4. Simple recursive parser

Now let's see a small example. We will create a parser that can evaluate expressions with additions. That means we only need to recognize one operator, "+".

In the code below you can see that the function Eval calls itself twice by calculating the answers of part1 and part2 of the expression. This is the recursive part of the parser. It does not matter if part1 and part2 are also expressions, in that case the function Eval will be called again and again until the expression is solved. That is when the end of all brances of the expression tree are reached.

Example 1
Recursive expression parser, Example 1.
Written with IBasic Professional
By Jos de Jong, may 2006

Supports expressions with additions
DEF inputexpr:STRING


'print some examples of expressions with their answers
PRINT "Examples:"
PRINT "2 + 3 = ", Eval("2 + 3")
PRINT "2 + 3 + 4 + 5 = ", Eval("2 + 3 + 4 + 5")
PRINT "2.5 + 3.25 = ", Eval("2.5 + 3.25")

PRINT "Enter an expression and press Enter to calculate it."
PRINT "Enter an empty expression to quit"
    'ask the user to enter an expression. After this the expression
    'will be evaluated and the answer will be printed
    INPUT ">>", inputexpr
    IF RTRIM$(inputexpr)<>""
        PRINT "    Ans = ", Eval(inputexpr)
UNTIL RTRIM$(inputexpr)=""

'end the program

SUB Eval(Expression:STRING), DOUBLE
    DEF pos:INT
    DEF expr:STRING
    DEF part1, part2:STRING
    'remove spaces at start and end of the expression
    expr = LTRIM$(RTRIM$(Expression))
    'search for an operator
    pos = INSTR(expr, "+")
    IF pos
        'there is an operator found at position pos. Split up the
        'expression in two parts and calculate the result of that two
        'parts. Then calculate the result for the complete expression.
        part1 = LEFT$(expr, pos-1)
        part2 = RIGHT$(expr, LEN(expr)-pos)
        'calculate the result and return the answer
        RETURN Eval(part1) + Eval(part2)

    'there are no more operators left in the expression. so the
    'expression must be a value. return the value of the expression
    RETURN VAL(expr)

Copyright 2006 SpeQ Mathematics