lean2/src/kernel/normalize.cpp

/*
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 "free_vars.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);
    // 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);
        if (is_var(arg(new_b, n - 1), 0) &&
            std::all_of(begin_args(new_b),
                        end_args(new_b) - 1,
                        [](expr const & arg) { return !has_free_var(arg, 0); })) {
            if (n == 2)
                return lower_free_vars(arg(new_b, 0), 1);
            else
                return lower_free_vars(app(n - 1, begin_args(new_b)), 1);
        }
        return lambda(abst_name(a), new_t, new_b);
    }
    else {
        return lambda(abst_name(a), new_t, new_b);
    }
}
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);
}
}