Compare relations

We can compare relations. Since the restrict operation returns a relation, we can compare two filtered results.

S[STATUS=20]

SNO SNAME STATUS CITY

S1 Smith 20 London
S4 Clark 20 London

SNO	SNAME	STATUS	CITY
S1	Smith	20	London
S4	Clark	20	London

S[CITY="London"]

SNO SNAME STATUS CITY

S1 Smith 20 London
S4 Clark 20 London

SNO	SNAME	STATUS	CITY
S1	Smith	20	London
S4	Clark	20	London

The equality comparison, using = will return true for this case.

S[STATUS=20] = S[CITY="London"]

true

We can also test whether one relation is a subset of another, using <=. This symbol is meant to resemble the subset symbol, ⊆ (which you can use instead, if your keyboard can create it).

S[STATUS=20] <= S[CITY="London"]

true

S[STATUS=20] <= S

true

S[STATUS=20] <= S[STATUS=30]

false

There is also a superset operator: >= (or ⊇). And there are pure subset and pure superset operators (i.e. excluding the cases when both are equal): < and > (or ⊂ and ⊃)

Heading

We can use the heading function to get the set of attributes for a relation.

heading(S)

attr type

CITY str
SNAME str
SNO str
STATUS int

attr	type
CITY	str
SNAME	str
SNO	str
STATUS	int

And because this returns a relation we can do further operations on it. For example, to find the common attributes in S and SP:

heading(S) & heading(SP)

attr type

SNO str

attr	type
SNO	str

Using heading with no parameter will return the heading for the current scope, i.e. each local variable plus globals (which includes persisted relvars for the current schema).

heading()

attr type

Constraint {name:str,rule:str}
P {PNO:str,PNAME:str,COLOR:str,WEIGHT:int,CITY:str}
S {SNO:str,SNAME:str,STATUS:int,CITY:str}
SP {SNO:str,PNO:str,QTY:int}
error {message:str}

attr	type
Constraint	{name:str,rule:str}
P	{PNO:str,PNAME:str,COLOR:str,WEIGHT:int,CITY:str}
S	{SNO:str,SNAME:str,STATUS:int,CITY:str}
SP	{SNO:str,PNO:str,QTY:int}
error	{message:str}

Cardinality

We can count how many tuples are in a relation using count().

count(S[STATUS=20])

We can check if a relation has no tuples using empty().

empty(dee)

false

empty(dum)

true

Degree

We can count how many attributes are in a relation using count and heading.

count(heading(S))

Quantification

We can add a boolean attribute to a relation (or use an existing one). Then we can use the all or exists (or ∀ or ∃ if your keyboard can create them) operators to check if all or any tuples have the attribute set true.

exists(S{*, test:=(STATUS=20)}, test)

true

all(S{test:=(STATUS=20)})

false

all(S{test:=(STATUS<100)})

true

exists and all should be more efficient than counting filtered matches since they can short-circuit and finish early without necessarily checking all the tuples.