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 "kernel/free_vars.h"
#include "kernel/replace.h"
#include "kernel/metavar.h"

namespace lean {
expr instantiate_with_closed(expr const & a, unsigned n, expr const * s) {
    lean_assert(std::all_of(s, s+n, closed));

    auto f = [=](expr const & m, unsigned offset) -> expr {
        if (is_var(m)) {
            unsigned vidx = var_idx(m);
            if (vidx >= offset) {
                if (vidx < offset + n)
                    return s[n - (vidx - offset) - 1];
                else
                    return mk_var(vidx - n);
            } else {
                return m;
            }
        } else if (is_metavar(m)) {
            expr r = m;
            for (unsigned i = 0; i < n; i++)
                r = add_inst(r, offset + n - i - 1, s[i]);
            return r;
        } else {
            return m;
        }
    };
    return replace_fn<decltype(f)>(f)(a);
}
expr instantiate(expr const & a, unsigned s, unsigned n, expr const * subst) {
    auto f = [=](expr const & m, unsigned offset) -> expr {
        if (is_var(m)) {
            unsigned vidx = var_idx(m);
            if (vidx >= offset + s) {
                if (vidx < offset + s + n)
                    return lift_free_vars(subst[n - (vidx - s - offset) - 1], offset);
                else
                    return mk_var(vidx - n);
            } else {
                return m;
            }
        } else if (is_metavar(m)) {
            expr r = m;
            for (unsigned i = 0; i < n; i++)
                r = add_inst(r, offset + s + n - i - 1, lift_free_vars(subst[i], offset + n - i - 1));
            return r;
        } else {
            return m;
        }
    };
    return replace_fn<decltype(f)>(f)(a);
}
expr instantiate(expr const & e, unsigned n, expr const * s) {
    return instantiate(e, 0, n, s);
}
expr instantiate(expr const & e, unsigned i, expr const & s) {
    return instantiate(e, i, 1, &s);
}

bool is_head_beta(expr const & t) {
    return is_app(t) && is_lambda(arg(t, 0));
}

expr head_beta_reduce(expr const & t) {
    if (!is_head_beta(t)) {
        return t;
    } else {
        unsigned num  = num_args(t);
        unsigned num1 = num - 1;
        expr const * f = &arg(t, 0);
        lean_assert(is_lambda(*f));
        unsigned m = 1;
        while (is_lambda(abst_body(*f)) && m < num1) {
            f = &abst_body(*f);
            m++;
        }
        lean_assert(m <= num1);
        expr r = instantiate(abst_body(*f), m, &arg(t, 1));
        if (m == num1) {
            return r;
        } else {
            buffer<expr> args;
            args.push_back(r);
            m++;
            for (; m < num; m++)
                args.push_back(arg(t, m));
            return mk_app(args.size(), args.data());
        }
    }
}

expr beta_reduce(expr t) {
    auto f = [=](expr const & m, unsigned) -> expr {
        if (is_head_beta(m))
            return head_beta_reduce(m);
        else
            return m;
    };
    while (true) {
        expr new_t = replace_fn<decltype(f)>(f)(t);
        if (new_t == t)
            return new_t;
        else
            t = new_t;
    }
}
}