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test(lua): add inductive datatype simple tests

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-05-17 09:25:03 -07:00
parent 36b070cb5b
commit 989bcdc7ad
1 changed files with 50 additions and 0 deletions
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tests/lua/ind1.lua Normal file
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local env = empty_environment()
local l = mk_param_univ("l")
local A = Const("A")
local U_l = mk_sort(l)
local U_l1 = mk_sort(mk_level_max(l, mk_level_one()))
local list_l = Const("list", {l})
local Nat = Const("Nat")
local vec_l = Const("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")
add_inductive(env, "nat", Type, "zero", Nat, "succ", mk_arrow(Nat, Nat))
add_inductive(env,
"list", {l}, 1, mk_arrow(U_l, U_l1),
"nil", Pi({{A, U_l, true}}, list_l(A)),
"cons", Pi({{A, U_l, true}}, mk_arrow(A, list_l(A), list_l(A))))
add_inductive(env,
"vec", {l}, 1,
mk_arrow(U_l, Nat, U_l1),
"vnil", Pi({{A, U_l, true}}, vec_l(A, zero)),
"vcons", Pi({{A, U_l, true}, {n, Nat, true}}, mk_arrow(A, vec_l(A, n), vec_l(A, succ(n)))))
local And = Const("and")
local Or = Const("or")
local B = Const("B")
add_inductive(env, "false", Bool)
add_inductive(env, "true", Bool, "trivial", Const("true"))
add_inductive(env,
"and", mk_arrow(Bool, Bool, Bool),
"and_intro", Pi({{A, Bool, true}, {B, Bool, true}}, mk_arrow(A, B, And(A, B))))
add_inductive(env,
"or", mk_arrow(Bool, Bool, Bool),
"or_intro_left", Pi({{A, Bool, true}, {B, Bool, true}}, mk_arrow(A, Or(A, B))),
"or_intro_right", Pi({{A, Bool, true}, {B, Bool, true}}, mk_arrow(B, Or(A, B))))
local P = Const("P")
local a = Const("a")
local exists_l = Const("exists", {l})
add_inductive(env,
"exists", {l}, 2, Pi({{A, U_l}}, mk_arrow(mk_arrow(A, Bool), Bool)),
"exists_intro", Pi({{A, U_l, true}, {P, mk_arrow(A, Bool), true}, {a, A}}, mk_arrow(P(a), exists_l(A, P))))
add_inductive(env, {l}, 1,
{"tree", mk_arrow(U_l, U_l1),
"node", Pi({{A, U_l, true}}, mk_arrow(A, forest_l(A), tree_l(A)))
},
{"forest", mk_arrow(U_l, U_l1),
"emptyf", Pi({{A, U_l, true}}, forest_l(A)),
"consf", Pi({{A, U_l, true}}, mk_arrow(tree_l(A), forest_l(A), forest_l(A)))})