calculus-solver

Design the structure

Based on our data type, we build the program with some modules. -- Expressions: parse the input string and output the Expression type. -- Laws: -- Match: Match the current expression with the left hand side equation. If they are match, return a substitution list. -- Printer: Print the data types. -- Substitutions: Substitude the right hand side equation with the pairs in Subst. -- Rewrites: Match the expression with the equation then get the new expression according to the law. -- Calculations: Do the calculations and get many steps of the derivition.

Data structures

data UnaryOp = Sin | Cos | Tan | Ln | Neg deriving Show
data BinaryOp = Add | Sub | Mul | Div | Pow | Log deriving Show
data Expression = Con String | Var String | Derivative Expression Expression | SinExpr UnaryOp Expression | BiExpr BinaryOp Expression Expression deriving Show


data Law = Law String Equation
type Equation = (Expression, Expression)
data Step = Step LawName Expression
data Calculation = Calc Expression [Step]

For calculation, we have binary operators like Add(+), Sub(-), Pow(^), etc. We also have unary operators like Sin, Cos, Ln, etc. For inputs with multiple operations like "2*x", we cannot ignore the *s. Otherwise, it will parse as "2x", a variable.

Basic Parsing

We updated the parser using the method in book. This time, we can parse something like "3+4+5". The basic idea is we use 3 helper functions rest, more and powexpr to deal with addOp, mulOp and powOp. And it follows the order from powOp to addOp. This ensures the right order of calculation.
Here is the example for parsing an expression.

Input: parseTest expr "(x, ((3 log x)+6))"
Output: Derivative (Var "x") (BiExpr Add (BiExpr Log (Con 3) (Var "x")) (Con 6))

Run the program

First run the program using

stack run

Then input your question, for example, (x, 2*x). Press the enter and then you can get the steps. Be careful, you cannot use key left, key right. You can only solve one problem in this program.

For unary expressions like sin(x), you need to type as (sin (x)) with the outer brackets.

Reason with configurable rules

how??

Problems / To do

configurable rules: How can we decide the order of the rules?
simplify the result How can can we simplify the result such as "1+2"? --((x ^ 2) * (2 * (1 / x)))
space, seems fixed ??

Bugs fixed

dz x^y
deriv const law
parse input for para in calculate
compatible for multi-variables
pretty print

sjcjoosten/Tyronezzz-calculus-solver