-module(function_relations_test).
-include_lib("eunit/include/eunit.hrl").
-include("operations.hrl").
%%% Function Relations Test Suite
%%%
%%% Testing infinite relations that represent arithmetic operations.
%%% These work like functions but backwards too (Prolog-style)
%%%
%%% - Plus: {(a, b, sum) | sum = a + b }
%%% - Times: {(a, b, product) | product = a * b}
%%% - Minus: {(a, b, difference) | difference = a - b}
%%% - Divide: {(a, b, quotient, remainder) | a = b*quotient + remainder}
function_relations_test_() ->
{foreach,
fun setup/0,
fun cleanup/1,
[
fun test_plus_both_operands_constrained/1,
fun test_plus_a_and_sum_constrained/1,
fun test_plus_b_and_sum_constrained/1,
fun test_plus_only_sum_constrained/1,
fun test_plus_sum_range_constrained/1,
fun test_plus_insufficient_constraints/1,
fun test_times_both_operands_constrained/1,
fun test_times_insufficient_constraints/1,
fun test_minus_both_operands_constrained/1,
fun test_divide_both_operands_constrained/1,
fun test_divide_avoids_zero/1,
fun test_plus_join_with_finite/1,
fun test_materialized_plus_relation/1
]}.
%%% Setup and Cleanup
setup() ->
operations:setup(),
DB = operations:create_database(test_db),
% First set up the basic number types (integers, naturals, etc)
{DB1, _Integers} = operations:create_infinite_relation(DB, #{
name => integers,
schema => #{}, % empty schema - this is a base type
cardinality => aleph_zero,
generator => {primitive, integers}
}),
{DB2, _Naturals} = operations:create_infinite_relation(DB1, #{
name => naturals,
schema => #{},
cardinality => aleph_zero,
generator => {primitive, naturals}
}),
% Now create the function relations - note how their schemas reference the domain relations above
{DB3, _Plus} = operations:create_infinite_relation(DB2, #{
name => plus,
schema => #{a => integers, b => integers, sum => integers},
cardinality => aleph_zero,
generator => {primitive, plus}
}),
{DB4, _Times} = operations:create_infinite_relation(DB3, #{
name => times,
schema => #{a => integers, b => integers, product => integers},
cardinality => aleph_zero,
generator => {primitive, times}
}),
{DB5, _Minus} = operations:create_infinite_relation(DB4, #{
name => minus,
schema => #{a => integers, b => integers, difference => integers},
cardinality => aleph_zero,
generator => {primitive, minus}
}),
{DB6, _Divide} = operations:create_infinite_relation(DB5, #{
name => divide,
schema => #{a => integers, b => integers, quotient => integers, remainder => naturals},
cardinality => aleph_zero,
generator => {primitive, divide}
}),
DB6.
cleanup(_DB) ->
ok.
%%% Plus Relation Tests
test_plus_both_operands_constrained(DB) ->
% Both operands bounded: a ∈ [1,3], b ∈ [2,4]
% TODO: eventually this should be a proper join like Integer[A], Integer[B], Plus[A,B,Sum]
% but for now just pass constraints directly
Iterator = operations:get_tuples_iterator(DB, plus, #{
a => {range, 1, 3},
b => {range, 2, 4}
}),
Results = operations:collect_all(Iterator),
% should get 9 tuples total (3 × 3 = 9)
% like (1,2,3), (1,3,4), (1,4,5), (2,2,4), ..., (3,4,7)
[
?_assertEqual(9, length(Results)),
?_assert(lists:member(#{a => 1, b => 2, sum => 3}, Results)),
?_assert(lists:member(#{a => 2, b => 3, sum => 5}, Results)),
?_assert(lists:member(#{a => 3, b => 4, sum => 7}, Results)),
?_assert(lists:all(fun(#{a := A, b := B, sum := S}) ->
S =:= A + B
end, Results))
].
test_plus_a_and_sum_constrained(DB) ->
% Test reversibility - given A and Sum, compute B
% a ∈ [1,3], sum ∈ [5,7], so b = sum - a
% This is like asking: Plus[A, ?, Sum]
Iterator = operations:get_tuples_iterator(DB, plus, #{
a => {range, 1, 3},
sum => {range, 5, 7}
}),
Results = operations:collect_all(Iterator),
% Expected tuples: (1,4,5), (1,5,6), (1,6,7), (2,3,5), (2,4,6), (2,5,7), (3,2,5), (3,3,6), (3,4,7)
% (filtered to only keep where b >= 0)
[
?_assert(length(Results) > 0),
?_assert(lists:all(fun(#{a := A, b := B, sum := S}) ->
S =:= A + B andalso B >= 0
end, Results)),
?_assert(lists:member(#{a => 1, b => 4, sum => 5}, Results)),
?_assert(lists:member(#{a => 3, b => 4, sum => 7}, Results))
].
test_plus_b_and_sum_constrained(DB) ->
% Another reversibility test - now given B and Sum, find A
% b ∈ [2,4], sum ∈ [5,6] → a = sum - b
% Like: Plus[?, B, Sum]
Iterator = operations:get_tuples_iterator(DB, plus, #{
b => {range, 2, 4},
sum => {range, 5, 6}
}),
Results = operations:collect_all(Iterator),
[
?_assert(length(Results) > 0),
?_assert(lists:all(fun(#{a := A, b := B, sum := S}) ->
S =:= A + B andalso A >= 0
end, Results)),
?_assert(lists:member(#{a => 3, b => 2, sum => 5}, Results)),
?_assert(lists:member(#{a => 2, b => 4, sum => 6}, Results))
].
test_plus_only_sum_constrained(DB) ->
% Only constrain the sum - should give us all ways to add up to 5
% Plus[?, ?, 5] generates: (0,5), (1,4), (2,3), (3,2), (4,1), (5,0)
Iterator = operations:get_tuples_iterator(DB, plus, #{
sum => {eq, 5}
}),
Results = operations:collect_all(Iterator),
[
?_assertEqual(6, length(Results)),
?_assert(lists:member(#{a => 0, b => 5, sum => 5}, Results)),
?_assert(lists:member(#{a => 2, b => 3, sum => 5}, Results)),
?_assert(lists:member(#{a => 5, b => 0, sum => 5}, Results)),
?_assert(lists:all(fun(#{a := A, b := B, sum := S}) ->
S =:= A + B andalso S =:= 5
end, Results))
].
test_plus_sum_range_constrained(DB) ->
% sum in a range [2,3] instead of single value
Iterator = operations:get_tuples_iterator(DB, plus, #{
sum => {range, 2, 3}
}),
Results = operations:collect_all(Iterator),
% For sum=2: (0,2), (1,1), (2,0) → 3 pairs
% For sum=3: (0,3), (1,2), (2,1), (3,0) → 4 pairs
% Total = 7
[
?_assertEqual(7, length(Results)),
?_assert(lists:all(fun(#{sum := S}) -> S >= 2 andalso S =< 3 end, Results)),
?_assert(lists:member(#{a => 0, b => 2, sum => 2}, Results)),
?_assert(lists:member(#{a => 3, b => 0, sum => 3}, Results))
].
test_plus_insufficient_constraints(DB) ->
% Try querying with zero constraints - should fail since we'd get infinite results
Iterator = operations:get_tuples_iterator(DB, plus, #{}),
Result = operations:next_tuple(Iterator),
[
?_assertMatch({error, {unbounded_plus, _}}, Result)
].
%%% Times (multiplication) Tests
test_times_both_operands_constrained(DB) ->
% Basic multiplication with both inputs bounded
Iterator = operations:get_tuples_iterator(DB, times, #{
a => {range, 2, 4},
b => {range, 3, 5}
}),
Results = operations:collect_all(Iterator),
% 3×3 = 9 tuples
[
?_assertEqual(9, length(Results)),
?_assert(lists:member(#{a => 2, b => 3, product => 6}, Results)),
?_assert(lists:member(#{a => 3, b => 4, product => 12}, Results)),
?_assert(lists:member(#{a => 4, b => 5, product => 20}, Results)),
?_assert(lists:all(fun(#{a := A, b := B, product := P}) ->
P =:= A * B
end, Results))
].
test_times_insufficient_constraints(DB) ->
% Times doesn't support full reversibility yet (would need factorization)
% So constraining just one operand should error
Iterator = operations:get_tuples_iterator(DB, times, #{a => {range, 1, 5}}),
Result = operations:next_tuple(Iterator),
[
?_assertMatch({error, {unbounded_times, _}}, Result)
].
%%% Minus (subtraction) Tests
test_minus_both_operands_constrained(DB) ->
% subtraction with both operands bounded
Iterator = operations:get_tuples_iterator(DB, minus, #{
a => {range, 5, 7},
b => {range, 2, 3}
}),
Results = operations:collect_all(Iterator),
% 3 × 2 = 6 tuples
[
?_assertEqual(6, length(Results)),
?_assert(lists:member(#{a => 5, b => 2, difference => 3}, Results)),
?_assert(lists:member(#{a => 7, b => 3, difference => 4}, Results)),
?_assert(lists:all(fun(#{a := A, b := B, difference := D}) ->
D =:= A - B
end, Results))
].
%%% Divide (integer division) Tests
test_divide_both_operands_constrained(DB) ->
% Integer division with quotient and remainder
Iterator = operations:get_tuples_iterator(DB, divide, #{
a => {range, 10, 12},
b => {range, 3, 4}
}),
Results = operations:collect_all(Iterator),
% 3 × 2 = 6 tuples
[
?_assertEqual(6, length(Results)),
?_assert(lists:member(#{a => 10, b => 3, quotient => 3, remainder => 1}, Results)),
?_assert(lists:member(#{a => 12, b => 4, quotient => 3, remainder => 0}, Results)),
?_assert(lists:all(fun(#{a := A, b := B, quotient := Q, remainder := R}) ->
A =:= B * Q + R andalso R >= 0 andalso R < abs(B)
end, Results))
].
test_divide_avoids_zero(DB) ->
% Make sure we don't try to divide by zero
% even if the range includes 0
Iterator = operations:get_tuples_iterator(DB, divide, #{
a => {range, 5, 7},
b => {range, 0, 2}
}),
Results = operations:collect_all(Iterator),
% 3 × 2 = 6 (skips b=0, only uses b=1,2)
[
?_assertEqual(6, length(Results)),
?_assert(lists:all(fun(#{b := B}) -> B =/= 0 end, Results))
].
%%% Integration Tests
test_plus_join_with_finite(DB) ->
% Simulate joining an infinite relation with a finite one
{DB1, _Employees} = operations:create_relation(DB, employees, #{
name => string,
age => integer
}),
{DB2, _} = operations:create_tuple(DB1, employees, #{name => "Alice", age => 30}),
{DB3, _} = operations:create_tuple(DB2, employees, #{name => "Bob", age => 35}),
EmployeeIter = operations:get_tuples_iterator(DB3, employees, #{}),
Employees = operations:collect_all(EmployeeIter),
% For each employee's age, find all the ways to add up to it
% (simulating: Employee JOIN Plus ON Plus.sum = Employee.age)
Results = lists:flatmap(fun(#{age := Age}) ->
PlusIter = operations:get_tuples_iterator(DB3, plus, #{
a => {range, 0, 15},
b => {range, 0, 15},
sum => {eq, Age}
}),
Tuples = operations:collect_all(PlusIter),
[#{age => Age, plus_tuple => T} || T <- Tuples]
end, Employees),
% verify we got some results
[
?_assert(length(Results) > 0),
?_assert(lists:any(fun(#{age := Age, plus_tuple := #{sum := S}}) ->
Age =:= S
end, Results))
].
test_materialized_plus_relation(DB) ->
% Take an infinite relation, constrain it, and materialize into a finite one
PlusIter = operations:get_tuples_iterator(DB, plus, #{
a => {range, 0, 2},
b => {range, 0, 2}
}),
% Turn it into an actual stored relation
{DB1, SmallPlus} = operations:materialize(DB, PlusIter, small_plus),
% check that it worked
ResultIter = operations:get_tuples_iterator(DB1, small_plus, #{}),
Results = operations:collect_all(ResultIter),
[
?_assertEqual({finite, 9}, SmallPlus#relation.cardinality),
?_assertEqual(9, length(Results)),
?_assert(lists:all(fun(#{a := A, b := B, sum := S}) ->
S =:= A + B andalso A >= 0 andalso A =< 2 andalso B >= 0 andalso B =< 2
end, Results))
].
