Book of programming problems

Complexity (1-100): 90

Translate a program on the programming language Beta to the equivalent program on the programming language Psi.

Beta language syntax & semantics

A Beta program consists of a sequence of operators, each on separate line of text, and each starting with a natural number - a label, - in the range [1;10000]. All labels are different and in ascending order. An operator is separated from its label with spaces.

A variable name consists of one or more latin letters (no more than 8 letters), case-insensitive. Variable names should differ from keywords.

Program starts with the first operator, the last operator in the program should be END.

Variable, constant and intermediate values are integer and ranged from -32768 to 32767. At the start, all variables are set to 0.

A program may contain any number of spaces between its lexemes, but it does not contain empty lines.

Operators of Beta language:

Operator	Syntax	Semantic
Assignment	variable=expression	an expression is an arithmetic formula consisting of variable names, constants, parenthesis, and operations +, -, *. The operator assigns a value of the expression to the left-hand variable.
Jump	WALKTO label	Continues execution of the program from the given label. The label is constant and cannot contain expressions.
Conditional	IF condition THEN assignment or jump	A condition is a couple of expressions, divided by one of the relation operations =, <, >, and <>. The operator checks the condition, and, if its true, executes the operator after THEN in the same line.
Output	TYPE expression	Prints the expression value starting from a new line.
Ending operator	END	Always comes at the end of a program and stops the program execution.

Psi language syntax & semantics

A Psi program consists variable definitions and a body. Variable definitions starts with the keyword DEF, followed by variable names used in the body.Variable names are divided by comma and cannot repeat. Definitions end with a semicolon.

The program body consists of an operator sequence, enclosed in keywords START and FINISH. Operators are separated by a semicolon.

The notion of variable, constant, expression, and condition are the same as in Beta.

A Psi program can contain empty lines and extra spaces. Variable values at the start are random.

Operators of Psi language:

Operator	Syntax	Semantic
Assignment	variable:=expression	Assigns a value of the expression to the left-hand variable.
Conditional	IF condition THEN operator; ...;operator; FI	Checks the condition, and, if its true, executes one or more operators between THEN and FI
Output	PRINT expression	Prints the expression value starting from a new line.
Loop	WHILE condition DO operator; ...;operator; OD	Executed one or more operators between DO and OD while the condition is true.

An example of translation

    Beta program                     an equivalent Psi program

  10 N=5                           DEF N, Var, C;
  20 SUM=SUM+N                     START
  35 N=N-1                          Var := 0; c := 1;
  40 IF N>0 THEN WALKTO 20          WHILE c < 6 DO
  70 TYPE Sum                        IF c=1 THEN N:= 5; c:=c+1; FI;
  999 END                            IF c = 4 THEN Var:=Var+N; c:=c+1; FI;
                                     IF c=4 THEN
                                       c:=c+1;
                                       IF N>0 THEN c:=2; FI;
                                     FI;
                                     IF c=5 THEN Print (Var);
                                     c:=c+1;
                                     FI;
                                    OD;
                                   FINISH

Note. The input text is always syntactically correct and contains no more than 100 lines with up to 80 characters in each line.