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feat(library/elaborator): add support for proj/pair/sigma in the the higher-order unification procedure

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-02-04 13:53:30 -08:00
parent 413391b2b4
commit f03c09c10b
3 changed files with 58 additions and 4 deletions
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46
src/library/elaborator/elaborator.cpp
View file

@ -620,11 +620,29 @@ class elaborator::imp {
}
}
void process_proj(context const & ctx, expr & a) {
if (is_proj(a)) {
expr const & arg = proj_arg(a);
expr new_arg = arg;
if (m_use_normalizer)
new_arg = normalize(ctx, arg);
if (is_pair(new_arg)) {
if (proj_first(a))
a = pair_first(new_arg);
else
a = pair_second(new_arg);
} else {
a = update_proj(a, new_arg);
}
}
}
expr normalize_step(context const & ctx, expr const & a) {
expr new_a = a;
process_let(new_a);
process_var(ctx, new_a);
process_app(ctx, new_a);
process_proj(ctx, new_a);
return new_a;
}
@ -908,6 +926,12 @@ class elaborator::imp {
state new_state(m_state);
justification new_assumption = mk_assumption();
expr imitation;
// Auxiliary function for creating the term
// (h[lift:0:num_a-1] #0 ... #(num_a-1))
auto mk_app_h_vars = [&](expr const & h) {
lean_assert(is_metavar(h));
return mk_app_vars(add_lift(h, 0, num_a - 1), num_a - 1);
};
lean_assert(arg_types.size() == num_a - 1);
if (is_app(b)) {
// Imitation for applications
@ -919,12 +943,12 @@ class elaborator::imp {
imitation_args.push_back(lift_free_vars(f_b, 0, num_a - 1, new_state.m_menv));
for (unsigned i = 1; i < num_b; i++) {
expr h_i = new_state.m_menv->mk_metavar(ctx);
imitation_args.push_back(mk_app_vars(add_lift(h_i, 0, num_a - 1), num_a - 1));
imitation_args.push_back(mk_app_h_vars(h_i));
push_new_eq_constraint(new_state.m_active_cnstrs, ctx, update_app(a, 0, h_i), arg(b, i), new_assumption);
}
imitation = mk_lambda(arg_types, mk_app(imitation_args));
} else if (is_abstraction(b)) {
// Imitation for lambdas and Pis
// Imitation for lambdas, Pis, and Sigmas
// Assign f_a <- fun (x_1 : T_1) ... (x_{num_a} : T_{num_a}),
// fun (x_b : (?h_1 x_1 ... x_{num_a})), (?h_2 x_1 ... x_{num_a} x_b)
// New constraints (h_1 a_1 ... a_{num_a}) == abst_domain(b)
@ -936,12 +960,26 @@ class elaborator::imp {
if (is_arrow(b)) {
push_new_eq_constraint(new_state.m_active_cnstrs, new_ctx,
update_app(lift_free_vars(a, 1), 0, h_2), abst_body(b), new_assumption);
imitation = mk_lambda(arg_types, update_abstraction(b, mk_app_vars(add_lift(h_1, 0, num_a - 1), num_a - 1), mk_app_vars(add_lift(h_2, 1, num_a - 1), num_a - 1, 1)));
imitation = mk_lambda(arg_types, update_abstraction(b, mk_app_h_vars(h_1), mk_app_vars(add_lift(h_2, 1, num_a - 1), num_a - 1, 1)));
} else {
push_new_eq_constraint(new_state.m_active_cnstrs, new_ctx,
mk_app(update_app(lift_free_vars(a, 1), 0, h_2), mk_var(0)), abst_body(b), new_assumption);
imitation = mk_lambda(arg_types, update_abstraction(b, mk_app_vars(add_lift(h_1, 0, num_a - 1), num_a - 1), mk_app_vars(add_lift(h_2, 1, num_a - 1), num_a)));
imitation = mk_lambda(arg_types, update_abstraction(b, mk_app_h_vars(h_1), mk_app_vars(add_lift(h_2, 1, num_a - 1), num_a)));
}
} else if (is_pair(b)) {
// Imitation for dependent pairs
expr h_f = new_state.m_menv->mk_metavar(ctx);
expr h_s = new_state.m_menv->mk_metavar(ctx);
expr h_t = new_state.m_menv->mk_metavar(ctx);
push_new_eq_constraint(new_state.m_active_cnstrs, ctx, update_app(a, 0, h_f), pair_first(b), new_assumption);
push_new_eq_constraint(new_state.m_active_cnstrs, ctx, update_app(a, 0, h_s), pair_second(b), new_assumption);
push_new_eq_constraint(new_state.m_active_cnstrs, ctx, update_app(a, 0, h_t), pair_type(b), new_assumption);
imitation = mk_lambda(arg_types, mk_pair(mk_app_h_vars(h_f), mk_app_h_vars(h_s), mk_app_h_vars(h_t)));
} else if (is_proj(b)) {
// Imitation for pair-projection
expr h_a = new_state.m_menv->mk_metavar(ctx);
push_new_eq_constraint(new_state.m_active_cnstrs, ctx, update_app(a, 0, h_a), proj_arg(b), new_assumption);
imitation = mk_lambda(arg_types, mk_proj(proj_first(b), mk_app_h_vars(h_a)));
} else {
// "Dumb imitation" aka the constant function
// Assign f_a <- fun (x_1 : T_1) ... (x_{num_a} : T_{num_a}), b

8
tests/lean/sig6.lean Normal file
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@ -0,0 +1,8 @@
variables A B : (Type U)
variables t1 t2 : A ⨯ B
axiom pair_Ax {A : (Type U)} {B : A → (Type U)} (p : sig x, B x) : (tuple (sig x, B x) : (proj1 p), (proj2 p)) = p
theorem spairext {A B : (Type U)} {p1 p2 : A ⨯ B} (H1 : proj1 p1 = proj1 p2) (H2 : proj2 p1 = proj2 p2) : p1 = p2
:= calc p1 = tuple (proj1 p1), (proj2 p1) : symm (pair_Ax p1)
... = tuple (proj1 p2), (proj2 p1) : { H1 }
... = tuple (proj1 p2), (proj2 p2) : { H2 }
... = p2 : pair_Ax p2

8
tests/lean/sig6.lean.expected.out Normal file
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@ -0,0 +1,8 @@
Set: pp::colors
Set: pp::unicode
Assumed: A
Assumed: B
Assumed: t1
Assumed: t2
Assumed: pair_Ax
Proved: spairext