complement notes in 10.02

notes/4.md

@@ -83,12 +83,12 @@ L -> S | L,S
 
 It can be represented as a NFA:
 
-```python {cmd matplotlib}
+```python {cmd matplotlib hide}
 import sys
 import pymupdf
 from PIL import Image
 doc = pymupdf.open("../pdf/L4.pdf")
-pix = doc[22].get_pixmap(dpi=500)
+pix = doc[22].get_pixmap(dpi=360)
 img = Image.frombytes("RGB", [pix.width, pix.height], pix.samples)
 
 plt.imshow(img)
@@ -97,8 +97,73 @@ plt.tight_layout()
 plt.show()
 ```
 
-
+* SLR(1) Parsing
-
-
 
 * LR(1) Grammar
+
+
+```python {cmd matplotlib hide}
+import sys
+import pymupdf
+from PIL import Image
+doc = pymupdf.open("../pdf/L4.pdf")
+pix = doc[47].get_pixmap(dpi=360)
+img = Image.frombytes("RGB", [pix.width, pix.height], pix.samples)
+
+plt.imshow(img)
+plt.axis('off')
+plt.tight_layout()
+plt.show()
+```
+
+LR(1) Parsing Table
+
+is same as LR(0) parsing table construction except for reductions:
+
+
+* LALR(1) Grammar
+
+LALR(1) generally has the same number of states as SLR (much less than LR(1))
+for Pascal language, SLR requires several hundred states, LR(1) requires several thousand states.
+
+#### Ambiguous Grammar
+
+Ambiguity is mainly from
+
+* Precedence
+  * The production at higher levels will have operators with lower priorities (and vice versa).
+  * we can insert non-terminals to enforce precendence.
+* Associativity
+  * we should determine where to place recursion depending on the associativity
+
+
+for example: `if-then-else`
+
+
+**Automatic Disambiguation**
+
+We can define precedence to use ambiguous grammars w/o shift-reduce conflicts.
+
+
+## AST
+
+### AST Construction LL
+
+```c
+expr parse_S() {
+    switch(token) {
+        case num:
+        case '(':
+            expr child1 = parse_E();
+            expr child2 = parse_Sp();
+            return new S(child1, child2);
+        default:
+            parseError();
+
+    }
+}
+
+```
+
+### AST Construction LR
+