lean2/src/kernel/instantiate.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 <limits>
#include "kernel/free_vars.h"
#include "kernel/replace_fn.h"
#include "kernel/declaration.h"
#include "kernel/instantiate.h"

namespace lean {
template<bool rev>
struct instantiate_easy_fn {
    unsigned n;
    expr const * subst;
    instantiate_easy_fn(unsigned _n, expr const * _subst):n(_n), subst(_subst) {}
    optional<expr> operator()(expr const & a, bool app) const {
        if (closed(a))
            return some_expr(a);
        if (is_var(a) && var_idx(a) < n)
            return some_expr(subst[rev ? n - var_idx(a) - 1 : var_idx(a)]);
        if (app && is_app(a))
        if (auto new_a = operator()(app_arg(a), false))
        if (auto new_f = operator()(app_fn(a), true))
            return some_expr(copy_tag(a, mk_app(*new_f, *new_a)));
        return none_expr();
    }
};

expr instantiate(expr const & a, unsigned s, unsigned n, expr const * subst) {
    if (s >= get_free_var_range(a) || n == 0)
        return a;
    if (s == 0)
        if (auto r = instantiate_easy_fn<false>(n, subst)(a, true))
            return *r;
    return replace(a, [=](expr const & m, unsigned offset) -> optional<expr> {
            unsigned s1 = s + offset;
            if (s1 < s)
                return some_expr(m); // overflow, vidx can't be >= max unsigned
            if (s1 >= get_free_var_range(m))
                return some_expr(m); // expression m does not contain free variables with idx >= s1
            if (is_var(m)) {
                unsigned vidx = var_idx(m);
                if (vidx >= s1) {
                    unsigned h = s1 + n;
                    if (h < s1 /* overflow, h is bigger than any vidx */ || vidx < h) {
                        return some_expr(lift_free_vars(subst[vidx - s1], offset));
                    } else {
                        return some_expr(mk_var(vidx - n));
                    }
                }
            }
            return none_expr();
        });
}

expr instantiate(expr const & e, unsigned n, expr const * s) { return instantiate(e, 0, n, s); }
expr instantiate(expr const & e, std::initializer_list<expr> const & l) {  return instantiate(e, l.size(), l.begin()); }
expr instantiate(expr const & e, unsigned i, expr const & s) { return instantiate(e, i, 1, &s); }
expr instantiate(expr const & e, expr const & s) { return instantiate(e, 0, s); }

expr instantiate_rev(expr const & a, unsigned n, expr const * subst) {
    if (closed(a))
        return a;
    if (auto r = instantiate_easy_fn<true>(n, subst)(a, true))
        return *r;
    return replace(a, [=](expr const & m, unsigned offset) -> optional<expr> {
            if (offset >= get_free_var_range(m))
                return some_expr(m); // expression m does not contain free variables with idx >= offset
            if (is_var(m)) {
                unsigned vidx = var_idx(m);
                if (vidx >= offset) {
                    unsigned h = offset + n;
                    if (h < offset /* overflow, h is bigger than any vidx */ || vidx < h) {
                        return some_expr(lift_free_vars(subst[n - (vidx - offset) - 1], offset));
                    } else {
                        return some_expr(mk_var(vidx - n));
                    }
                }
            }
            return none_expr();
        });
}

bool is_head_beta(expr const & t) {
    expr const * it = &t;
    while (is_app(*it)) {
        expr const & f = app_fn(*it);
        if (is_lambda(f)) {
            return true;
        } else if (is_app(f)) {
            it = &f;
        } else {
            return false;
        }
    }
    return false;
}

expr apply_beta(expr f, unsigned num_args, expr const * args) {
    if (num_args == 0) {
        return f;
    } else if (!is_lambda(f)) {
        return mk_rev_app(f, num_args, args);
    } else {
        unsigned m = 1;
        while (is_lambda(binding_body(f)) && m < num_args) {
            f = binding_body(f);
            m++;
        }
        lean_assert(m <= num_args);
        return mk_rev_app(instantiate(binding_body(f), m, args + (num_args - m)), num_args - m, args);
    }
}

expr head_beta_reduce(expr const & t) {
    if (!is_head_beta(t)) {
        return t;
    } else {
        buffer<expr> args;
        expr const * it = &t;
        while (true) {
            lean_assert(is_app(*it));
            expr const & f = app_fn(*it);
            args.push_back(app_arg(*it));
            if (is_lambda(f)) {
                return apply_beta(f, args.size(), args.data());
            } else {
                lean_assert(is_app(f));
                it = &f;
            }
        }
    }
}

expr beta_reduce(expr t) {
    auto f = [=](expr const & m, unsigned) -> optional<expr> {
        if (is_head_beta(m))
            return some_expr(head_beta_reduce(m));
        else if (is_local(m) || is_metavar(m))
            return some_expr(m); // do not simplify local constants and metavariables types.
        else
            return none_expr();
    };
    while (true) {
        expr new_t = replace(t, f);
        if (new_t == t)
            return new_t;
        else
            t = new_t;
    }
}

expr instantiate_univ_params(expr const & e, level_param_names const & ps, levels const & ls) {
    if (!has_param_univ(e))
        return e;
    return replace(e, [&](expr const & e) -> optional<expr> {
            if (!has_param_univ(e))
                return some_expr(e);
            if (is_constant(e)) {
                return some_expr(update_constant(e, map_reuse(const_levels(e),
                                                              [&](level const & l) { return instantiate(l, ps, ls); },
                                                              [](level const & l1, level const & l2) { return is_eqp(l1, l2); })));
            } else if (is_sort(e)) {
                return some_expr(update_sort(e, instantiate(sort_level(e), ps, ls)));
            } else {
                return none_expr();
            }
        });
}

expr instantiate_type_univ_params(declaration const & d, levels const & ls) {
    lean_assert(length(d.get_univ_params()) == length(ls));
    return instantiate_univ_params(d.get_type(), d.get_univ_params(), ls);
}

expr instantiate_value_univ_params(declaration const & d, levels const & ls) {
    lean_assert(length(d.get_univ_params()) == length(ls));
    return instantiate_univ_params(d.get_value(), d.get_univ_params(), ls);
}
}