Discussion 12: Regular Expressions, BNF, SQL

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Backus-Naur Form (BNF) is a syntax for describing a context-free grammar. It was invented for describing the syntax of programming languages, and is still commonly used in documentation and language parsers. EBNF is a dialect of BNF which contains some convenient shorthands.

An EBNF grammar contains symbols and a set of recursive production rules. In 61A, we are using the Python Lark library to write EBNF grammars, which has a few specific rules for grammar writing.

There are two types of symbols: Non-terminal symbols can expand into non-terminals (including themselves) or terminals. In the Python Lark library, non-terminal symbols are always lowercase. Terminal symbols can be strings or regular expressions. In Lark, terminals are always uppercase.

Consider these two production rules:

numbers: INTEGER | numbers "," INTEGER
INTEGER: /-?\d+/

The symbol numbers is a non-terminal with a recursive production rule. It corresponds to either an INTEGER terminal or to the numbers symbol (itself) plus a comma plus an INTEGER terminal. The INTEGER terminal is defined using a regular expression which matches any number of digits with an optional - sign in front.

This grammar can describe strings like:


And so on, with any number of integers in front.

A grammar should also specify a start symbol, which corresponds to the whole expression being parsed (or the whole sentence, for a spoken language).

For the simple example of comma-separated numbers, the start symbol could just be the numbers terminal itself:

?start: numbers
numbers: numbers "," INTEGER | INTEGER
INTEGER: /-?\d+/

EBNF grammars can use these shorthand notations for specifying how many symbols to match:

EBNF Notation Meaning Pure BNF Equivalent
item* Zero or more items items: | items item
item+ One or more items items: item | items item
Optional item optitem: | item

Lark also includes a few handy features:

  • You can specify tokens to complete ignore by using the ignore directive at the bottom of a grammar. For example, %ignore /\s+/ ignores all whitespace (tabs/spaces/new lines).
  • You can import pre-defined terminals for common types of data to match. For example, %import common.NUMBER imports a terminal that matches any integer or decimal number.

Q1: lambda BNF

We've written a simple BNF grammar to handle lambda expressions. The body of our lambda has to consist of a single expression, which can be a number, word, or another lambda expression.

?start: lambda_expression
lambda_expression:  "lambda " arguments ":" body
arguments: WORD ("," WORD)*
body: expression
?expression: value | lambda_expression
?value: WORD | NUMBER

%import common.WORD
%import common.NUMBER
%ignore /\s+/

For each of the given examples, draw the resulting tree created by this BNF.

lark> lambda x: 5
lark> lambda x, y: x
lark> lambda x: lambda y: x


SQL is an example of a declarative programming language. Statements do not describe computations directly, but instead describe the desired result of some computation. It is the role of the query interpreter of the database system to plan and perform a computational process to produce such a result.

For this discussion, you can test out your code at sql.cs61a.org. The records table should already be loaded in.

Select Statements

We can use a SELECT statement to create tables. The following statement creates a table with a single row, with columns named “first” and “last”:

sqlite> SELECT "Ben" AS first, "Bitdiddle" AS last;

Given two tables with the same number of columns, we can combine their rows into a larger table with UNION:

sqlite> SELECT "Ben" AS first, "Bitdiddle" AS last UNION
...> SELECT "Louis", "Reasoner";

We can SELECT specific values from an existing table using a FROM clause. This query creates a table with two columns, with a row for each row in the records table:

sqlite> SELECT name, division FROM records;
Alyssa P Hacker|Computer
Robert Cratchet|Accounting

The special syntax SELECT * will select all columns from a table. It’s an easy way to print the contents of a table.

sqlite> SELECT * FROM records;
Alyssa P Hacker|Computer|Programmer|40000|Ben Bitdiddle
Robert Cratchet|Accounting|Scrivener|18000|Eben Scrooge

We can choose which columns to show in the first part of the SELECT, we can filter out rows using a WHERE clause, and sort the resulting rows with an ORDER BY clause. In general the syntax is:

SELECT [columns] FROM [tables]
WHERE [condition] ORDER BY [criteria];

For instance, the following statement lists all information about employees with the “Programmer” title.

sqlite> SELECT * FROM records WHERE title = "Programmer";
Alyssa P Hacker|Computer|Programmer|40000|Ben Bitdiddle
Cy D Fect|Computer|Programmer|35000|Ben Bitdiddle

The following statement lists the names and salaries of each employee under the accounting division, sorted in descending order by their salaries.

sqlite> SELECT name, salary FROM records
...> WHERE division = "Accounting" ORDER BY salary desc;
Eben Scrooge|75000
Robert Cratchet|18000

Note that all valid SQL statements must be terminated by a semicolon (;). Additionally, you can split up your statement over many lines and add as much whitespace as you want, much like Scheme. But keep in mind that having consistent indentation and line breaking does make your code a lot more readable to others (and your future self)!



Let's write a BNF grammar that describes SELECT statements in SQL. Your grammar should support the following:

  • selecting one or more columns from a single table
  • an optional WHERE clause
  • any number of additional AND clauses if a WHERE clause is present
  • the WHERE and AND clauses only need to support comparisons between column(s) and numbers

The SQLite documentation actually uses BNF via railroad diagrams, which are a way of representing the grammar. Check out the diagram for a complete SELECT statement on the SQLite site here.

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SQL Queries

For the following questions, you will be referring to the records table:

Name Division Title Salary Supervisor
Alyssa P Hacker Computer Programmer 40000 Ben Bitdiddle
... ... ... ... ...

Q3: Oliver Employees

Write a query that outputs the names of employees that Oliver Warbucks directly supervises.

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Q4: Self Supervisor

Write a query that outputs all information about employees that supervise themselves.

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Q5: Rich Employees

Write a query that outputs the names of all employees with salary greater than 50,000 in alphabetical order.

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Regular Expressions

Q6: Email Domain Validator

Create a regular expression that makes sure a given string email is a valid email address and that its domain name is in the provided list of domains.

An email address is valid if it contains letters, number, or underscores, followed by an @ symbol, then a domain.

All domains will have a 3 letter extension following the period.

Hint: For this problem, you will have to make a regex pattern based on the inputs domains. A for loop can help with that.

Extra: There is a particularly elegant solution that utilizes join and replace instead of a for loop.

Note: The skeleton code is just a suggestion; feel free to use your own structure if you prefer.

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