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fix(library/tactic/unfold_rec): support indexed families at unfold_rec

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This commit also removes many (now unnecessary) folds from the HoTT
library.

See issue #692

We still have to implement support for recursive definitions based on
brec_on that recurse over inductive families.
This commit is contained in:
Leonardo de Moura 2015-07-12 12:32:58 -04:00
parent 7fa5c3e5da
commit 584f9e3f49
3 changed files with 59 additions and 37 deletions
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21
hott/algebra/e_closure.hlean
View file

@ -84,27 +84,16 @@ section
(ap_e_closure_elim_h e' (λa a' s, (ap (ap h) (p s))⁻¹) t) :=
begin
induction t,
{ unfold [ap_e_closure_elim_h,e_closure.elim],
{ unfold [ap_e_closure_elim_h, e_closure.elim],
apply square_of_eq, exact !con.right_inv ⬝ !con.left_inv⁻¹},
{ apply ids},
{ rewrite [↑e_closure.elim,↓e_closure.elim e r,
↑ap_e_closure_elim_h,
↓ap_e_closure_elim_h e p r,
↓ap_e_closure_elim_h e (λa a' s, ap_compose h g (e s)) r,
↓ap_e_closure_elim_h e' (λa a' s, (ap (ap h) (p s))⁻¹) r,
ap_con (ap h)],
{ unfold [e_closure.elim, ap_e_closure_elim_h],
rewrite [ap_con (ap h)],
refine (transpose !ap_compose_inv)⁻¹ᵛ ⬝h _,
rewrite [con_inv,inv_inv,-inv2_inv],
exact !ap_inv2 ⬝v square_inv2 v_0},
{ rewrite [↑e_closure.elim,↓e_closure.elim e r, ↓e_closure.elim e r',
↑ap_e_closure_elim_h,
↓ap_e_closure_elim_h e p r,
↓ap_e_closure_elim_h e (λa a' s, ap_compose h g (e s)) r,
↓ap_e_closure_elim_h e' (λa a' s, (ap (ap h) (p s))⁻¹) r,
↓ap_e_closure_elim_h e p r',
↓ap_e_closure_elim_h e (λa a' s, ap_compose h g (e s)) r',
↓ap_e_closure_elim_h e' (λa a' s, (ap (ap h) (p s))⁻¹) r',
ap_con (ap h)],
{ unfold [e_closure.elim, ap_e_closure_elim_h],
rewrite [ap_con (ap h)],
refine (transpose !ap_compose_con)⁻¹ᵛ ⬝h _,
rewrite [con_inv,inv_inv,con2_inv],
refine !ap_con2 ⬝v square_con2 v_0 v_1},

2
hott/hit/two_quotient.hlean
View file

@ -273,7 +273,7 @@ namespace two_quotient
{ exact P0 a},
{ exact P1 s},
{ exact abstract [unfold 10] begin induction q with a a' t t' q,
rewrite [↑e_closure.elim,↓e_closure.elim P1 t,↓e_closure.elim P1 t'],
rewrite [↑e_closure.elim],
apply con_inv_eq_idp, exact P2 q end end},
end
local attribute elim [unfold 8]

57
src/library/tactic/unfold_rec.cpp
View file

@ -90,7 +90,8 @@ class unfold_rec_fn : public replace_visitor_aux {
}
// return true if e is of the form (C.rec ...)
bool is_rec_app(expr const & e, buffer<expr> const & locals, name & rec_name, unsigned & main_arg_pos, buffer<unsigned> & rec_arg_pos) {
bool is_rec_app(expr const & e, buffer<expr> const & locals, name & rec_name, buffer<unsigned> & indices_pos,
unsigned & main_arg_pos, buffer<unsigned> & rec_arg_pos) {
buffer<expr> args;
expr fn = get_app_args(e, args);
if (!is_constant(fn))
@ -102,10 +103,33 @@ class unfold_rec_fn : public replace_visitor_aux {
if (!is_recursive_datatype(m_env, *I))
return false;
unsigned major_idx = *inductive::get_elim_major_idx(m_env, const_name(fn));
if (major_idx >= args.size())
unsigned nindices = *inductive::get_num_indices(m_env, *I);
lean_assert(nindices <= major_idx);
unsigned rel_idx = major_idx - nindices; // first index we should track
// Collect position of indices (at least the ones that occur in e)
while (rel_idx < args.size() && rel_idx < major_idx) {
if (auto it2 = get_local_pos(locals, args[rel_idx])) {
indices_pos.push_back(*it2);
} else {
return false;
}
rel_idx++;
}
if (major_idx >= args.size()) {
// Some indices and the major premise may not occur in e because of eta-reduction
main_arg_pos = locals.size() + major_idx - args.size();
for (unsigned i = rel_idx; i < major_idx; i++)
indices_pos.push_back(locals.size() + i - args.size());
return true;
}
if (auto it = get_local_pos(locals, args[major_idx])) {
main_arg_pos = *it;
} else {
return false;
}
for (unsigned i = major_idx+1; i < args.size(); i++) {
if (auto it2 = get_local_pos(locals, args[i])) {
rec_arg_pos.push_back(*it2);
@ -115,21 +139,22 @@ class unfold_rec_fn : public replace_visitor_aux {
}
return true;
}
return false;
}
enum rec_kind { BREC, REC, NOREC };
// try to detect the kind of recursive definition
rec_kind get_rec_kind(expr const & e, buffer<expr> const & locals, name & rec_name, unsigned & main_arg_pos, buffer<unsigned> & rec_arg_pos) {
if (is_rec_app(e, locals, rec_name, main_arg_pos, rec_arg_pos))
rec_kind get_rec_kind(expr const & e, buffer<expr> const & locals, name & rec_name,
buffer<unsigned> & indices_pos, unsigned & main_arg_pos, buffer<unsigned> & rec_arg_pos) {
if (is_rec_app(e, locals, rec_name, indices_pos, main_arg_pos, rec_arg_pos))
return REC;
buffer<expr> args;
expr fn = get_app_args(e, args);
if (is_constant(fn) && const_name(fn) == inductive::get_elim_name(get_prod_name()) &&
args.size() >= 5) {
// try do detect brec_on pattern
if (is_rec_app(args[4], locals, rec_name, main_arg_pos, rec_arg_pos)) {
if (is_rec_app(args[4], locals, rec_name, indices_pos, main_arg_pos, rec_arg_pos) &&
// for brec, eta is not applicable, so main_arg_pos must be < locals.size()
main_arg_pos < locals.size()) {
for (unsigned i = 5; i < args.size(); i++) {
if (auto it2 = get_local_pos(locals, args[i])) {
rec_arg_pos.push_back(*it2);
@ -176,14 +201,16 @@ class unfold_rec_fn : public replace_visitor_aux {
rec_kind m_kind;
name m_rec_name;
unsigned m_major_idx; // position of the major premise in the recursor
buffer<unsigned> const & m_indices_pos; // position of the datatype indices in the function being unfolded
unsigned m_main_pos; // position of the (recursive) argument in the function being unfolded
buffer<unsigned> const & m_rec_arg_pos; // position of the other arguments that are not fixed in the recursion
name m_prod_rec_name;
fold_rec_fn(type_checker_ptr & tc, expr const & fn, buffer<expr> const & args, rec_kind k, name const & rec_name,
unsigned main_pos, buffer<unsigned> const & rec_arg_pos):
buffer<unsigned> const & indices_pos, unsigned main_pos, buffer<unsigned> const & rec_arg_pos):
m_tc(tc), m_fn(fn), m_args(args), m_kind(k), m_rec_name(rec_name),
m_major_idx(*inductive::get_elim_major_idx(m_tc->env(), rec_name)),
m_indices_pos(indices_pos),
m_main_pos(main_pos), m_rec_arg_pos(rec_arg_pos) {
m_prod_rec_name = inductive::get_elim_name(get_prod_name());
lean_assert(m_main_pos < args.size());
@ -197,6 +224,10 @@ class unfold_rec_fn : public replace_visitor_aux {
throw fold_failed();
buffer<expr> new_args;
new_args.append(m_args);
unsigned nindices = m_indices_pos.size();
for (unsigned i = 0; i < m_indices_pos.size(); i++) {
new_args[m_indices_pos[i]] = args[m_major_idx - nindices + i];
}
new_args[m_main_pos] = args[m_major_idx];
for (unsigned i = 0; i < m_rec_arg_pos.size(); i++) {
new_args[m_rec_arg_pos[i]] = args[m_major_idx + 1 + i];
@ -265,13 +296,15 @@ class unfold_rec_fn : public replace_visitor_aux {
}
name rec_name;
unsigned main_pos;
buffer<unsigned> indices_pos;
buffer<unsigned> rec_arg_pos;
rec_kind k = get_rec_kind(fn_body, fn_locals, rec_name, main_pos, rec_arg_pos);
if (k == NOREC) {
rec_kind k = get_rec_kind(fn_body, fn_locals, rec_name, indices_pos, main_pos, rec_arg_pos);
if (k == NOREC || main_pos >= args.size()) {
// norecursive definition
return unfold_simple(fn, args);
}
for (unsigned i = fn_locals.size(); i < args.size(); i++)
unsigned rest = main_pos >= fn_locals.size() ? main_pos+1 : fn_locals.size();
for (unsigned i = rest; i < args.size(); i++)
rec_arg_pos.push_back(i);
auto new_main_cs = m_tc->whnf(args[main_pos]);
if (!is_constructor_app(m_env, new_main_cs.first) || new_main_cs.second) {
@ -294,7 +327,7 @@ class unfold_rec_fn : public replace_visitor_aux {
// //head is a recursor... so the unfold is probably not generating a nice result...
// throw fold_failed();
// }
return fold_rec_fn(m_tc, fn, args, k, rec_name, main_pos, rec_arg_pos)(new_e);
return fold_rec_fn(m_tc, fn, args, k, rec_name, indices_pos, main_pos, rec_arg_pos)(new_e);
}
bool unfold_cnst(expr const & e) {