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Asked: 2026-05-20T01:06:12+00:00

I am given a bunch of expressions in prefix notation in an ANSI text

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I am given a bunch of expressions in prefix notation in an ANSI text file. I would like to produce another ANSI text file containing the step-by-step evaluation of these expressions. For example:

- + ^ x 2 ^ y 2 1

should be turned into

t1 = x^2
t2 = y^2
t3 = t1 + t2
t4 = t3 - 1
t4 is the result

I also have to identify common subexpressions. For example given

expression_1: z = ^ x 2
expression_2: - + z ^ y 2 1
expression_3: - z y

I have to generate an output saying that x appears in expressions 1, 2 and 3 (through z).

I have to identify dependecies: expression_1 depends only on x, expression_2 depends on x and y, etc.

The original problem is more difficult than the examples above and I have no control over the input format, it is in prefix notation in a much more complicated way than the above ones.

I already have a working implementation in C++ however it is a lot of pain doing such things in C++.

What programming language is best suited for these type problems?

Could you recommend a tutorial / website / book where I could start?

What keywords should I look for?

UPDATE: Based on the answers, the above examples are somewhat unfortunate, I have unary, binary and n-ary operators in the input. (If you are wondering, exp is an unary operator, sum over a range is an n-ary operator.)

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1 Answer

  1. Editorial Team

    The problem consists of two subproblems: parsing and symbolic manipulation. It seems to me the answer boils down to two possible solutions.

    One is to implement everything from scratch: “I do recommend creating the full expression tree if you want to retain maximum flexibility for handling tricky cases.” – proposed by Rex. As Sven points out: “any of the high-level languages you listed are almost equally suited for the task,” however “Python (or any of the high-level languages you listed) won’t take away the complexity of the problem.”
    I have received very nice solutions in Scala (many thanks for Rex and Daniel), a nice little example in Python (from Sven). However, I am still interested in Lisp, Haskell or Erlang solutions.

    The other solution is to use some existing library/software for the task, with all the implied pros and cons. Candidates are Maxima (Common Lisp), SymPy (Python, proposed by payne) and GiNaC (C++).

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