Express SQL statements in Relational Algebra

select name as "Beer", manf as "Brewer"
from Beers;

Res = rename[Beer,Brewer](Beers)


select * from Bars where addr = 'Coogee'

Res = Sel[addr=Coogee](Bars)


select addr from Bars where addr = 'Coogee'

Res = Proj[addr](Sel[addr=Coogee](Bars))

Tmp = Sel[addr=Coogee](Bars)
Res = Proj[addr](Tmp)


select price from Sells
where bar = 'CBH' and beer = 'New'

Res = Proj[price](Sel[bar=CBH && beer=New](Sells))


select * from Sells
where price = (select price from Sells
               where bar = 'CBH' and beer = 'New')

P = Proj[price](Sel[bar=CBH && beer=New](Sells))
Res = Sel[(price) in P](Sells)

-- Res = Sel[price = P](Sells) (not quite accurate)

select b.name as beer, b.manf as brewer, d.name as drinker
from   Beers b join Likes L on b.name = L.beer
       join Drinkers d on L.drinker = d.name

Tmp1(name,manf,beer,drinker) = Beers join[name=beer] Likes
Tmp0 Rename[dname,addr)(Drinkers)
Tmp2(name,manf,beer,drinker,dname,addr) = Tmp0 join[drinker=dname] Tmp1
Tmp3 = Proj[name,manf,dname](Tmp2)
Res = Rename[beer,brewer,drinker]Tmp3