104 lines
2.6 KiB
Markdown
104 lines
2.6 KiB
Markdown
# Syntax Anlysis 2
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## Bottom-Up Parsing
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Bottom-up Parsing is more efficient than Top-down parsing.
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it uses LR grammars: Left-recursive and right-most derivation.
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Rely on **Shift-reduce Parsers**.
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example:
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```c
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E -> T | T + E
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T -> int | int * T | (E)
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```
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```c
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// reduce
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int * int + int | T -> int
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int * T + int | T -> int * T
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T + int | T -> int
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T + T | E -> T
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T + E | E -> T + E
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E |
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// view as reversed, it seems right-most derivation
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```
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### Shift-Reudce Parsing
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```c
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E -> T | T + E
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T -> int | int * T | (E)
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```
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| Stack | Input | Applied Production |
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| ----------- | ----------------- | --------------------- |
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| | `int * int + int` | shift |
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| `int` | `* int + int` | shift |
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| `int *` | `int + int` | shift |
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| `int * int` | `+ int` | reduce `T -> int` |
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| `int * T` | `+ int` | reduce `T -> int * T` |
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| `T` | `+ int` | shift |
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| `T +` | `int` | shift |
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| `T + int` | | reduce `T -> int` |
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| `T + T` | | reduce `E -> T` |
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| `T + E` | | reduce `E -> T + E` |
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| `E` | | |
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**Action Selection Problem**
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Which action should we take?
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when shift, when reduce, which production applied?
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#### LR-Style Grammars
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* LR(k): left-toright scanning, right most derivation and k symbol lookahead
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* LR(0) Grammar
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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**.
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represent shift-reduce parsing using an **NFA**, whose states are production with separator '`.`' on RHS.
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for eample, a production `T -> (E)` has four states: `T -> .(E)`, `T -> (.E)`, `T -> (E.)`, `T -> (E.)`.
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before `.` means already in stack, next item means expecting item.
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plus an additional dummy production `S' -> S$` for a start and end state.
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there are two types of transitions between the stats
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- shift transition
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- $\epsilon$ transition:
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example:
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```
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S -> (L) | id
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L -> LS | L,S
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```
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```
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S' -> S$
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S -> (L) | id
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L -> S | L,S
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```
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It can be represented as a NFA:
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```python {cmd matplotlib}
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import sys
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import pymupdf
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from PIL import Image
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doc = pymupdf.open("../pdf/L4.pdf")
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pix = doc[22].get_pixmap(dpi=500)
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img = Image.frombytes("RGB", [pix.width, pix.height], pix.samples)
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plt.imshow(img)
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plt.axis('off')
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plt.tight_layout()
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plt.show()
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```
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* LR(1) Grammar |