local env     = environment()
local l       = param_univ("l")
env = add_decl(env, mk_var_decl("group", {l}, mk_sort(l+1)))
env = add_decl(env, mk_var_decl("abelian_group", {l}, mk_sort(l+1)))
env = add_decl(env, mk_var_decl("ring", {l}, mk_sort(l+1)))
env = add_decl(env, mk_var_decl("abelian_ring", {l}, mk_sort(l+1)))
local group    = Const("group", {l})
local ring     = Const("ring", {l})
local ab_group = Const("abelian_group", {l})
local ab_ring  = Const("abelian_ring", {l})
env = add_decl(env, mk_var_decl("carrier", {l}, mk_arrow(group, mk_sort(l))))
env = add_coercion(env, "carrier")

env = add_decl(env, mk_var_decl("ag2g", {l}, mk_arrow(ab_group, group)))
env = add_decl(env, mk_var_decl("r2g", {l},   mk_arrow(ring, group)))
env = add_decl(env, mk_var_decl("ar2r", {l}, mk_arrow(ab_ring, ring)))
env = add_decl(env, mk_var_decl("ar2ag", {l}, mk_arrow(ab_ring, ab_group)))
env = add_coercion(env, "ag2g")
env = add_coercion(env, "r2g")
env = add_coercion(env, "ar2r")
env = add_coercion(env, "ar2ag")
for_each_coercion_sort(env, function(C, f) print(tostring(C) .. " >-> sort : " .. tostring(f)) end)
for_each_coercion_user(env, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D) .. " : " .. tostring(f)) end)

print(get_coercions_to_sort(env, Const("abelian_ring", {1})):head())
assert(env:type_check(get_coercions_to_sort(env, Const("abelian_ring", {1})):head()))
print("Coercions (abelian ring): ")
cs = get_coercions_from(env, ab_ring)
for i = 1, #cs do
   print(tostring(cs[i][2]) .. " : " .. tostring(cs[i][4]) .. " : " .. tostring(cs[i][3]))
end
