lean2/src/library/tactic/expr_to_tactic.cpp

/*
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.

Author: Leonardo de Moura
*/
#include <unordered_map>
#include <string>
#include "util/sstream.h"
#include "kernel/instantiate.h"
#include "kernel/type_checker.h"
#include "library/string.h"
#include "library/num.h"
#include "library/tactic/expr_to_tactic.h"
#include "library/tactic/apply_tactic.h"

namespace lean {
typedef std::unordered_map<name, expr_to_tactic_fn, name_hash, name_eq> expr_to_tactic_map;
expr_to_tactic_map & get_expr_to_tactic_map() {
    static expr_to_tactic_map g_map;
    return g_map;
}

void register_expr_to_tactic(name const & n, expr_to_tactic_fn const & fn) {
    get_expr_to_tactic_map().insert(mk_pair(n, fn));
}

static name g_tac("tactic"), g_tac_name(g_tac, "tactic"), g_builtin_tac_name(g_tac, "builtin_tactic");
static name g_exact_tac_name(g_tac, "exact"), g_and_then_tac_name(g_tac, "and_then");
static name g_or_else_tac_name(g_tac, "or_else"), g_repeat_tac_name(g_tac, "repeat"), g_fixpoint_name(g_tac, "fixpoint");
static expr g_exact_tac_fn(Const(g_exact_tac_name)), g_and_then_tac_fn(Const(g_and_then_tac_name));
static expr g_or_else_tac_fn(Const(g_or_else_tac_name)), g_repeat_tac_fn(Const(g_repeat_tac_name));
static expr g_tac_type(Const(g_tac_name)), g_builtin_tac(Const(g_builtin_tac_name)), g_fixpoint_tac(Const(g_fixpoint_name));
expr const & get_exact_tac_fn() { return g_exact_tac_fn; }
expr const & get_and_then_tac_fn() { return g_and_then_tac_fn; }
expr const & get_or_else_tac_fn() { return g_or_else_tac_fn; }
expr const & get_repeat_tac_fn() { return g_repeat_tac_fn; }
expr const & get_tactic_type() { return g_tac_type; }

bool has_tactic_decls(environment const & env) {
    try {
        type_checker tc(env);
        return
            tc.infer(g_builtin_tac) == g_tac_type &&
            tc.infer(g_and_then_tac_fn) == g_tac_type >> (g_tac_type >> g_tac_type) &&
            tc.infer(g_or_else_tac_fn) == g_tac_type >> (g_tac_type >> g_tac_type) &&
            tc.infer(g_repeat_tac_fn) == g_tac_type >> g_tac_type;
    } catch (...) {
        return false;
    }
}

static void throw_failed(expr const & e) {
    throw expr_to_tactic_exception(e, "failed to convert expression into tactic");
}

/** \brief Return true if v is the constant tactic.builtin_tactic or the constant function that returns tactic.builtin_tactic */
static bool is_builtin_tactic(expr const & v) {
    if (is_lambda(v))
        return is_builtin_tactic(binding_body(v));
    else if (v == g_builtin_tac)
        return true;
    else
        return false;
}

tactic expr_to_tactic(type_checker & tc, expr e, pos_info_provider const * p) {
    e = tc.whnf(e);
    expr f = get_app_fn(e);
    if (!is_constant(f))
        throw_failed(e);
    optional<declaration> it = tc.env().find(const_name(f));
    if (!it || !it->is_definition())
        throw_failed(e);
    expr v = it->get_value();
    if (is_builtin_tactic(v)) {
        auto const & map = get_expr_to_tactic_map();
        auto it2 = map.find(const_name(f));
        if (it2 != map.end())
            return it2->second(tc, e, p);
        else
            throw expr_to_tactic_exception(e, sstream() << "implementation for builtin tactic '" << const_name(f) << "' was not found");
    } else {
        // unfold definition
        buffer<expr> locals;
        get_app_rev_args(e, locals);
        level_param_names const & ps = it->get_univ_params();
        levels ls = const_levels(f);
        unsigned num_ps = length(ps);
        unsigned num_ls = length(ls);
        if (num_ls > num_ps)
            throw expr_to_tactic_exception(e, sstream() << "invalid number of universes");
        if (num_ls < num_ps) {
            buffer<level> extra_ls;
            name_generator ngen = tc.mk_ngen();
            for (unsigned i = num_ls; i < num_ps; i++)
                extra_ls.push_back(mk_meta_univ(ngen.next()));
            ls = append(ls, to_list(extra_ls.begin(), extra_ls.end()));
        }
        v = instantiate_univ_params(v, ps, ls);
        v = apply_beta(v, locals.size(), locals.data());
        return expr_to_tactic(tc, v, p);
    }
}

static name g_tmp_prefix = name::mk_internal_unique_name();
MK_THREAD_LOCAL_GET(unsigned, get_expr_tac_id, 0)
static name_generator next_name_generator() {
    unsigned & c = get_expr_tac_id();
    unsigned r = c;
    c++;
    return name_generator(name(g_tmp_prefix, r));
}

tactic expr_to_tactic(environment const & env, expr const & e, pos_info_provider const * p) {
    type_checker tc(env, next_name_generator());
    return expr_to_tactic(tc, e, p);
}

tactic fixpoint(expr const & b) {
    return tactic([=](environment const & env, io_state const & ios, proof_state const & s) -> proof_state_seq {
            return expr_to_tactic(env, b, nullptr)(env, ios, s);
        });
}

register_simple_tac::register_simple_tac(name const & n, std::function<tactic()> f) {
    register_expr_to_tactic(n, [=](type_checker &, expr const & e, pos_info_provider const *) {
            if (!is_constant(e))
                throw expr_to_tactic_exception(e, "invalid constant tactic");
            return f();
        });
}

register_bin_tac::register_bin_tac(name const & n, std::function<tactic(tactic const &, tactic const &)> f) {
    register_expr_to_tactic(n, [=](type_checker & tc, expr const & e, pos_info_provider const * p) {
            buffer<expr> args;
            get_app_args(e, args);
            if (args.size() != 2)
                throw expr_to_tactic_exception(e, "invalid binary tactic, it must have two arguments");
            return f(expr_to_tactic(tc, args[0], p),
                     expr_to_tactic(tc, args[1], p));
        });
}

register_unary_tac::register_unary_tac(name const & n, std::function<tactic(tactic const &)> f) {
    register_expr_to_tactic(n, [=](type_checker & tc, expr const & e, pos_info_provider const * p) {
            buffer<expr> args;
            get_app_args(e, args);
            if (args.size() != 1)
                throw expr_to_tactic_exception(e, "invalid unary tactic, it must have one argument");
            return f(expr_to_tactic(tc, args[0], p));
        });
}

register_unary_num_tac::register_unary_num_tac(name const & n, std::function<tactic(tactic const &, unsigned k)> f) {
    register_expr_to_tactic(n, [=](type_checker & tc, expr const & e, pos_info_provider const * p) {
            buffer<expr> args;
            get_app_args(e, args);
            if (args.size() != 2)
                throw expr_to_tactic_exception(e, "invalid tactic, it must have two arguments");
            tactic t = expr_to_tactic(tc, args[0], p);
            optional<mpz> k = to_num(args[1]);
            if (!k)
                k = to_num(tc.whnf(args[1]));
            if (!k)
                throw expr_to_tactic_exception(e, "invalid tactic, second argument must be a numeral");
            if (!k->is_unsigned_int())
                throw expr_to_tactic_exception(e, "invalid tactic, second argument does not fit in a machine unsigned integer");
            return f(t, k->get_unsigned_int());
        });
}

static register_simple_tac reg_id(name(g_tac, "id"), []() { return id_tactic(); });
static register_simple_tac reg_now(name(g_tac, "now"), []() { return now_tactic(); });
static register_simple_tac reg_assumption(name(g_tac, "assumption"), []() { return assumption_tactic(); });
static register_simple_tac reg_eassumption(name(g_tac, "eassumption"), []() { return eassumption_tactic(); });
static register_simple_tac reg_fail(name(g_tac, "fail"), []() { return fail_tactic(); });
static register_simple_tac reg_beta(name(g_tac, "beta"), []() { return beta_tactic(); });
static register_bin_tac reg_then(g_and_then_tac_name, [](tactic const & t1, tactic const & t2) { return then(t1, t2); });
static register_bin_tac reg_append(name(g_tac, "append"), [](tactic const & t1, tactic const & t2) { return append(t1, t2); });
static register_bin_tac reg_interleave(name(g_tac, "interleave"), [](tactic const & t1, tactic const & t2) { return interleave(t1, t2); });
static register_bin_tac reg_par(name(g_tac, "par"), [](tactic const & t1, tactic const & t2) { return par(t1, t2); });
static register_bin_tac reg_orelse(g_or_else_tac_name, [](tactic const & t1, tactic const & t2) { return orelse(t1, t2); });
static register_unary_tac reg_repeat(g_repeat_tac_name, [](tactic const & t1) { return repeat(t1); });
static register_tac reg_state(name(g_tac, "state"), [](type_checker &, expr const & e, pos_info_provider const * p) {
        if (p)
            return trace_state_tactic(std::string(p->get_file_name()), p->get_pos_info(e));
        else
            return trace_state_tactic("unknown", mk_pair(0, 0));
    });
static register_tac reg_trace(name(g_tac, "trace"), [](type_checker & tc, expr const & e, pos_info_provider const *) {
        buffer<expr> args;
        get_app_args(e, args);
        if (args.size() != 1)
            throw expr_to_tactic_exception(e, "invalid trace tactic, argument expected");
        if (auto str = to_string(args[0]))
            return trace_tactic(*str);
        else if (auto str = to_string(tc.whnf(args[0])))
            return trace_tactic(*str);
        else
            throw expr_to_tactic_exception(e, "invalid trace tactic, string value expected");
    });
static register_tac reg_apply(name(g_tac, "apply"), [](type_checker &, expr const & e, pos_info_provider const *) {
        return apply_tactic(app_arg(e));
    });
static register_tac reg_exact(g_exact_tac_name, [](type_checker &, expr const & e, pos_info_provider const *) {
        return exact_tactic(app_arg(e));
    });
static register_tac reg_unfold(name(g_tac, "unfold"), [](type_checker &, expr const & e, pos_info_provider const *) {
        expr id = get_app_fn(app_arg(e));
        if (!is_constant(id))
            return fail_tactic();
        else
            return unfold_tactic(const_name(id));
    });
static register_unary_num_tac reg_at_most(name(g_tac, "at_most"), [](tactic const & t, unsigned k) { return take(t, k); });
static register_unary_num_tac reg_discard(name(g_tac, "discard"), [](tactic const & t, unsigned k) { return discard(t, k); });
static register_unary_num_tac reg_focus_at(name(g_tac, "focus_at"), [](tactic const & t, unsigned k) { return focus(t, k); });
static register_unary_num_tac reg_try_for(name(g_tac, "try_for"), [](tactic const & t, unsigned k) { return try_for(t, k); });
static register_tac reg_fixpoint(g_fixpoint_name, [](type_checker & tc, expr const & e, pos_info_provider const *) {
        if (!is_constant(app_fn(e)))
            throw expr_to_tactic_exception(e, "invalid fixpoint tactic, it must have one argument");
        expr r = tc.whnf(mk_app(app_arg(e), e));
        return fixpoint(r);
    });

// We encode the 'by' expression that is used to trigger tactic execution.
// This is a trick to avoid creating a new kind of expression.
// 'by' macros are temporary objects used by the elaborator,
// and have no semantic significance.
[[ noreturn ]] static void throw_ex() { throw exception("unexpected occurrence of 'by' expression"); }
static name g_by_name("by");
class by_macro_cell : public macro_definition_cell {
public:
    virtual name get_name() const { return g_by_name; }
    virtual expr get_type(expr const &, expr const *, extension_context &) const { throw_ex(); }
    virtual optional<expr> expand(expr const &, extension_context &) const { throw_ex(); }
    virtual void write(serializer &) const { throw_ex(); }
};

static macro_definition g_by(new by_macro_cell());
expr mk_by(expr const & e) {
    return mk_macro(g_by, 1, &e);
}

bool is_by(expr const & e) {
    return is_macro(e) && macro_def(e) == g_by;
}

expr const & get_by_arg(expr const & e) {
    lean_assert(is_by(e));
    return macro_arg(e, 0);
}
}