lean2/src/kernel/normalize.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 <algorithm>
#include "expr.h"
#include "list.h"
#include "buffer.h"
#include "trace.h"
#include "exception.h"
namespace lean {
class value;
typedef list<value> context;
enum class value_kind { Expr, Closure, BoundedVar };
class value {
unsigned m_kind:2;
unsigned m_bvar:30;
expr m_expr;
context m_ctx;
public:
value() {}
explicit value(expr const & e):m_kind(static_cast<unsigned>(value_kind::Expr)), m_expr(e) {}
explicit value(unsigned k):m_kind(static_cast<unsigned>(value_kind::BoundedVar)), m_bvar(k) {}
value(expr const & e, context const & c):m_kind(static_cast<unsigned>(value_kind::Closure)), m_expr(e), m_ctx(c) { lean_assert(is_lambda(e)); }
value_kind kind() const { return static_cast<value_kind>(m_kind); }
bool is_expr() const { return kind() == value_kind::Expr; }
bool is_closure() const { return kind() == value_kind::Closure; }
bool is_bounded_var() const { return kind() == value_kind::BoundedVar; }
expr const & get_expr() const { lean_assert(is_expr() || is_closure()); return m_expr; }
context const & get_ctx() const { lean_assert(is_closure()); return m_ctx; }
unsigned get_var_idx() const { lean_assert(is_bounded_var()); return m_bvar; }
};
value_kind kind(value const & v) { return v.kind(); }
expr const & to_expr(value const & v) { return v.get_expr(); }
context const & ctx_of(value const & v) { return v.get_ctx(); }
unsigned to_bvar(value const & v) { return v.get_var_idx(); }
value lookup(context const & c, unsigned i) {
context const * curr = &c;
while (!is_nil(*curr)) {
if (i == 0)
return head(*curr);
--i;
curr = &tail(*curr);
}
throw exception("unknown free variable");
}
context extend(context const & c, value const & v) { return cons(v, c); }
value normalize(expr const & a, context const & c, unsigned k);
expr reify(value const & v, unsigned k);
expr reify_closure(expr const & a, context const & c, unsigned k) {
lean_assert(is_lambda(a));
expr new_t = reify(normalize(abst_type(a), c, k), k);
expr new_b = reify(normalize(abst_body(a), extend(c, value(k)), k+1), k+1);
return lambda(abst_name(a), new_t, new_b);
#if 0
// TODO: ETA-reduction
if (is_app(new_b)) {
// (lambda (x:T) (app f ... (var 0)))
// check eta-rule applicability
unsigned n = num_args(new_b);
lean_assert(n >= 2);
expr const & last_arg = arg(new_b, n - 1);
if (is_var(last_arg) && var_idx(last_arg) == 0) {
if (n == 2)
return arg(new_b, 0);
else
return app(n - 1, begin_args(new_b));
}
return lambda(abst_name(a), new_t, new_b);
}
else {
return lambda(abst_name(a), new_t, new_b);
}
#endif
}
expr reify(value const & v, unsigned k) {
lean_trace("normalize", tout << "Reify kind: " << static_cast<unsigned>(v.kind()) << "\n";
if (v.is_bounded_var()) tout << "#" << to_bvar(v); else tout << to_expr(v); tout << "\n";);
switch (v.kind()) {
case value_kind::Expr: return to_expr(v);
case value_kind::BoundedVar: return var(k - to_bvar(v) - 1);
case value_kind::Closure: return reify_closure(to_expr(v), ctx_of(v), k);
}
lean_unreachable();
return expr();
}
value normalize(expr const & a, context const & c, unsigned k) {
lean_trace("normalize", tout << "Normalize, k: " << k << "\n" << a << "\n";);
switch (a.kind()) {
case expr_kind::Var:
return lookup(c, var_idx(a));
case expr_kind::Constant: case expr_kind::Prop: case expr_kind::Type: case expr_kind::Numeral:
return value(a);
case expr_kind::App: {
value f = normalize(arg(a, 0), c, k);
unsigned i = 1;
unsigned n = num_args(a);
while (true) {
if (f.is_closure()) {
// beta reduction
expr const & fv = to_expr(f);
lean_trace("normalize", tout << "beta reduction...\n" << fv << "\n";);
context new_c = extend(ctx_of(f), normalize(arg(a, i), c, k));
f = normalize(abst_body(fv), new_c, k);
if (i == n - 1)
return f;
i++;
}
else {
// TODO: support for interpreted symbols
buffer<expr> new_args;
new_args.push_back(reify(f, k));
for (; i < n; i++)
new_args.push_back(reify(normalize(arg(a, i), c, k), k));
return value(app(new_args.size(), new_args.data()));
}
}
}
case expr_kind::Lambda:
return value(a, c);
case expr_kind::Pi: {
expr new_t = reify(normalize(abst_type(a), c, k), k);
expr new_b = reify(normalize(abst_body(a), extend(c, value(k)), k+1), k+1);
return value(pi(abst_name(a), new_t, new_b));
}}
lean_unreachable();
return value(a);
}
expr normalize(expr const & e) {
return reify(normalize(e, context(), 0), 0);
}
}