NB. Relational Database Definitions

first =: {.
rest =: }.
open =: >
box =: <
head =: open@first
rank =: "
bond =: &
link =: ;

NB. A relation is a collection of tuples which we represent as a table.

csg =: ('course';'studentid';'grade');('cs101';12345;'A');('cs101';67890;'B');('ee200';12345;'C');('ee200';22222;'B+');('cs101';333333;'A-');box('ph100';67890;'C+')

NB. In the definition of the relation csg we have 
NB. incorporated additional information attributes (a set of column names called
NB. scheme) at the beginning of our representation for a relation.

head csg NB. course_studentid_grade scheme
rest csg NB. course_studentid_grade relation

NB. The order of tuples in a relation is not significant.
NB. csg2 =:({. csg) , (? ~ <: # csg) { }. csg
NB. is the same relation
NB. The order of columns in a relation is not significant.
NB. csg1 =: 1 2 0 & { &. > csg
NB. csg1 is the same relation
NB. We do assume that column names are distinct.

NB. access column of a relation by name
NB. relation col 'column_name'

col =: dyad def '((head x.) i. box y.) bond from rank 1 open rest x.'

NB. access row of a relation by row_index
NB. relation row row_index

row =: dyad def 'open y. from rest x.'

NB. Some other sample relations.

snap =: ('studentid';'name';'address';'phone');(12345;'C. Brown';'12 Apple St.';'555-1234');(67890;'L. Van Pelt';'34 Pear Ave.';'555-5678');box(22222;'P. Patty';'56 Grape Blvd';'555-9999')

cp =: ('course';'prerequisite');('cs101';'cs100');('ee200';'ee005');('ee200';'cs100');('cs120';'cs101');('cs121';'cs120');('cs205';'cs101');('cs206';'cs121');box('cs206';'cs205')

cdh =: ('course';'day';'hour');('cs101';'M';'9AM');('cs101';'W';'9AM');('cs101';'F';'9AM');('ee200';'Tu';'10AM');('ee200';'W';'1PM');box('ee200';'W';'10AM')

cr =: ('course';'room');('cs101';'Turing Aud.');('ee200';'25 Ohm Hall');box('ph100';'Newton Lab.')

NB. A database is a collection of relations

NB. Problem 1.  Implement relation insert tuple
NB. Problem 2.  Implement relation delete tuple_spec
NB.             where '*' in a tuple_spec means match anything.
NB. Problem 3.  Implement relation lookup tuple_spec
NB.             where '*' in a tuple_spec means match anything.

NB. A key for a relation is a set of one or more attributes such that
NB. under no circumstances will the relation have two tuples whose
NB. values agree in each column headed by a key attribute.

NB. Problem 4.  Devise a solution to the kind of problem "What grade did C. Brown
NB.             receive in cs101?"