Use of Tools for Parsing

(構文解析用のツールの詳細)

10th lecture, June 27, 2018

Language Theory and Compilers

http://www.sw.it.aoyama.ac.jp/2018/Compiler/lecture10.html

Martin J. Dürst

Today's Schedule

About last lecture's homework
Summary of last lecture
How to write a grammar:
- Priorities
- Associativity
- Repetition (lists)
- Other constructs
How bison works:
- Different orders of derivation
- LALR parsing
- How to read the .output file
- How to debug bison grammars

Last Lecture's Homework

Deadline is June 28, 2018 (Thursday)

Complete calc.y so that with test.in as an input, it produces test.check

Caution: How to deal with unary MINUS

Summary of Last Lecture

Creating a program with bison and flex needs many steps, so using make is important
The input format for bison is very similar to the input format for flex, but there are also some differences
bison uses attribute grammars to calculate the result of parsing
The attributes are referenced as $$ (left hand side) and $1, $2,... (right hand side) in the C program fragments
Priority and associativity of operators are expressed in the rewriting rules of the grammar

How to Express Priorities

Use a separate nonterminal symbol for each priority level
Write the grammar starting with the lowest priority (outside)
On the right hand side of the rewriting rule for a given priority's nonterminal,
use nonterminals of the same or one level higher priority
How to select names for nonterminals:
- Use mathematical terms (用語): term (項), factor (因子)
- Use the type of operator, or one representative operator
  (shift_expression, mulExpression,...)

How to Express Associativity

Left associative:
- Use the same nonterminal on the left hand side of the rewriting rule and on the right hand side to the left of the operator
- Use the one level higher priority nonterminal to the right of the operator
- (unless this operator is required) Also create a rewriting rule with just the one level higher nonterminal as the right hand side
Right associative:
- Exchange the nonterminals to the right and the left of the operator

How to Express Repetition (Lists)

Example: A list of statements (statementList or statements)
Two rewriting rules are needed
Base rule:
- Repetition of 0 or more times: A rewriting rule with an empty right hand side
- Repetition of 1 or more times: A rewriting rule with a single element (e.g. statement) of the list on the right hand side
Inductive rule:
- Right hand side uses both list and single element nonterminals
- If associativity is important, it determines the order of the two nonterminals
- If associativity is not important, there are two choices:
  - List first: Left recursion; advantage: smaller stack
  - Element first: Right recursion
Examples:
- 0 or more times:
```
things : {}
       | things thing {};
```
- 1 or more times:
  things : thing {} | things thing {};

How to Express Other Constructs (e.g. if statement)

Write as is, carefully distinguishing alternatives and terminal/non-terminal symbols

if_statement : IF OPENPAREN cond CLOSEPAREN statement
             | IF OPENPAREN cond CLOSEPAREN statement
               ELSE statement
;

Grammar Patterns: Repetition

One or more times:

items: items item
     | item 
;

Zero or more times:

items: items item
     |
;

Instead of "items item", "item items" is also possible, but bison's stack may become a problem

Grammar Patterns: Associativity

Left associative:

big_exp: big_exp left_associative_operator small_exp
       | small_exp
;

Right associative:

big_exp: small_exp right_associative_operator big_exp
       | small_exp
;

Grammar Patterns: Priority

(priority is small_exp > middle_exp > big_exp; assuming left associative)

big_exp: big_exp operator middle_exp
       | middle_exp
;
middle_exp: middle_exp operator small_exp
          | small_exp
;

Grammar Patterns: Parentheses

small_exp: open_paren big_exp close_paren
         | literal 
;

Order of Derivation: Leftmost and Rightmost Derivation

With leftmost derivation, the leftmost nonterminal in the syntax tree is always expanded first

With rightmost derivation, the rightmost nonterminal in the syntax tree is always expanded first

Simple example grammar:

E → E '+' T| T T → integer

Example of input: 5 + 7 + 3

Derivation Choices

Different choices may generate:

Different words:
This is necessary to be able to process different inputs
Different syntax trees (same word):
Ambiguous grammar, try to avoid
Different orders (leftmost/rightmost/... derivation; same syntax tree):
Different parsing algorithm

Kinds of Analysis Methods

LL: Read input from the left, use leftmost derivation (used in top-down parsing)
LR: Read input from the left, use rightmost derivation, in reverse order)
LL(1): LL, with one token lookahead
LR(1): LR, with one token lookahead
LALR: A kind of LR (1), used widely in yacc and bison

The labels are also used for grammars:
This grammar is LL(1). ⇔ This grammar can be used with an LL(1) parser.

Understanding `bison`: The `.output` File

bison -v creates a file with extension .output, containing the following interesting details:

[Problems: Unused terminal symbols, conflicts]
Grammar: Numbered rewriting rules; rule number 0 is $accept: start_symbol $end)
Terminals: Numbered terminal symbols; numbers are ASCII codes or ≧256)
Nonterminals, with numbers of rules where they appear
States, with the following information for each state:
- Rewriting rules (. shows current position)
- Terminal symbols (or $default) and the action (shift, reduce, goto) if this symbol is the next symbol in the input
- Nonterminal symbols: goal state of transition after reduction

Understanding `bison`: Debuging

#define YYDEBUG 1 switches on debugging

The output shows how bison works:

A (pushdown) stack is used to store:
- States (of an automaton)
- Already read terminals and reduced nonterminals
The automaton and the next input token decide the action to be taken
There are three possible actions:
- shift: Read a token and put it on the stack (together with a state)
- reduce: Convert some tokens and/or nonterminals on the stack to a single nonterminal using a rewriting rule
  (a reduce action is always followed by a goto to another state)
- accept: Stop processing and accept the input

Conflicts and Ambiguous Grammars

When running bison, it may show some conflicts:
- shift/reduce conflicts: Both shift and reduce are possible; shift is always choosen
- reduce/reduce conflicts: There is more than one way to reduce
bison just chooses one of the selections:
- If this is the right selection, we are fine
  (but we may want to fix the grammar anyway)
- If this is the wrong selection, we need to fix the grammar
Grammar example: E → E '-' E | integer
For 5 - 3 - 7, this grammar allows two interpretations: (5-3) - 7 and 5 - (3-7)

Another Example of Ambiguity

The grammar for if-else is a famous example of ambiguity:

if (...) if (...) ...; else ...;

can be parsed in two ways:

if (...) {
    if (...)  ...;
    else      ...;
}

if (...) {
    if (...)  ...;
}
else  ...;

This creates a shift-reduce conflict.

The first way of parsing is correct (for C), and is choosen by Bison because in a shift-reduce conflict, shift is selected.

Grammar of `bison` Rewriting Rules

rewritingRule → nonterminalSymbol ":" rightHandList ";"
rightHandList → rightHand | rightHand "|" rightHandList
rightHand → symbolList "{" CFragment "}"
symbolList → symbol | symbol symbolList
symbol → nonterminalSimbol | terminalSymbol

How to Combine `flex` and `bison`

In the .y file, list all token types:
%token NUM PLUS ASTERISK ...
In the .y file, define the type of the attributes
#define YYSTYPE int
In the .lex file, define one or more rules for each token type
In the .y file, define the rewriting rules of the grammar
In the .y file, write the program fragments to calculate attribute values
Process (with flex/bison), compile, and test

Advantages and Problems of Bottom-Up Parsing

Advantages:
- No fear of left recursion
- Wider range of grammars
- Automatic creation of parser
Problems:
- Very hard to create parser by hand
- Ambiguity needs attention

Homework: A Calculator for Dates

Deadline: July 12, 2018 (Thursday in two weeks), 19:00

Prepare questions so that you can ask them in next week's lecture!

Where to submit: Box in front of room O-529 (building O, 5th floor)

Format: Submit the files dates.lex and dates.y, A4 using BOTH sides (↓↓, not ↓↑), stapled in upper left if more than one page, NO cover page, NO wrapping lines, legible font size, non-proportional font, portrait (not landscape), formatted (indents,...) for easy visibility, name (kanji and kana) and student number as a comment at the top right

Expand the simple calculator of calc.y to a calculator for dates and time periods (numbers of days).

Data types: dates, number of days, integers
- For dates, use the form yyyy-mm-dd from the flex exercise (no need to check for leap years)
- For number of days, use PnnD (where nn is the number of days; see http://en.wikipedia.org/wiki/ISO_8601#Durations)
A multiplication of a number of days with an integer produces a number of days
Numbers of days can be added/subtracted to/from each other, producing a number of days
A number of days can be added/subtracted to/from a date, producing a date
Subtracting a date from another date produces a number of days
Use the grammar to define priorities and associativities (do NOT use %left, %right,...)
Statements are separated with ;. Print out the result of each statement.

Bonus points (発展問題) for dealing with hours, months, years,...

Hints for Homework

Start from the calc files, but change the file names (including in the makefile)
Use YYSTYPE to define a type that can handle dates, numbers of days, and integers (both in .lex and .y)
Define additional tokens in .y (%token rule)
Write rules for additional tokens in .lex
If you have a shift/reduce or reduce/reduce conflict:
- Check the .output file
- Check using different inputs
Expand your grammar little by little, always carefully testing
Build up your own test file, and expand it together with expansions to the grammar
Create tests that check important aspects of the grammar (priorities, associativity, errors)
Save test outputs and use them for automatic comparison

Glossary

unary (operator): 単項 (演算子)
leftmost derivation: 最左導出
rightmost derivation: 最右導出
reverse order: 逆順
lookahead: 先読み
non-proportional font: 等幅のフォント
number of days: 日数