ladnik / ocalc

A program implemented in the functional programming language OCaml for parsing and evaluating simple arithmetic expressions using a recursive descent parser.

OCalc 🐫

OCalc is a simple program for parsing and evaluating arithmetic expressions like "1+2*3". The calculator works on float values for in- and output.

Supported operations: addition, subtraction, multiplication, division, modulus and exponentiation.

Not supported: unary operations such as -, ! and logical operations such as AND, OR, ..., as well as other useful functions like sin, cos, sqrt, ...

If you have any questions regarding this project or ideas on improving it, feel free to contact me.

Implementation

As the name suggests, OCalc is implemented in the functional programming language OCaml. The algorithm itself consists of three parts:

I. Lexer

The lexer performs a lexical analysis of the input string i.e. it converts the input into a list of tokens and detects syntactically erroneous inputs (indicated by an 'Invalid' token).

It recognizes the following symbols:

• Binary operators: +, -, *, /, %, ^
• Parentheses: (, )
• Values: floating point constants

(% denotes the modulus operator, ^ exponentiation)

II. Parser

The parser takes the output token list of the lexer and converts it to an abstract syntax tree (AST) whilst respecting operator precedence. This is achieved by using a recursive descent parser. [Wikipedia] [craftinginterpreters]. A function to convert the AST to its graphviz representation (viewable with Webgraphviz is provided.

III. Evaluator

Evaluation of the generated abstract syntax tree is the simplest part, it only consists in recursively evaluating all subtrees by replacing the arithmetic operation nodes by their respective function (+), (-), etc. Evaluation will performed with floats.

Usage

To get the correct OCaml environment with utop, OUnit2 and Dune, install opam with your package manager and install the following packages:

opam init --bare
opam switch create 5.0.0
eval $(opam env)
opam install ocaml-lsp-server dune utop ocamlformat ounit2

UTop

To run the program in the toplevel utop, nagivate to the source directory ocalc/ and execute

dune utop

In the toplevel, run

#use "calc.ml";;

After that the following commands are available:

• generate_token_list: Generates the list of lexer tokens from a given string. Signature: string -> float token list
• generate_syntax_tree: Generates the AST from a list of lexer tokens. Signature: float token list -> float expr
• eval_syntax_tree: Evaluates a given AST. Signature: float expr -> float
• eval_string_expr: Evaluates a given string expression, combines the three previously listed commands. Signature: string -> float
• print_ast_to_file: Prints an AST in the graphviz format to the specified file. Signature: string -> float expr -> unit

Dune

With the build system dune installed, an executable can be built from the source as follows: Navigate to the source directory ocalc/ and execute

dune build calc.exe

The executable can be run with

dune exec _build/default/calc.exe

OCaml compiler

To compile the program to a binary, use the ocamlopt compiler:

• Make sure your ocaml libraries are up to date by running the following three commands:

opam update
opam upgrade
eval $(opam env)

• Build the modules:

ocamlopt -c lexer/lexer.ml
ocamlopt -c -I lexer parser/parser.ml
ocamlopt -c -I lexer -I parser -I $(opam var lib)/ounit2 calc.mli
ocamlopt -c -I lexer -I parser -I $(opam var lib)/ounit2 calc.ml

• Link the modules:

ocamlfind ocamlopt -o out -package ounit2 -linkpkg lexer/lexer.cmx parser/parser.cmx calc.cmx

• Run the program:

./out

A pre-built executable can be found here. (TODO)

Examples

• "1+2+3" -> 6.0
• "1+2-3" -> 0.0
• "2/3*3" -> 2.0
• ".0+.1" -> 0.1
• "1.+.1" -> 1.1
• "2^(2-2)" -> 1.0
• "1+1/1+1/2+1/(1*2*3)+1/(1*2*3*4)+1/(1*2*3*4*5)" -> 2.71666666667
• "5%(2*2)" -> 1.0