function test_unify_simple(lhs, rhs, expected)
   print(tostring(lhs) .. " =?= " .. tostring(rhs) .. ", expected: " .. tostring(expected))
   r, s = unify_simple(substitution(), lhs, rhs, justification())
   if r == unify_status.Solved then
      s:for_each_expr(function(n, v, j)
                         print("  " .. tostring(n) .. " := " .. tostring(v))
      end)
      s:for_each_level(function(n, v, j)
                          print("  " .. tostring(n) .. " := " .. tostring(v))
      end)
   end
   if r ~= expected then print("r: " .. r) end
   assert(r == expected)
end

local f  = Const("f")
local a  = Const("a")
local l1 = mk_local("l1", "x", Prop)
local l2 = mk_local("l2", "y", Prop)
local l3 = mk_local("l3", "z", Prop)
local m  = mk_metavar("m", Prop)

test_unify_simple(m(l1, l2), f(f(a, l1), l1), unify_status.Solved)
test_unify_simple(m(l1, l2), m(l1, l2), unify_status.Solved)
test_unify_simple(m(l1, l2), m(l2, l2), unify_status.Unsupported)
test_unify_simple(m(l1, l2), f(f(l2, l1), l1), unify_status.Solved)
test_unify_simple(m(l1, a), f(f(a), l1), unify_status.Unsupported)
test_unify_simple(f(m, a), f(f(a), l1), unify_status.Unsupported)
test_unify_simple(m(l1, l2), f(f(m), l1), unify_status.Failed)
test_unify_simple(m(l1, l2), f(f(l3), l1), unify_status.Failed)
test_unify_simple(m, f(a), unify_status.Solved)
test_unify_simple(f(a), f(a), unify_status.Solved)
test_unify_simple(f(a), f(f(a)), unify_status.Failed)
test_unify_simple(f(f(a, l1), l1), m(l1, l2), unify_status.Solved)
test_unify_simple(m(l1, l1), f(f(l2, l1), l1), unify_status.Unsupported)
test_unify_simple(m(l1, l2, l1), f(f(l2, l1), l1), unify_status.Unsupported)
test_unify_simple(m(l1, l2), Fun(l3, f(f(a, l1), l3)), unify_status.Solved)

local zero = level()
local one  = zero+1
local l    = mk_param_univ("l")
local u    = mk_global_univ("u")
local m    = mk_meta_univ("m")
test_unify_simple(m+1, u+1, unify_status.Solved)
test_unify_simple(u+1, u+1, unify_status.Solved)
test_unify_simple(u+1, m+1, unify_status.Solved)
test_unify_simple(m, u+1, unify_status.Solved)
test_unify_simple(m, max_univ(u, l), unify_status.Solved)
test_unify_simple(max_univ(u, l), max_univ(u, l), unify_status.Solved)
test_unify_simple(m+1, m+1, unify_status.Solved)
test_unify_simple(l, l+1, unify_status.Failed)
test_unify_simple(m, m+1, unify_status.Failed)
test_unify_simple(m, max_univ(m, u), unify_status.Unsupported)
test_unify_simple(m, max_univ(m, u)+1, unify_status.Failed)
test_unify_simple(m+2, m+1, unify_status.Failed)
test_unify_simple(u+2, m+1, unify_status.Solved)