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Update fo_match

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This commit is contained in:
Soonho Kong 2013-09-19 12:21:29 -07:00
parent f89ededddc
commit 9ba6068858
5 changed files with 270 additions and 189 deletions
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314
src/library/rewrite/fo_match.cpp
View file

@ -10,172 +10,238 @@ Author: Soonho Kong
#include "library/all/all.h" #include "library/all/all.h"
#include "library/arith/nat.h" #include "library/arith/nat.h"
#include "library/arith/arith.h" #include "library/arith/arith.h"
#include "library/rewrite/fo_match.h"
#include "library/rewrite/rewrite.h" #include "library/rewrite/rewrite.h"
#include "library/printer.h"
using std::cout;
using std::endl;
namespace lean { namespace lean {
std::ostream & operator<<(std::ostream & out, subst_map & s) {
std::ostream & operator<<(std::ostream & out, expr_pair const & p) { out << "{";
out << "(" for (auto it = s.begin(); it != s.end(); it++) {
<< p.first << ", " out << it->first << " => ";
<< p.second << ")"; out << it->second << "; ";
}
out << "}";
return out; return out;
} }
bool fo_match::match_var(context & ctx, expr const & p, expr const & t, subst_map & s) { bool fo_match::match_var(expr const & p, expr const & t, unsigned o, subst_map & s) {
std::cerr << "match_var : (" cout << "match_var : ("
<< ctx << " ," << p << ", "
<< p << ", " << t << ", "
<< t << ", " << o << ", "
// << s << ")" << s << ")"
<< std::endl; << endl;
s.insert(std::make_pair(var_idx(p), t));
return true; unsigned idx = var_idx(p);
} if (idx < o) {
bool fo_match::match_constant(context & ctx, expr const & p, expr const & t, subst_map & s) { // Current variable is the one created by lambda inside of pattern
std::cerr << "match_constant : (" // and it is not a target of pattern matching.
<< ctx << " ," return p == t;
<< p << ", "
<< t << ", "
// << s << ")"
<< std::endl;
if (is_constant(t) && const_name(p) == const_name(t)) {
return true;
} else { } else {
return false; auto it = s.find(p);
if (it != s.end()) {
// This variable already has an entry in the substitution
// map. We need to make sure that 't' and s[idx] are the
// same
cout << "match_var exist:" << p << " |-> " << it->second << endl;
return it->second == t;
}
// This variable has no entry in the substituition map. Let's
// add one.
s.insert(std::make_pair(p, t));
cout << "match_var MATCHED : " << s << endl;
return true;
} }
} }
bool fo_match::match_value(context & ctx, expr const & p, expr const & t, subst_map & s) {
std::cerr << "match_value : (" bool fo_match::match_constant(expr const & p, expr const & t, unsigned o, subst_map & s) {
<< ctx << " ," cout << "match_constant : ("
<< p << ", " << p << ", "
<< t << ", " << t << ", "
// << s << ")" << o << ", "
<< std::endl; << s << ")"
if (is_value(t) && to_value(p) == to_value(t)) { << endl;
return true; return p == t;
} else {
return false;
}
} }
bool fo_match::match_app(context & ctx, expr const & p, expr const & t, subst_map & s) {
std::cerr << "match_app : (" bool fo_match::match_value(expr const & p, expr const & t, unsigned o, subst_map & s) {
<< ctx << " ," cout << "match_value : ("
<< p << ", " << p << ", "
<< t << ", " << t << ", "
// << s << ")" << o << ", "
<< std::endl; << s << ")"
<< endl;
return p == t;
}
bool fo_match::match_app(expr const & p, expr const & t, unsigned o, subst_map & s) {
cout << "match_app : ("
<< p << ", "
<< t << ", "
<< o << ", "
<< s << ")"
<< endl;
unsigned num_p = num_args(p); unsigned num_p = num_args(p);
unsigned num_t = num_args(p); unsigned num_t = num_args(p);
if (num_p != num_t) { if (num_p != num_t) {
return false; return false;
} }
for unsigned i = 0; i <= num_p; i++) { for (unsigned i = 0; i < num_p; i++) {
if (!match(ctx, arg(p, i), arg(t, i), s)) if (!match(arg(p, i), arg(t, i), o, s))
return false; return false;
} }
return true; return true;
} }
bool fo_match::match_lambda(context & ctx, expr const & p, expr const & t, subst_map & s) {
std::cerr << "match_lambda : (" bool fo_match::match_lambda(expr const & p, expr const & t, unsigned o, subst_map & s) {
<< ctx << " ," cout << "match_lambda : ("
<< p << ", " << p << ", "
<< t << ", " << t << ", "
// << s << ")" << o << ", "
<< std::endl; << s << ")"
// TODO(soonho) << endl;
std::cerr << "fun (" << abst_name(p) cout << "fun (" << abst_name(p)
<< " : " << abst_domain(p) << " : " << abst_domain(p)
<< "), " << abst_body(p) << std::endl; << "), " << abst_body(p) << endl;
if (!is_lambda(t)) { if (!is_lambda(t)) {
return false; return false;
} } else {
// First match the domain part
auto p_domain = abst_domain(p);
auto t_domain = abst_domain(t);
if (!match(p_domain, t_domain, o, s))
return false;
return true; // Then match the body part, increase offset by 1.
auto p_body = abst_body(p);
auto t_body = abst_body(t);
return match(p_domain, t_domain, o + 1, s);
}
} }
bool fo_match::match_pi(context & ctx, expr const & p, expr const & t, subst_map & s) {
std::cerr << "match_pi : (" bool fo_match::match_pi(expr const & p, expr const & t, unsigned o, subst_map & s) {
<< ctx << " ," cout << "match_pi : ("
<< p << ", " << p << ", "
<< t << ", " << t << ", "
// << s << ")" << o << ", "
<< std::endl; << s << ")"
// TODO(soonho) << endl;
std::cerr << "Pi (" << abst_name(p) cout << "Pi (" << abst_name(p)
<< " : " << abst_domain(p) << " : " << abst_domain(p)
<< "), " << abst_body(p) << std::endl; << "), " << abst_body(p) << endl;
return true;
if (!is_pi(t)) {
return false;
} else {
// First match the domain part
auto p_domain = abst_domain(p);
auto t_domain = abst_domain(t);
if (!match(p_domain, t_domain, o, s))
return false;
// Then match the body part, increase offset by 1.
auto p_body = abst_body(p);
auto t_body = abst_body(t);
return match(p_domain, t_domain, o + 1, s);
}
} }
bool fo_match::match_type(context & ctx, expr const & p, expr const & t, subst_map & s) {
std::cerr << "match_type : (" bool fo_match::match_type(expr const & p, expr const & t, unsigned o, subst_map & s) {
<< ctx << " ," cout << "match_type : ("
<< p << ", " << p << ", "
<< t << ", " << t << ", "
// << s << ")" << o << ", "
<< std::endl; << s << ")"
// TODO(soonho) << endl;
return true; return p == t;
} }
bool fo_match::match_eq(context & ctx, expr const & p, expr const & t, subst_map & s) {
std::cerr << "match_eq : (" bool fo_match::match_eq(expr const & p, expr const & t, unsigned o, subst_map & s) {
<< ctx << " ," cout << "match_eq : ("
<< p << ", " << p << ", "
<< t << ", " << t << ", "
// << s << ")" << o << ", "
<< std::endl; << s << ")"
// TODO(soonho) << endl;
return true; return match(eq_lhs(p), eq_lhs(t), o, s) && match(eq_rhs(p), eq_rhs(t), o, s);
} }
bool fo_match::match_let(context & ctx, expr const & p, expr const & t, subst_map & s) {
std::cerr << "match_let : (" bool fo_match::match_let(expr const & p, expr const & t, unsigned o, subst_map & s) {
<< ctx << " ," cout << "match_let : ("
<< p << ", " << p << ", "
<< t << ", " << t << ", "
// << s << ")" << o << ", "
<< std::endl; << s << ")"
// TODO(soonho) << endl;
return true;
if (!is_let(t)) {
return false;
} else {
// First match the type part
auto p_type = let_type(p);
auto t_type = let_type(t);
if (!match(p_type, t_type, o, s))
return false;
// then match the value part
auto p_value = let_value(p);
auto t_value = let_value(t);
if (!match(p_value, t_value, o, s))
return false;
// then match the value part
auto p_body = let_body(p);
auto t_body = let_body(t);
return match(p_body, t_body, o + 1, s);
}
} }
bool fo_match::match_metavar(context & ctx, expr const & p, expr const & t, subst_map & s) { bool fo_match::match_metavar(expr const & p, expr const & t, unsigned o, subst_map & s) {
std::cerr << "match_meta : (" cout << "match_meta : ("
<< ctx << " ," << p << ", "
<< p << ", " << t << ", "
<< t << ", " << o << ", "
// << s << ")" << s << ")"
<< std::endl; << endl;
// TODO(soonho) return p == t;
return true;
} }
bool fo_match::match(context & ctx, expr const & p, expr const & t, subst_map & s) {
std::cerr << "match : (" bool fo_match::match(expr const & p, expr const & t, unsigned o, subst_map & s) {
<< ctx << " ," cout << "match : ("
<< p << ", " << p << ", "
<< t << ", " << t << ", "
// << s << ")" << o << ", "
<< std::endl; << s << ")"
<< endl;
switch (p.kind()) { switch (p.kind()) {
case expr_kind::Var: case expr_kind::Var:
return match_var(ctx, p, t, s); return match_var(p, t, o, s);
case expr_kind::Constant: case expr_kind::Constant:
return match_constant(ctx, p, t, s); return match_constant(p, t, o, s);
case expr_kind::Value: case expr_kind::Value:
return match_value(ctx, p, t, s); return match_value(p, t, o, s);
case expr_kind::App: case expr_kind::App:
return match_app(ctx, p, t, s); return match_app(p, t, o, s);
case expr_kind::Lambda: case expr_kind::Lambda:
return match_lambda(ctx, p, t, s); return match_lambda(p, t, o, s);
case expr_kind::Pi: case expr_kind::Pi:
return match_pi(ctx, p, t, s); return match_pi(p, t, o, s);
case expr_kind::Type: case expr_kind::Type:
return match_type(ctx, p, t, s); return match_type(p, t, o, s);
case expr_kind::Eq: case expr_kind::Eq:
return match_eq(ctx, p, t, s); return match_eq(p, t, o, s);
case expr_kind::Let: case expr_kind::Let:
return match_let(ctx, p, t, s); return match_let(p, t, o, s);
case expr_kind::MetaVar: case expr_kind::MetaVar:
return match_metavar(ctx, p, t, s); return match_metavar(p, t, o, s);
} }
lean_unreachable();
return false;
} }
} }

26
src/library/rewrite/fo_match.h
View file

@ -7,6 +7,7 @@ Author: Soonho Kong
#pragma once #pragma once
#include <unordered_map> #include <unordered_map>
#include "kernel/expr.h" #include "kernel/expr.h"
#include "kernel/expr_maps.h"
#include "kernel/context.h" #include "kernel/context.h"
#include "util/list.h" #include "util/list.h"
#include "library/all/all.h" #include "library/all/all.h"
@ -16,21 +17,22 @@ Author: Soonho Kong
namespace lean { namespace lean {
typedef std::unordered_map<unsigned, expr const &> subst_map; typedef expr_map<expr> subst_map;
class fo_match { class fo_match {
private: private:
bool match_var(context & ctx, expr const & p, expr const & t, subst_map & s); bool match_var(expr const & p, expr const & t, unsigned o, subst_map & s);
bool match_constant(context & ctx, expr const & p, expr const & t, subst_map & s); bool match_constant(expr const & p, expr const & t, unsigned o, subst_map & s);
bool match_value(context & ctx, expr const & p, expr const & t, subst_map & s); bool match_value(expr const & p, expr const & t, unsigned o, subst_map & s);
bool match_app(context & ctx, expr const & p, expr const & t, subst_map & s); bool match_app(expr const & p, expr const & t, unsigned o, subst_map & s);
bool match_lambda(context & ctx, expr const & p, expr const & t, subst_map & s); bool match_lambda(expr const & p, expr const & t, unsigned o, subst_map & s);
bool match_pi(context & ctx, expr const & p, expr const & t, subst_map & s); bool match_pi(expr const & p, expr const & t, unsigned o, subst_map & s);
bool match_type(context & ctx, expr const & p, expr const & t, subst_map & s); bool match_type(expr const & p, expr const & t, unsigned o, subst_map & s);
bool match_eq(context & ctx, expr const & p, expr const & t, subst_map & s); bool match_eq(expr const & p, expr const & t, unsigned o, subst_map & s);
bool match_let(context & ctx, expr const & p, expr const & t, subst_map & s); bool match_let(expr const & p, expr const & t, unsigned o, subst_map & s);
bool match_metavar(context & ctx, expr const & p, expr const & t, subst_map & s); bool match_metavar(expr const & p, expr const & t, unsigned o, subst_map & s);
public: public:
bool match(context & ctx, expr const & p, expr const & t, subst_map & s); bool match(expr const & p, expr const & t, unsigned o, subst_map & s);
}; };
} }

59
src/library/rewrite/rewrite.cpp
View file

@ -4,14 +4,15 @@ Released under Apache 2.0 license as described in the file LICENSE.
Author: Soonho Kong Author: Soonho Kong
*/ */
#include "kernel/environment.h"
#include "kernel/abstract.h" #include "kernel/abstract.h"
#include "kernel/builtin.h" #include "kernel/builtin.h"
#include "kernel/context.h"
#include "kernel/environment.h"
#include "library/printer.h"
#include "library/rewrite/fo_match.h"
#include "library/rewrite/rewrite.h" #include "library/rewrite/rewrite.h"
// Term Rewriting // Term Rewriting
//
// ORELSE // ORELSE
// APP_RW // APP_RW
// LAMBDA_RW // LAMBDA_RW
@ -23,4 +24,54 @@ Author: Soonho Kong
// FORALL // FORALL
// FAIL // FAIL
// FAIL_IF // FAIL_IF
//
using std::cout;
using std::endl;
namespace lean {
theorem_rw::theorem_rw(expr const & t, expr const & v)
: thm_t(t), thm_v(v), num_args(0) {
cout << "================= Theorem Rewrite Constructor Start ===================" << endl;
cout << "Type = " << thm_t << endl;
cout << "Body = " << thm_v << endl;
// We expect the theorem is in the form of
// Pi (x_1 : t_1 ... x_n : t_n), t = s
expr tmp = t;
while (is_pi(tmp)) {
tmp = abst_body(tmp);
num_args++;
}
if (!is_eq(tmp)) {
cout << "Theorem " << t << " is not in the form of "
<< "Pi (x_1 : t_1 ... x_n : t_n), t = s" << endl;
}
cout << "OK. Number of Arg = " << num_args << endl;
cout << "================= Theorem Rewrite Constructor END ===================" << endl;
}
void theorem_rw::operator()(context & ctx, expr const & t) {
cout << "================= Theorem Rewrite () START ===================" << endl;
cout << "Context = " << ctx << endl;
cout << "Term = " << t << endl;
expr tmp = thm_t;
while (is_pi(tmp)) {
tmp = abst_body(tmp);
num_args++;
}
if (!is_eq(tmp)) {
cout << "Theorem " << t << " is not in the form of "
<< "Pi (x_1 : t_1 ... x_n : t_n), t = s" << endl;
}
expr const & lhs = eq_lhs(tmp);
expr const & rhs = eq_rhs(tmp);
fo_match fm;
subst_map s;
fm.match(lhs, t, 0, s);
// apply s to rhs
cout << "================= Theorem Rewrite () END ===================" << endl;
}
}

50
src/library/rewrite/rewrite.h
View file

@ -5,61 +5,17 @@ Released under Apache 2.0 license as described in the file LICENSE.
Author: Soonho Kong Author: Soonho Kong
*/ */
#pragma once #pragma once
#include <iostream>
#include "kernel/context.h"
#include "kernel/environment.h"
#include "library/printer.h"
#include "library/rewrite/fo_match.h"
namespace lean { namespace lean {
/**
\brief Format
uses `sexpr` as an internal representation.
nil = ["NIL"]
text s = ("TEXT" . s)
choice f1 f2 = ("CHOICE" f1 . f2)
compose f1 ... fn = ["COMPOSE" f1 ... fn]
line = ["LINE"]
nest n f = ("NEST" n . f)
highlight c f = ("HIGHLIGHT" c . f)
*/
class theorem_rw { class theorem_rw {
private: private:
expr const & thm_t; expr const & thm_t;
expr const & thm_v; expr const & thm_v;
unsigned num_args; unsigned num_args;
public:
theorem_rw(expr const & t, expr const & v)
: thm_t(t), thm_v(v), num_args(0) {
std::cout << "Theorem_Rewrite "
<< "(" << thm_v << " : " << thm_t << ")"
<< std::endl;
// We expect the theorem is in the form of
// Pi (x_1 : t_1 ... x_n : t_n), t = s
expr tmp = t;
while (is_pi(tmp)) {
tmp = abst_body(tmp);
num_args++;
}
if (!is_eq(tmp)) {
std::cout << "Theorem " << t << " is not in the form of "
<< "Pi (x_1 : t_1 ... x_n : t_n), t = s" << std::endl;
}
std::cout << "Theorem " << t << " is OK. Number of Arg = " << num_args << std::endl;
}
void operator()(context & ctx, expr const & t) { public:
std::cout << "Theorem_Rewrite: (" theorem_rw(expr const & t, expr const & v);
<< "Context : " << ctx void operator()(context & ctx, expr const & t);
<< ", Term : " << t
<< ")" << std::endl;
fo_match fm;
subst_map s;
fm.match(ctx, thm_t, t, s);
}
}; };
} }

10
src/tests/library/rewrite/rewrite.cpp
View file

@ -12,6 +12,7 @@ Author: Soonho Kong
#include "library/arith/nat.h" #include "library/arith/nat.h"
#include "library/rewrite/fo_match.h" #include "library/rewrite/fo_match.h"
#include "library/rewrite/rewrite.h" #include "library/rewrite/rewrite.h"
#include "library/printer.h"
using namespace lean; using namespace lean;
using std::cout; using std::cout;
@ -25,12 +26,17 @@ int main() {
expr zero = nVal(0); // 0 : Nat expr zero = nVal(0); // 0 : Nat
expr x_plus_zero = nAdd(x, zero); // x_plus_zero := x + 0 expr x_plus_zero = nAdd(x, zero); // x_plus_zero := x + 0
expr y_plus_zero = nAdd(y, zero); // y_plus_zero := y + 0 expr y_plus_zero = nAdd(y, zero); // y_plus_zero := y + 0
std::cout << x_plus_zero << std::endl; cout << "x := " << x << endl;
env.display(std::cout); cout << "y := " << y << endl;
cout << "x + 0 := " << x_plus_zero << endl;
cout << "x + 0 := " << y_plus_zero << endl;
//env.display(cout);
expr thm_t = Pi("x", Nat, Eq(nAdd(Const("x"), nVal(0)), Const("x"))); // Pi (x : Z), x + 0 = x expr thm_t = Pi("x", Nat, Eq(nAdd(Const("x"), nVal(0)), Const("x"))); // Pi (x : Z), x + 0 = x
cout << "theorem := " << thm_t << endl;
env.add_axiom("H1", thm_t); // H1 : Pi (x : N), x = x + 0 env.add_axiom("H1", thm_t); // H1 : Pi (x : N), x = x + 0
expr thm_v = Const("H1"); expr thm_v = Const("H1");
cout << "axiom := " << thm_v << endl;
theorem_rw trw(thm_t, thm_v); theorem_rw trw(thm_t, thm_v);
context ctx; context ctx;