1. Project Overview
Cat.js is a lightweight, state-of-the-art engine designed to build powerful User Interfaces (UIs). It prioritizes the highest performance and efficiency, based exclusively on modern native browser APIs, primarily Web Components.

- Version: 0.1.0 (as of October 1, 2024)

2. Core Concepts and Principles
- Utilizes modern native browser APIs, especially Web Components
- Focuses on maximum performance and efficiency
- Promotes a lightweight approach to UI development
- Emphasizes simplicity and ease of use

3. Technical Details

Key Features
- Client-Side Compiler (CSC) before loading the DOM
- Attachment through a script:src tag in the head of HTML documents
- Written in vanilla, low-level JavaScript optimized for browser runtime
- Beautiful and easy-to-use syntax
- Efficient project tree structure
- 0 dependencies, neither of Cat.js after compilation. 

Implementation Details
- No Virtual DOM or similar abstractions
- Avoids use of bundlers, node modules, Webpack, polyfills, etc.
- Discourages writing HTML or CSS code within JavaScript files
- Eliminates render methods for components and logic that trigger unnecessary reflows and repainting

4. Code

```

// cat.js

// Immediately Invoked Function Expression (IIFE) to encapsulate the engine
(function() {
  'use strict';

  /**
   * Internal module for tracking loaded files.
   */
  const Registry = (function() {
    const loadedFiles = new Set();

    return {
      isFileLoaded: (path) => loadedFiles.has(path),
      markFileAsLoaded: (path) => loadedFiles.add(path),
    };
  })();

  /**
   * Compiler module for generating self-contained component classes.
   */
  const Compiler = (function() {
    /**
     * Compiles the component's template and script into a component class definition.
     * @param {string} name - The name of the component (e.g., 'my-component').
     * @param {string} templateContent - The inner HTML of the component's <template>.
     * @param {string} scriptContent - The content of the component's <script>.
     * @returns {Function} - A function that defines and registers the component.
     */
    function compileComponent(name, templateContent, scriptContent) {
      // Process the templateContent here, parse it into DOM nodes, and find bindings.

      // Create a template element
      const templateElement = document.createElement('template');
      templateElement.innerHTML = templateContent;

      // Now, process the template content to find bindings
      const bindings = []; // Array to hold binding info
      const propertyNames = new Set();

      const processNode = (node) => {
        if (node.nodeType === Node.TEXT_NODE) {
          const text = node.textContent;
          const parts = text.split(/(\{|\})/);
          let hasBinding = false;

          // Collect variable names inside { }
          for (let i = 0; i < parts.length; i++) {
            if (parts[i] === '{' && parts[i + 2] === '}') {
              const varName = parts[i + 1].trim();
              propertyNames.add(varName);
              hasBinding = true;

              i += 2; // Skip over the { varName }
            }
          }

          if (hasBinding) {
            bindings.push({
              type: 'text',
              nodePath: getNodePath(node),
              varNames: getVariableNamesFromParts(parts),
              parts: parts,
            });
          }
        } else if (node.nodeType === Node.ELEMENT_NODE) {
          if (node.nodeName.toLowerCase() === 'style') {
            // Do not process the content of style tags
            return;
          }

          // Process attributes
          for (let attr of Array.from(node.attributes)) {
            const value = attr.value;
            const parts = value.split(/(\{|\})/);
            let hasBinding = false;

            // Collect variable names inside { }
            for (let i = 0; i < parts.length; i++) {
              if (parts[i] === '{' && parts[i + 2] === '}') {
                const varName = parts[i + 1].trim();
                propertyNames.add(varName);
                hasBinding = true;

                i += 2; // Skip over the { varName }
              }
            }

            if (hasBinding) {
              bindings.push({
                type: 'attribute',
                nodePath: getNodePath(node),
                attributeName: attr.name,
                varNames: getVariableNamesFromParts(parts),
                parts: parts,
              });
            }
          }

          // Process child nodes
          node.childNodes.forEach(childNode => {
            processNode(childNode);
          });
        }
      };

      // Helper function to get the path to a node
      const getNodePath = (node) => {
        const path = [];
        let current = node;
        while (current !== templateElement.content) {
          const parent = current.parentNode;
          const index = Array.prototype.indexOf.call(parent.childNodes, current);
          path.unshift(index);
          current = parent;
        }
        return path;
      };

      // Helper function to extract variable names from parts
      const getVariableNamesFromParts = (parts) => {
        const varNames = [];
        for (let i = 0; i < parts.length; i++) {
          if (parts[i] === '{' && parts[i + 2] === '}') {
            varNames.push(parts[i + 1].trim());
            i += 2; // Skip over the { varName }
          }
        }
        return varNames;
      };

      // Start processing from templateElement.content
      templateElement.content.childNodes.forEach(node => processNode(node));

      // Precompute propertyNames
      const properties = Array.from(propertyNames);

      // Generate the ComponentClass
      class ComponentClass extends HTMLElement {
        constructor() {
          super();
          const shadowRoot = this.attachShadow({ mode: 'open' });

          // Clone the template content into the shadowRoot
          shadowRoot.appendChild(templateElement.content.cloneNode(true));

          // Map from property name to array of bindings
          this._bindingsMap = {};

          // Setup bindings
          this._bindings = this._createBindings(shadowRoot);

          // Initialize properties and their setters/getters
          properties.forEach(varName => {
            this._defineReactiveProperty(varName);
            this[varName] = ''; // Initialize property
          });

          // Execute user script in the context of 'this' safely
          if (scriptContent.trim()) {
            try {
              const scriptFunction = new Function(scriptContent);
              scriptFunction.call(this);
            } catch (error) {
              console.error(`Error executing script in component ${name}: ${error.message}`);
            }
          }
        }

        _createBindings(shadowRoot) {
          const instanceBindings = [];

          bindings.forEach(binding => {
            const node = getNodeByPath(shadowRoot, binding.nodePath);

            // Create a copy of the binding for this instance
            const instanceBinding = Object.assign({}, binding);
            instanceBinding.node = node;

            // For each varName in the binding, add the binding to _bindingsMap
            instanceBinding.varNames.forEach(varName => {
              if (!this._bindingsMap[varName]) {
                this._bindingsMap[varName] = [];
              }
              this._bindingsMap[varName].push(instanceBinding);
            });

            instanceBindings.push(instanceBinding);
          });

          return instanceBindings;
        }

        _defineReactiveProperty(varName) {
          let value = '';
          Object.defineProperty(this, varName, {
            get: () => value,
            set: newValue => {
              value = newValue;
              this._updateProperty(varName);
            },
          });
        }

        _updateProperty(varName) {
          const bindings = this._bindingsMap[varName];
          if (bindings) {
            bindings.forEach(binding => {
              if (binding.type === 'text') {
                const newText = this._computeBindingText(binding);
                binding.node.textContent = newText;
              } else if (binding.type === 'attribute') {
                const newValue = this._computeBindingText(binding);
                binding.node.setAttribute(binding.attributeName, newValue);
              }
            });
          }
        }

        _computeBindingText(binding) {
          const computedParts = [];
          for (let i = 0; i < binding.parts.length; i++) {
            if (binding.parts[i] === '{' && binding.parts[i + 2] === '}') {
              const varName = binding.parts[i + 1].trim();
              computedParts.push(this[varName]);
              i += 2; // Skip over { varName }
            } else if (binding.parts[i] !== '{' && binding.parts[i] !== '}') {
              computedParts.push(binding.parts[i]);
            }
          }
          return computedParts.join('');
        }

        connectedCallback() {
          // Component is connected to the DOM
          // Any additional initialization can be done here
        }

        disconnectedCallback() {
          // Clean up if necessary
        }
      }

      // Helper function to get node by path
      function getNodeByPath(root, path) {
        let current = root;
        path.forEach(index => {
          current = current.childNodes[index];
        });
        return current;
      }

      return function() {
        customElements.define(name, ComponentClass);
      };
    }

    return {
      compileComponent,
    };
  })();

  /**
   * Internal module for loading and parsing HTML files.
   */
  const Loader = (function() {
    /**
     * Loads an HTML file from the given path.
     * @param {string} path - The path to the HTML file (without .html extension).
     * @returns {Promise<string>} - A promise that resolves to the content of the HTML file.
     */
    async function loadFile(path) {
      const fullPath = `${path}.html`;

      try {
        const response = await fetch(fullPath);
        if (!response.ok) {
          throw new Error(`Failed to load: ${fullPath} (Status: ${response.status})`);
        }
        const content = await response.text();
        return content;
      } catch (error) {
        console.error(error.message);
        throw error;
      }
    }

    /**
     * Parses an HTML string into a Document object.
     * @param {string} htmlString - The HTML string to parse.
     * @returns {Document} - The parsed Document object.
     */
    function parseHTML(htmlString) {
      const parser = new DOMParser();
      const doc = parser.parseFromString(htmlString, 'text/html');
      return doc;
    }

    return {
      loadFile,
      parseHTML,
    };
  })();

  /**
   * Global load function.
   * @param {string} path - The path to the HTML file (without .html extension).
   * @returns {Promise<void>}
   */
  window.load = async function(path) {
    console.log(`Loading: ${path}`);

    if (Registry.isFileLoaded(path)) {
      console.log(`Already loaded: ${path}`);
      return;
    }

    try {
      const responseText = await Loader.loadFile(path);
      const doc = Loader.parseHTML(responseText);

      Registry.markFileAsLoaded(path);

      // Extract the <template> with the 'name' attribute
      const template = doc.querySelector('template[name]');
      if (!template) {
        console.error(`No <template name="..."> found in ${path}.html`);
        return;
      }

      const componentName = template.getAttribute('name');
      const templateContent = template.innerHTML;

      // Extract the <script> content
      const script = doc.querySelector('script');
      const scriptContent = script ? script.textContent : '';

      // Use compiler to generate and define the component
      const defineComponent = Compiler.compileComponent(componentName, templateContent, scriptContent);

      // Execute the function to define the component
      defineComponent();

      console.log(`Component registered: ${componentName}`);
    } catch (error) {
      console.error(`Error loading component from ${path}: ${error.message}`);
    }
  };
})();

```

5. Sample component:

```
<!-- app/comp/counter.html -->
<template name="my-counter">
    <style>
        .on {
            background-color: blue;
        }
        .off {
            background-color: aliceblue;
        }
        .btn {
            padding: 20px;
        }
    </style>

    <button class="{status} btn">Count: {count}</button>
</template>

<script>
    this.count = 0;
    this.status = 'on';
    
    const button = this.shadowRoot.querySelector('button');
    const span = button.querySelector('span');

    const component = this; // To maintain correct context inside functions

    function updateCount() {
        component.count++;

        component.status = component.status === 'on' ? 'off' : 'on';
        // The reactive system will automatically update the DOM elements where {count} and {status} are used
    }

    button.addEventListener('click', updateCount);
</script>
```

Your first task it's updating the compiler to be a Build-time compiler, instead of a Runtime compiler. Important points, our compiler won't affect the JavaScript of a component, only if the component make use of a dynamic / reactive value, there our compiler compiles the native JavaScript highly efficient logic that make possible such behavior. Creating highly optimized, lightweight components that can work perfectly without any type of dependency, neither from cat.js after compilation.

Provide the cat.js with the implementations.