Data

Compare relations

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

S[STATUS=20]
SNOSNAMESTATUSCITY


S1Smith20London


S4Clark20London


S[CITY="London"]
SNOSNAMESTATUSCITY


S1Smith20London


S4Clark20London

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)
attrtype


CITYstr


SNAMEstr


SNOstr


STATUSint

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)
attrtype


SNOstr

Cardinality

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

count(S[STATUS=20])
2

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))
4

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.