Update documentations.

Add background for sudoku demo for better style in dark mode.

Fix a typo in the documentation.

Remove the architecture ascii graph since it looks not good.

Author: hzhangxyz

docs/examples/Sudoku.vue

@@ -38,6 +38,7 @@
   flex-direction: column;
   align-items: center;
   padding: 20px;
+  background-color: #f0f2f5;
   min-height: 100vh;
   box-sizing: border-box;
 }
@@ -116,7 +117,8 @@ h1 {
 /* 浅色背景宫 */
 .sudoku-grid > div:nth-child(-n + 3) span:nth-child(-n + 3),
 .sudoku-grid > div:nth-child(-n + 3) span:nth-child(n + 7),
-.sudoku-grid > div:nth-child(n + 4):nth-child(-n + 6)
+.sudoku-grid
+  > div:nth-child(n + 4):nth-child(-n + 6)
   span:nth-child(n + 4):nth-child(-n + 6),
 .sudoku-grid > div:nth-child(n + 7) span:nth-child(-n + 3),
 .sudoku-grid > div:nth-child(n + 7) span:nth-child(n + 7) {
@@ -159,7 +161,9 @@ button {
   margin: 0 10px 20px;
   font-size: 1.1em;
   cursor: pointer;
-  transition: background-color 0.3s ease, transform 0.2s ease;
+  transition:
+    background-color 0.3s ease,
+    transform 0.2s ease;
   box-shadow: 0 4px 8px rgba(0, 0, 0, 0.1);
 }
 
@@ -174,14 +178,26 @@ button:active {
   box-shadow: 0 2px 4px rgba(0, 0, 0, 0.1);
 }
 
-button:nth-of-type(1) { background-color: #2ecc71; }
-button:nth-of-type(1):hover { background-color: #27ae60; }
+button:nth-of-type(1) {
+  background-color: #2ecc71;
+}
+button:nth-of-type(1):hover {
+  background-color: #27ae60;
+}
 
-button:nth-of-type(2) { background-color: #f39c12; }
-button:nth-of-type(2):hover { background-color: #e67e22; }
+button:nth-of-type(2) {
+  background-color: #f39c12;
+}
+button:nth-of-type(2):hover {
+  background-color: #e67e22;
+}
 
-button:nth-of-type(3) { background-color: #e74c3c; }
-button:nth-of-type(3):hover { background-color: #c0392b; }
+button:nth-of-type(3) {
+  background-color: #e74c3c;
+}
+button:nth-of-type(3):hover {
+  background-color: #c0392b;
+}
 
 /* ----------------------------------------------
    Log 区域
@@ -196,7 +212,7 @@ h3 {
 textarea {
   width: 80%;
   max-width: 1000px;
-  height: 150px;
+  height: 450px;
   padding: 15px;
   border: 1px solid #ccc;
   border-radius: 8px;

docs/examples/basic.md

@@ -11,7 +11,7 @@ The classic example demonstrates double negation elimination using propositional
 - **Axiom 2**: (P → (Q → R)) → ((P → Q) → (P → R))
 - **Axiom 3**: (¬P → ¬Q) → (Q → P)
 
-Given the premise !!X (double negation of X), we can derive X.
+Given the premise ¬¬X (double negation of X), we can derive X.
 
 === "Python"
 

docs/index.md

@@ -12,20 +12,6 @@ A deductive system for logical inference, implemented in C++. The library provid
 - **WebAssembly**: Run inference in the browser or Node.js environments
 - **Type-Safe**: Strong typing support in TypeScript and Python
 
-## Architecture
-
-```
-┌────────────────────────────────────────────────────────────┐
-│                     Application Layer                      │
-├────────────────────┬────────────────────┬──────────────────┤
-│ TypeScript (atsds) │   Python (apyds)   │    C++ Direct    │
-│   via WebAssembly  │    via pybind11    │                  │
-├────────────────────┴────────────────────┴──────────────────┤
-│                       C++ Core Library                     │
-│                     (include/ds/, src/)                    │
-└────────────────────────────────────────────────────────────┘
-```
-
 ## Quick Links
 
 - **[Installation](getting-started/installation.md)** - Install DS for your preferred language