lean2/src/kernel/instantiate.cpp

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/*
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;
}
}
}