SQL

Tuple Relational Calculus

Description of the data

Relational Algebra

Procedure to retrieve data

Selection

select * from r where

{ R |  r(R)  and    }

{ t | t  r and }

Projection

select distinct A from r

{ R.a_i . . . R.a_j  |  r(R) }
   with a_i . . . a_j    A

{ t.A | t   r }

Union

select * from r
union
select * from s

{T | r(T) or s(T) }

{ t | t   r  or  t   s }

Minus

select * from r
minus
select * from s

{T | r(T) and not s(T) }

{ t | t   r  and  t   s }

Cartesian Product

select * from r, q

{ R,Q | r(R) and q(Q) }

{ t_r t_q | t_r   r and t_q   q  }

Join

select * from p, q where

{ P,Q | p(P) and q(Q) and }

{t_pt_q | t_p  p and t_q   q and }