lean2/src/library/hop_match.cpp

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/*
Copyright (c) 2013 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include "util/optional.h"
#include "util/buffer.h"
#include "kernel/free_vars.h"
#include "kernel/instantiate.h"
#include "kernel/kernel.h"
#include "library/equality.h"
#include "library/kernel_bindings.h"
#include "library/hop_match.h"
namespace lean {
class hop_match_fn {
buffer<optional<expr>> & m_subst;
buffer<expr> m_vars;
optional<ro_environment> m_env;
bool is_free_var(expr const & x, unsigned ctx_size) const {
return is_var(x) && var_idx(x) >= ctx_size;
}
bool is_locally_bound(expr const & x, unsigned ctx_size) const {
return is_var(x) && var_idx(x) < ctx_size;
}
optional<expr> get_subst(expr const & x, unsigned ctx_size) const {
lean_assert(is_free_var(x, ctx_size));
unsigned vidx = var_idx(x) - ctx_size;
unsigned sz = m_subst.size();
if (vidx >= sz)
throw exception("ill-formed higher-order matching problem");
return m_subst[sz - vidx - 1];
}
bool has_locally_bound_var(expr const & t, unsigned ctx_size) const {
return has_free_var(t, 0, ctx_size);
}
void assign(expr const & p, expr const & t, unsigned ctx_size) {
lean_assert(is_free_var(p, ctx_size));
lean_assert(!get_subst(p, ctx_size));
unsigned vidx = var_idx(p) - ctx_size;
unsigned sz = m_subst.size();
m_subst[sz - vidx - 1] = t;
}
bool args_are_distinct_locally_bound_vars(expr const & p, unsigned ctx_size, buffer<expr> & vars) {
lean_assert(is_app(p));
vars.clear();
unsigned num = num_args(p);
for (unsigned i = 1; i < num; i++) {
expr const & v = arg(p, i);
if (!is_locally_bound(v, ctx_size))
return false;
if (std::find(vars.begin(), vars.end(), v) != vars.end())
return false;
vars.push_back(v);
}
return true;
}
/**
\brief Return t' when all locally bound variables in \c t occur in vars at positions [0, vars_size).
The locally bound variables occurring in \c t are replaced using the following mapping:
vars[vars_size - 1] ==> #0
...
vars[0] ==> #vars_size - 1
None is returned if \c t contains a locally bound variable that does not occur in \c vars.
Remark: vars_size <= vars.size()
*/
optional<expr> proj_core(expr const & t, unsigned ctx_size, buffer<expr> const & vars, unsigned vars_size) {
bool failed = false;
expr r = replace(t, [&](expr const & e, unsigned offset) -> expr {
if (is_var(e)) {
unsigned vidx = var_idx(e);
if (vidx < offset)
return e;
vidx -= offset;
if (vidx < ctx_size) {
// e is locally bound
for (unsigned i = 0; i < vars_size; i++) {
if (var_idx(vars[i]) == vidx)
return mk_var(offset + vars_size - i - 1);
}
failed = true;
return e;
} else if (ctx_size != vars_size) {
return mk_var(offset + vidx - ctx_size + vars_size);
} else {
return e;
}
} else {
return e;
}
});
if (failed)
return none_expr();
else
return some_expr(r);
}
// We say \c t has a simple projection when it is of the form (f v1 ... vn)
// where f does no contain locally bound variables, and v1 ... vn are exactly the variables in vars.
// In this case, the proj procedure can return f instead of (fun xn .... x1, f x1 ... xn)
bool is_simple_proj(expr const & t, unsigned ctx_size, buffer<expr> const & vars) {
if (is_app(t) && !has_locally_bound_var(arg(t, 0), ctx_size) && num_args(t) == vars.size() + 1) {
for (unsigned i = 0; i < vars.size(); i++)
if (arg(t, i+1) != vars[i])
return false;
return true;
} else {
return false;
}
}
/**
\brief Return <tt>(fun (x1 ... xn) t')</tt> if all locally bound variables in \c t occur in vars.
\c n is the size of \c vars.
None is returned if \c t contains a locally bound variable that does not occur in \c vars.
*/
optional<expr> proj(expr const & t, context const & ctx, unsigned ctx_size, buffer<expr> const & vars) {
if (is_simple_proj(t, ctx_size, vars)) {
return some_expr(lower_free_vars(arg(t, 0), ctx_size, ctx_size));
}
optional<expr> t_prime = proj_core(t, ctx_size, vars, vars.size());
if (!t_prime)
return none_expr();
expr r = *t_prime;
unsigned i = vars.size();
while (i > 0) {
--i;
unsigned vidx = var_idx(vars[i]);
auto p = lookup_ext(ctx, vidx);
context_entry const & entry = p.first;
context entry_ctx = p.second;
if (!entry.get_domain())
return none_expr();
expr d = *entry.get_domain();
optional<expr> new_d = proj_core(d, entry_ctx.size(), vars, i);
if (!new_d)
return none_expr();
r = mk_lambda(entry.get_name(), *new_d, r);
}
return some_expr(r);
}
optional<expr> unfold_constant(expr const & c) {
if (is_constant(c)) {
auto obj = (*m_env)->find_object(const_name(c));
if (obj && (obj->is_definition() || obj->is_builtin()))
return some_expr(obj->get_value());
}
return none_expr();
}
bool match_constant(expr const & p, expr const & t) {
if (p == t)
return true;
auto new_p = unfold_constant(p);
if (new_p)
return match_constant(*new_p, t);
return false;
}
bool match(expr const & p, expr const & t, context const & ctx, unsigned ctx_size) {
lean_assert(ctx.size() == ctx_size);
if (is_free_var(p, ctx_size)) {
auto s = get_subst(p, ctx_size);
if (s) {
return lift_free_vars(*s, ctx_size) == t;
} else if (has_locally_bound_var(t, ctx_size)) {
return false;
} else {
assign(p, lower_free_vars(t, ctx_size, ctx_size), ctx_size);
return true;
}
} else if (is_app(p) && is_free_var(arg(p, 0), ctx_size) && args_are_distinct_locally_bound_vars(p, ctx_size, m_vars)) {
// higher-order pattern case
auto s = get_subst(arg(p, 0), ctx_size);
unsigned num = num_args(p);
if (s) {
expr f = lift_free_vars(*s, ctx_size);
expr new_p = apply_beta(f, num - 1, &(arg(p, 1)));
return new_p == t;
} else {
optional<expr> new_t = proj(t, ctx, ctx_size, m_vars);
if (new_t) {
assign(arg(p, 0), *new_t, ctx_size);
return true;
}
// fallback to the first-order case
}
}
if (p == t && !has_free_var_ge(p, ctx_size)) {
return true;
}
if (m_env && is_constant(p)) {
return match_constant(p, t);
}
if (is_equality(p) && is_equality(t) && (!is_eq(p) || !is_eq(t))) {
// Remark: if p and t are homogeneous equality, then we handle as an application (in the else branch)
// We do that because we can get more information. For example, the pattern
// may be (eq #1 a b).
// This branch ignores the type.
expr_pair p1 = get_equality_args(p);
expr_pair p2 = get_equality_args(t);
return match(p1.first, p2.first, ctx, ctx_size) && match(p1.second, p2.second, ctx, ctx_size);
} else {
if (p.kind() != t.kind())
return false;
switch (p.kind()) {
case expr_kind::Var: case expr_kind::Constant: case expr_kind::Type:
case expr_kind::Value: case expr_kind::MetaVar:
return false;
case expr_kind::App: {
unsigned i1 = num_args(p);
unsigned i2 = num_args(t);
while (i1 > 0 && i2 > 0) {
--i1;
--i2;
if (i1 == 0 && i2 > 0) {
return match(arg(p, i1), mk_app(i2+1, begin_args(t)), ctx, ctx_size);
} else if (i2 == 0 && i1 > 0) {
return match(mk_app(i1+1, begin_args(p)), arg(t, i2), ctx, ctx_size);
} else {
if (!match(arg(p, i1), arg(t, i2), ctx, ctx_size))
return false;
}
}
return true;
}
case expr_kind::Lambda: case expr_kind::Pi:
return
match(abst_domain(p), abst_domain(t), ctx, ctx_size) &&
match(abst_body(p), abst_body(t), extend(ctx, abst_name(t), abst_domain(t)), ctx_size+1);
case expr_kind::Let:
// TODO(Leo)
return false;
}
}
lean_unreachable();
}
public:
hop_match_fn(buffer<optional<expr>> & subst, optional<ro_environment> const & env):m_subst(subst), m_env(env) {}
bool operator()(expr const & p, expr const & t) {
return match(p, t, context(), 0);
}
};
bool hop_match(expr const & p, expr const & t, buffer<optional<expr>> & subst, optional<ro_environment> const & env) {
return hop_match_fn(subst, env)(p, t);
}
static int hop_match_core(lua_State * L, optional<ro_environment> const & env) {
int nargs = lua_gettop(L);
expr p = to_expr(L, 1);
expr t = to_expr(L, 2);
int k = 0;
if (nargs >= 4) {
k = luaL_checkinteger(L, 4);
if (k < 0)
throw exception("hop_match, arg #4 must be non-negative");
} else {
k = free_var_range(p);
}
buffer<optional<expr>> subst;
subst.resize(k);
if (hop_match(p, t, subst, env)) {
lua_newtable(L);
int i = 1;
for (auto s : subst) {
if (s) {
push_expr(L, *s);
} else {
lua_pushboolean(L, false);
}
lua_rawseti(L, -2, i);
i = i + 1;
}
} else {
lua_pushnil(L);
}
return 1;
}
static int hop_match(lua_State * L) {
int nargs = lua_gettop(L);
if (nargs >= 3) {
if (!lua_isnil(L, 3)) {
ro_shared_environment env(L, 3);
return hop_match_core(L, optional<ro_environment>(env));
} else {
return hop_match_core(L, optional<ro_environment>());
}
} else {
ro_shared_environment env(L);
return hop_match_core(L, optional<ro_environment>(env));
}
}
void open_hop_match(lua_State * L) {
SET_GLOBAL_FUN(hop_match, "hop_match");
}
}