Simple command line equation parser and evaluator written in Scala to practice functional programming in Scala

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The equation parser comes with a simple CLI. To evaluate an expression, run

# start the sbt server
sbt

run "<expression>"

Numbers can be specified as integers (e.g. 42) or decimals (e.g. 1.23) and are evaluated as doubles.

Negative numbers must always be wrapped in parentheses (i.e. write (-42)+2 instead of -42+2).

The following operations are allowed:

+    Addition
-    Difference
*    Multiplication
/    Division
^    Power

You can also use left ( and right ) parentheses. Whitespaces are ignored.

sbt:equation-parser> run "1+2"
3.0

sbt:equation-parser> run "3 * (1 + 2) ^ 7"
6561.0

sbt:equation-parser> run "100 / 8 - (2 * 3) + 4 ^ 3"
70.5

sbt:equation-parser> run "((3 + 2) * (2 + 1)) ^ 2"
225.0

sbt:equation-parser> run "(-42)^3+(-42)"
-74130.0

Evaluating an expression works in two steps:

1. Tokenizing
2. Parsing

The tokenizer converts the raw string into individual tokens. This is quite straightforward and implemented in the Tokenizer.scala.

The parser in turn also works in two stages. Firstly, the list of tokens is converted from infix notation (as put in by the user) to RPN using the Shunting Yard algorithm. Parsing the RPN to the final expression is then straightforward. This is implemented in Parser.scala.

For example, parsing the equation 3+4*2/(1-5)^2^3 creates the following syntax tree.