lean4-htt/src/kernel/expr.cpp
2019-07-26 12:39:35 -07:00

873 lines
31 KiB
C++

/*
Copyright (c) 2013-2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
Soonho Kong
*/
#include <vector>
#include <sstream>
#include <string>
#include <algorithm>
#include <limits>
#include "runtime/hash.h"
#include "util/list_fn.h"
#include "util/buffer.h"
#include "kernel/expr.h"
#include "kernel/expr_eq_fn.h"
#include "kernel/expr_sets.h"
#include "kernel/for_each_fn.h"
#include "kernel/replace_fn.h"
#include "kernel/abstract.h"
#include "kernel/instantiate.h"
#ifndef LEAN_INITIAL_EXPR_CACHE_CAPACITY
#define LEAN_INITIAL_EXPR_CACHE_CAPACITY 1024*16
#endif
namespace lean {
/* Expression literal values */
literal::literal(char const * v):
object_ref(mk_cnstr(static_cast<unsigned>(literal_kind::String), mk_string(v))) {
}
literal::literal(unsigned v):
object_ref(mk_cnstr(static_cast<unsigned>(literal_kind::Nat), mk_nat_obj(v))) {
}
literal::literal(mpz const & v):
object_ref(mk_cnstr(static_cast<unsigned>(literal_kind::Nat), mk_nat_obj(v))) {
}
literal::literal(nat const & v):
object_ref(mk_cnstr(static_cast<unsigned>(literal_kind::Nat), v)) {
}
bool operator==(literal const & a, literal const & b) {
if (a.kind() != b.kind()) return false;
switch (a.kind()) {
case literal_kind::String: return a.get_string() == b.get_string();
case literal_kind::Nat: return a.get_nat() == b.get_nat();
}
lean_unreachable();
}
bool operator<(literal const & a, literal const & b) {
if (a.kind() != b.kind()) return static_cast<unsigned>(a.kind()) < static_cast<unsigned>(b.kind());
switch (a.kind()) {
case literal_kind::String: return a.get_string() < b.get_string();
case literal_kind::Nat: return a.get_nat() < b.get_nat();
}
lean_unreachable();
}
static inline unsigned literal_hash(b_obj_arg l) {
switch (literal::kind(l)) {
case literal_kind::Nat: return nat::hash(cnstr_get(l, 0));
case literal_kind::String: return hash_str(string_size(cnstr_get(l, 0)) - 1, string_cstr(cnstr_get(l, 0)), 17);
}
lean_unreachable();
}
static unsigned levels_hash(object * ls) {
unsigned r = 23;
while (!is_scalar(ls)) {
r = hash(level::hash(cnstr_get(ls, 0)), r);
ls = cnstr_get(ls, 1);
}
return r;
}
// =======================================
// Safe arithmetic
static unsigned safe_add(unsigned w1, unsigned w2) {
unsigned r = w1 + w2;
if (r < w1)
r = std::numeric_limits<unsigned>::max(); // overflow
return r;
}
static unsigned safe_inc(unsigned w) {
if (w < std::numeric_limits<unsigned>::max())
return w+1;
else
return w;
}
static unsigned safe_dec(unsigned k) {
return k == 0 ? 0 : k - 1;
}
// =======================================
// Scalar data offset calculation and setters/getters
inline constexpr unsigned num_obj_fields(expr_kind k) {
return
k == expr_kind::App ? 2 :
k == expr_kind::Const ? 2 :
k == expr_kind::FVar ? 3 : // TODO(Leo): it should be 1 after we remove support for legacy code
k == expr_kind::Lambda ? 3 :
k == expr_kind::Pi ? 3 :
k == expr_kind::BVar ? 1 :
k == expr_kind::Let ? 4 :
k == expr_kind::MVar ? 2 :
k == expr_kind::Sort ? 1 :
k == expr_kind::Lit ? 1 :
k == expr_kind::MData ? 2 :
k == expr_kind::Proj ? 3 :
/* k == expr_kind::Quote */ 1;
}
/* Expression scalar data offset. */
inline constexpr unsigned scalar_offset(expr_kind k) { return num_obj_fields(k) * sizeof(object*); }
inline constexpr unsigned binder_info_offset(expr_kind k) {
// Only for: k == expr_kind::Pi || k == expr_kind::Lambda || k == expr_kind::FVar
return scalar_offset(k);
}
/* Legacy support */
inline constexpr unsigned reflected_offset(expr_kind k) {
// Only for: k == expr_kind::Quote
return scalar_offset(k);
}
inline constexpr unsigned hash_offset(expr_kind k) {
return
k == expr_kind::FVar ? scalar_offset(k) + sizeof(unsigned) : // for binder_info, TODO(Leo): delete after we remove support for legacy code
k == expr_kind::Lambda ? scalar_offset(k) + sizeof(unsigned) : // for binder_info
k == expr_kind::Pi ? scalar_offset(k) + sizeof(unsigned) : // for binder_info
scalar_offset(k);
}
inline constexpr size_t flags_offset(expr_kind k) { return hash_offset(k) + sizeof(unsigned); }
inline constexpr size_t weight_offset(expr_kind k) { return flags_offset(k) + sizeof(unsigned); }
inline constexpr size_t depth_offset(expr_kind k) { return weight_offset(k) + sizeof(unsigned); }
inline constexpr size_t loose_bvar_range_offset(expr_kind k) { return depth_offset(k) + sizeof(unsigned); }
/* Size for scalar value area for non recursive expression. */
inline constexpr size_t expr_scalar_size(expr_kind k) { return flags_offset(k) + sizeof(unsigned); }
/* Size for scalar value area for recursive expression. */
inline constexpr size_t rec_expr_scalar_size(expr_kind k) { return loose_bvar_range_offset(k) + sizeof(unsigned); }
static inline unsigned expr_hash(object * e) { return cnstr_get_scalar<unsigned>(e, hash_offset(expr::kind(e))); }
unsigned hash(expr const & e) { return expr_hash(e.raw()); }
extern "C" size_t lean_expr_hash(object * e) { return expr_hash(e); }
/* Set expr cached hash code and flags. All expressions contain them.
We provide the kind `k` to allow the compiler to compute offsets at compilation time. */
template<expr_kind k> void set_scalar(object * e, unsigned hash, bool has_expr_mvar, bool has_univ_mvar,
bool has_fvar, bool has_univ_param) {
lean_assert(expr::kind(e) == k);
unsigned char d =
(has_expr_mvar ? 1 : 0) +
(has_univ_mvar ? 2 : 0) +
(has_fvar ? 4 : 0) +
(has_univ_param ? 8 : 0);
cnstr_set_scalar<unsigned>(e, hash_offset(k), hash);
cnstr_set_scalar<unsigned char>(e, flags_offset(k), d);
}
/* Set expr cached weight, depth and loose bvar range. We only store this information in recursive expr constructors.
We provide the kind `k` to allow the compiler to compute offsets at compilation time. */
template<expr_kind k> void set_rec_scalar(object * e, unsigned weight, unsigned depth, unsigned loose_bvar_range) {
lean_assert(expr::kind(e) == k);
cnstr_set_scalar<unsigned>(e, weight_offset(k), weight);
cnstr_set_scalar<unsigned>(e, depth_offset(k), depth);
cnstr_set_scalar<unsigned>(e, loose_bvar_range_offset(k), loose_bvar_range);
}
template<expr_kind k> void set_binder_info(object * e, binder_info bi) {
lean_assert(expr::kind(e) == k);
cnstr_set_scalar<unsigned char>(e, binder_info_offset(k), static_cast<unsigned char>(bi));
}
static inline unsigned char get_flags(object * e) { return cnstr_get_scalar<unsigned char>(e, flags_offset(expr::kind(e))); }
static inline bool has_expr_mvar(object * e) { return (get_flags(e) & 1) != 0; }
static inline bool has_univ_mvar(object * e) { return (get_flags(e) & 2) != 0; }
static inline bool has_fvar(object * e) { return (get_flags(e) & 4) != 0; }
static inline bool has_univ_param(object * e) { return (get_flags(e) & 8) != 0; }
bool has_expr_mvar(expr const & e) { return has_expr_mvar(e.raw()); }
bool has_univ_mvar(expr const & e) { return has_univ_mvar(e.raw()); }
bool has_fvar(expr const & e) { return has_fvar(e.raw()); }
bool has_univ_param(expr const & e) { return has_univ_param(e.raw()); }
template<expr_kind k> unsigned get_weight_core(object * e) { return cnstr_get_scalar<unsigned>(e, weight_offset(k)); }
unsigned expr_get_weight(object * e) {
switch (expr::kind(e)) {
case expr_kind::BVar: case expr_kind::Const: case expr_kind::Sort:
case expr_kind::MVar: case expr_kind::FVar: case expr_kind::Lit:
return 1;
case expr_kind::Lambda: return get_weight_core<expr_kind::Lambda>(e);
case expr_kind::Pi: return get_weight_core<expr_kind::Pi>(e);
case expr_kind::App: return get_weight_core<expr_kind::App>(e);
case expr_kind::Let: return get_weight_core<expr_kind::Let>(e);
case expr_kind::MData: return get_weight_core<expr_kind::MData>(e);
case expr_kind::Proj: return get_weight_core<expr_kind::Proj>(e);
}
lean_unreachable(); // LCOV_EXCL_LINE
}
extern "C" object * lean_expr_get_weight(b_obj_arg e) { return mk_nat_obj(expr_get_weight(e)); }
template<expr_kind k> unsigned get_depth_core(object * e) { return cnstr_get_scalar<unsigned>(e, depth_offset(k)); }
unsigned expr_get_depth(object * e) {
switch (expr::kind(e)) {
case expr_kind::BVar: case expr_kind::Const: case expr_kind::Sort:
case expr_kind::MVar: case expr_kind::FVar: case expr_kind::Lit:
return 1;
case expr_kind::Lambda: return get_depth_core<expr_kind::Lambda>(e);
case expr_kind::Pi: return get_depth_core<expr_kind::Pi>(e);
case expr_kind::App: return get_depth_core<expr_kind::App>(e);
case expr_kind::Let: return get_depth_core<expr_kind::Let>(e);
case expr_kind::MData: return get_depth_core<expr_kind::MData>(e);
case expr_kind::Proj: return get_depth_core<expr_kind::Proj>(e);
}
lean_unreachable(); // LCOV_EXCL_LINE
}
extern "C" object * lean_expr_get_depth(b_obj_arg e) { return mk_nat_obj(expr_get_depth(e)); }
template<expr_kind k> unsigned get_loose_bvar_range_core(object * e) { return cnstr_get_scalar<unsigned>(e, loose_bvar_range_offset(k)); }
unsigned expr_get_loose_bvar_range(object * e) {
switch (expr::kind(e)) {
case expr_kind::Const: case expr_kind::Sort:
case expr_kind::Lit:
return 0;
case expr_kind::BVar: {
object * idx = cnstr_get(e, 0);
if (is_scalar(idx))
return safe_inc(unbox(idx));
else
return std::numeric_limits<unsigned>::max();
}
case expr_kind::MVar: return get_loose_bvar_range_core<expr_kind::MVar>(e);
case expr_kind::FVar: return get_loose_bvar_range_core<expr_kind::FVar>(e);
case expr_kind::Lambda: return get_loose_bvar_range_core<expr_kind::Lambda>(e);
case expr_kind::Pi: return get_loose_bvar_range_core<expr_kind::Pi>(e);
case expr_kind::App: return get_loose_bvar_range_core<expr_kind::App>(e);
case expr_kind::Let: return get_loose_bvar_range_core<expr_kind::Let>(e);
case expr_kind::MData: return get_loose_bvar_range_core<expr_kind::MData>(e);
case expr_kind::Proj: return get_loose_bvar_range_core<expr_kind::Proj>(e);
}
lean_unreachable(); // LCOV_EXCL_LINE
}
extern "C" object * lean_expr_get_loose_bvar_range(b_obj_arg e) { return mk_nat_obj(expr_get_loose_bvar_range(e)); }
bool is_atomic(expr const & e) {
switch (e.kind()) {
case expr_kind::Const: case expr_kind::Sort:
case expr_kind::BVar: case expr_kind::Lit:
return true;
case expr_kind::App: case expr_kind::MVar:
case expr_kind::FVar: case expr_kind::Lambda:
case expr_kind::Pi: case expr_kind::Let:
case expr_kind::MData: case expr_kind::Proj:
return false;
}
lean_unreachable(); // LCOV_EXCL_LINE
}
binder_info binding_info(expr const & e) {
lean_assert(is_lambda(e) || is_pi(e));
// Remark: lambda and Pi have the same memory layout
return static_cast<binder_info>(cnstr_get_scalar<unsigned char>(e.raw(), binder_info_offset(expr_kind::Lambda)));
}
/* Legacy */
binder_info local_info(expr const & e) {
lean_assert(is_local(e));
return static_cast<binder_info>(cnstr_get_scalar<unsigned char>(e.raw(), binder_info_offset(expr_kind::FVar)));
}
static expr * g_nat_type = nullptr;
static expr * g_string_type = nullptr;
expr const & lit_type(expr const & e) {
switch (lit_value(e).kind()) {
case literal_kind::String: return *g_string_type;
case literal_kind::Nat: return *g_nat_type;
}
lean_unreachable();
}
// =======================================
// Constructors
static expr * g_dummy = nullptr;
expr::expr():expr(*g_dummy) {}
extern "C" object * lean_expr_mk_lit(obj_arg l) {
object * r = alloc_cnstr(static_cast<unsigned>(expr_kind::Lit), 1, expr_scalar_size(expr_kind::Lit));
cnstr_set(r, 0, l);
set_scalar<expr_kind::Lit>(r, literal_hash(l), false, false, false, false);
return r;
}
expr mk_lit(literal const & l) {
inc(l.raw());
return expr(lean_expr_mk_lit(l.raw()));
}
extern "C" object * lean_expr_mk_mdata(obj_arg m, obj_arg e) {
object * r = alloc_cnstr(static_cast<unsigned>(expr_kind::MData), 2, expr_scalar_size(expr_kind::MData));
cnstr_set(r, 0, m);
cnstr_set(r, 1, e);
unsigned w = safe_inc(expr_get_weight(e));
unsigned d = expr_get_depth(e) + 1;
unsigned h = hash(expr_hash(e), hash(w, d));
set_scalar<expr_kind::MData>(r, h, has_expr_mvar(e), has_univ_mvar(e), has_fvar(e), has_univ_param(e));
set_rec_scalar<expr_kind::MData>(r, w, d, expr_get_loose_bvar_range(e));
return r;
}
expr mk_mdata(kvmap const & m, expr const & e) {
inc(m.raw()); inc(e.raw());
return expr(lean_expr_mk_mdata(m.raw(), e.raw()));
}
extern "C" object * lean_expr_mk_proj(obj_arg s, obj_arg idx, obj_arg e) {
object * r = alloc_cnstr(static_cast<unsigned>(expr_kind::Proj), 3, rec_expr_scalar_size(expr_kind::Proj));
cnstr_set(r, 0, s);
cnstr_set(r, 1, idx);
cnstr_set(r, 2, e);
unsigned w = safe_inc(expr_get_weight(e));
unsigned d = expr_get_depth(e) + 1;
unsigned h = hash(expr_hash(e), hash(nat::hash(idx), w));
set_scalar<expr_kind::Proj>(r, h, has_expr_mvar(e), has_univ_mvar(e), has_fvar(e), has_univ_param(e));
set_rec_scalar<expr_kind::Proj>(r, w, d, expr_get_loose_bvar_range(e));
return r;
}
expr mk_proj(name const & s, nat const & idx, expr const & e) {
inc(s.raw()); inc(idx.raw()); inc(e.raw());
return expr(lean_expr_mk_proj(s.raw(), idx.raw(), e.raw()));
}
extern "C" object * lean_expr_mk_bvar(obj_arg idx) {
object * r = alloc_cnstr(static_cast<unsigned>(expr_kind::BVar), 1, expr_scalar_size(expr_kind::BVar));
cnstr_set(r, 0, idx);
set_scalar<expr_kind::BVar>(r, nat::hash(idx), false, false, false, false);
return r;
}
expr mk_bvar(nat const & idx) {
inc(idx.raw());
return expr(lean_expr_mk_bvar(idx.raw()));
}
/* Legacy */
static inline object * mk_local(obj_arg n, obj_arg pp_n, obj_arg t, binder_info bi) {
object * r = alloc_cnstr(static_cast<unsigned>(expr_kind::FVar), 3, rec_expr_scalar_size(expr_kind::FVar));
cnstr_set(r, 0, n);
cnstr_set(r, 1, pp_n);
cnstr_set(r, 2, t);
set_binder_info<expr_kind::FVar>(r, bi);
set_scalar<expr_kind::FVar>(r, name::hash(n), has_expr_mvar(t), has_univ_mvar(t), true, has_univ_param(t));
set_rec_scalar<expr_kind::FVar>(r, 1, 1, expr_get_loose_bvar_range(t));
return r;
}
extern "C" object * lean_expr_mk_fvar(obj_arg n) {
inc(n);
inc(g_dummy->raw());
return mk_local(n, n, g_dummy->raw(), mk_binder_info());
}
expr mk_local(name const & n, name const & pp_n, expr const & t, binder_info bi) {
inc(n.raw()); inc(pp_n.raw()); inc(t.raw());
return expr(mk_local(n.raw(), pp_n.raw(), t.raw(), bi));
}
expr mk_fvar(name const & n) {
return mk_local(n, n, expr(), mk_binder_info());
}
extern "C" object * lean_expr_mk_const(obj_arg n, obj_arg ls) {
object * r = alloc_cnstr(static_cast<unsigned>(expr_kind::Const), 2, expr_scalar_size(expr_kind::Const));
cnstr_set(r, 0, n);
cnstr_set(r, 1, ls);
set_scalar<expr_kind::Const>(r, hash(name::hash(n), levels_hash(ls)), false, levels_has_mvar(ls), false, levels_has_param(ls));
return r;
}
expr mk_const(name const & n, levels const & ls) {
inc(n.raw()); inc(ls.raw());
return expr(lean_expr_mk_const(n.raw(), ls.raw()));
}
extern "C" object * lean_expr_mk_app(obj_arg f, obj_arg a) {
object * r = alloc_cnstr(static_cast<unsigned>(expr_kind::App), 2, rec_expr_scalar_size(expr_kind::App));
cnstr_set(r, 0, f);
cnstr_set(r, 1, a);
unsigned w = safe_inc(safe_add(expr_get_weight(f), expr_get_weight(a)));
unsigned d = std::max(expr_get_depth(f), expr_get_depth(a)) + 1;
unsigned h = hash(hash(expr_hash(f), expr_hash(a)), hash(d, w));
set_scalar<expr_kind::App>(r, h,
has_expr_mvar(f) || has_expr_mvar(a),
has_univ_mvar(f) || has_univ_mvar(a),
has_fvar(f) || has_fvar(a),
has_univ_param(f) || has_univ_param(a));
set_rec_scalar<expr_kind::App>(r, w, d, std::max(expr_get_loose_bvar_range(f), expr_get_loose_bvar_range(a)));
return r;
}
expr mk_app(expr const & f, expr const & a) {
inc(f.raw()); inc(a.raw());
return expr(lean_expr_mk_app(f.raw(), a.raw()));
}
extern "C" object * lean_expr_mk_sort(obj_arg l) {
object * r = alloc_cnstr(static_cast<unsigned>(expr_kind::Sort), 1, expr_scalar_size(expr_kind::Sort));
cnstr_set(r, 0, l);
set_scalar<expr_kind::Sort>(r, level::hash(l), false, level_has_mvar(l), false, level_has_param(l));
return r;
}
expr mk_sort(level const & l) {
inc(l.raw());
return expr(lean_expr_mk_sort(l.raw()));
}
template<expr_kind k>
static object * mk_binding(obj_arg n, obj_arg t, obj_arg e, binder_info bi) {
lean_assert(k == expr_kind::Pi || k == expr_kind::Lambda);
object * r = alloc_cnstr(static_cast<unsigned>(k), 3, rec_expr_scalar_size(k));
cnstr_set(r, 0, n);
cnstr_set(r, 1, t);
cnstr_set(r, 2, e);
unsigned w = safe_inc(safe_add(expr_get_weight(t), expr_get_weight(e)));
unsigned d = std::max(expr_get_depth(t), expr_get_depth(e)) + 1;
unsigned h = hash(hash(d, w), hash(expr_hash(t), expr_hash(e)));
unsigned lbvr = std::max(expr_get_loose_bvar_range(t), safe_dec(expr_get_loose_bvar_range(e)));
set_binder_info<k>(r, bi);
set_scalar<k>(r, h,
has_expr_mvar(t) || has_expr_mvar(e),
has_univ_mvar(t) || has_univ_mvar(e),
has_fvar(t) || has_fvar(e),
has_univ_param(t) || has_univ_param(e));
set_rec_scalar<k>(r, w, d, lbvr);
return r;
}
extern "C" object * lean_expr_mk_lambda(obj_arg n, uint8 bi, obj_arg t, obj_arg e) {
return mk_binding<expr_kind::Lambda>(n, t, e, static_cast<binder_info>(bi));
}
expr mk_lambda(name const & n, expr const & t, expr const & e, binder_info bi) {
inc(n.raw()); inc(t.raw()); inc(e.raw());
return expr(mk_binding<expr_kind::Lambda>(n.raw(), t.raw(), e.raw(), bi));
}
extern "C" object * lean_expr_mk_pi(obj_arg n, uint8 bi, obj_arg t, obj_arg e) {
return mk_binding<expr_kind::Pi>(n, t, e, static_cast<binder_info>(bi));
}
expr mk_pi(name const & n, expr const & t, expr const & e, binder_info bi) {
inc(n.raw()); inc(t.raw()); inc(e.raw());
return expr(mk_binding<expr_kind::Pi>(n.raw(), t.raw(), e.raw(), bi));
}
static name * g_default_name = nullptr;
expr mk_arrow(expr const & t, expr const & e) {
return mk_pi(*g_default_name, t, e, mk_binder_info());
}
extern "C" object * lean_expr_mk_let(object * n, object * t, object * v, object * b) {
object * r = alloc_cnstr(static_cast<unsigned>(expr_kind::Let), 4, rec_expr_scalar_size(expr_kind::Let));
cnstr_set(r, 0, n);
cnstr_set(r, 1, t);
cnstr_set(r, 2, v);
cnstr_set(r, 3, b);
unsigned w = safe_inc(safe_add(safe_add(expr_get_weight(t), expr_get_weight(v)), expr_get_weight(b)));
unsigned d = std::max(expr_get_depth(t), std::max(expr_get_depth(v), expr_get_depth(b))) + 1;
unsigned h = hash(hash(w, d), hash(hash(expr_hash(t), expr_hash(v)), expr_hash(b)));
unsigned lbvr = std::max(expr_get_loose_bvar_range(t), std::max(expr_get_loose_bvar_range(v), safe_dec(expr_get_loose_bvar_range(b))));
set_scalar<expr_kind::Let>(r, h,
has_expr_mvar(t) || has_expr_mvar(v) || has_expr_mvar(b),
has_univ_mvar(t) || has_univ_mvar(v) || has_univ_mvar(b),
has_fvar(t) || has_fvar(v) || has_fvar(b),
has_univ_param(t) || has_univ_param(v) || has_univ_param(b));
set_rec_scalar<expr_kind::Let>(r, w, d, lbvr);
return r;
}
expr mk_let(name const & n, expr const & t, expr const & v, expr const & b) {
inc(n.raw()); inc(t.raw()); inc(v.raw()); inc(b.raw());
return expr(lean_expr_mk_let(n.raw(), t.raw(), v.raw(), b.raw()));
}
extern "C" object * lean_expr_mk_mvar(object * n, object * t) {
object * r = alloc_cnstr(static_cast<unsigned>(expr_kind::MVar), 2, rec_expr_scalar_size(expr_kind::MVar));
cnstr_set(r, 0, n);
cnstr_set(r, 1, t);
set_scalar<expr_kind::MVar>(r, name::hash(n), true, has_univ_mvar(t), has_fvar(t), has_univ_param(t));
set_rec_scalar<expr_kind::MVar>(r, 1, 1, expr_get_loose_bvar_range(t));
return r;
}
expr mk_mvar(name const & n, expr const & t) {
inc(n.raw()); inc(t.raw());
return expr(lean_expr_mk_mvar(n.raw(), t.raw()));
}
static expr * g_Prop = nullptr;
static expr * g_Type0 = nullptr;
expr mk_Prop() { return *g_Prop; }
expr mk_Type() { return *g_Type0; }
// =======================================
// Auxiliary constructors and accessors
expr mk_app(expr const & f, unsigned num_args, expr const * args) {
expr r = f;
for (unsigned i = 0; i < num_args; i++)
r = mk_app(r, args[i]);
return r;
}
expr mk_app(unsigned num_args, expr const * args) {
lean_assert(num_args >= 2);
return mk_app(mk_app(args[0], args[1]), num_args - 2, args+2);
}
expr mk_app(expr const & f, list<expr> const & args) {
buffer<expr> _args;
to_buffer(args, _args);
return mk_app(f, _args);
}
expr mk_rev_app(expr const & f, unsigned num_args, expr const * args) {
expr r = f;
unsigned i = num_args;
while (i > 0) {
--i;
r = mk_app(r, args[i]);
}
return r;
}
expr mk_rev_app(unsigned num_args, expr const * args) {
lean_assert(num_args >= 2);
return mk_rev_app(mk_app(args[num_args-1], args[num_args-2]), num_args-2, args);
}
expr const & get_app_args(expr const & e, buffer<expr> & args) {
unsigned sz = args.size();
expr const * it = &e;
while (is_app(*it)) {
args.push_back(app_arg(*it));
it = &(app_fn(*it));
}
std::reverse(args.begin() + sz, args.end());
return *it;
}
expr const & get_app_args_at_most(expr const & e, unsigned num, buffer<expr> & args) {
unsigned sz = args.size();
expr const * it = &e;
unsigned i = 0;
while (is_app(*it)) {
if (i == num)
break;
args.push_back(app_arg(*it));
it = &(app_fn(*it));
i++;
}
std::reverse(args.begin() + sz, args.end());
return *it;
}
expr const & get_app_rev_args(expr const & e, buffer<expr> & args) {
expr const * it = &e;
while (is_app(*it)) {
args.push_back(app_arg(*it));
it = &(app_fn(*it));
}
return *it;
}
expr const & get_app_fn(expr const & e) {
expr const * it = &e;
while (is_app(*it)) {
it = &(app_fn(*it));
}
return *it;
}
unsigned get_app_num_args(expr const & e) {
expr const * it = &e;
unsigned n = 0;
while (is_app(*it)) {
it = &(app_fn(*it));
n++;
}
return n;
}
bool is_arrow(expr const & t) {
if (!is_pi(t)) return false;
if (has_loose_bvars(t)) {
return !has_loose_bvar(binding_body(t), 0);
} else {
lean_assert(has_loose_bvars(binding_body(t)) == has_loose_bvar(binding_body(t), 0));
return !has_loose_bvars(binding_body(t));
}
}
bool is_default_var_name(name const & n) {
return n == *g_default_name;
}
/* Legacy */
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;
}
// =======================================
// Update
expr update_mdata(expr const & e, expr const & t) {
if (!is_eqp(mdata_expr(e), t))
return mk_mdata(mdata_data(e), t);
else
return e;
}
expr update_proj(expr const & e, expr const & t) {
if (!is_eqp(proj_expr(e), t))
return mk_proj(proj_sname(e), proj_idx(e), t);
else
return e;
}
expr update_app(expr const & e, expr const & new_fn, expr const & new_arg) {
if (!is_eqp(app_fn(e), new_fn) || !is_eqp(app_arg(e), new_arg))
return mk_app(new_fn, new_arg);
else
return e;
}
expr update_binding(expr const & e, expr const & new_domain, expr const & new_body) {
if (!is_eqp(binding_domain(e), new_domain) || !is_eqp(binding_body(e), new_body))
return mk_binding(e.kind(), binding_name(e), new_domain, new_body, binding_info(e));
else
return e;
}
expr update_binding(expr const & e, expr const & new_domain, expr const & new_body, binder_info bi) {
if (!is_eqp(binding_domain(e), new_domain) || !is_eqp(binding_body(e), new_body) || bi != binding_info(e))
return mk_binding(e.kind(), binding_name(e), new_domain, new_body, bi);
else
return e;
}
expr update_sort(expr const & e, level const & new_level) {
if (!is_eqp(sort_level(e), new_level))
return mk_sort(new_level);
else
return e;
}
expr update_const(expr const & e, levels const & new_levels) {
if (!is_eqp(const_levels(e), new_levels))
return mk_const(const_name(e), new_levels);
else
return e;
}
expr update_mvar(expr const & e, expr const & new_type) {
if (is_eqp(mvar_type(e), new_type))
return e;
else
return mk_mvar(mvar_name(e), new_type);
}
expr update_let(expr const & e, expr const & new_type, expr const & new_value, expr const & new_body) {
if (!is_eqp(let_type(e), new_type) || !is_eqp(let_value(e), new_value) || !is_eqp(let_body(e), new_body))
return mk_let(let_name(e), new_type, new_value, new_body);
else
return e;
}
/* Legacy */
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);
}
/* Legacy */
expr update_local(expr const & e, binder_info bi) {
return update_local(e, local_type(e), bi);
}
/* Legacy */
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));
}
// =======================================
// Loose bound variable management
static bool has_loose_bvars_in_domain(expr const & b, unsigned vidx, bool strict) {
if (is_pi(b)) {
return
(has_loose_bvar(binding_domain(b), vidx) && is_explicit(binding_info(b))) ||
has_loose_bvars_in_domain(binding_body(b), vidx+1, strict);
} else if (!strict) {
return has_loose_bvar(b, vidx);
} else {
return false;
}
}
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;
}
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);
}
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);
}
// =======================================
// 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() {
g_dummy = new expr(mk_constant("__expr_for_default_constructor__"));
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. */
g_nat_type = new expr(mk_constant("Nat"));
g_string_type = new expr(mk_constant("String"));
}
void finalize_expr() {
delete g_Prop;
delete g_Type0;
delete g_dummy;
delete g_default_name;
delete g_nat_type;
delete g_string_type;
}
#if 0
// Expr metavariables and local variables
expr_mlocal::expr_mlocal(bool is_meta, name const & n, name const & pp_n, expr const & t):
expr_composite(is_meta ? expr_kind::MVar : expr_kind::FVar, n.hash(), is_meta || t.has_expr_metavar(), t.has_univ_metavar(),
!is_meta || t.has_fvar(), t.has_param_univ(),
1, get_loose_bvar_range(t)),
m_name(n),
m_pp_name(pp_n),
m_type(t) {}
void expr_mlocal::dealloc(buffer<expr_cell*> & todelete) {
dec_ref(m_type, todelete);
delete this;
}
#endif
}