READ 1,A DO 10 J=1,11 I=11-J Y=FUNF(A(I+1)) IF(400.0-Y)4,8,8 4 PRINT 5,I 5 FORMAT(I10,10H TOO LARGE) GOTO 10 8 PRINT 9,I,Y 9 FORMAT(I10,F12.7) 10 CONTINUE STOP 52525This was the first programming language with comments. The statement function is used and the backward loop has to be simulated, since a backward loop (negative index) was not permitted, and neither was index zero. The conditional statement is the arithmetical one, with jumps to three different positions depending on whether the arithmetic expression is less than zero, equal to zero or greater than zero. All function names have to end with an

C THE TPK ALGORITHM C FORTRAN IV STYLE DIMENSION A(11) FUN(T) = SQRT(ABS(T)) + 5.)*T**3 READ (5,1) A 1 FORMAT(5F10.2) DO 10 J = 1, 11 I = 11 - J Y = FUN(A(I+1)) IF (400.0-Y) 4, 8, 8 4 WRITE (6,5) I 5 FORMAT(I10, 10H TOO LARGE) GO TO 10 8 WRITE(6,9) I, Y FORMAT(I10, F12.6) 10 CONTINUE STOP ENDAlso here a statement function is being used and the backward loop is still simulated. The structured layout has been used. The notation Fortran 66 started to be used in 1978, previously it was just called Standard FORTRAN or the IBM-notation FORTRAN IV was used also by other vendors.

PROGRAM TPK C THE TPK ALGORITHM C FORTRAN 77 STYLE REAL A(0:10) READ (5,*) A DO 10 I = 10, 0, -1 Y = FUN(A(I)) IF ( Y . LT. 400) THEN WRITE(6,9) I,Y 9 FORMAT(I10. F12.6) ELSE WRITE (6,5) I 5 FORMAT(I10,' TOO LARGE') ENDIF 10 CONTINUE END REAL FUNCTION FUN(T) REAL T FUN = SQRT(ABS(T)) + 5.0*T**3 ENDAlso here a statement function ought be used, but is was not popular at that time, and therefore an external function was being used instead. The backward loop no longer has to be simulated and the conditional statement can be given in a more natural way. Structured layout is now the normal case. The character string can be given within apostrophes so that you no longer have to count manually the number of characters in the character string. The statement

PROGRAM TPK ! The TPK Algorithm ! Fortran 90 style IMPLICIT NONE INTEGER :: I REAL :: Y REAL, DIMENSION(0:10) :: A READ (*,*) A DO I = 10, 0, -1 ! Backwards Y = FUN(A(I)) IF ( Y < 400.0 ) THEN WRITE(*,*) I, Y ELSE WRITE(*,*) I, ' Too large' END IF END DO CONTAINS ! Local function FUNCTION FUN(T) REAL :: FUN REAL, INTENT(IN) :: T FUN = SQRT(ABS(T)) + 5.0*T**3 END FUNCTION FUN END PROGRAM TPKInstead of an external function a local function is now used. The backward loop has not to be simulated. The conditional statement can be given in a more natural way and the symbol < (less than) has returned from Fortran 0. The specifications have a new appearance. Structured layout is used always and all statement numbers have been removed. The character string is given within apostrophes and the standard formats and standard units are used. Comments can be given on the same line as the statement, and comments are now indicated by an exclamation mark ! Implicit specification can (and should) be avoided.

This example is not changed in Fortran 95!

module Functions public :: fun contains function fun(t) result (r) real, intent(in) :: t real :: r r = sqrt(abs(t)) + 5.0*t**3 end function fun end module Functions program TPK ! The TPK Algorithm ! F style use Functions integer :: i real :: y real, dimension(0:10) :: a read *, a do i = 10, 0, -1 ! Backwards y = fun(a(i)) if ( y < 400.0 ) then print *, i, y else print *, i, " Too large" end if end do end program TPK

The new language F has been developed as a possible replacement of Pascal at the teaching of programming, but at the same it is a pure subset of Fortran 90 and Fortran 95.

A free F compiler for Linux is now available.

Keywords are reserved words and are required to be lower case letters,
other identifiers may be mixed. Functions and subroutines are only permitted
via modules. By default all variables have to be declared (the statement
`IMPLICIT NONE ` is therefore implicit, and was previously not permitted explicitly, it is however now optional).
When available, the compiler switch `-u ` is therefore very useful if
you run an F program with a Fortran 90 compiler.

This example is a first attempt at writing in F!

Last modified: 8 January 1997