lean2/src/library/rewriter/rewriter.h

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/*
Copyright (c) 2013 Microsoft Corporation.
Copyright (c) 2013 Carnegie Mellon University.
All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Soonho Kong
*/
#pragma once
#include <algorithm>
#include <utility>
#include "kernel/abstract.h"
#include "kernel/context.h"
#include "kernel/environment.h"
#include "kernel/expr.h"
#include "kernel/replace_fn.h"
#include "kernel/type_checker.h"
#include "kernel/builtin.h"
#include "library/rewriter/rewriter.h"
#include "util/exception.h"
#include "util/scoped_map.h"
// TODO(soonhok)
// FORALL
// FAIL_IF
namespace lean {
class rewriter_exception : public exception {
public:
virtual exception * clone() const { return new rewriter_exception(); }
virtual void rethrow() const { throw *this; }
};
enum class rewriter_kind { Theorem, OrElse, Then, Try, App,
LambdaType, LambdaBody, Lambda,
PiType, PiBody, Pi,
LetType, LetValue, LetBody, Let,
Fail, Success, Repeat, Depth };
std::pair<expr, expr> rewrite_lambda_type(environment const & env, context & ctx, expr const & v, std::pair<expr, expr> const & result_ty);
std::pair<expr, expr> rewrite_lambda_body(environment const & env, context & ctx, expr const & v, std::pair<expr, expr> const & result_body);
std::pair<expr, expr> rewrite_lambda(environment const & env, context & ctx, expr const & v, std::pair<expr, expr> const & result_ty, std::pair<expr, expr> const & result_body);
std::pair<expr, expr> rewrite_pi_type(environment const & env, context & ctx, expr const & v, std::pair<expr, expr> const & result_ty);
std::pair<expr, expr> rewrite_pi_body(environment const & env, context & ctx, expr const & v, std::pair<expr, expr> const & result_body);
std::pair<expr, expr> rewrite_pi(environment const & env, context & ctx, expr const & v, std::pair<expr, expr> const & result_ty, std::pair<expr, expr> const & result_body);
std::pair<expr, expr> rewrite_eq_lhs(environment const & env, context & ctx, expr const & v, std::pair<expr, expr> const & result_lhs);
std::pair<expr, expr> rewrite_eq_rhs(environment const & env, context & ctx, expr const & v, std::pair<expr, expr> const & result_rhs);
std::pair<expr, expr> rewrite_eq(environment const & env, context & ctx, expr const & v, std::pair<expr, expr> const & result_lhs, std::pair<expr, expr> const & result_rhs);
std::pair<expr, expr> rewrite_let_type(environment const & env, context & ctx, expr const & v, std::pair<expr, expr> const & result_ty);
std::pair<expr, expr> rewrite_let_value(environment const & env, context & ctx, expr const & v, std::pair<expr, expr> const & result_value);
std::pair<expr, expr> rewrite_let_body(environment const & env, context & ctx, expr const & v, std::pair<expr, expr> const & result_body);
std::pair<expr, expr> rewrite_app(environment const & env, context & ctx, expr const & v, buffer<std::pair<expr, expr>> const & results );
class rewriter;
class rewriter_cell {
protected:
rewriter_kind m_kind;
MK_LEAN_RC();
void dealloc();
virtual std::ostream & display(std::ostream & out) const = 0;
public:
rewriter_cell(rewriter_kind k);
virtual ~rewriter_cell();
rewriter_kind kind() const { return m_kind; }
// unsigned hash() const { return m_hash; }
virtual std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception) = 0;
friend std::ostream & operator<<(std::ostream & out, rewriter_cell const & rw);
};
class rewriter {
private:
rewriter_cell * m_ptr;
public:
explicit rewriter(rewriter_cell * ptr):m_ptr(ptr) {}
rewriter():m_ptr(nullptr) {}
rewriter(rewriter const & r):m_ptr(r.m_ptr) {
if (m_ptr) m_ptr->inc_ref();
}
rewriter(rewriter && r):m_ptr(r.m_ptr) { r.m_ptr = nullptr; }
~rewriter() { if (m_ptr) m_ptr->dec_ref(); }
void release() { if (m_ptr) m_ptr->dec_ref(); m_ptr = nullptr; }
friend void swap(rewriter & a, rewriter & b) { std::swap(a.m_ptr, b.m_ptr); }
rewriter_kind kind() const { return m_ptr->kind(); }
rewriter & operator=(rewriter const & s) { LEAN_COPY_REF(s); }
rewriter & operator=(rewriter && s) { LEAN_MOVE_REF(s); }
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const {
return (*m_ptr)(env, ctx, v);
}
friend std::ostream & operator<<(std::ostream & out, rewriter const & rw);
};
class theorem_rewriter_cell : public rewriter_cell {
private:
expr const & m_type;
expr const & m_body;
expr m_pattern;
expr m_rhs;
unsigned m_num_args;
std::ostream & display(std::ostream & out) const;
public:
theorem_rewriter_cell(expr const & type, expr const & body);
~theorem_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class orelse_rewriter_cell : public rewriter_cell {
private:
list<rewriter> m_rwlist;
std::ostream & display(std::ostream & out) const;
public:
orelse_rewriter_cell(rewriter const & rw1, rewriter const & rw2);
orelse_rewriter_cell(std::initializer_list<rewriter> const & l);
~orelse_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class then_rewriter_cell : public rewriter_cell {
private:
list<rewriter> m_rwlist;
std::ostream & display(std::ostream & out) const;
public:
then_rewriter_cell(rewriter const & rw1, rewriter const & rw2);
then_rewriter_cell(std::initializer_list<rewriter> const & l);
~then_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class try_rewriter_cell : public rewriter_cell {
private:
list<rewriter> m_rwlist;
std::ostream & display(std::ostream & out) const;
public:
try_rewriter_cell(rewriter const & rw1, rewriter const & rw2);
try_rewriter_cell(std::initializer_list<rewriter> const & l);
~try_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class app_rewriter_cell : public rewriter_cell {
private:
rewriter m_rw;
std::ostream & display(std::ostream & out) const;
public:
app_rewriter_cell(rewriter const & rw);
~app_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class lambda_type_rewriter_cell : public rewriter_cell {
private:
rewriter m_rw;
std::ostream & display(std::ostream & out) const;
public:
lambda_type_rewriter_cell(rewriter const & rw);
~lambda_type_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class lambda_body_rewriter_cell : public rewriter_cell {
private:
rewriter m_rw;
std::ostream & display(std::ostream & out) const;
public:
lambda_body_rewriter_cell(rewriter const & rw);
~lambda_body_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class lambda_rewriter_cell : public rewriter_cell {
private:
rewriter m_rw;
std::ostream & display(std::ostream & out) const;
public:
lambda_rewriter_cell(rewriter const & rw);
~lambda_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class pi_type_rewriter_cell : public rewriter_cell {
private:
rewriter m_rw;
std::ostream & display(std::ostream & out) const;
public:
pi_type_rewriter_cell(rewriter const & rw);
~pi_type_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class pi_body_rewriter_cell : public rewriter_cell {
private:
rewriter m_rw;
std::ostream & display(std::ostream & out) const;
public:
pi_body_rewriter_cell(rewriter const & rw);
~pi_body_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class pi_rewriter_cell : public rewriter_cell {
private:
rewriter m_rw;
std::ostream & display(std::ostream & out) const;
public:
pi_rewriter_cell(rewriter const & rw);
~pi_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class let_type_rewriter_cell : public rewriter_cell {
private:
rewriter m_rw;
std::ostream & display(std::ostream & out) const;
public:
let_type_rewriter_cell(rewriter const & rw);
~let_type_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class let_value_rewriter_cell : public rewriter_cell {
private:
rewriter m_rw;
std::ostream & display(std::ostream & out) const;
public:
let_value_rewriter_cell(rewriter const & rw);
~let_value_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class let_body_rewriter_cell : public rewriter_cell {
private:
rewriter m_rw;
std::ostream & display(std::ostream & out) const;
public:
let_body_rewriter_cell(rewriter const & rw);
~let_body_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class let_rewriter_cell : public rewriter_cell {
private:
rewriter m_rw;
std::ostream & display(std::ostream & out) const;
public:
let_rewriter_cell(rewriter const & rw);
~let_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class fail_rewriter_cell : public rewriter_cell {
private:
std::ostream & display(std::ostream & out) const;
public:
fail_rewriter_cell();
~fail_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class success_rewriter_cell : public rewriter_cell {
private:
std::ostream & display(std::ostream & out) const;
public:
success_rewriter_cell();
~success_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class repeat_rewriter_cell : public rewriter_cell {
private:
rewriter m_rw;
std::ostream & display(std::ostream & out) const;
public:
repeat_rewriter_cell(rewriter const & rw);
~repeat_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
class depth_rewriter_cell : public rewriter_cell {
private:
rewriter m_rw;
std::ostream & display(std::ostream & out) const;
public:
depth_rewriter_cell(rewriter const & rw);
~depth_rewriter_cell();
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) const throw(rewriter_exception);
};
/** \brief (For debugging) Display the content of this rewriter */
inline std::ostream & operator<<(std::ostream & out, rewriter_cell const & rc) { rc.display(out); return out; }
inline std::ostream & operator<<(std::ostream & out, rewriter const & rw) { out << *(rw.m_ptr); return out; }
rewriter mk_theorem_rewriter(expr const & type, expr const & body);
rewriter mk_then_rewriter(rewriter const & rw1, rewriter const & rw2);
rewriter mk_then_rewriter(std::initializer_list<rewriter> const & l);
rewriter mk_try_rewriter(rewriter const & rw);
rewriter mk_try_rewriter(rewriter const & rw1, rewriter const & rw2);
rewriter mk_try_rewriter(std::initializer_list<rewriter> const & l);
rewriter mk_orelse_rewriter(rewriter const & rw1, rewriter const & rw2);
rewriter mk_orelse_rewriter(std::initializer_list<rewriter> const & l);
rewriter mk_app_rewriter(rewriter const & rw);
rewriter mk_lambda_type_rewriter(rewriter const & rw);
rewriter mk_lambda_body_rewriter(rewriter const & rw);
rewriter mk_lambda_rewriter(rewriter const & rw);
rewriter mk_pi_type_rewriter(rewriter const & rw);
rewriter mk_pi_body_rewriter(rewriter const & rw);
rewriter mk_pi_rewriter(rewriter const & rw);
rewriter mk_let_type_rewriter(rewriter const & rw);
rewriter mk_let_value_rewriter(rewriter const & rw);
rewriter mk_let_body_rewriter(rewriter const & rw);
rewriter mk_let_rewriter(rewriter const & rw);
rewriter mk_fail_rewriter();
rewriter mk_success_rewriter();
rewriter mk_repeat_rewriter(rewriter const & rw);
rewriter mk_depth_rewriter(rewriter const & rw);
/**
\brief Functional for applying <tt>F</tt> to the subexpressions of a given expression.
The signature of \c F is
expr const &, context const & ctx, unsigned n -> expr
F is invoked for each subexpression \c s of the input expression e.
In a call <tt>F(s, c, n)</tt>, \c c is the context where \c s occurs,
and \c n is the size of \c c.
P is a "post-processing" functional object that is applied to each
pair (old, new)
*/
template<typename RW, typename P = default_replace_postprocessor>
class apply_rewriter_fn {
// the return type of RW()(env, ctx, e) should be std::pair<expr, expr>
static_assert(std::is_same<typename std::result_of<decltype(std::declval<RW>())(environment const &, context &, expr const &)>::type,
std::pair<expr, expr>>::value,
"apply_rewriter_fn: the return type of RW()(env, ctx, e) should be std::pair<expr, expr>");
// the return type of P()(e1, e2) should be void
static_assert(std::is_same<typename std::result_of<decltype(std::declval<P>())(expr const &, expr const &)>::type,
void>::value,
"apply_rewriter_fn: the return type of P()(e1, e2) is not void");
typedef scoped_map<expr, std::pair<expr, expr>, expr_hash, expr_eqp> cache;
cache m_cache;
RW m_rw;
P m_post;
std::pair<expr, expr> apply(environment const & env, context & ctx, expr const & v) {
bool shared = false;
if (is_shared(v)) {
shared = true;
auto it = m_cache.find(v);
if (it != m_cache.end())
return it->second;
}
std::pair<expr, expr> result; // m_rw(env, ctx, v);
// if (is_eqp(v, result.first))
type_inferer ti(env);
expr ty_v = ti(v, ctx);
switch (v.kind()) {
case expr_kind::Type:
result = m_rw(env, ctx, v);
break;
case expr_kind::Value:
result = m_rw(env, ctx, v);
break;
case expr_kind::Constant:
result = m_rw(env, ctx, v);
break;
case expr_kind::Var:
result = m_rw(env, ctx, v);
break;
case expr_kind::MetaVar:
result = m_rw(env, ctx, v);
break;
case expr_kind::App: {
buffer<std::pair<expr, expr>> results;
for (unsigned i = 0; i < num_args(v); i++) {
results.push_back(apply(env, ctx, arg(v, i)));
}
result = rewrite_app(env, ctx, v, results);
std::pair<expr, expr> tmp = m_rw(env, ctx, result.first);
if (result.first != tmp.first) {
tmp.second = Trans(ty_v, v, result.first, tmp.first, result.second, tmp.second);
result = tmp;
}
}
break;
case expr_kind::Eq: {
expr const & lhs = eq_lhs(v);
expr const & rhs = eq_rhs(v);
std::pair<expr, expr> result_lhs = apply(env, ctx, lhs);
std::pair<expr, expr> result_rhs = apply(env, ctx, rhs);
expr const & new_lhs = result_lhs.first;
expr const & new_rhs = result_rhs.first;
if (lhs != new_lhs) {
if (rhs != new_rhs) {
// lhs & rhs changed
result = rewrite_eq(env, ctx, v, result_lhs, result_rhs);
} else {
// only lhs changed
result = rewrite_eq_lhs(env, ctx, v, result_lhs);
}
} else {
if (rhs != new_rhs) {
// only rhs changed
result = rewrite_eq_rhs(env, ctx, v, result_rhs);
} else {
// nothing changed
result = std::make_pair(v, Refl(ti(v, ctx), v));
}
}
std::pair<expr, expr> tmp = m_rw(env, ctx, result.first);
if (result.first != tmp.first) {
tmp.second = Trans(ty_v, v, result.first, tmp.first, result.second, tmp.second);
result = tmp;
}
}
break;
case expr_kind::Lambda: {
name const & n = abst_name(v);
expr const & ty = abst_domain(v);
expr const & body = abst_body(v);
context new_ctx = extend(ctx, n, ty);
std::pair<expr, expr> result_ty = apply(env, ctx, ty);
std::pair<expr, expr> result_body = apply(env, new_ctx, body);
if (ty != result_ty.first) {
if (body != result_body.first) {
// ty and body changed
result = rewrite_lambda(env, ctx, v, result_ty, result_body);
} else {
// ty changed
result = rewrite_lambda_type(env, ctx, v, result_ty);
}
} else {
if (body != result_body.first) {
// body changed
result = rewrite_lambda_body(env, ctx, v, result_body);
} else {
// nothing changed
result = std::make_pair(v, Refl(ti(v, ctx), v));
}
}
std::pair<expr, expr> tmp = m_rw(env, ctx, result.first);
if (result.first != tmp.first) {
tmp.second = Trans(ty_v, v, result.first, tmp.first, result.second, tmp.second);
result = tmp;
}
}
break;
case expr_kind::Pi: {
name const & n = abst_name(v);
expr const & ty = abst_domain(v);
expr const & body = abst_body(v);
context new_ctx = extend(ctx, n, ty);
std::pair<expr, expr> result_ty = apply(env, ctx, ty);
std::pair<expr, expr> result_body = apply(env, new_ctx, body);
if (ty != result_ty.first) {
if (body != result_body.first) {
// ty and body changed
result = rewrite_pi(env, ctx, v, result_ty, result_body);
} else {
// ty changed
result = rewrite_pi_type(env, ctx, v, result_ty);
}
} else {
if (body != result_body.first) {
// body changed
result = rewrite_pi_body(env, ctx, v, result_body);
} else {
// nothing changed
result = std::make_pair(v, Refl(ti(v, ctx), v));
}
}
std::pair<expr, expr> tmp = m_rw(env, ctx, result.first);
if (result.first != tmp.first) {
tmp.second = Trans(ty_v, v, result.first, tmp.first, result.second, tmp.second);
result = tmp;
}
}
break;
case expr_kind::Let: {
name const & n = let_name(v);
optional<expr> const & ty = let_type(v);
expr const & val = let_value(v);
expr const & body = let_body(v);
expr new_v = v;
expr ty_v = ti(v, ctx);
expr pf = Refl(ty_v, v);
bool changed = false;
if (ty) {
std::pair<expr, expr> result_ty = apply(env, ctx, *ty);
if (*ty != result_ty.first) {
// ty changed
result = rewrite_let_type(env, ctx, new_v, result_ty);
new_v = result.first;
pf = result.second;
changed = true;
}
}
std::pair<expr, expr> result_val = apply(env, ctx, val);
if (val != result_val.first) {
result = rewrite_let_value(env, ctx, new_v, result_val);
if (changed) {
pf = Trans(ty_v, v, new_v, result.first, pf, result.second);
} else {
pf = result.second;
}
new_v = result.first;
changed = true;
}
context new_ctx = extend(ctx, n, ty, val);
std::pair<expr, expr> result_body = apply(env, new_ctx, body);
if (body != result_body.first) {
result = rewrite_let_body(env, ctx, new_v, result_body);
if (changed) {
pf = Trans(ty_v, v, new_v, result.first, pf, result.second);
} else {
pf = result.second;
}
new_v = result.first;
changed = true;
}
result = std::make_pair(new_v, pf);
std::pair<expr, expr> tmp = m_rw(env, ctx, result.first);
if (result.first != tmp.first) {
tmp.second = Trans(ty_v, v, result.first, tmp.first, result.second, tmp.second);
result = tmp;
}
}
break;
}
if (shared)
m_cache.insert(std::make_pair(v, result));
return result;
}
public:
apply_rewriter_fn(RW const & rw, P const & p = P()):
m_rw(rw),
m_post(p) {
}
std::pair<expr, expr> operator()(environment const & env, context & ctx, expr const & v) {
return apply(env, ctx, v);
}
};
}