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lean2/src/frontend/pp.cpp
Leonardo de Moura 7ec7b4dce8 Fix bug in pretty printer 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-08-18 11:02:29 -07:00

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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 <limits>
#include <memory>
#include "pp.h"
#include "frontend.h"
#include "context.h"
#include "scoped_map.h"
#include "occurs.h"
#include "instantiate.h"
#include "builtin_notation.h"
#include "context_to_lambda.h"
#include "printer.h"
#include "options.h"
#ifndef LEAN_DEFAULT_PP_MAX_DEPTH
#define LEAN_DEFAULT_PP_MAX_DEPTH std::numeric_limits<unsigned>::max()
#endif
#ifndef LEAN_DEFAULT_PP_MAX_STEPS
#define LEAN_DEFAULT_PP_MAX_STEPS std::numeric_limits<unsigned>::max()
#endif
#ifndef LEAN_DEFAULT_PP_IMPLICIT
#define LEAN_DEFAULT_PP_IMPLICIT false
#endif
#ifndef LEAN_DEFAULT_PP_NOTATION
#define LEAN_DEFAULT_PP_NOTATION true
#endif
#ifndef LEAN_DEFAULT_PP_EXTRA_LETS
#define LEAN_DEFAULT_PP_EXTRA_LETS true
#endif
#ifndef LEAN_DEFAULT_PP_ALIAS_MIN_DEPTH
#define LEAN_DEFAULT_PP_ALIAS_MIN_DEPTH 1000 //TODO: fix to reasonable value
#endif
namespace lean {
static format g_Type_fmt = highlight_builtin(format("Type"));
static format g_eq_fmt = format("=");
static char const * g_eq_sym = "eq";
static unsigned g_eq_sz = strlen(g_eq_sym);
static format g_eq_sym_fmt = format(g_eq_sym);
static format g_lambda_fmt = highlight_keyword(format("\u03BB"));
static format g_Pi_fmt = highlight_keyword(format("\u03A0"));
static format g_arrow_fmt = highlight_keyword(format("\u2192"));
static format g_ellipsis_fmt = highlight(format("\u2026"));
static format g_let_fmt = highlight_keyword(format("let"));
static format g_in_fmt = highlight_keyword(format("in"));
static format g_assign_fmt = highlight_keyword(format(":="));
static format g_geq_fmt = format("\u2265");
static name g_pp_max_depth {"pp", "max_depth"};
static name g_pp_max_steps {"pp", "max_steps"};
static name g_pp_implicit {"pp", "implicit"};
static name g_pp_notation {"pp", "notation"};
static name g_pp_extra_lets {"pp", "extra_lets"};
static name g_pp_alias_min_depth {"pp", "alias_min_depth"};
unsigned get_pp_max_depth(options const & opts) { return opts.get_unsigned(g_pp_max_depth, LEAN_DEFAULT_PP_MAX_DEPTH); }
unsigned get_pp_max_steps(options const & opts) { return opts.get_unsigned(g_pp_max_steps, LEAN_DEFAULT_PP_MAX_STEPS); }
bool get_pp_implicit(options const & opts) { return opts.get_bool(g_pp_implicit, LEAN_DEFAULT_PP_IMPLICIT); }
bool get_pp_notation(options const & opts) { return opts.get_bool(g_pp_notation, LEAN_DEFAULT_PP_NOTATION); }
bool get_pp_extra_lets(options const & opts) { return opts.get_bool(g_pp_extra_lets, LEAN_DEFAULT_PP_EXTRA_LETS); }
unsigned get_pp_alias_min_depth(options const & opts) { return opts.get_unsigned(g_pp_alias_min_depth, LEAN_DEFAULT_PP_ALIAS_MIN_DEPTH); }
/**
\brief Return a fresh name for the given abstraction.
By fresh, we mean a name that is not used for any constant in abst_body(e).
The resultant name is based on abst_name(e).
*/
name get_unused_name(expr const & e) {
name const & n = abst_name(e);
name n1 = n;
unsigned i = 1;
while (occurs(n1, abst_body(e))) {
n1 = name(n, i);
i++;
}
return n1;
}
/** \brief Functional object for pretty printing expressions */
class pp_fn {
typedef scoped_map<expr, name, expr_hash, expr_eqp> aliases;
typedef std::vector<std::pair<name, format>> aliases_defs;
frontend const & m_frontend;
// State
aliases m_aliases;
aliases_defs m_aliases_defs;
unsigned m_num_steps;
name m_aux;
// Configuration
unsigned m_indent;
unsigned m_max_depth;
unsigned m_max_steps;
bool m_implict;
bool m_notation; //!< if true use notation
bool m_extra_lets; //!< introduce extra let-expression to cope with sharing.
unsigned m_alias_min_depth; //!< minimal depth to create an alias
// Create a scope for local definitions
struct mk_scope {
pp_fn & m_fn;
unsigned m_old_size;
mk_scope(pp_fn & fn):m_fn(fn), m_old_size(fn.m_aliases_defs.size()) {
m_fn.m_aliases.push();
}
~mk_scope() {
lean_assert(m_old_size <= m_fn.m_aliases_defs.size());
m_fn.m_aliases.pop();
m_fn.m_aliases_defs.resize(m_old_size);
}
};
format nest(unsigned i, format const & f) { return ::lean::nest(i, f); }
typedef std::pair<format, unsigned> result;
/**
\brief Return true iff \c e is an atomic operation.
*/
bool is_atomic(expr const & e) {
switch (e.kind()) {
case expr_kind::Var: case expr_kind::Constant: case expr_kind::Value: case expr_kind::Type:
return true;
case expr_kind::App: case expr_kind::Lambda: case expr_kind::Pi: case expr_kind::Eq: case expr_kind::Let:
return false;
}
return false;
}
result mk_result(format const & fmt, unsigned depth) {
return mk_pair(fmt, depth);
}
result pp_ellipsis() {
return mk_result(g_ellipsis_fmt, 1);
}
result pp_var(expr const & e) {
unsigned vidx = var_idx(e);
return mk_result(compose(format("#"), format(vidx)), 1);
}
result pp_constant(expr const & e) {
return mk_result(::lean::pp(const_name(e)), 1);
}
result pp_value(expr const & e) {
return mk_result(to_value(e).pp(), 1);
}
result pp_type(expr const & e) {
if (e == Type()) {
return mk_result(g_Type_fmt, 1);
} else {
return mk_result(format{g_Type_fmt, space(), ::lean::pp(ty_level(e))}, 1);
}
}
/**
\brief Return the operator associated with \c e.
Return the nil operator if there is none.
We say \c e has an operator associated with it, if:
1) It is a constant and there is an operator associated with it.
2) It is an application, and the function is a constant \c c with an
operator associated with \c c.
*/
operator_info get_operator(expr const & e) {
if (is_constant(e))
return m_frontend.find_op_for(const_name(e));
else if (is_app(e) && is_constant(arg(e, 0)))
return m_frontend.find_op_for(const_name(arg(e, 0)));
else
return operator_info();
}
/** \brief Return true if the application \c e has the number of arguments expected by the operator \c op. */
bool has_expected_num_args(expr const & e, operator_info const & op) {
switch (op.get_fixity()) {
case fixity::Infix: case fixity::Infixl: case fixity::Infixr:
return num_args(e) == 3;
case fixity::Prefix: case fixity::Postfix:
return num_args(e) == 2;
case fixity::Mixfixl: case fixity::Mixfixr:
return num_args(e) == length(op.get_op_name_parts()) + 1;
case fixity::Mixfixc:
return num_args(e) == length(op.get_op_name_parts());
}
lean_unreachable();
return false;
}
/**
\brief Pretty print given expression and put parenthesis around it.
*/
result pp_child_with_paren(expr const & e, unsigned depth) {
result r = pp(e, depth + 1);
return mk_result(format{lp(), r.first, rp()}, r.second);
}
/**
\brief Pretty print given expression and put parenthesis around
it if it is not atomic.
*/
result pp_child(expr const & e, unsigned depth) {
if (is_atomic(e))
return pp(e, depth + 1);
else
return pp_child_with_paren(e, depth);
}
/**
\brief Pretty print the child of an infix, prefix, postfix or
mixfix operator. It will add parethesis when needed.
*/
result pp_mixfix_child(operator_info const & op, expr const & e, unsigned depth) {
if (is_atomic(e)) {
return pp(e, depth + 1);
} else {
operator_info op_child = get_operator(e);
if (op_child && op.get_precedence() < op_child.get_precedence())
return pp(e, depth + 1);
else
return pp_child_with_paren(e, depth);
}
}
/**
\brief Pretty print the child of an associative infix
operator. It will add parethesis when needed.
*/
result pp_infix_child(operator_info const & op, expr const & e, unsigned depth) {
if (is_atomic(e)) {
return pp(e, depth + 1);
} else {
operator_info op_child = get_operator(e);
if (op_child && (op == op_child || op.get_precedence() < op_child.get_precedence()))
return pp(e, depth + 1);
else
return pp_child_with_paren(e, depth);
}
}
result mk_infix(operator_info const & op, result const & lhs, result const & rhs) {
unsigned r_depth = std::max(lhs.second, rhs.second) + 1;
format r_format = group(format{lhs.first, space(), format(op.get_op_name()), line(), rhs.first});
return mk_result(r_format, r_depth);
}
/**
\brief Pretty print an application.
*/
result pp_app(expr const & e, unsigned depth) {
operator_info op;
if (m_notation && (op = get_operator(e)) && has_expected_num_args(e, op)) {
result p_arg;
format r_format;
unsigned sz;
unsigned r_depth = 0;
switch (op.get_fixity()) {
case fixity::Infix:
return mk_infix(op, pp_mixfix_child(op, arg(e, 1), depth), pp_mixfix_child(op, arg(e, 2), depth));
case fixity::Infixr:
return mk_infix(op, pp_mixfix_child(op, arg(e, 1), depth), pp_infix_child(op, arg(e, 2), depth));
case fixity::Infixl:
return mk_infix(op, pp_infix_child(op, arg(e, 1), depth), pp_mixfix_child(op, arg(e, 2), depth));
case fixity::Prefix:
p_arg = pp_infix_child(op, arg(e, 1), depth);
sz = op.get_op_name().size();
return mk_result(group(format{format(op.get_op_name()), nest(sz+1, format{line(), p_arg.first})}),
p_arg.second + 1);
case fixity::Postfix:
p_arg = pp_mixfix_child(op, arg(e, 1), depth);
return mk_result(group(format{p_arg.first, space(), format(op.get_op_name())}),
p_arg.second + 1);
case fixity::Mixfixr: {
// _ ID ... _ ID
list<name> parts = op.get_op_name_parts();
auto it = parts.begin();
for (unsigned i = 1; i < num_args(e); i++) {
result p_arg = pp_mixfix_child(op, arg(e, i), depth);
r_format += format{p_arg.first, space(), format(*it), line()};
r_depth = std::max(r_depth, p_arg.second);
++it;
}
return mk_result(group(r_format), r_depth + 1);
}
case fixity::Mixfixl: case fixity::Mixfixc: {
// ID _ ... _
// ID _ ... _ ID
list<name> parts = op.get_op_name_parts();
auto it = parts.begin();
for (unsigned i = 1; i < num_args(e); i++) {
result p_arg = pp_mixfix_child(op, arg(e, i), depth);
unsigned sz = it->size();
if (i > 1) r_format += space();
r_format += format{format(*it), nest(sz+1, format{line(), p_arg.first})};
r_depth = std::max(r_depth, p_arg.second);
++it;
}
if (it != parts.end()) {
// it is Mixfixc
r_format += format{space(), format(*it)};
}
return mk_result(group(r_format), r_depth + 1);
}}
lean_unreachable();
return mk_result(format(), 0);
} else {
// standard function application
result p = pp_child(arg(e, 0), depth);
format r_format = p.first;
unsigned r_depth = p.second;
for (unsigned i = 1; i < num_args(e); i++) {
result p_arg = pp_child(arg(e, i), depth);
r_format += format{line(), p_arg.first};
r_depth = std::max(r_depth, p_arg.second);
}
return mk_result(group(nest(m_indent, r_format)), r_depth + 1);
}
}
/**
\brief Collect nested Lambdas (or Pis), and instantiate
variables with unused names. Store in \c r the selected names
and associated domains. Return the body of the sequence of
Lambda (of Pis).
\remark The argument B is only relevant when processing
condensed definitions. \see pp_abstraction_core.
*/
std::pair<expr, expr> collect_nested(expr const & e, expr T, expr_kind k, buffer<std::pair<name, expr>> & r) {
if (e.kind() == k) {
name n1 = get_unused_name(e);
r.push_back(mk_pair(n1, abst_domain(e)));
expr b = instantiate_with_closed(abst_body(e), mk_constant(n1));
if (T)
T = instantiate_with_closed(abst_body(T), mk_constant(n1));
return collect_nested(b, T, k, r);
} else {
return mk_pair(e, T);
}
}
result pp_scoped_child(expr const & e, unsigned depth) {
if (is_atomic(e)) {
return pp(e, depth + 1);
} else {
mk_scope s(*this);
// TODO: create Let with new aliases
return pp(e, depth+1);
}
}
result pp_arrow_body(expr const & e, unsigned depth) {
if (is_atomic(e) || is_arrow(e)) {
return pp(e, depth + 1);
} else {
return pp_child_with_paren(e, depth);
}
}
template<typename It>
format pp_bnames(It const & begin, It const & end, bool use_line) {
auto it = begin;
format r = format(it->first);
++it;
for (; it != end; ++it) {
r += compose(use_line ? line() : space(), format(it->first));
}
return r;
}
/**
\brief Pretty print Lambdas, Pis and compact definitions.
When T != 0, it is a compact definition.
A compact definition is of the form
Defintion Name Pi(x : A), B := Lambda (x : A), C
it is printed as
Defintion Name (x : A) : B := C
This method only generates the
(x : A) : B := C
for compact definitions.
\remark if T != 0, then T is Pi(x : A), B
*/
result pp_abstraction_core(expr const & e, unsigned depth, expr T) {
if (is_arrow(e)) {
lean_assert(!T);
result p_lhs = pp_child(abst_domain(e), depth);
result p_rhs = pp_arrow_body(abst_body(e), depth);
format r_format = group(format{p_lhs.first, space(), g_arrow_fmt, line(), p_rhs.first});
return mk_result(r_format, std::max(p_lhs.second, p_rhs.second) + 1);
} else {
buffer<std::pair<name, expr>> nested;
auto p = collect_nested(e, T, e.kind(), nested);
expr b = p.first;
T = p.second;
lean_assert(b.kind() != e.kind());
format head;
if (!T) {
head = is_lambda(e) ? g_lambda_fmt : g_Pi_fmt;
}
format body_sep;
if (T) {
format T_f = pp(T, 0).first;
body_sep = format{space(), colon(), space(), T_f, space(), g_assign_fmt};
} else {
body_sep = comma();
}
expr domain0 = nested[0].second;
if (std::all_of(nested.begin() + 1, nested.end(), [&](std::pair<name, expr> const & p) { return p.second == domain0; })) {
// Domain of all binders is the same
format names = pp_bnames(nested.begin(), nested.end(), false);
result p_domain = pp_scoped_child(domain0, depth);
result p_body = pp_scoped_child(b, depth);
format sig = format{names, space(), colon(), space(), p_domain.first};
if (T)
sig = format{lp(), sig, rp()};
format r_format = group(nest(m_indent, format{head, space(), sig, body_sep, line(), p_body.first}));
return mk_result(r_format, std::max(p_domain.second, p_body.second)+1);
} else {
auto it = nested.begin();
auto end = nested.end();
unsigned r_depth = 0;
// PP binders in blocks (names ... : type)
bool first = true;
format bindings;
while (it != end) {
auto it2 = it;
++it2;
while (it2 != end && it2->second == it->second) {
++it2;
}
result p_domain = pp_scoped_child(it->second, depth);
r_depth = std::max(r_depth, p_domain.second);
format block = group(nest(m_indent, format{lp(), pp_bnames(it, it2, true), space(), colon(), space(), p_domain.first, rp()}));
if (first) {
bindings = block;
first = false;
} else {
bindings += compose(line(), block);
}
it = it2;
}
result p_body = pp_scoped_child(b, depth);
format r_format = group(nest(m_indent, format{head, space(), group(bindings), body_sep, line(), p_body.first}));
return mk_result(r_format, std::max(r_depth, p_body.second)+1);
}
}
}
result pp_abstraction(expr const & e, unsigned depth) {
return pp_abstraction_core(e, depth, expr());
}
result pp_let(expr const & e, unsigned depth) {
// TODO
return mk_result(format("TODO"), 1);
}
/** \brief Pretty print the child of an equality. */
result pp_eq_child(expr const & e, unsigned depth) {
if (is_atomic(e)) {
return pp(e, depth + 1);
} else {
operator_info op_child = get_operator(e);
if (op_child && g_eq_precedence < op_child.get_precedence())
return pp(e, depth + 1);
else
return pp_child_with_paren(e, depth);
}
}
/** \brief Pretty print an equality */
result pp_eq(expr const & e, unsigned depth) {
result p_arg1, p_arg2;
format r_format;
if (m_notation) {
p_arg1 = pp_eq_child(eq_lhs(e), depth);
p_arg2 = pp_eq_child(eq_rhs(e), depth);
r_format = group(format{p_arg1.first, space(), g_eq_fmt, line(), p_arg2.first});
} else {
p_arg1 = pp_child(eq_lhs(e), depth);
p_arg2 = pp_child(eq_rhs(e), depth);
r_format = group(format{g_eq_sym_fmt, nest(g_eq_sz + 1,
format{line(), p_arg1.first,
line(), p_arg2.first})});
}
return mk_result(r_format, std::max(p_arg1.second, p_arg2.second) + 1);
}
result pp(expr const & e, unsigned depth) {
if (m_num_steps > m_max_steps || depth > m_max_depth) {
return pp_ellipsis();
} else {
m_num_steps++;
if (m_extra_lets && is_shared(e)) {
auto it = m_aliases.find(e);
if (it != m_aliases.end())
return mk_result(format(it->second), 1);
}
result r;
switch (e.kind()) {
case expr_kind::Var: r = pp_var(e); break;
case expr_kind::Constant: r = pp_constant(e); break;
case expr_kind::Value: r = pp_value(e); break;
case expr_kind::App: r = pp_app(e, depth); break;
case expr_kind::Lambda:
case expr_kind::Pi: r = pp_abstraction(e, depth); break;
case expr_kind::Type: r = pp_type(e); break;
case expr_kind::Eq: r = pp_eq(e, depth); break;
case expr_kind::Let: r = pp_let(e, depth); break;
}
if (m_extra_lets && is_shared(e) && r.second > m_alias_min_depth) {
lean_unreachable(); // TODO: remove
std::cout << "DEPTH: " << r.second << "\n";
name new_aux = name(m_aux, m_aliases.size());
m_aliases.insert(e, new_aux);
return mk_result(format(new_aux), 1);
}
return r;
}
}
void set_options(options const & opts) {
m_indent = get_pp_indent(opts);
m_max_depth = get_pp_max_depth(opts);
m_max_steps = get_pp_max_steps(opts);
m_implict = get_pp_implicit(opts);
m_notation = get_pp_notation(opts);
m_extra_lets = get_pp_extra_lets(opts);
m_alias_min_depth = get_pp_alias_min_depth(opts);
}
void init() {
m_aliases.clear();
m_aliases_defs.clear();
m_num_steps = 0;
m_aux = name("aux"); // TODO: find non used prefix
}
public:
pp_fn(frontend const & fe, options const & opts):
m_frontend(fe) {
set_options(opts);
}
format operator()(expr const & e) {
init();
return pp(e, 0).first;
}
format pp_definition(expr const & v, expr const & t) {
init();
expr T(t);
return pp_abstraction_core(v, 0, T).first;
}
};
class pp_formatter_cell : public formatter_cell {
frontend m_frontend;
options m_options;
unsigned m_indent;
format pp(expr const & e) {
return pp_fn(m_frontend, m_options)(e);
}
format pp(context const & c, expr const & e, bool include_e) {
format r;
bool first = true;
expr c2 = context_to_lambda(c, e);
while (is_fake_context(c2)) {
name n1 = get_unused_name(c2);
format entry = format{format(n1), space(), colon(), space(), pp(fake_context_domain(c2))};
expr val = fake_context_value(c2);
if (val)
entry += format{space(), g_assign_fmt, nest(m_indent, format{line(), pp(val)})};
if (first) {
r = group(entry);
first = false;
} else {
r += format{line(), group(entry)};
}
c2 = instantiate_with_closed(fake_context_rest(c2), mk_constant(n1));
}
if (include_e) {
if (first)
r += format{line(), pp(c2)};
else
r = pp(c2);
} else {
return r;
}
return r;
}
format pp_definition(char const * kwd, name const & n, expr const & t, expr const & v) {
format def = format{highlight_command(format(kwd)), space(), format(n), space(), colon(), space(),
pp(t), space(), g_assign_fmt, line(), pp(v)};
return group(nest(m_indent, def));
}
format pp_compact_definition(char const * kwd, name const & n, expr const & t, expr const & v) {
expr it1 = t;
expr it2 = v;
while (is_pi(it1) && is_lambda(it2)) {
if (abst_domain(it1) != abst_domain(it2))
return pp_definition(kwd, n, t, v);
it1 = abst_body(it1);
it2 = abst_body(it2);
}
if (!is_lambda(v) || is_pi(it1) || is_lambda(it2)) {
return pp_definition(kwd, n, t, v);
} else {
lean_assert(is_lambda(v));
format def = pp_fn(m_frontend, m_options).pp_definition(v, t);
return format{highlight_command(format(kwd)), space(), format(n), def};
}
}
format pp_uvar_decl(object const & obj) {
return format{highlight_command(format(obj.keyword())), space(), format(obj.get_name()), space(), format("\u2265"), space(), ::lean::pp(obj.get_cnstr_level())};
}
format pp_postulate(object const & obj) {
return format{highlight_command(format(obj.keyword())), space(), format(obj.get_name()), space(), colon(), space(), pp(obj.get_type())};
}
format pp_definition(object const & obj) {
return pp_compact_definition(obj.keyword(), obj.get_name(), obj.get_type(), obj.get_value());
}
format pp_notation_decl(object const & obj) {
return ::lean::pp(*(static_cast<notation_declaration const *>(obj.cell())));
}
public:
pp_formatter_cell(frontend const & fe, options const & opts):
m_frontend(fe),
m_options(opts) {
m_indent = get_pp_indent(opts);
}
virtual ~pp_formatter_cell() {
}
virtual format operator()(expr const & e) {
return pp(e);
}
virtual format operator()(context const & c) {
return pp(c, Type(), false);
}
virtual format operator()(context const & c, expr const & e, bool format_ctx) {
if (format_ctx) {
return pp(c, e, true);
} else {
expr c2 = context_to_lambda(c, e);
while (is_fake_context(c2)) {
expr const & rest = fake_context_rest(c2);
name n1 = get_unused_name(rest);
c2 = instantiate_with_closed(rest, mk_constant(n1));
}
return pp(c2);
}
}
virtual format operator()(object const & obj) {
switch (obj.kind()) {
case object_kind::UVarDeclaration: return pp_uvar_decl(obj);
case object_kind::Postulate: return pp_postulate(obj);
case object_kind::Definition: return pp_definition(obj);
case object_kind::Neutral:
if (dynamic_cast<notation_declaration const *>(obj.cell())) {
// If the object is not notation, then the object was
// created in different frontend, and we ignore it.
return pp_notation_decl(obj);
} else {
return format("Unknown neutral object");
}
}
lean_unreachable();
return format();
}
virtual format operator()(environment const & env) {
format r;
bool first = true;
std::for_each(env.begin_objects(),
env.end_objects(),
[&](object const & obj) {
if (first) first = false; else r += line();
r += operator()(obj);
});
return r;
}
};
formatter mk_pp_formatter(frontend const & fe, options const & opts) {
return formatter(new pp_formatter_cell(fe, opts));
}
std::ostream & operator<<(std::ostream & out, frontend const & fe) {
formatter fmt = mk_pp_formatter(fe, options());
out << fmt(fe.get_environment());
return out;
}
}
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