set.seed(34523)

test_that('kleene', {
    a <- kleene(algebra('luk'))
    expect_that(a$algebratype, equals(c('lukasiewicz', 'kleene')))


    a <- kleene(algebra('gog'))

    expect_that(a$algebratype, equals(c('goguen', 'kleene')))
    expect_that(a$t(), equals(NA_real_))
    expect_that(a$t(NA), equals(NA_real_))
    expect_that(a$t(NaN), equals(NA_real_))
    expect_that(a$t(0.5, NA), equals(NA_real_))
    expect_that(a$t(0.5, NaN), equals(NA_real_))
    expect_that(a$t(0, NA), equals(0))
    expect_that(a$t(1, NA), equals(NA_real_))
    expect_that(a$t(0.5, 0.4), equals(0.2))
    expect_that(a$t(c(0.5, NA, NA, 0.8, NA)), equals(NA_real_))
    expect_that(a$t(c(0, 0.5, NA, NA, 0.8, NA)), equals(0))

    expect_true(is.null(a$pt()))
    expect_that(a$pt(NA, 0.8), equals(NA_real_))
    expect_that(a$pt(NaN, 0.8), equals(NA_real_))
    expect_that(a$pt(c(0.5, NA, 0.4, NA, NA),
                     c(NA, 0.4, 0.5, NA, 0)),
                equals(c(NA_real_, NA_real_, 0.2, NA_real_, 0)))

    expect_that(a$c(), equals(NA_real_))
    expect_that(a$c(NA), equals(NA_real_))
    expect_that(a$c(NaN), equals(NA_real_))
    expect_that(a$c(NA, 0), equals(NA_real_))
    expect_that(a$c(NA, 0.5), equals(NA_real_))
    expect_that(a$c(NA, 1), equals(1))
    expect_that(a$c(0.5, NA, NaN, 0.8, NA), equals(NA_real_))
    expect_that(a$c(c(0.5, NA, NA, 0.8, NA)), equals(NA_real_))
    expect_that(a$c(c(1, 0.5, NA, NA, 0.8, NA)), equals(1))

    expect_true(is.null(a$pc()))
    expect_that(a$pc(NA, 0.8), equals(NA_real_))
    expect_that(a$pc(NaN, 0.8), equals(NA_real_))
    expect_that(a$pc(NA, 0), equals(NA_real_))
    expect_that(a$pc(NA, 1), equals(1))
    expect_that(a$pc(c(0.5, NA, 0.4, 1),
                     c(NA, 0.4, 0.5, NA)),
                equals(c(NA_real_, NA_real_, 0.7, 1)))

    expect_that(a$r(c(0.5, 0.8,   NA,      0.3,       NA,      0, NA, NA),
                    c(0.8, 0.5,   0.4,      NA,       NA,      NA, 1,  0)),
             equals(c(1.0, 0.625, NA_real_, NA_real_, NA_real_, 1, 1, NA_real_)))

    expect_that(a$b(c(0.5,   0.8,   NA,       0.4,      NA,       0,        1),
                    c(0.8,   0.5,   0.4,      NA,       NA,       NA,       NA)),
             equals(c(0.625, 0.625, NA_real_, NA_real_, NA_real_, NA_real_, NA_real_)))

    expect_that(a$i(), equals(NA_real_))
    expect_that(a$i(NA), equals(NA_real_))
    expect_that(a$i(NaN), equals(NA_real_))
    expect_that(a$i(0.5, NA, NaN, 0.8, NA), equals(NA_real_))
    expect_that(a$i(0, 0.5, NA, NaN, 0.8, NA), equals(0))
    expect_that(a$i(c(0.5, NA, NA, 0.8, NA)), equals(NA_real_))
    expect_that(a$i(c(0.5, 0, NA, NA, 0.8, NA)), equals(0))

    expect_true(is.null(a$pi()))
    expect_that(a$pi(NA, 0.8), equals(NA_real_))
    expect_that(a$pi(NaN, 0.8), equals(NA_real_))
    expect_that(a$pi(NA, 1), equals(NA_real_))
    expect_that(a$pi(NA, 0), equals(0))
    expect_that(a$pi(c(0.5, NA, 0.4, 0, 1),
                     c(NA, 0.4, 0.5, NA, NA)),
                equals(c(NA_real_, NA_real_, 0.4, 0, NA_real_)))

    expect_that(a$s(), equals(NA_real_))
    expect_that(a$s(NA), equals(NA_real_))
    expect_that(a$s(NaN), equals(NA_real_))
    expect_that(a$s(0.5, NA, NaN, 0.8, NA), equals(NA_real_))
    expect_that(a$s(1, 0.5, NA, NaN, 0.8, NA), equals(1))
    expect_that(a$s(c(0.5, NA, NA, 0.8, NA)), equals(NA_real_))
    expect_that(a$s(c(0.5, 1, NA, NA, 0.8, NA)), equals(1))

    expect_true(is.null(a$ps()))
    expect_that(a$ps(NA, 0.8), equals(NA_real_))
    expect_that(a$ps(NaN, 0.8), equals(NA_real_))
    expect_that(a$ps(NA, 0), equals(NA_real_))
    expect_that(a$ps(NA, 1), equals(1))
    expect_that(a$ps(c(0.5, NA, 0.4, NA, NA),
                     c(NA, 0.4, 0.5, 0, 1)),
                equals(c(NA_real_, NA_real_, 0.5, NA_real_, 1)))

    expect_that(a$n(NA), equals(NA_real_))
    expect_that(a$n(1), equals(0))
    expect_that(a$n(0), equals(1))
    expect_that(a$n(0.8), equals(a$r(0.8, 0)))

    expect_that(a$ni(NA), equals(NA_real_))
    expect_that(a$ni(1), equals(0))
    expect_that(a$ni(0), equals(1))
    expect_that(a$ni(0.8), equals(0.2))
})


test_that('kleene 2', {
    a <- kleene(algebra('gog'))

    expect_equal(a$t(0.4, 0.5), 0.2)
    expect_equal(a$t(0, NA), 0)
    expect_equal(a$t(0.5, NA), NA_real_)
    expect_equal(a$t(1, NA), NA_real_)
    expect_equal(a$t(NA, 0), 0)
    expect_equal(a$t(NA, 0.5), NA_real_)
    expect_equal(a$t(NA, 1), NA_real_)
    expect_equal(a$t(NA, NA), NA_real_)

    expect_equal(a$pt(0.4, 0.5), 0.2)
    expect_equal(a$pt(0, NA), 0)
    expect_equal(a$pt(0.5, NA), NA_real_)
    expect_equal(a$pt(1, NA), NA_real_)
    expect_equal(a$pt(NA, 0), 0)
    expect_equal(a$pt(NA, 0.5), NA_real_)
    expect_equal(a$pt(NA, 1), NA_real_)
    expect_equal(a$pt(NA, NA), NA_real_)

    expect_equal(a$c(0.4, 0.5), 0.7)
    expect_equal(a$c(0, NA), NA_real_)
    expect_equal(a$c(0.5, NA), NA_real_)
    expect_equal(a$c(1, NA), 1)
    expect_equal(a$c(NA, 0), NA_real_)
    expect_equal(a$c(NA, 0.5), NA_real_)
    expect_equal(a$c(NA, 1), 1)
    expect_equal(a$c(NA, NA), NA_real_)

    expect_equal(a$pc(0.4, 0.5), 0.7)
    expect_equal(a$pc(0, NA), NA_real_)
    expect_equal(a$pc(0.5, NA), NA_real_)
    expect_equal(a$pc(1, NA), 1)
    expect_equal(a$pc(NA, 0), NA_real_)
    expect_equal(a$pc(NA, 0.5), NA_real_)
    expect_equal(a$pc(NA, 1), 1)
    expect_equal(a$pc(NA, NA), NA_real_)

    expect_equal(a$i(0.4, 0.5), 0.4)
    expect_equal(a$i(0, NA), 0)
    expect_equal(a$i(0.5, NA), NA_real_)
    expect_equal(a$i(1, NA), NA_real_)
    expect_equal(a$i(NA, 0), 0)
    expect_equal(a$i(NA, 0.5), NA_real_)
    expect_equal(a$i(NA, 1), NA_real_)
    expect_equal(a$i(NA, NA), NA_real_)

    expect_equal(a$pi(0.4, 0.5), 0.4)
    expect_equal(a$pi(0, NA), 0)
    expect_equal(a$pi(0.5, NA), NA_real_)
    expect_equal(a$pi(1, NA), NA_real_)
    expect_equal(a$pi(NA, 0), 0)
    expect_equal(a$pi(NA, 0.5), NA_real_)
    expect_equal(a$pi(NA, 1), NA_real_)
    expect_equal(a$pi(NA, NA), NA_real_)

    expect_equal(a$s(0.4, 0.5), 0.5)
    expect_equal(a$s(0, NA), NA_real_)
    expect_equal(a$s(0.5, NA), NA_real_)
    expect_equal(a$s(1, NA), 1)
    expect_equal(a$s(NA, 0), NA_real_)
    expect_equal(a$s(NA, 0.5), NA_real_)
    expect_equal(a$s(NA, 1), 1)
    expect_equal(a$s(NA, NA), NA_real_)

    expect_equal(a$ps(0.4, 0.5), 0.5)
    expect_equal(a$ps(0, NA), NA_real_)
    expect_equal(a$ps(0.5, NA), NA_real_)
    expect_equal(a$ps(1, NA), 1)
    expect_equal(a$ps(NA, 0), NA_real_)
    expect_equal(a$ps(NA, 0.5), NA_real_)
    expect_equal(a$ps(NA, 1), 1)
    expect_equal(a$ps(NA, NA), NA_real_)

    expect_equal(a$n(c(0, 0.5, 1, NA)),
                     c(1,   0, 0, NA_real_))
    expect_equal(a$ni(c(0, 0.5, 1, NA)),
                      c(1, 0.5, 0, NA_real_))

    expect_equal(a$b(0.4, 0.5), 4/5)
    expect_equal(a$b(0, NA), NA_real_)
    expect_equal(a$b(0.5, NA), NA_real_)
    expect_equal(a$b(1, NA), NA_real_)
    expect_equal(a$b(0.5, 0.4), 4/5)
    expect_equal(a$b(NA, 0), NA_real_)
    expect_equal(a$b(NA, 0.5), NA_real_)
    expect_equal(a$b(NA, 1), NA_real_)
    expect_equal(a$b(NA, NA), NA_real_)
    expect_equal(a$b(0.5, 0.5), 1)

    expect_equal(a$r(0.4, 0.5), 1)
    expect_equal(a$r(0, NA), 1)
    expect_equal(a$r(0.5, NA), NA_real_)
    expect_equal(a$r(1, NA), NA_real_)
    expect_equal(a$r(NA, 0), NA_real_)
    expect_equal(a$r(NA, 0.5), NA_real_)
    expect_equal(a$r(NA, 1), 1)
    expect_equal(a$r(NA, NA), NA_real_)

    a <- kleene(algebra('lukasiewicz'))
    expect_equal(a$r(0.5, NA), NA_real_)
})


test_that('kleene is non-associative', {
    a <- kleene(algebra('lukasiewicz'))

    expect_equal(a$t(0.3, 0.2, NA), 0)
    expect_equal(a$t(NA, 0.3, 0.2), 0)
})


test_that('kleene order', {
    a <- kleene(algebra('lukasiewicz'))
    expect_error(a$order(0))
})