lean2/tests/lua/ind2.lua

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local env = environment()
function bad_add_inductive(...)
arg = {...}
ok, msg = pcall(function() add_inductive(unpack(arg)) end)
assert(not ok)
print("\nExpected error: " .. msg:what())
end
local l = mk_param_univ("l")
local U_l = mk_sort(l)
local U_l1 = mk_sort(max_univ(l, 1)) -- Make sure U_l1 is not Prop
local list_l = Const("list", {l}) -- list.{l}
local Nat = Const("nat")
local vec_l = Const("vec", {l}) -- vec.{l}
local zero = Const("zero")
local succ = Const("succ")
local forest_l = Const("forest", {l})
local tree_l = Const("tree", {l})
local n = Const("n")
bad_add_inductive(env,
"nat", Type,
"zero", Prop, -- Incorrect result type
"succ", mk_arrow(Nat, Nat))
local A = Local("A", U_l)
bad_add_inductive(env, {l}, 1,
{"tree", mk_arrow(U_l, U_l1),
"node", Pi(A, mk_arrow(A, forest_l(A), tree_l(A)))
},
{"forest", mk_arrow(U_l1, U_l1), -- Parameters of all inductive types must match
"emptyf", Pi(A, forest_l(A)),
"consf", Pi(A, mk_arrow(tree_l(A), forest_l(A), forest_l(A)))})
bad_add_inductive(env, {l}, 1,
{"tree", mk_arrow(U_l, U_l), -- Result may be in universe zero (e.g., l is instantiated with zero)
"node", Pi(A, mk_arrow(A, forest_l(A), tree_l(A)))
},
{"forest", mk_arrow(U_l, U_l1),
"emptyf", Pi(A, forest_l(A)),
"consf", Pi(A, mk_arrow(tree_l(A), forest_l(A), forest_l(A)))})
bad_add_inductive(env,
"nat", 1, Type, -- mismatch in the number of arguments claimed
"zero", Nat,
"succ", mk_arrow(Nat, Nat))
env = add_inductive(env,
"nat", Type,
"zero", Nat,
"succ", mk_arrow(Nat, Nat))
local Even = Const("Even")
local Odd = Const("Odd")
local b = Local("b", Nat)
bad_add_inductive(env, {},
{"Even", mk_arrow(Nat, Type),
"zero_is_even", Even(zero),
"succ_odd", Pi(b, mk_arrow(Odd(b), Even(succ(b))))},
{"Odd", mk_arrow(Nat, Prop), -- if one datatype lives in Prop, then all must live in Prop
"succ_even", Pi(b, mk_arrow(Even(b), Odd(succ(b))))})
bad_add_inductive(env,
"list", {l}, 1, mk_arrow(U_l, U_l1),
"nil", Pi(A, mk_arrow(mk_arrow(list_l(A), Prop), list_l(A))), -- nonpositive occurrence of inductive datatype
"cons", Pi(A, mk_arrow(A, list_l(A), list_l(A))))
bad_add_inductive(env,
"list", {l}, 1, mk_arrow(U_l, U_l1),
"nil", Pi(A, list_l(mk_arrow(A, A))),
"cons", Pi(A, mk_arrow(A, list_l(A), list_l(A))))
local list_1 = Const("list", {mk_level_one()})
bad_add_inductive(env,
"list", {l}, 1, mk_arrow(U_l, U_l1),
"nil", Pi(A, list_l(A)),
"cons", Pi(A, mk_arrow(A, list_1(Nat), list_l(A)))) -- all list occurrences must be of the form list_l(A)
bad_add_inductive(env,
"list", {l}, 1, mk_arrow(U_l, U_l1),
"nil", Pi(A, list_l(A)),
"cons", Pi(A, mk_arrow(A, list_1(A), list_1(A))))
bad_add_inductive(env,
"list", {l}, 1, mk_arrow(U_l, U_l1),
"nil", Pi(A, mk_arrow(U_l, list_l(A))),
"cons", Pi(A, mk_arrow(A, list_l(A), list_l(A))))
bad_add_inductive(env,
"list", {l}, 1, mk_arrow(U_l, U_l1),
"nil", Pi(A, list_l(A)),
"cons", Pi(A, mk_arrow(list_l(A), A, list_l(A))))
local A = Local("A", Type)
env = add_decl(env, mk_constant_assumption("eq", Pi(A, mk_arrow(A, A, Prop))))
local eq = Const("eq")
local Nat2 = Const("nat2")
local a = Local("a", Nat2)
bad_add_inductive(env,
"nat2", Type,
"zero2", Nat2,
"succ2", Pi(a, mk_arrow(eq(Nat2, a, a), Nat2)))
local env = bare_environment()
bad_add_inductive(env, -- Environment does not support inductive datatypes
"nat", Type,
"zero", Nat,
"succ", mk_arrow(Nat, Nat))