Update readme.

Author: rudlorenz

README.md

@@ -16,7 +16,8 @@ https://github.com/rudlorenz/mathParser
 ```
 
 To use Expressions in your project add src folder with `add_subdirectory()` command to your `CmakeLists.txt` file and
-include `Expressions.h` and `Parser.h` in source files.
+include `Expression.h` and `Parser.h` in source files.
+Cmake will automatically fetch gtest and fmt library. 
 
 Alternatively you can use supplied `main.cpp`.
 
@@ -26,51 +27,76 @@ Parsing expression from string:
 
 ```c++
 #include <Parser.h>
+#include <fmt/core.h>
 
-auto result = parser::parse("x + y");
-if (result != nullptr) {
-    std::cout << "result : " << result->to_string();
+std::optional<mexpr::Expression> result = parser::parse("x + y");
+if (!result.has_value()) {
+    fmt::print(stderr, "Something wrong!");
+    return 0;
 }
+
+fmt::print(stdout, "input : {}\n", result->to_string());
+fmt::print(stdout, "as expressions : {}\n", result->to_expr_string());
 ```
 
 Parse expression from string and find derivative:
 
 ```c++
 #include <Parser.h>
 
-auto result = parser::parse("x * x + 2*x + 10");
-if (result != nullptr)
-{
-    auto derivative = result->diff("x");
-    std::cout << "expression : " << result->to_string() << "\n"
-        << "derivative : " << derivative->to_string(); 
+std::optional<mexpr::Expression> result = parser::parse("x * x + 2*x + 10");
+if (!result.has_value()) {
+    fmt::print(stderr, "Something wrong!");
+    return 0;
 }
+
+fmt::print(stdout, "input : {}\n", input);
+fmt::print(stdout, "as expressions : {}\n", result->to_expr_string());
+fmt::print(stdout, "d/dx : {}\n", result->diff("x").to_string());
 ```
 
 Calls are chainable:
 
 ```c++
 auto result = parser::parse("x*x*y + x*y*y");
-auto as_string = result != nullptr
-    ? result->diff(x)->diff(y)->to_string();
+auto as_string = result
+    ? result->diff(x).diff(y).to_string();
+    : "empty"; 
 ```
 
 You can create expressions directly, but it's highly discouraged:
 
 ```c++
 #include "Expressions.h"
-    // x * x + y
-    auto var_x = std::make_shared<Variable>("x");
-    auto var_y = std::make_shared<Variable>("y"); 
-    auto result = std::make_shared<Sum>(
-        std::make_shared<Mul>(var_x, var_x),
-        var_y
-    );
+using namespace mexpr;
+
+// x * x + y
+auto var_x = Expression{"x"};
+auto var_y = Expression{"y"};
+auto two_expr = Expression{2};
+auto var_x_squared = Expression{
+    binary_expr_type::mul,
+    var_x.clone(),
+    var_x.clone(),
+}
+auto result = Expression{
+    binary_expr_type::sub,
+    Expression{
+        binary_expr_type::sum,
+        std::move(var_x_squared),
+        std::move(var_y)
+    },
+    std::move(two_expr)
+}
 ```
 
 ## TODO
 
 1. Unit testing.
-2. Proper lexical and synax analysis i.e. input expression validation. Right now it works "garbage in --> garbage out".
+2. ~~Proper lexical and syntax analysis i.e. input expression validation. Right now it works "garbage in --> garbage out".~~
 3. Expression simplification.
-4. Proper parser errors.
+4. ~~Proper parser errors.~~
+5. More unit tests.
+6. POW operation.
+7. Check for proper "unary" function parsing.
+8. Expression evaluation.