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-[attr]lfs-file filter=lfs diff=lfs merge=lfs -text
-
-*.pdf lfs-file
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+++ b/notes/3.md
@@ -34,8 +34,22 @@ One of the purposes of the compiler is error handling.
 
 ## Parsing
 
-### Top-down Parsing
+* Top-down Parsing
 
 **Recursive Descent Parsing**
 
-### Predictive Parsing
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+by using backtracking
+
+* Predictive Parsing
+
+
+Parsing Table: no need to backtrack.
+
+
+
+### Parser Implement
+
+
+
+
+
diff --git a/notes/4.md b/notes/4.md
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@@ -0,0 +1,104 @@
+# Syntax Anlysis 2
+
+## Bottom-Up Parsing
+
+Bottom-up Parsing is more efficient than Top-down parsing.
+it uses LR grammars: Left-recursive and right-most derivation.
+
+Rely on **Shift-reduce Parsers**.
+
+example:
+
+```c
+E -> T | T + E
+T -> int | int * T | (E)
+```
+
+```c
+// reduce
+int * int + int | T -> int
+int * T + int   | T -> int * T
+T + int         | T -> int
+T + T           | E -> T
+T + E           | E -> T + E
+E               |
+// view as reversed, it seems right-most derivation
+```
+
+### Shift-Reudce Parsing
+
+```c
+E -> T | T + E
+T -> int | int * T | (E)
+```
+
+| Stack       | Input             | Applied Production    |
+| ----------- | ----------------- | --------------------- |
+|             | `int * int + int` | shift                 |
+| `int`       | `* int + int`     | shift                 |
+| `int *`     | `int + int`       | shift                 |
+| `int * int` | `+ int`           | reduce `T -> int`     |
+| `int * T`   | `+ int`           | reduce `T -> int * T` |
+| `T`         | `+ int`           | shift                 |
+| `T +`       | `int`             | shift                 |
+| `T + int`   |                   | reduce `T -> int`     |
+| `T + T`     |                   | reduce `E -> T`       |
+| `T + E`     |                   | reduce `E -> T + E`   |
+| `E`         |                   |                       |
+
+
+**Action Selection Problem**
+Which action should we take?
+when shift, when reduce, which production applied?
+
+#### LR-Style Grammars
+
+* LR(k): left-toright scanning, right most derivation and k symbol lookahead
+
+* LR(0) Grammar
+
+LR(0) indicates grammars that can determine actions without any lookahead: there are no reduce-reduce and shift-reduce conflicts when using **only the symbols in the stack**.
+
+represent shift-reduce parsing using an **NFA**, whose states are production with separator '`.`' on RHS.
+for eample, a production `T -> (E)` has four states: `T -> .(E)`, `T -> (.E)`, `T -> (E.)`, `T -> (E.)`.
+before `.` means already in stack, next item means expecting item.
+plus an additional dummy production `S' -> S$` for a start and end state.
+
+there are two types of transitions between the stats
+- shift transition
+- $\epsilon$ transition:
+
+example:
+
+```
+S -> (L) | id
+L -> LS | L,S
+```
+
+```
+S' -> S$
+S -> (L) | id
+L -> S | L,S
+```
+
+It can be represented as a NFA:
+
+```python {cmd matplotlib}
+import sys
+import pymupdf
+from PIL import Image
+doc = pymupdf.open("../pdf/L4.pdf")
+pix = doc[22].get_pixmap(dpi=500)
+img = Image.frombytes("RGB", [pix.width, pix.height], pix.samples)
+
+plt.imshow(img)
+plt.axis('off')
+plt.tight_layout()
+plt.show()
+```
+
+
+
+
+
+* LR(1) Grammar
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