Overview

Relational Operators

Relational operators take relations as input and produce relations as output.

Category	Operator	Description	Ruby	TS
Selection	restrict	Filter tuples matching a predicate (aka where)	✓	✓
	exclude	Filter tuples NOT matching a predicate	✓	✓
	matching	Semi join (where exists)	✓	✓
	not_matching	Inverse semi join (where not exists)	✓	✓
Projection	project	Keep specified attributes only	✓	✓
	allbut	Remove specified attributes	✓	✓
Joining	join	Natural join on a join key	✓	✓
	left_join	Left join with optional default tuple	✓	✓
	cross_product	Cross product (aka cross_join)	✓	✓
Set Operations	union	Set union	✓	✓
	minus	Set difference	✓	✓
	intersect	Set intersection		✓
Renaming	rename	Rename some attributes	✓	✓
	prefix	Add prefix to attribute names	✓	✓
	suffix	Add suffix to attribute names	✓	✓
Extension	extend	Add computed attributes	✓	✓
	constants	Add constant attributes	✓	✓
	transform	Transform attribute values	✓	✓
Summarization	summarize	Relational summarization (group by + aggregate)	✓	✓
Structuring	group	Create relation-valued attribute from attributes	✓	✓
	ungroup	Flatten relation-valued attributes	✓	✓
	image	Create relation-valued attribute from another relation	✓	✓
	wrap	Wrap attributes into tuple-valued attribute		✓
	autowrap	Structure a flat relation (e.g. split on _)	✓	✓
	unwrap	Merge tuple-valued attributes into parent tuple	✓	✓
Pagination	page	Pagination with explicit ordering	✓

Non-Relational Operators

Non-relational operators take relations as input but produce other values (tuples, arrays, booleans, objects).

Operator	Description	Ruby	TS
one	Extract single tuple from relation		✓
toArray	Convert relation to array (Ruby: to_a)	✓	✓
isEqual	Check set equality of two relations		✓
yByX	Create mapping object from relation (Ruby: y_by_x)	✓	✓

Suppliers and Parts

Some examples for the individual operations available in Bmg use a version of the well-known Suppliers and Parts database. It contains the following four relations:

cities

city	country
London	England
Paris	France
Athens	Greece
Brussels	Belgium

parts

pid	name	color	weight	city
P1	Nut	Red	12.0	London
P2	Bolt	Green	17.0	Paris
P3	Screw	Blue	17.0	Oslo
P4	Screw	Red	14.0	London
P5	Cam	Blue	12.0	Paris
P6	Cog	Red	19.0	London

suppliers

sid	name	status	city
S1	Smith	20	London
S2	Jones	10	Paris
S3	Blake	30	Paris
S4	Clark	20	London
S5	Adams	30	Athens

supplies

sid	pid	qty
S1	P1	300
S1	P2	200
S1	P3	400
S1	P4	200
S1	P5	100
S1	P6	100
S2	P1	300
S2	P2	400
S3	P2	200
S4	P2	200
S4	P4	300
S4	P5	400

Here’s are some examples to illustrate what the relations represent:

• Supplier S1 (Smith) supplies 6 different parts
• There are 2 types of screw, one which weighs 17.0 and the other 14.0 (grams, let’s say)
• There are 2 suppliers in London, 2 in Paris, and 1 in Athens
• Supplier S4 (Clark) has 900 parts in stock, in total
• For the part P5 (Cam), there are 500 items in stock in total, accross all suppliers

Our examples assume the four relations are referenced by variables by the same names: cities, parts, etc.

Get part numbers for all parts supplied by more than one supplier