lean2/src/kernel/metavar.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 <limits>
#include <algorithm>
#include "util/exception.h"
#include "kernel/metavar.h"
#include "kernel/free_vars.h"
#include "kernel/instantiate.h"
#include "kernel/occurs.h"
#include "kernel/for_each.h"

namespace lean {
void swap(substitution & s1, substitution & s2) {
    swap(s1.m_subst, s2.m_subst);
    std::swap(s1.m_size, s2.m_size);
}

substitution::substitution(bool beta_reduce_mv):
    m_size(0),
    m_beta_reduce_mv(beta_reduce_mv) {
}

bool substitution::is_assigned(name const & m) const {
    return const_cast<substitution*>(this)->m_subst.splay_find(m);
}

bool substitution::is_assigned(expr const & m) const {
    return is_assigned(metavar_name(m));
}

void substitution::assign(name const & m, expr const & t) {
    lean_assert(!is_assigned(m));
    m_subst.insert(m, t);
    m_size++;
}

void substitution::assign(expr const & m, expr const & t) {
    lean_assert(is_metavar(m));
    lean_assert(!has_local_context(m));
    assign(metavar_name(m), t);
}

expr apply_local_context(expr const & a, local_context const & lctx) {
    if (lctx) {
        if (is_metavar(a)) {
            return mk_metavar(metavar_name(a), append(lctx, metavar_lctx(a)));
        } else {
            expr r = apply_local_context(a, tail(lctx));
            local_entry const & e = head(lctx);
            if (e.is_lift()) {
                return lift_free_vars(r, e.s(), e.n());
            } else {
                lean_assert(e.is_inst());
                return instantiate(r, e.s(), e.v());
            }
        }
    } else {
        return a;
    }
}

expr substitution::get_subst(expr const & m) const {
    lean_assert(is_metavar(m));
    name2expr::entry const * e = const_cast<substitution*>(this)->m_subst.splay_find(metavar_name(m));
    if (e) {
        expr r = e->second;
        if (has_assigned_metavar(r, *this)) {
            r = instantiate_metavars(r, *this);
            const_cast<substitution*>(this)->m_subst.insert(metavar_name(m), r);
        }
        local_context const & lctx = metavar_lctx(m);
        if (lctx) {
            r = apply_local_context(r, lctx);
            if (has_assigned_metavar(r, *this))
                r = instantiate_metavars(r, *this);
        }
        return r;
    } else {
        return expr();
    }
}

static name g_unique_name = name::mk_internal_unique_name();

void swap(metavar_env & a, metavar_env & b) {
    swap(a.m_name_generator,         b.m_name_generator);
    swap(a.m_substitution,           b.m_substitution);
    swap(a.m_metavar_types,          b.m_metavar_types);
    swap(a.m_metavar_contexts,       b.m_metavar_contexts);
    swap(a.m_metavar_justifications, b.m_metavar_justifications);
    std::swap(a.m_timestamp,         b.m_timestamp);
}

void metavar_env::inc_timestamp() {
    if (m_timestamp == std::numeric_limits<unsigned>::max()) {
        // This should not happen in real examples. We add it just to be safe.
        throw exception("metavar_env timestamp overflow");
    }
    m_timestamp++;
}

metavar_env::metavar_env(name const & prefix):
    m_name_generator(prefix),
    m_timestamp(0) {
}

metavar_env::metavar_env():
    metavar_env(g_unique_name) {
}

expr metavar_env::mk_metavar(context const & ctx, expr const & type) {
    inc_timestamp();
    name m = m_name_generator.next();
    expr r = ::lean::mk_metavar(m);
    if (ctx)
        m_metavar_contexts.insert(m, ctx);
    if (type)
        m_metavar_types.insert(m, type);
    return r;
}

context metavar_env::get_context(expr const & m) const {
    lean_assert(is_metavar(m));
    lean_assert(!has_local_context(m));
    return get_context(metavar_name(m));
}

context metavar_env::get_context(name const & m) const {
    auto e = const_cast<metavar_env*>(this)->m_metavar_contexts.splay_find(m);
    if (e)
        return e->second;
    else
        return context();
}

expr metavar_env::get_type(expr const & m) {
    lean_assert(is_metavar(m));
    expr t = get_type(metavar_name(m));
    if (has_local_context(m)) {
        if (is_metavar(t)) {
            return update_metavar(t, append(metavar_lctx(m), metavar_lctx(t)));
        } else {
            return apply_local_context(t, metavar_lctx(m));
        }
    } else {
        return t;
    }
}

expr metavar_env::get_type(name const & m) {
    auto e = const_cast<metavar_env*>(this)->m_metavar_types.splay_find(m);
    if (e) {
        return e->second;
    } else {
        expr t = mk_metavar(get_context(m));
        m_metavar_types.insert(m, t);
        return t;
    }
}

bool metavar_env::has_type(name const & m) const {
    auto e = const_cast<metavar_env*>(this)->m_metavar_types.splay_find(m);
    return e;
}

bool metavar_env::has_type(expr const & m) const {
    lean_assert(is_metavar(m));
    return has_type(metavar_name(m));
}


justification metavar_env::get_justification(expr const & m) const {
    lean_assert(is_metavar(m));
    return get_justification(metavar_name(m));
}

justification metavar_env::get_justification(name const & m) const {
    auto e = const_cast<metavar_env*>(this)->m_metavar_justifications.splay_find(m);
    if (e) {
        return e->second;
    } else {
        return justification();
    }
}

bool metavar_env::is_assigned(name const & m) const {
    return m_substitution.is_assigned(m);
}

bool metavar_env::is_assigned(expr const & m) const {
    lean_assert(is_metavar(m));
    return is_assigned(metavar_name(m));
}

void metavar_env::assign(name const & m, expr const & t, justification const & j) {
    lean_assert(!is_assigned(m));
    inc_timestamp();
    m_substitution.assign(m, t);
    if (j)
        m_metavar_justifications.insert(m, j);
}

void metavar_env::assign(expr const & m, expr const & t, justification const & j) {
    lean_assert(is_metavar(m));
    lean_assert(!has_local_context(m));
    assign(metavar_name(m), t, j);
}

struct found_unassigned{};
name metavar_env::find_unassigned_metavar() const {
    name r;
    try {
        m_metavar_types.for_each([&](name const & m, expr const &) {
                if (!m_substitution.is_assigned(m)) {
                    r = m;
                    throw found_unassigned();
                }
            });
    } catch (found_unassigned &) {
    }
    return r;
}


void instantiate_metavars_proc::instantiated_metavar(expr const &) {
}

expr instantiate_metavars_proc::visit_metavar(expr const & m, context const &) {
    if (is_metavar(m) && m_subst.is_assigned(m)) {
        instantiated_metavar(m);
        return m_subst.get_subst(m);
    } else {
        return m;
    }
}

expr instantiate_metavars_proc::visit_app(expr const & e, context const & ctx) {
    if (m_subst.beta_reduce_metavar_application() && is_metavar(arg(e, 0)) && m_subst.is_assigned(arg(e, 0))) {
        instantiated_metavar(arg(e, 0));
        expr new_f = m_subst.get_subst(arg(e, 0));
        if (is_lambda(new_f)) {
            buffer<expr> new_args;
            for (unsigned i = 1; i < num_args(e); i++)
                new_args.push_back(visit(arg(e, i), ctx));
            return apply_beta(new_f, new_args.size(), new_args.data());
        }
    }
    return replace_visitor::visit_app(e, ctx);
}

instantiate_metavars_proc::instantiate_metavars_proc(substitution const & s):m_subst(s) {
}

expr instantiate_metavars(expr const & e, substitution const & s) {
    if (!has_metavar(e)) {
        return e;
    } else {
        return instantiate_metavars_proc(s)(e);
    }
}

struct found_assigned {};
bool has_assigned_metavar(expr const & e, substitution const & s) {
    if (!has_metavar(e)) {
        return false;
    } else {
        auto proc = [&](expr const & n, unsigned) {
            if (is_metavar(n) && s.is_assigned(n))
                throw found_assigned();
        };
        for_each_fn<decltype(proc)> visitor(proc);
        try {
            visitor(e);
            return false;
        } catch (found_assigned&) {
            return true;
        }
    }
}

local_context add_lift(local_context const & lctx, unsigned s, unsigned n) {
    if (n == 0) {
        return lctx;
    } else if (lctx) {
        local_entry e = head(lctx);
        // Simplification rule
        //    lift:(s1+n1):n2 lift:s1:n1 --->  lift:s1:n1+n2
        if (e.is_lift() && s == e.s() + e.n()) {
            return add_lift(tail(lctx), e.s(), e.n() + n);
        }
    }
    return cons(mk_lift(s, n), lctx);
}

expr add_lift(expr const & m, unsigned s, unsigned n) {
    return update_metavar(m, add_lift(metavar_lctx(m), s, n));
}

local_context add_inst(local_context const & lctx, unsigned s, expr const & v) {
    if (lctx) {
        local_entry e = head(lctx);
        if (e.is_lift() && e.s() <= s && s < e.s() + e.n()) {
            return add_lift(tail(lctx), e.s(), e.n() - 1);
        }
        // Simplifications such as
        //   inst:4 #6  lift:5:3  -->  lift:4:2
        //   inst:3 #7  lift:4:5 -->   lift:3:4
        // General rule is:
        //   inst:(s-1) #(s+n-2)  lift:s:n  --> lift:s-1:n-1
        if (e.is_lift() && is_var(v) && e.s() > 0 && s == e.s() - 1 && e.s() + e.n() > 2 && var_idx(v) == e.s() + e.n() - 2) {
            return add_lift(tail(lctx), e.s() - 1, e.n() - 1);
        }
    }
    return cons(mk_inst(s, v), lctx);
}

expr add_inst(expr const & m, unsigned s, expr const & v) {
    return update_metavar(m, add_inst(metavar_lctx(m), s, v));
}

bool has_local_context(expr const & m) {
    return metavar_lctx(m);
}

expr pop_meta_context(expr const & m) {
    lean_assert(has_local_context(m));
    return update_metavar(m, tail(metavar_lctx(m)));
}

/**
   \brief Auxiliary exception used to sign that a metavariable was
   found in an expression.
*/
struct found_metavar {};

bool has_metavar(expr const & e, expr const & m, substitution const & s) {
    if (has_metavar(e)) {
        lean_assert(is_metavar(m));
        lean_assert(!s.is_assigned(m));
        auto f = [&](expr const & m2, unsigned) {
            if (is_metavar(m2)) {
                if (metavar_name(m) == metavar_name(m2))
                    throw found_metavar();
                if (s.is_assigned(m2) &&
                    has_metavar(s.get_subst(m2), m, s))
                    throw found_metavar();
            }
        };
        try {
            for_each_fn<decltype(f)> proc(f);
            proc(e);
            return false;
        } catch (found_metavar) {
            return true;
        }
    } else {
        return false;
    }
}
}