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 <limits>
#include "kernel/free_vars.h"
#include "kernel/replace_fn.h"
#include "kernel/instantiate.h"
namespace lean {
expr instantiate(expr const & a, unsigned s, unsigned n, expr const * subst) {
if (s >= get_free_var_range(a) || n == 0)
return a;
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); }
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
return none_expr();
};
while (true) {
expr new_t = replace_fn(f)(t);
if (new_t == t)
return new_t;
else
t = new_t;
}
}
expr instantiate_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, unsigned) -> 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();
}
});
}
}