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feat(library/tactic/rewrite_tactic): try to fold nested recursive applications after unfolding a recursive function

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See issue #692.
The implementation still has some rough spots.
It is not clear what the right semantic is.
Moreover, the folds in e_closure could not be eliminated automatically.
This commit is contained in:
Leonardo de Moura 2015-07-08 21:08:24 -04:00
parent 7f1993be41
commit a9515ac7a4
14 changed files with 498 additions and 52 deletions
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2
hott/types/hprop_trunc.hlean
View file

@ -31,7 +31,7 @@ namespace is_trunc
{ intro H x y, apply is_trunc_eq},
{ intro H, cases H, apply idp},
{ intro P, apply eq_of_homotopy, intro a, apply eq_of_homotopy, intro b,
esimp [function.id,compose,is_trunc_succ_intro,is_trunc_eq],
esimp [is_trunc_eq], esimp[compose,is_trunc_succ_intro],
generalize (P a b), intro H, cases H, apply idp},
end

4
hott/types/pointed.hlean
View file

@ -206,9 +206,7 @@ namespace pointed
begin
revert A B f, induction n with n IH,
{ intros A B f, exact f},
{ intros A B f, rewrite [↑Iterated_loop_space,↓Iterated_loop_space n (Ω A),
↑Iterated_loop_space, ↓Iterated_loop_space n (Ω B)],
apply IH (Ω A),
{ intros A B f, esimp [Iterated_loop_space], apply IH (Ω A),
{ esimp, fconstructor,
intro q, refine !respect_pt⁻¹ ⬝ ap f q ⬝ !respect_pt,
esimp, apply con.left_inv}}

5
library/data/real/order.lean
View file

@ -725,11 +725,12 @@ theorem not_lt_self (s : seq) : ¬ s_lt s s :=
intro Hlt,
rewrite [↑s_lt at Hlt, ↑pos at Hlt],
apply exists.elim Hlt,
intro n Hn,
rewrite [↑sadd at Hn, ↑sneg at Hn, sub_self at Hn],
intro n Hn, esimp at Hn,
rewrite [↑sadd at Hn,↑sneg at Hn, sub_self at Hn],
apply absurd Hn (rat.not_lt_of_ge (rat.le_of_lt !inv_pos))
end
theorem not_sep_self (s : seq) : ¬ s ≢ s :=
begin
intro Hsep,

6
library/data/stream.lean
View file

@ -251,13 +251,15 @@ coinduction
rfl
(λ B fr ch, by rewrite [tail_iterate, tail_const]; exact ch)
local attribute stream [reducible]
theorem map_iterate (f : A → A) (a : A) : iterate f (f a) = map f (iterate f a) :=
begin
apply funext, intro n,
induction n with n' IH,
{reflexivity},
{esimp [map, iterate, nth] at *,
rewrite IH}
{ esimp [map, iterate, nth] at *,
rewrite IH }
end
section corec

2
library/logic/examples/cont.lean
View file

@ -59,7 +59,7 @@ lemma not_all_continuous : false :=
let β := znkω (M f + 1) 1 in
let α := znkω m (M f + 1) in
assert βeq₁ : zω =[M f + 1] β, from
λ (a : nat) (h : a < M f + 1), begin esimp [zω, znkω], rewrite [if_pos h] end,
λ (a : nat) (h : a < M f + 1), begin unfold zω, unfold znkω, rewrite [if_pos h] end,
assert βeq₂ : zω =[M f] β, from pred_beq βeq₁,
assert m_eq_fβ : m = f β, from M_spec f β βeq₂,
assert aux : ∀ α, zω =[m] α → β 0 = β (α m), by rewrite m_eq_fβ at {1}; exact (β0_eq β),

24
src/frontends/lean/parse_rewrite_tactic.cpp
View file

@ -44,7 +44,7 @@ static void check_not_in_theorem_queue(parser & p, name const & n, pos_info cons
}
}
static expr parse_rewrite_unfold_core(parser & p) {
static expr parse_rewrite_unfold_core(parser & p, bool force_unfold) {
buffer<name> to_unfold;
if (p.curr_is_token(get_lbracket_tk())) {
p.next();
@ -63,19 +63,21 @@ static expr parse_rewrite_unfold_core(parser & p) {
check_not_in_theorem_queue(p, to_unfold.back(), pos);
}
location loc = parse_tactic_location(p);
return mk_rewrite_unfold(to_list(to_unfold), loc);
return mk_rewrite_unfold(to_list(to_unfold), force_unfold, loc);
}
static expr parse_rewrite_unfold(parser & p) {
static expr parse_rewrite_unfold(parser & p, bool force_unfold) {
lean_assert(p.curr_is_token(get_up_tk()) || p.curr_is_token(get_caret_tk()));
p.next();
return parse_rewrite_unfold_core(p);
return parse_rewrite_unfold_core(p, force_unfold);
}
// If use_paren is true, then lemmas must be identifiers or be wrapped with parenthesis
static expr parse_rewrite_element(parser & p, bool use_paren) {
if (p.curr_is_token(get_up_tk()) || p.curr_is_token(get_caret_tk()))
return parse_rewrite_unfold(p);
if (p.curr_is_token(get_up_tk()) || p.curr_is_token(get_caret_tk())) {
bool force_unfold = false;
return parse_rewrite_unfold(p, force_unfold);
}
if (p.curr_is_token(get_down_tk())) {
p.next();
expr e = p.parse_tactic_expr_arg();
@ -170,10 +172,11 @@ expr parse_krewrite_tactic(parser & p) {
expr parse_esimp_tactic(parser & p) {
buffer<expr> elems;
auto pos = p.pos();
bool force_unfold = false;
if (p.curr_is_token(get_up_tk()) || p.curr_is_token(get_caret_tk())) {
elems.push_back(p.save_pos(parse_rewrite_unfold(p), pos));
elems.push_back(p.save_pos(parse_rewrite_unfold(p, force_unfold), pos));
} else if (p.curr_is_token(get_lbracket_tk())) {
elems.push_back(p.save_pos(parse_rewrite_unfold_core(p), pos));
elems.push_back(p.save_pos(parse_rewrite_unfold_core(p, force_unfold), pos));
} else {
location loc = parse_tactic_location(p);
elems.push_back(p.save_pos(mk_rewrite_reduce(loc), pos));
@ -184,13 +187,14 @@ expr parse_esimp_tactic(parser & p) {
expr parse_unfold_tactic(parser & p) {
buffer<expr> elems;
auto pos = p.pos();
bool force_unfold = true;
if (p.curr_is_identifier()) {
name c = p.check_constant_next("invalid unfold tactic, identifier expected");
check_not_in_theorem_queue(p, c, pos);
location loc = parse_tactic_location(p);
elems.push_back(p.save_pos(mk_rewrite_unfold(to_list(c), loc), pos));
elems.push_back(p.save_pos(mk_rewrite_unfold(to_list(c), force_unfold, loc), pos));
} else if (p.curr_is_token(get_lbracket_tk())) {
elems.push_back(p.save_pos(parse_rewrite_unfold_core(p), pos));
elems.push_back(p.save_pos(parse_rewrite_unfold_core(p, force_unfold), pos));
} else {
throw parser_error("invalid unfold tactic, identifier or `[` expected", pos);
}

2
src/library/tactic/CMakeLists.txt
View file

@ -6,6 +6,6 @@ expr_to_tactic.cpp location.cpp rewrite_tactic.cpp util.cpp
init_module.cpp change_tactic.cpp check_expr_tactic.cpp let_tactic.cpp
contradiction_tactic.cpp exfalso_tactic.cpp constructor_tactic.cpp
injection_tactic.cpp congruence_tactic.cpp relation_tactics.cpp
induction_tactic.cpp subst_tactic.cpp)
induction_tactic.cpp subst_tactic.cpp unfold_rec.cpp)
target_link_libraries(tactic ${LEAN_LIBS})

82
src/library/tactic/rewrite_tactic.cpp
View file

@ -38,7 +38,7 @@ Author: Leonardo de Moura
#include "library/tactic/rewrite_tactic.h"
#include "library/tactic/expr_to_tactic.h"
#include "library/tactic/relation_tactics.h"
#include "library/tactic/unfold_rec.h"
// #define TRACE_MATCH_PLUGIN
#ifndef LEAN_DEFAULT_REWRITER_MAX_ITERATIONS
@ -57,7 +57,6 @@ Author: Leonardo de Moura
#define LEAN_DEFAULT_REWRITER_BETA_ETA true
#endif
namespace lean {
static name * g_rewriter_max_iterations = nullptr;
static name * g_rewriter_syntactic = nullptr;
@ -82,24 +81,27 @@ bool get_rewriter_beta_eta(options const & opts) {
class unfold_info {
list<name> m_names;
bool m_force_unfold;
location m_location;
public:
unfold_info() {}
unfold_info(list<name> const & l, location const & loc):m_names(l), m_location(loc) {}
unfold_info(list<name> const & l, bool force_unfold, location const & loc):
m_names(l), m_force_unfold(force_unfold), m_location(loc) {}
list<name> const & get_names() const { return m_names; }
location const & get_location() const { return m_location; }
bool force_unfold() const { return m_force_unfold; }
friend serializer & operator<<(serializer & s, unfold_info const & e) {
write_list<name>(s, e.m_names);
s << e.m_location;
s << e.m_force_unfold << e.m_location;
return s;
}
friend deserializer & operator>>(deserializer & d, unfold_info & e) {
e.m_names = read_list<name>(d);
d >> e.m_location;
d >> e.m_force_unfold >> e.m_location;
return d;
}
bool operator==(unfold_info const & i) const { return m_names == i.m_names && m_location == i.m_location; }
bool operator==(unfold_info const & i) const { return m_names == i.m_names && m_location == i.m_location && m_force_unfold == i.m_force_unfold; }
bool operator!=(unfold_info const & i) const { return !operator==(i); }
};
@ -308,8 +310,8 @@ public:
}
};
expr mk_rewrite_unfold(list<name> const & ns, location const & loc) {
macro_definition def(new rewrite_unfold_macro_cell(unfold_info(ns, loc)));
expr mk_rewrite_unfold(list<name> const & ns, bool force_unfold, location const & loc) {
macro_definition def(new rewrite_unfold_macro_cell(unfold_info(ns, force_unfold, loc)));
return mk_macro(def);
}
@ -626,16 +628,30 @@ class rewrite_fn {
}
};
optional<expr> reduce(expr const & e, list<name> const & to_unfold) {
bool unfolded = !to_unfold;
type_checker_ptr tc(new type_checker(m_env, m_ngen.mk_child(),
std::unique_ptr<converter>(new rewriter_converter(m_env, to_unfold, unfolded))));
optional<expr> reduce(expr const & e, list<name> const & to_unfold, bool force_unfold) {
constraint_seq cs;
bool use_eta = true;
expr r = normalize(*tc, e, cs, use_eta);
if (!unfolded || cs) // FAIL if didn't unfolded or generated constraints
return none_expr();
return some_expr(r);
bool unfolded = !to_unfold;
bool use_eta = true;
// TODO(Leo): should we add add an option that will not try to fold recursive applications
if (to_unfold) {
auto new_e = unfold_rec(m_env, m_ngen.mk_child(), force_unfold, e, to_unfold);
if (!new_e)
return none_expr();
type_checker_ptr tc(new type_checker(m_env, m_ngen.mk_child(),
std::unique_ptr<converter>(new rewriter_converter(m_env, list<name>(), unfolded))));
expr r = normalize(*tc, *new_e, cs, use_eta);
if (cs) // FAIL if generated constraints
return none_expr();
return some_expr(r);
} else {
type_checker_ptr tc(new type_checker(m_env, m_ngen.mk_child(),
std::unique_ptr<converter>(new rewriter_converter(m_env, to_unfold, unfolded))));
expr r = normalize(*tc, e, cs, use_eta);
if (!unfolded || cs) // FAIL if didn't unfolded or generated constraints
return none_expr();
return some_expr(r);
}
}
// Replace goal with definitionally equal one
@ -646,8 +662,8 @@ class rewrite_fn {
update_goal(new_g);
}
bool process_reduce_goal(list<name> const & to_unfold) {
if (auto new_type = reduce(m_g.get_type(), to_unfold)) {
bool process_reduce_goal(list<name> const & to_unfold, bool force_unfold) {
if (auto new_type = reduce(m_g.get_type(), to_unfold, force_unfold)) {
replace_goal(*new_type);
return true;
} else {
@ -683,9 +699,9 @@ class rewrite_fn {
update_goal(new_g);
}
bool process_reduce_hypothesis(name const & hyp_internal_name, list<name> const & to_unfold) {
bool process_reduce_hypothesis(name const & hyp_internal_name, list<name> const & to_unfold, bool force_unfold) {
expr hyp = m_g.find_hyp_from_internal_name(hyp_internal_name)->first;
if (auto new_hyp_type = reduce(mlocal_type(hyp), to_unfold)) {
if (auto new_hyp_type = reduce(mlocal_type(hyp), to_unfold, force_unfold)) {
replace_hypothesis(hyp, *new_hyp_type);
return true;
} else {
@ -693,20 +709,20 @@ class rewrite_fn {
}
}
bool process_reduce_step(list<name> const & to_unfold, location const & loc) {
bool process_reduce_step(list<name> const & to_unfold, bool force_unfold, location const & loc) {
if (loc.is_goal_only())
return process_reduce_goal(to_unfold);
return process_reduce_goal(to_unfold, force_unfold);
bool progress = false;
buffer<expr> hyps;
m_g.get_hyps(hyps);
for (expr const & h : hyps) {
if (!loc.includes_hypothesis(local_pp_name(h)))
continue;
if (process_reduce_hypothesis(mlocal_name(h), to_unfold))
if (process_reduce_hypothesis(mlocal_name(h), to_unfold, force_unfold))
progress = true;
}
if (loc.includes_goal()) {
if (process_reduce_goal(to_unfold))
if (process_reduce_goal(to_unfold, force_unfold))
progress = true;
}
return progress;
@ -715,7 +731,7 @@ class rewrite_fn {
bool process_unfold_step(expr const & elem) {
lean_assert(is_rewrite_unfold_step(elem));
auto info = get_rewrite_unfold_info(elem);
return process_reduce_step(info.get_names(), info.get_location());
return process_reduce_step(info.get_names(), info.force_unfold(), info.get_location());
}
optional<pair<expr, constraints>> elaborate_core(expr const & e, bool fail_if_cnstrs) {
@ -874,7 +890,7 @@ class rewrite_fn {
lean_assert(is_rewrite_reduce_step(elem));
if (macro_num_args(elem) == 0) {
auto info = get_rewrite_reduce_info(elem);
return process_reduce_step(list<name>(), info.get_location());
return process_reduce_step(list<name>(), false, info.get_location());
} else {
auto info = get_rewrite_reduce_info(elem);
return process_reduce_to_step(macro_arg(elem, 0), info.get_location());
@ -946,7 +962,7 @@ class rewrite_fn {
expr reduce_rule_type(expr const & e) {
if (m_apply_reduce) {
if (auto it = reduce(e, list<name>()))
if (auto it = reduce(e, list<name>(), false))
return *it;
else // TODO(Leo): we should fail instead of doing trying again
return head_beta_reduce(e);
@ -1257,6 +1273,10 @@ class rewrite_fn {
add_target_failure(src, t, failure::Unification);
return unify_result();
}
} catch (kernel_exception & ex) {
regular(m_env, m_ios) << ">> " << ex << "\n";
add_target_failure(orig_elem, t, ex.what());
return unify_result();
} catch (exception & ex) {
add_target_failure(orig_elem, t, ex.what());
return unify_result();
@ -1620,9 +1640,9 @@ public:
lean_assert(gs);
update_goal(head(gs));
m_subst = m_ps.get_subst();
m_max_iter = get_rewriter_max_iterations(ios.get_options());
m_use_trace = get_rewriter_trace(ios.get_options());
m_beta_eta = get_rewriter_beta_eta(ios.get_options());
m_max_iter = get_rewriter_max_iterations(ios.get_options());
m_use_trace = get_rewriter_trace(ios.get_options());
m_beta_eta = get_rewriter_beta_eta(ios.get_options());
m_apply_reduce = false;
}

2
src/library/tactic/rewrite_tactic.h
View file

@ -9,7 +9,7 @@ Author: Leonardo de Moura
#include "library/tactic/location.h"
namespace lean {
expr mk_rewrite_unfold(list<name> const & ns, location const & loc);
expr mk_rewrite_unfold(list<name> const & ns, bool force_unfold, location const & loc);
expr mk_rewrite_reduce(location const & loc);
expr mk_rewrite_reduce_to(expr const & e, location const & loc);
expr mk_rewrite_fold(expr const & e, location const & loc);

338
src/library/tactic/unfold_rec.cpp Normal file
View file

@ -0,0 +1,338 @@
/*
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include "kernel/type_checker.h"
#include "kernel/abstract.h"
#include "kernel/instantiate.h"
#include "kernel/inductive/inductive.h"
#include "library/util.h"
#include "library/replace_visitor.h"
#include "library/constants.h"
extern void pp_detail(lean::environment const & env, lean::expr const & e);
extern void pp(lean::environment const & env, lean::expr const & e);
namespace lean {
// Auxiliary visitor the implements the common parts for unfold_rec_fn and fold_rec_fn
class replace_visitor_aux : public replace_visitor {
protected:
virtual name mk_fresh_name() = 0;
expr visit_app_default(expr const & e, expr const & fn, buffer<expr> & args) {
bool modified = false;
for (expr & arg : args) {
expr new_arg = visit(arg);
if (arg != new_arg)
modified = true;
arg = new_arg;
}
if (!modified)
return e;
return mk_app(fn, args);
}
virtual expr visit_binding(expr const & b) {
expr new_domain = visit(binding_domain(b));
expr l = mk_local(mk_fresh_name(), new_domain);
expr new_body = abstract(visit(instantiate(binding_body(b), l)), l);
return update_binding(b, new_domain, new_body);
}
};
class unfold_rec_fn : public replace_visitor_aux {
environment const & m_env;
name_generator m_ngen;
bool m_force_unfold;
type_checker_ptr m_tc;
type_checker_ptr m_norm_decl_tc;
list<name> m_to_unfold;
virtual name mk_fresh_name() { return m_ngen.next(); }
static void throw_ill_formed() {
throw exception("ill-formed expression");
}
static bool is_rec_building_part(name const & n) {
if (n == get_prod_pr1_name() || n == get_prod_pr2_name())
return true;
if (n.is_atomic() || !n.is_string())
return false;
char const * str = n.get_string();
return
strcmp(str, "rec_on") == 0 ||
strcmp(str, "cases_on") == 0 ||
strcmp(str, "brec_on") == 0 ||
strcmp(str, "below") == 0 ||
strcmp(str, "no_confusion") == 0;
}
optional<unsigned> get_local_pos(buffer<expr> const & locals, expr const & e) {
if (!is_local(e))
return optional<unsigned>();
unsigned i = 0;
for (expr const & local : locals) {
if (mlocal_name(local) == mlocal_name(e))
return optional<unsigned>(i);
i++;
}
return optional<unsigned>();
}
// 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) {
buffer<expr> args;
expr fn = get_app_args(e, args);
if (!is_constant(fn))
return false;
optional<name> I = inductive::is_elim_rule(m_env, const_name(fn));
rec_name = const_name(fn);
if (!I)
return false;
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())
return false;
if (auto it = get_local_pos(locals, args[major_idx])) {
main_arg_pos = *it;
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);
} else {
return false;
}
}
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))
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)) {
for (unsigned i = 5; i < args.size(); i++) {
if (auto it2 = get_local_pos(locals, args[i])) {
rec_arg_pos.push_back(*it2);
} else {
return NOREC;
}
}
return BREC;
}
}
return NOREC;
}
// just unfold the application without trying to fold recursive call
expr unfold_simple(expr const & fn, buffer<expr> & args) {
expr new_app = mk_app(fn, args);
if (auto r = unfold_term(m_env, new_app)) {
return visit(*r);
} else {
return new_app;
}
}
expr get_fn_decl(expr const & fn, buffer<expr> & locals) {
lean_assert(is_constant(fn));
declaration decl = m_env.get(const_name(fn));
if (length(const_levels(fn)) != decl.get_num_univ_params())
throw_ill_formed();
expr fn_body = instantiate_value_univ_params(decl, const_levels(fn));
while (is_lambda(fn_body)) {
expr local = mk_local(m_ngen.next(), binding_domain(fn_body));
locals.push_back(local);
fn_body = instantiate(binding_body(fn_body), local);
}
return m_norm_decl_tc->whnf(fn_body).first;
}
struct fold_failed {};
struct fold_rec_fn : public replace_visitor_aux {
type_checker_ptr & m_tc;
expr m_fn; // function being unfolded
buffer<expr> const & m_args; // arguments of the function being unfolded
rec_kind m_kind;
name m_rec_name;
unsigned m_major_idx; // position of the major premise in the recursor
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
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):
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_main_pos(main_pos), m_rec_arg_pos(rec_arg_pos) {
lean_assert(m_main_pos < args.size());
lean_assert(std::all_of(rec_arg_pos.begin(), rec_arg_pos.end(), [&](unsigned pos) { return pos < args.size(); }));
}
virtual name mk_fresh_name() { return m_tc->mk_fresh_name(); }
expr fold_rec(expr const & e, buffer<expr> const & args) {
if (args.size() != m_major_idx + 1 + m_rec_arg_pos.size())
throw fold_failed();
buffer<expr> new_args;
new_args.append(m_args);
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];
}
expr folded_app = mk_app(m_fn, new_args);
if (!m_tc->is_def_eq(folded_app, e).first)
throw fold_failed();
return folded_app;
}
expr fold_brec(expr const & e, buffer<expr> const & args) {
if (args.size() != 3 + m_rec_arg_pos.size())
throw fold_failed();
buffer<expr> nested_args;
get_app_args(args[1], nested_args);
if (nested_args.size() != m_major_idx+1)
throw fold_failed();
buffer<expr> new_args;
new_args.append(m_args);
new_args[m_main_pos] = nested_args[m_major_idx];
for (unsigned i = 0; i < m_rec_arg_pos.size(); i++) {
new_args[m_rec_arg_pos[i]] = args[3 + i];
}
expr folded_app = mk_app(m_fn, new_args);
if (!m_tc->is_def_eq(folded_app, e).first)
throw fold_failed();
return folded_app;
}
virtual expr visit_app(expr const & e) {
buffer<expr> args;
expr fn = get_app_args(e, args);
if (m_kind == REC && is_constant(fn) && const_name(fn) == m_rec_name)
return fold_rec(e, args);
if (m_kind == BREC && is_constant(fn) && const_name(fn) == get_prod_pr1_name() && args.size() >= 3) {
expr rec_fn = get_app_fn(args[1]);
if (is_constant(rec_fn) && const_name(rec_fn) == m_rec_name)
return fold_brec(e, args);
}
return visit_app_default(e, fn, args);
}
};
expr unfold(expr const & fn, buffer<expr> args) {
buffer<expr> fn_locals;
expr fn_body = get_fn_decl(fn, fn_locals);
if (args.size() < fn_locals.size()) {
// insufficient args
return unfold_simple(fn, args);
}
name rec_name;
unsigned main_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) {
// norecursive definition
return unfold_simple(fn, args);
}
for (unsigned i = fn_locals.size(); 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) {
// argument is not a constructor or constraints were generated
throw fold_failed();
}
args[main_pos] = new_main_cs.first;
expr fn_body_abst = abstract_locals(fn_body, fn_locals.size(), fn_locals.data());
expr new_e = instantiate_rev(fn_body_abst, fn_locals.size(), args.data());
new_e = mk_app(new_e, args.size() - fn_locals.size(), args.data() + fn_locals.size());
auto new_e_cs = m_norm_decl_tc->whnf(new_e);
if (new_e_cs.second) {
// constraints were generated
throw fold_failed();
}
new_e = new_e_cs.first;
expr const new_head = get_app_fn(new_e);
// TODO(Leo): create an option for the following conditions?
// if (is_constant(new_head) && inductive::is_elim_rule(m_env, const_name(new_head))) {
// //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);
}
bool unfold_cnst(expr const & e) {
return is_constant(e) && std::find(m_to_unfold.begin(), m_to_unfold.end(), const_name(e)) != m_to_unfold.end();
}
virtual expr visit_app(expr const & e) {
buffer<expr> args;
expr fn = get_app_args(e, args);
bool modified = false;
for (expr & arg : args) {
expr new_arg = visit(arg);
if (arg != new_arg)
modified = true;
arg = new_arg;
}
if (unfold_cnst(fn)) {
try {
return unfold(fn, args);
} catch (fold_failed &) {
if (m_force_unfold)
return unfold_simple(fn, args);
}
}
if (!modified) {
return e;
} else {
return mk_app(fn, args);
}
}
virtual expr visit_constant(expr const & e) {
if (unfold_cnst(e)) {
if (auto r = unfold_term(m_env, e))
return *r;
}
return e;
}
public:
unfold_rec_fn(environment const & env, name_generator && ngen, bool force_unfold, list<name> const & to_unfold):
m_env(env),
m_ngen(ngen),
m_force_unfold(force_unfold),
m_tc(mk_type_checker(m_env, m_ngen.mk_child(), [](name const &) { return false; })),
m_norm_decl_tc(mk_type_checker(m_env, m_ngen.mk_child(), [](name const & n) { return !is_rec_building_part(n); })),
m_to_unfold(to_unfold)
{}
expr operator()(expr const & e) {
return replace_visitor_aux::operator()(e);
}
};
optional<expr> unfold_rec(environment const & env, name_generator && ngen, bool force_unfold, expr const & e, list<name> const & to_unfold) {
try {
expr r = unfold_rec_fn(env, std::move(ngen), force_unfold, to_unfold)(e);
if (r == e)
return none_expr();
return some_expr(r);
} catch (exception &) {
return none_expr();
}
}
}

11
src/library/tactic/unfold_rec.h Normal file
View file

@ -0,0 +1,11 @@
/*
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#pragma once
#include "kernel/environment.h"
namespace lean {
optional<expr> unfold_rec(environment const & env, name_generator && ngen, bool force_unfold, expr const & e, list<name> const & to_unfold);
}

2
tests/lean/run/esimp1.lean
View file

@ -10,12 +10,14 @@ definition foo [irreducible] (a : nat) := a
example (x y : nat) (H : (fun (a : nat), sigma.pr1 ⟨foo a, y⟩) x = 0) : x = 0 :=
begin
esimp at H,
esimp ↑foo at H,
exact H
end
example (x y : nat) (H : x = 0) : (fun (a : nat), sigma.pr1 ⟨foo a, y⟩) x = 0 :=
begin
esimp,
esimp ↑foo,
exact H
end

50
tests/lean/unfold_rec.lean Normal file
View file

@ -0,0 +1,50 @@
import data.vector
open nat vector
variables {A B : Type}
variable {n : nat}
theorem tst1 : ∀ n m, succ n + succ m = succ (succ (n + m)) :=
begin
intro n m,
esimp [add],
state,
rewrite [succ_add]
end
definition add2 (x y : nat) : nat :=
nat.rec_on x (λ y, y) (λ x r y, succ (r y)) y
local infix + := add2
theorem tst2 : ∀ n m, succ n + succ m = succ (succ (n + m)) :=
begin
intro n m,
esimp [add2],
state,
apply sorry
end
definition fib (A : Type) : nat → nat → nat → nat
| b 0 c := b
| b 1 c := c
| b (succ (succ a)) c := fib b a c + fib b (succ a) c
theorem fibgt0 : ∀ b n c, fib nat b n c > 0
| b 0 c := sorry
| b 1 c := sorry
| b (succ (succ m)) c :=
begin
unfold fib,
state,
apply sorry
end
theorem unzip_zip : ∀ {n : nat} (v₁ : vector A n) (v₂ : vector B n), unzip (zip v₁ v₂) = (v₁, v₂)
| 0 [] [] := rfl
| (succ m) (a::va) (b::vb) :=
begin
unfold [zip, unzip],
state,
rewrite [unzip_zip]
end

20
tests/lean/unfold_rec.lean.expected.out Normal file
View file

@ -0,0 +1,20 @@
unfold_rec.lean:11:2: proof state
n m : ℕ
⊢ succ (succ n + m) = succ (succ (n + m))
unfold_rec.lean:24:2: proof state
n m : ℕ
⊢ succ (n + succ m) = succ (succ (n + m))
unfold_rec.lean:39:2: proof state
fibgt0 : ∀ (b n c : ℕ), fib ℕ b n c > 0,
b m c : ℕ
⊢ fib ℕ b m c + fib ℕ b (succ m) c > 0
unfold_rec.lean:48:2: proof state
A : Type,
B : Type,
unzip_zip : ∀ {n : ℕ} (v₁ : vector A n) (v₂ : vector B n), unzip (zip v₁ v₂) = (v₁, v₂),
m : ℕ,
a : A,
va : vector A m,
b : B,
vb : vector B m
⊢ (a :: prod.pr1 (unzip (zip va vb)), b :: prod.pr2 (unzip (zip va vb))) = (a :: va, b :: vb)