/*
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.

Author: Leonardo de Moura
*/
#include "kernel/instantiate.h"
#include "kernel/abstract.h"
#include "kernel/find_fn.h"
#include "kernel/inductive/inductive.h"
#include "library/util.h"
#include "library/equations_compiler/equations.h"
#include "library/equations_compiler/util.h"

namespace lean {
[[ noreturn ]] void throw_ill_formed_eqns() {
    throw exception("ill-formed match/equations expression");
}

static optional<pair<expr, unsigned>> get_eqn_fn_and_arity(expr e) {
    while (is_lambda(e))
        e = binding_body(e);
    if (!is_equation(e) && !is_no_equation(e)) throw_ill_formed_eqns();
    if (is_no_equation(e)) {
        return optional<pair<expr, unsigned>>();
    } else {
        expr const & lhs = equation_lhs(e);
        expr const & fn  = get_app_fn(lhs);
        lean_assert(is_local(fn));
        return optional<pair<expr, unsigned>>(fn, get_app_num_args(lhs));
    }
}

static expr consume_fn_prefix(expr eq, buffer<expr> const & fns) {
    for (unsigned i = 0; i < fns.size(); i++) {
        if (!is_lambda(eq)) throw_ill_formed_eqns();
        eq = binding_body(eq);
    }
    return instantiate_rev(eq, fns);
}

unpack_eqns::unpack_eqns(type_context & ctx, expr const & e):
    m_locals(ctx) {
    lean_assert(is_equations(e));
    m_src = e;
    buffer<expr> eqs;
    unsigned num_fns = equations_num_fns(e);
    to_equations(e, eqs);
    /* Extract functions. */
    lean_assert(eqs.size() > 0);
    expr eq = eqs[0];
    for (unsigned i = 0; i < num_fns; i++) {
        if (!is_lambda(eq)) throw_ill_formed_eqns();
        if (!closed(binding_domain(eq))) throw_ill_formed_eqns();
        m_fns.push_back(m_locals.push_local(binding_name(eq), binding_domain(eq)));
        eq = binding_body(eq);
    }
    /* Extract equations */
    unsigned eqidx = 0;
    for (unsigned fidx = 0; fidx < num_fns; fidx++) {
        m_eqs.push_back(buffer<expr>());
        buffer<expr> & fn_eqs = m_eqs.back();
        if (eqidx >= eqs.size()) throw_ill_formed_eqns();
        expr eq = consume_fn_prefix(eqs[eqidx], m_fns);
        fn_eqs.push_back(eq);
        eqidx++;
        if (auto p = get_eqn_fn_and_arity(eq)) {
            if (p->first != m_fns[fidx]) throw_ill_formed_eqns();
            unsigned arity = p->second;
            m_arity.push_back(arity);
            while (eqidx < eqs.size()) {
                expr eq = consume_fn_prefix(eqs[eqidx], m_fns);
                if (auto p = get_eqn_fn_and_arity(eq)) {
                    if (p->first == m_fns[fidx]) {
                        if (p->second != arity) throw_ill_formed_eqns();
                        fn_eqs.push_back(eq);
                        eqidx++;
                    } else {
                        break;
                    }
                } else {
                    break;
                }
            }
        } else {
            /* noequation, guess arity using type of function */
            expr type = ctx.infer(m_fns[fidx]);
            unsigned arity = 0;
            while (is_pi(type)) {
                arity++;
                type = binding_body(type);
            }
            if (arity == 0) throw_ill_formed_eqns();
            m_arity.push_back(arity);
        }
    }
    if (eqs.size() != eqidx) throw_ill_formed_eqns();
    lean_assert(m_arity.size() == m_fns.size());
    lean_assert(m_eqs.size() == m_fns.size());
}

expr unpack_eqns::update_fn_type(unsigned fidx, expr const & type) {
    expr new_fn = m_locals.push_local(local_pp_name(m_fns[fidx]), type);
    m_fns[fidx] = new_fn;
    return new_fn;
}

expr unpack_eqns::repack() {
    buffer<expr> new_eqs;
    for (buffer<expr> const & fn_eqs : m_eqs) {
        for (expr const & eq : fn_eqs) {
            new_eqs.push_back(m_locals.ctx().mk_lambda(m_fns, eq));
        }
    }
    return update_equations(m_src, new_eqs);
}

unpack_eqn::unpack_eqn(type_context & ctx, expr const & eqn):
    m_src(eqn), m_locals(ctx) {
    expr it = eqn;
    while (is_lambda(it)) {
        expr d = instantiate_rev(binding_domain(it), m_locals.as_buffer().size(), m_locals.as_buffer().data());
        m_vars.push_back(m_locals.push_local(binding_name(it), d, binding_info(it)));
        it = binding_body(it);
    }
    it = instantiate_rev(it, m_locals.as_buffer().size(), m_locals.as_buffer().data());
    if (!is_equation(it)) throw_ill_formed_eqns();
    m_nested_src = it;
    m_lhs = equation_lhs(it);
    m_rhs = equation_rhs(it);
}

expr unpack_eqn::add_var(name const & n, expr const & type) {
    m_modified_vars = true;
    m_vars.push_back(m_locals.push_local(n, type));
    return m_vars.back();
}

expr unpack_eqn::repack() {
    if (!m_modified_vars &&
        equation_lhs(m_nested_src) == m_lhs &&
        equation_rhs(m_nested_src) == m_rhs) return m_src;
    expr new_eq = copy_tag(m_nested_src, mk_equation(m_lhs, m_rhs));
    return copy_tag(m_src, m_locals.ctx().mk_lambda(m_vars, new_eq));
}

bool is_recursive_eqns(type_context & ctx, expr const & e) {
    unpack_eqns ues(ctx, e);
    for (unsigned fidx = 0; fidx < ues.get_num_fns(); fidx++) {
        buffer<expr> const & eqns = ues.get_eqns_of(fidx);
        for (expr const & eqn : eqns) {
            expr it = eqn;
            while (is_lambda(it)) {
                it = binding_body(it);
            }
            if (!is_equation(it) && !is_no_equation(it)) throw_ill_formed_eqns();
            if (is_equation(it)) {
                expr const & rhs = equation_rhs(it);
                if (find(rhs, [&](expr const & e, unsigned) {
                            if (is_local(e)) {
                                for (unsigned fidx = 0; fidx < ues.get_num_fns(); fidx++) {
                                    if (mlocal_name(e) == mlocal_name(ues.get_fn(fidx)))
                                        return true;
                                }
                            }
                            return false;
                        })) {
                    return true;
                }
            }
        }
    }
    return false;
}
}