603 lines
20 KiB
C++
603 lines
20 KiB
C++
/*
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Copyright (c) 2013-2014 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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Soonho Kong
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*/
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#include <vector>
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#include <sstream>
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#include <string>
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#include <algorithm>
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#include <limits>
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#include "runtime/hash.h"
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#include "util/list_fn.h"
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#include "util/buffer.h"
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#include "kernel/expr.h"
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#include "kernel/expr_eq_fn.h"
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#include "kernel/expr_sets.h"
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#include "kernel/for_each_fn.h"
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#include "kernel/replace_fn.h"
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#include "kernel/abstract.h"
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#include "kernel/instantiate.h"
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namespace lean {
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/* Expression literal values */
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literal::literal(char const * v):
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object_ref(mk_cnstr(static_cast<unsigned>(literal_kind::String), mk_string(v))) {
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}
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literal::literal(unsigned v):
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object_ref(mk_cnstr(static_cast<unsigned>(literal_kind::Nat), mk_nat_obj(v))) {
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}
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literal::literal(mpz const & v):
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object_ref(mk_cnstr(static_cast<unsigned>(literal_kind::Nat), mk_nat_obj(v))) {
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}
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literal::literal(nat const & v):
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object_ref(mk_cnstr(static_cast<unsigned>(literal_kind::Nat), v)) {
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}
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bool operator==(literal const & a, literal const & b) {
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if (a.kind() != b.kind()) return false;
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switch (a.kind()) {
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case literal_kind::String: return a.get_string() == b.get_string();
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case literal_kind::Nat: return a.get_nat() == b.get_nat();
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}
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lean_unreachable();
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}
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bool operator<(literal const & a, literal const & b) {
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if (a.kind() != b.kind()) return static_cast<unsigned>(a.kind()) < static_cast<unsigned>(b.kind());
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switch (a.kind()) {
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case literal_kind::String: return a.get_string() < b.get_string();
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case literal_kind::Nat: return a.get_nat() < b.get_nat();
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}
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lean_unreachable();
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}
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bool is_atomic(expr const & e) {
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switch (e.kind()) {
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case expr_kind::Const: case expr_kind::Sort:
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case expr_kind::BVar: case expr_kind::Lit:
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case expr_kind::MVar: case expr_kind::FVar:
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return true;
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case expr_kind::App:
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case expr_kind::Lambda:
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case expr_kind::Pi: case expr_kind::Let:
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case expr_kind::MData: case expr_kind::Proj:
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case expr_kind::Local:
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return false;
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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extern "C" uint8 lean_expr_binder_info(object * e);
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binder_info binding_info(expr const & e) { return static_cast<binder_info>(lean_expr_binder_info(e.to_obj_arg())); }
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extern "C" object * lean_lit_type(obj_arg e);
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expr lit_type(literal const & lit) { return expr(lean_lit_type(lit.to_obj_arg())); }
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extern "C" usize lean_expr_hash(obj_arg e);
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unsigned hash(expr const & e) { return lean_expr_hash(e.to_obj_arg()); }
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extern "C" uint8 lean_expr_has_fvar(obj_arg e);
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bool has_fvar(expr const & e) { return lean_expr_has_fvar(e.to_obj_arg()); }
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extern "C" uint8 lean_expr_has_expr_mvar(obj_arg e);
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bool has_expr_mvar(expr const & e) { return lean_expr_has_expr_mvar(e.to_obj_arg()); }
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extern "C" uint8 lean_expr_has_level_mvar(obj_arg e);
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bool has_univ_mvar(expr const & e) { return lean_expr_has_level_mvar(e.to_obj_arg()); }
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extern "C" uint8 lean_expr_has_level_param(obj_arg e);
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bool has_univ_param(expr const & e) { return lean_expr_has_level_param(e.to_obj_arg()); }
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extern "C" unsigned lean_expr_loose_bvar_range(object * e);
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unsigned get_loose_bvar_range(expr const & e) { return lean_expr_loose_bvar_range(e.to_obj_arg()); }
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// =======================================
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// Constructors
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static expr * g_dummy = nullptr;
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static expr const & get_dummy() {
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if (!g_dummy) {
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g_dummy = new expr(mk_constant("__expr_for_default_constructor__"));
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}
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return *g_dummy;
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}
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expr::expr():expr(get_dummy()) {}
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extern "C" object * lean_expr_mk_lit(obj_arg l);
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expr mk_lit(literal const & l) { return expr(lean_expr_mk_lit(l.to_obj_arg())); }
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extern "C" object * lean_expr_mk_mdata(obj_arg m, obj_arg e);
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expr mk_mdata(kvmap const & m, expr const & e) { return expr(lean_expr_mk_mdata(m.to_obj_arg(), e.to_obj_arg())); }
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extern "C" object * lean_expr_mk_proj(obj_arg s, obj_arg idx, obj_arg e);
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expr mk_proj(name const & s, nat const & idx, expr const & e) { return expr(lean_expr_mk_proj(s.to_obj_arg(), idx.to_obj_arg(), e.to_obj_arg())); }
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extern "C" object * lean_expr_mk_bvar(obj_arg idx);
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expr mk_bvar(nat const & idx) { return expr(lean_expr_mk_bvar(idx.to_obj_arg())); }
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extern "C" object * lean_expr_mk_fvar(obj_arg n);
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expr mk_fvar(name const & n) { return expr(lean_expr_mk_fvar(n.to_obj_arg())); }
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extern "C" object * lean_expr_mk_mvar(object * n);
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expr mk_mvar(name const & n) { return expr(lean_expr_mk_mvar(n.to_obj_arg())); }
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extern "C" object * lean_expr_mk_const(obj_arg n, obj_arg ls);
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expr mk_const(name const & n, levels const & ls) { return expr(lean_expr_mk_const(n.to_obj_arg(), ls.to_obj_arg())); }
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extern "C" object * lean_expr_mk_app(obj_arg f, obj_arg a);
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expr mk_app(expr const & f, expr const & a) { return expr(lean_expr_mk_app(f.to_obj_arg(), a.to_obj_arg())); }
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extern "C" object * lean_expr_mk_sort(obj_arg l);
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expr mk_sort(level const & l) { return expr(lean_expr_mk_sort(l.to_obj_arg())); }
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extern "C" object * lean_expr_mk_lambda(obj_arg n, obj_arg t, obj_arg e, uint8 bi);
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expr mk_lambda(name const & n, expr const & t, expr const & e, binder_info bi) {
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return expr(lean_expr_mk_lambda(n.to_obj_arg(), t.to_obj_arg(), e.to_obj_arg(), static_cast<uint8>(bi)));
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}
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extern "C" object * lean_expr_mk_forall(obj_arg n, obj_arg t, obj_arg e, uint8 bi);
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expr mk_pi(name const & n, expr const & t, expr const & e, binder_info bi) {
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return expr(lean_expr_mk_forall(n.to_obj_arg(), t.to_obj_arg(), e.to_obj_arg(), static_cast<uint8>(bi)));
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}
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static name * g_default_name = nullptr;
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expr mk_arrow(expr const & t, expr const & e) {
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return mk_pi(*g_default_name, t, e, mk_binder_info());
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}
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extern "C" object * lean_expr_mk_let(object * n, object * t, object * v, object * b);
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expr mk_let(name const & n, expr const & t, expr const & v, expr const & b) {
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return expr(lean_expr_mk_let(n.to_obj_arg(), t.to_obj_arg(), v.to_obj_arg(), b.to_obj_arg()));
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}
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static expr * g_Prop = nullptr;
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static expr * g_Type0 = nullptr;
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expr mk_Prop() { return *g_Prop; }
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expr mk_Type() { return *g_Type0; }
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// =======================================
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// Auxiliary constructors and accessors
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expr mk_app(expr const & f, unsigned num_args, expr const * args) {
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expr r = f;
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for (unsigned i = 0; i < num_args; i++)
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r = mk_app(r, args[i]);
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return r;
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}
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expr mk_app(unsigned num_args, expr const * args) {
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lean_assert(num_args >= 2);
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return mk_app(mk_app(args[0], args[1]), num_args - 2, args+2);
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}
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expr mk_app(expr const & f, list<expr> const & args) {
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buffer<expr> _args;
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to_buffer(args, _args);
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return mk_app(f, _args);
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}
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expr mk_rev_app(expr const & f, unsigned num_args, expr const * args) {
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expr r = f;
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unsigned i = num_args;
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while (i > 0) {
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--i;
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r = mk_app(r, args[i]);
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}
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return r;
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}
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expr mk_rev_app(unsigned num_args, expr const * args) {
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lean_assert(num_args >= 2);
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return mk_rev_app(mk_app(args[num_args-1], args[num_args-2]), num_args-2, args);
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}
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expr const & get_app_args(expr const & e, buffer<expr> & args) {
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unsigned sz = args.size();
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expr const * it = &e;
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while (is_app(*it)) {
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args.push_back(app_arg(*it));
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it = &(app_fn(*it));
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}
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std::reverse(args.begin() + sz, args.end());
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return *it;
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}
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expr const & get_app_args_at_most(expr const & e, unsigned num, buffer<expr> & args) {
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unsigned sz = args.size();
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expr const * it = &e;
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unsigned i = 0;
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while (is_app(*it)) {
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if (i == num)
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break;
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args.push_back(app_arg(*it));
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it = &(app_fn(*it));
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i++;
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}
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std::reverse(args.begin() + sz, args.end());
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return *it;
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}
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expr const & get_app_rev_args(expr const & e, buffer<expr> & args) {
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expr const * it = &e;
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while (is_app(*it)) {
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args.push_back(app_arg(*it));
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it = &(app_fn(*it));
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}
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return *it;
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}
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expr const & get_app_fn(expr const & e) {
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expr const * it = &e;
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while (is_app(*it)) {
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it = &(app_fn(*it));
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}
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return *it;
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}
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unsigned get_app_num_args(expr const & e) {
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expr const * it = &e;
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unsigned n = 0;
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while (is_app(*it)) {
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it = &(app_fn(*it));
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n++;
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}
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return n;
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}
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bool is_arrow(expr const & t) {
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if (!is_pi(t)) return false;
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if (has_loose_bvars(t)) {
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return !has_loose_bvar(binding_body(t), 0);
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} else {
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lean_assert(has_loose_bvars(binding_body(t)) == has_loose_bvar(binding_body(t), 0));
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return !has_loose_bvars(binding_body(t));
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}
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}
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bool is_default_var_name(name const & n) {
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return n == *g_default_name;
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}
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// =======================================
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// Update
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expr update_mdata(expr const & e, expr const & t) {
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if (!is_eqp(mdata_expr(e), t))
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return mk_mdata(mdata_data(e), t);
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else
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return e;
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}
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expr update_proj(expr const & e, expr const & t) {
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if (!is_eqp(proj_expr(e), t))
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return mk_proj(proj_sname(e), proj_idx(e), t);
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else
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return e;
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}
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expr update_app(expr const & e, expr const & new_fn, expr const & new_arg) {
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if (!is_eqp(app_fn(e), new_fn) || !is_eqp(app_arg(e), new_arg))
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return mk_app(new_fn, new_arg);
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else
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return e;
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}
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expr update_binding(expr const & e, expr const & new_domain, expr const & new_body) {
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if (!is_eqp(binding_domain(e), new_domain) || !is_eqp(binding_body(e), new_body))
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return mk_binding(e.kind(), binding_name(e), new_domain, new_body, binding_info(e));
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else
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return e;
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}
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expr update_binding(expr const & e, expr const & new_domain, expr const & new_body, binder_info bi) {
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if (!is_eqp(binding_domain(e), new_domain) || !is_eqp(binding_body(e), new_body) || bi != binding_info(e))
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return mk_binding(e.kind(), binding_name(e), new_domain, new_body, bi);
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else
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return e;
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}
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expr update_sort(expr const & e, level const & new_level) {
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if (!is_eqp(sort_level(e), new_level))
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return mk_sort(new_level);
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else
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return e;
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}
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expr update_const(expr const & e, levels const & new_levels) {
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if (!is_eqp(const_levels(e), new_levels))
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return mk_const(const_name(e), new_levels);
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else
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return e;
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}
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expr update_let(expr const & e, expr const & new_type, expr const & new_value, expr const & new_body) {
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if (!is_eqp(let_type(e), new_type) || !is_eqp(let_value(e), new_value) || !is_eqp(let_body(e), new_body))
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return mk_let(let_name(e), new_type, new_value, new_body);
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else
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return e;
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}
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extern "C" object * lean_expr_update_mdata(obj_arg e, obj_arg new_expr) {
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if (mdata_expr(TO_REF(expr, e)).raw() != new_expr) {
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object * r = lean_expr_mk_mdata(mdata_data(TO_REF(expr, e)).to_obj_arg(), new_expr);
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lean_dec_ref(e);
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return r;
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} else {
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lean_dec_ref(new_expr);
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return e;
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}
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}
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extern "C" object * lean_expr_update_const(obj_arg e, obj_arg new_levels) {
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if (const_levels(TO_REF(expr, e)).raw() != new_levels) {
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object * r = lean_expr_mk_const(const_name(TO_REF(expr, e)).to_obj_arg(), new_levels);
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lean_dec_ref(e);
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return r;
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} else {
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lean_dec(new_levels);
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return e;
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}
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}
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extern "C" object * lean_expr_update_sort(obj_arg e, obj_arg new_level) {
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if (sort_level(TO_REF(expr, e)).raw() != new_level) {
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object * r = lean_expr_mk_sort(new_level);
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lean_dec_ref(e);
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return r;
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} else {
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lean_dec(new_level);
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return e;
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}
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}
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extern "C" object * lean_expr_update_proj(obj_arg e, obj_arg new_expr) {
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if (proj_expr(TO_REF(expr, e)).raw() != new_expr) {
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object * r = lean_expr_mk_proj(proj_sname(TO_REF(expr, e)).to_obj_arg(), proj_idx(TO_REF(expr, e)).to_obj_arg(), new_expr);
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lean_dec_ref(e);
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return r;
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} else {
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lean_dec_ref(new_expr);
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return e;
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}
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}
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extern "C" object * lean_expr_update_app(obj_arg e, obj_arg new_fn, obj_arg new_arg) {
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if (app_fn(TO_REF(expr, e)).raw() != new_fn || app_arg(TO_REF(expr, e)).raw() != new_arg) {
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object * r = lean_expr_mk_app(new_fn, new_arg);
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lean_dec_ref(e);
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return r;
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} else {
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lean_dec_ref(new_fn); lean_dec_ref(new_arg);
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return e;
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}
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}
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extern "C" object * lean_expr_update_forall(obj_arg e, uint8 new_binfo, obj_arg new_domain, obj_arg new_body) {
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if (binding_domain(TO_REF(expr, e)).raw() != new_domain || binding_body(TO_REF(expr, e)).raw() != new_body ||
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binding_info(TO_REF(expr, e)) != static_cast<binder_info>(new_binfo)) {
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object * r = lean_expr_mk_forall(binding_name(TO_REF(expr, e)).to_obj_arg(), new_domain, new_body, new_binfo);
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lean_dec_ref(e);
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return r;
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} else {
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lean_dec_ref(new_domain); lean_dec_ref(new_body);
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return e;
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}
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}
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extern "C" object * lean_expr_update_lambda(obj_arg e, uint8 new_binfo, obj_arg new_domain, obj_arg new_body) {
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if (binding_domain(TO_REF(expr, e)).raw() != new_domain || binding_body(TO_REF(expr, e)).raw() != new_body ||
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binding_info(TO_REF(expr, e)) != static_cast<binder_info>(new_binfo)) {
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object * r = lean_expr_mk_lambda(binding_name(TO_REF(expr, e)).to_obj_arg(), new_domain, new_body, new_binfo);
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lean_dec_ref(e);
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return r;
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} else {
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lean_dec_ref(new_domain); lean_dec_ref(new_body);
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return e;
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}
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}
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extern "C" object * lean_expr_update_let(obj_arg e, obj_arg new_type, obj_arg new_val, obj_arg new_body) {
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if (let_type(TO_REF(expr, e)).raw() != new_type || let_value(TO_REF(expr, e)).raw() != new_val ||
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let_body(TO_REF(expr, e)).raw() != new_body) {
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object * r = lean_expr_mk_let(let_name(TO_REF(expr, e)).to_obj_arg(), new_type, new_val, new_body);
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lean_dec_ref(e);
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return r;
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} else {
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lean_dec_ref(new_type); lean_dec_ref(new_val); lean_dec_ref(new_body);
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return e;
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}
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}
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// =======================================
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// Loose bound variable management
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static bool has_loose_bvars_in_domain(expr const & b, unsigned vidx, bool strict) {
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if (is_pi(b)) {
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return
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(has_loose_bvar(binding_domain(b), vidx) && is_explicit(binding_info(b))) ||
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has_loose_bvars_in_domain(binding_body(b), vidx+1, strict);
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} else if (!strict) {
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return has_loose_bvar(b, vidx);
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} else {
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return false;
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}
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}
|
|
|
|
bool has_loose_bvar(expr const & e, unsigned i) {
|
|
bool found = false;
|
|
for_each(e, [&](expr const & e, unsigned offset) {
|
|
if (found)
|
|
return false; // already found
|
|
unsigned n_i = i + offset;
|
|
if (n_i < i)
|
|
return false; // overflow, vidx can't be >= max unsigned
|
|
if (n_i >= get_loose_bvar_range(e))
|
|
return false; // expression e does not contain bound variables with idx >= n_i
|
|
if (is_var(e)) {
|
|
nat const & vidx = bvar_idx(e);
|
|
if (vidx == n_i)
|
|
found = true;
|
|
}
|
|
return true; // continue search
|
|
});
|
|
return found;
|
|
}
|
|
|
|
extern "C" uint8 lean_expr_has_loose_bvar(b_obj_arg e, b_obj_arg i) {
|
|
if (!lean_is_scalar(i))
|
|
return false;
|
|
return has_loose_bvar(TO_REF(expr, e), lean_unbox(i));
|
|
}
|
|
|
|
expr lower_loose_bvars(expr const & e, unsigned s, unsigned d) {
|
|
if (d == 0 || s >= get_loose_bvar_range(e))
|
|
return e;
|
|
lean_assert(s >= d);
|
|
return replace(e, [=](expr const & e, unsigned offset) -> optional<expr> {
|
|
unsigned s1 = s + offset;
|
|
if (s1 < s)
|
|
return some_expr(e); // overflow, vidx can't be >= max unsigned
|
|
if (s1 >= get_loose_bvar_range(e))
|
|
return some_expr(e); // expression e does not contain bound variables with idx >= s1
|
|
if (is_bvar(e) && bvar_idx(e) >= s1) {
|
|
lean_assert(bvar_idx(e) >= offset + d);
|
|
return some_expr(mk_bvar(bvar_idx(e) - nat(d)));
|
|
} else {
|
|
return none_expr();
|
|
}
|
|
});
|
|
}
|
|
|
|
expr lower_loose_bvars(expr const & e, unsigned d) {
|
|
return lower_loose_bvars(e, d, d);
|
|
}
|
|
|
|
extern "C" object * lean_expr_lower_loose_bvars(b_obj_arg e, b_obj_arg s, b_obj_arg d) {
|
|
if (!lean_is_scalar(s) || !lean_is_scalar(d) || lean_unbox(s) < lean_unbox(d)) {
|
|
lean_inc(e);
|
|
return e;
|
|
}
|
|
return lower_loose_bvars(TO_REF(expr, e), lean_unbox(s), lean_unbox(d)).steal();
|
|
}
|
|
|
|
expr lift_loose_bvars(expr const & e, unsigned s, unsigned d) {
|
|
if (d == 0 || s >= get_loose_bvar_range(e))
|
|
return e;
|
|
return replace(e, [=](expr const & e, unsigned offset) -> optional<expr> {
|
|
unsigned s1 = s + offset;
|
|
if (s1 < s)
|
|
return some_expr(e); // overflow, vidx can't be >= max unsigned
|
|
if (s1 >= get_loose_bvar_range(e))
|
|
return some_expr(e); // expression e does not contain bound variables with idx >= s1
|
|
if (is_var(e) && bvar_idx(e) >= s + offset) {
|
|
return some_expr(mk_bvar(bvar_idx(e) + nat(d)));
|
|
} else {
|
|
return none_expr();
|
|
}
|
|
});
|
|
}
|
|
|
|
expr lift_loose_bvars(expr const & e, unsigned d) {
|
|
return lift_loose_bvars(e, 0, d);
|
|
}
|
|
|
|
extern "C" object * lean_expr_lift_loose_bvars(b_obj_arg e, b_obj_arg s, b_obj_arg d) {
|
|
if (!lean_is_scalar(s) || !lean_is_scalar(d)) {
|
|
lean_inc(e);
|
|
return e;
|
|
}
|
|
return lift_loose_bvars(TO_REF(expr, e), lean_unbox(s), lean_unbox(d)).steal();
|
|
}
|
|
|
|
// =======================================
|
|
// Implicit argument inference
|
|
|
|
expr infer_implicit(expr const & t, unsigned num_params, bool strict) {
|
|
if (num_params == 0) {
|
|
return t;
|
|
} else if (is_pi(t)) {
|
|
expr new_body = infer_implicit(binding_body(t), num_params-1, strict);
|
|
if (!is_explicit(binding_info(t))) {
|
|
// argument is already marked as implicit
|
|
return update_binding(t, binding_domain(t), new_body);
|
|
} else if (has_loose_bvars_in_domain(new_body, 0, strict)) {
|
|
return update_binding(t, binding_domain(t), new_body, mk_implicit_binder_info());
|
|
} else {
|
|
return update_binding(t, binding_domain(t), new_body);
|
|
}
|
|
} else {
|
|
return t;
|
|
}
|
|
}
|
|
|
|
expr infer_implicit(expr const & t, bool strict) {
|
|
return infer_implicit(t, std::numeric_limits<unsigned>::max(), strict);
|
|
}
|
|
|
|
// =======================================
|
|
// Initialization & Finalization
|
|
|
|
void initialize_expr() {
|
|
get_dummy();
|
|
g_default_name = new name("a");
|
|
g_Type0 = new expr(mk_sort(mk_level_one()));
|
|
g_Prop = new expr(mk_sort(mk_level_zero()));
|
|
/* TODO(Leo): add support for builtin constants in the kernel.
|
|
Something similar to what we have in the library directory. */
|
|
}
|
|
|
|
void finalize_expr() {
|
|
delete g_Prop;
|
|
delete g_Type0;
|
|
delete g_dummy;
|
|
delete g_default_name;
|
|
}
|
|
|
|
// =======================================
|
|
// Legacy
|
|
|
|
binder_info local_info(expr const & e) { lean_assert(is_local(e)); return static_cast<binder_info>(lean_expr_binder_info(e.to_obj_arg())); }
|
|
extern "C" object * lean_expr_mk_local(obj_arg n, obj_arg u, obj_arg t, uint8 bi);
|
|
expr mk_local(name const & n, name const & pp_n, expr const & t, binder_info bi) {
|
|
return expr(lean_expr_mk_local(n.to_obj_arg(), pp_n.to_obj_arg(), t.to_obj_arg(), static_cast<uint8>(bi)));
|
|
}
|
|
|
|
expr update_local(expr const & e, expr const & new_type, binder_info bi) {
|
|
if (is_eqp(local_type(e), new_type) && local_info(e) == bi)
|
|
return e;
|
|
else
|
|
return mk_local(local_name(e), local_pp_name(e), new_type, bi);
|
|
}
|
|
|
|
expr update_local(expr const & e, binder_info bi) {
|
|
return update_local(e, local_type(e), bi);
|
|
}
|
|
|
|
expr update_local(expr const & e, expr const & new_type) {
|
|
if (is_eqp(local_type(e), new_type))
|
|
return e;
|
|
else
|
|
return mk_local(local_name(e), local_pp_name(e), new_type, local_info(e));
|
|
}
|
|
|
|
optional<expr> has_expr_metavar_strict(expr const & e) {
|
|
if (!has_expr_metavar(e))
|
|
return none_expr();
|
|
optional<expr> r;
|
|
for_each(e, [&](expr const & e, unsigned) {
|
|
if (r || !has_expr_metavar(e)) return false;
|
|
if (is_metavar_app(e)) { r = e; return false; }
|
|
if (is_local(e)) return false; // do not visit type
|
|
return true;
|
|
});
|
|
return r;
|
|
}
|
|
}
|