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_fn.h"
#include "kernel/metavar.h"
namespace lean {
expr instantiate_with_closed_relaxed(expr const & a, unsigned n, expr const * s) {
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_with_closed(expr const & a, unsigned n, expr const * s) {
lean_assert(std::all_of(s, s+n, closed));
return instantiate_with_closed_relaxed(a, n, s);
}
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 apply_beta(expr f, unsigned num_args, expr const * args) {
lean_assert(is_lambda(f));
unsigned m = 1;
while (is_lambda(abst_body(f)) && m < num_args) {
f = abst_body(f);
m++;
}
lean_assert(m <= num_args);
expr r = instantiate(abst_body(f), m, args);
if (m == num_args) {
return r;
} else {
buffer<expr> new_args;
new_args.push_back(r);
for (; m < num_args; m++)
new_args.push_back(args[m]);
return mk_app(new_args);
}
}
expr head_beta_reduce(expr const & t) {
if (!is_head_beta(t)) {
return t;
} else {
return apply_beta(arg(t, 0), num_args(t) - 1, &arg(t, 1));
}
}
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;
}
}
}