Scicalc-rs

Rust crate for parsing and doing calculations with measurements, typically used in scientific contexts.

TODO

Lexing [OK]

Transform a string(i.e. the input as a sequence of characters) into a sequence of tokens, which can then be fed into the parser.

Parsing [OK]

Read a sequence of tokens — which has a linear structure — and transform it into a tree structure.

Evaluating [OK]

Read the tree structure of the expression and fold it, reducing it into it's final value.

Proper error handling [WIP]

don't panic!

Instead of panic!ing, it'd better if the evaluator and the parser returned a Result<...>

Calculator

• Parse and perform basic operations with measurements (DONE)

  • For example, addition (23.0 ± 0.1) + (1.5 ± 0.5)

• Add support for:

• Exponentiation

• Logarithms

• Add support for squareroots, n-th roots and many other functions

Significant figures & Scientific notation

• Parse and verify if a measured quantity has the correct representation, i.e. with corresponding amount of significant figures
• Parse different kinds of scientific notation, such as (23.0E+7 ± 1.0E6), (2.00 ± 0.01)E-10 and 2.00*10^9

Miscellaneous

• Add support for numeric constants with no uncertainty, such as 42, e, π, etc

  • Numeric literals
  • e
  • π

• Add support for the plus-minus digraph('+-' for ±)

BNF grammar for the expressions

      Expression ::= Value | UnaryExpression | BinaryExpression | Grouping
        Grouping ::= "(" Expression ")"
           Value ::= Constant | Number | Measurement
     Measurement ::= Number "±" PosNumber
          Number ::= PosNumber | UnaryMinus PosNumber
       PosNumber ::= (\d+)(\.\d+)?|(\.\d+)
        Constant ::= "e" | "π"
BinaryExpression ::= Expression BinaryOperator Expression
 UnaryExpression ::= UnaryOperator Expression
  BinaryOperator ::= "+" | "-" | "*" | "/" | "^"
   UnaryOperator ::= UnaryMinus
      UnaryMinus ::= "-"

Note: As observed by Pratt's paper on "Top Down Operator Precedence", a Backus-Naur Form(for which BNF is a shorthand) is very inept at capturing the precedence of infix operators. Even then, I still think that specifying a grammar with BNF is useful for providing a quick-and-easy guide, with which you can see the recursive structure of the language at a glance.

Acknowledgements & Further reading

These are some resources that I used to learn about programming language theory, algorithms and their implementations:

• Brief introduction to recursive descent parsing, by Ryan Flannery

• Crafting Interpreters, by Bob Nystrom

• Pratt parsing and precedence climbing are the same algorithm, by Oilshell

• Programming Language Theory, a huge list of resources about PLT maintained by Steven Shaw

• Simple but powerful Pratt parsing, by Aleksey Kladov(matklad)