34 lines
1.2 KiB
Lua
34 lines
1.2 KiB
Lua
|
local env = environment()
|
||
|
|
env = env:begin_section_scope()
|
||
|
|
env = env:begin_section_scope()
|
||
|
|
local nat = Const("nat")
|
||
|
|
env = add_inductive(env,
|
||
|
|
"nat", Type,
|
||
|
|
"zero", nat,
|
||
|
|
"succ", mk_arrow(nat, nat))
|
||
|
|
local zero = Const("zero")
|
||
|
|
local succ = Const("succ")
|
||
|
|
local one = succ(zero)
|
||
|
|
env = env:add_global_level("l")
|
||
|
|
local l = mk_global_univ("l")
|
||
|
|
env = env:add(check(env, mk_var_decl("A", mk_sort(l))), binder_info(true))
|
||
|
|
env = env:add(check(env, mk_var_decl("B", mk_sort(l))), binder_info(true))
|
||
|
|
local A = Const("A")
|
||
|
|
local l1 = mk_param_univ("l1")
|
||
|
|
local D = Const("D", {l1})
|
||
|
|
local n = Local("n", nat)
|
||
|
|
env = add_inductive(env,
|
||
|
|
"D", {l1}, 1, mk_arrow(nat, nat, mk_sort(max_univ(l1, l, 1))),
|
||
|
|
"mk1", Pi(n, mk_arrow(A, D(n, one))),
|
||
|
|
"mk0", Pi(n, mk_arrow(A, A, D(n, zero))))
|
||
|
|
print(env:find("D_rec"):type())
|
||
|
|
env = env:end_scope()
|
||
|
|
env = env:end_scope()
|
||
|
|
print(env:find("D_rec"):type())
|
||
|
|
|
||
|
|
local l = mk_param_univ("l")
|
||
|
|
local A = Local("A", mk_sort(l))
|
||
|
|
local D = Const("D", {l, l1})
|
||
|
|
print(env:find("mk1"):type())
|
||
|
|
assert(env:find("mk1"):type() == Pi({A, n}, mk_arrow(A, D(A, n, one))))
|