40 lines
1.4 KiB
Lua
40 lines
1.4 KiB
Lua
|
local env = environment()
|
||
|
|
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")
|
||
|
|
|
||
|
|
env = env:begin_section_scope()
|
||
|
|
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 vector = Const("vector")
|
||
|
|
local n = Local("n", nat)
|
||
|
|
env = add_inductive(env,
|
||
|
|
"vector", mk_arrow(nat, mk_sort(max_univ(l, 1))),
|
||
|
|
"nil", vector(zero),
|
||
|
|
"cons", Pi(n, mk_arrow(A, vector(n), vector(succ(n)))))
|
||
|
|
|
||
|
|
print(env:find("vector_rec"):type())
|
||
|
|
assert(env:find("cons"):type() == Pi(n, mk_arrow(A, vector(n), vector(succ(n)))))
|
||
|
|
env = env:end_scope()
|
||
|
|
print(env:find("vector_rec"):type())
|
||
|
|
print(env:find("cons"):type())
|
||
|
|
local l = mk_param_univ("l")
|
||
|
|
local A = Local("A", mk_sort(l))
|
||
|
|
local vector = Const("vector", {l})
|
||
|
|
assert(env:find("cons"):type() == Pi({A, n}, mk_arrow(A, vector(A, n), vector(A, succ(n)))))
|
||
|
|
env = env:end_scope()
|
||
|
|
|
||
|
|
print(env:find("vector_rec"):type())
|
||
|
|
print(env:find("cons"):type())
|
||
|
|
env:export("sect8_mod.olean")
|
||
|
|
local env2 = import_modules("sect8_mod")
|
||
|
|
assert(env:find("vector_rec"):type() == env2:find("vector_rec"):type())
|