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README.md
NimKalc  A math parsing library
NimKalc is a simple implementation of a recursivedescent topdown parser that can evaluate mathematical expressions.
Disclaimer: This library is in beta and is not fully tested yet. It will be soon, though. If you find any bugs or issues, please report them so we can fix them and make a proper test suite!
Features:
 Support for the following mathematical constants:
pi
tau
(pi * 2)e
(Euler's number)inf
(Infinity)nan
(Not a number)
 Support for the following of nim's math library functions:
sin
cos
tan
sinh
tanh
cosh
arccos
arcsin
arctan
arcsinh
arccosh
arctanh
hypot
sqrt
cbrt
log10
log2
ln
log
 Parentheses can be used to enforce different precedence levels
 Easy API for tokenization, parsing and evaluation of AST nodes
Note: Some procedures were not implemented because for any of the following reasons:
 They return booleans or other custom types that we don't support, like
classify
 They weren't useful enough or their functionality was already implemented in other ways (such as
pow
which we use as the^
operator)  They just haven't made their way into the library yet, be patient!
Current limitations
 No equationsolving (coming soon)
How to use it
NimKalc parses mathematical expressions following this process:
 Tokenize the input
 Generate an AST
 Visit the nodes
Each of these steps can be run separately, but for convenience a wrapper eval
procedure has been defined which takes in a string
and returns a single AST node containing the result of the given expression.
Supported operators
Beyond the classical 4 operators (+
, 
, /
and *
), NimKalc supports:
%
for modulo division^
for exponentiation unary

for negation
Exceptions
NimKalc defines various exceptions:
NimKalcException
is a generic superclass for all errorsParseError
is used when the expression is syntactically invalidMathError
is used when there is an arithmetical error such as division by 0 or domain errors (e.g.log(0)
)EvaluationError
is used when the runtime evaluation of an expression fails (e.g. trying to call something that isn't a function)
Design
NimKalc treats all numerical values as float
to simplify the implementation of the underlying operators. To tell integers
from floating point numbers the AstNode
object has a kind
discriminant which will be equal to NodeKind.Integer
for ints
and NodeKind.Float
for decimals. It is advised that you take this into account when using the library, since integers might
start losing precision when converted from their float counterpart due to the difference of the two types. Everything should
be fine as long as the value doesn't exceed 2 ^ 53 though.
Note: The string representation of integer nodes won't show the decimal part for clarity
Some other notable design choices (due to the underlying simplicity of the language we parse) are as follows:
 Identifiers are checked when tokenizing, since they're all constant
 Mathematical constants are immediately mapped to their real values when tokenizing with no intermediate steps or tokens
 Type errors (such as trying to call an integer) are detected statically at parse time
String representations
All of NimKalc's objects implement the $
operator and are therefore printable. Integer nodes will look like Integer(x)
, while
floats are represented with Float(x.x)
. Unary operators print as Unary(operator, right)
, while binary operators print as Binary(left, operator, right)
.
Parenthesized expressions print as Grouping(expr)
, where expr
is the expression enclosed in parentheses (as an AST node, obviously).
Token objects will print as Token(kind, lexeme)
: an example for the number 2 would be Token(Integer, '2')
. Function calls print like Call(name, args)
where name
is the function name and args
is a list of arguments
Example
Here is an example of a REPL using all of NimKalc's functionality to evaluate expressions from stdin (can be found at examples/repl.nim
)
import nimkalc
import strformat
import strutils
proc repl() =
## A simple REPL to demonstrate NimKalc's functionality
var line: string
var result: AstNode
var tokens: seq[Token]
let lexerObj = initLexer()
let parserObj = initParser()
let visitor = initNodeVisitor()
echo "Welcome to the NimKalc REPL, type a math expression and press enter"
while true:
try:
stdout.write("=> ")
line = stdin.readLine()
echo &"Parsing and evaluation of {line} below:"
tokens = lexerObj.lex(line)
# Noone cares about the EOF token after all
echo &"Tokenization of {line}: {tokens[0..^2].join(\", \")}"
result = parserObj.parse(tokens)
echo &"AST for {line}: {result}"
result = visitor.eval(result)
case result.kind:
# The result is an AstNode object, specifically
# either a node of type NodeKind.Float or a NodeKind.Integer
of NodeKind.Float:
echo &"Value of {line}: {result.value}"
of NodeKind.Integer:
echo &"Value of {line}: {int(result.value)}"
else:
discard # Unreachable
except IOError:
echo "\nGoodbye."
break
except ParseError:
echo &"A parsing error occurred: {getCurrentExceptionMsg()}"
except MathError:
echo &"An arithmetic error occurred: {getCurrentExceptionMsg()}"
except OverflowDefect:
echo &"Value overflow/underflow detected: {getCurrentExceptionMsg()}"
when isMainModule:
repl()
Note: If you don't need the intermediate representations shown here (tokens/AST) you can just import nimkalc
and use
the eval
procedure, which takes in a string and returns the evaluated result as a primary AST node like so:
import nimkalc
echo eval("2+2") # Prints Integer(4)
Installing
You can install the package via nimble with this command: nimble install nimkalc
Note: Nim 1.2.0 or higher is required to build NimKalc! Other versions are likely work if they're not too old, but they have not been tested