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feat(frontends/lean): add type notation for referencing hypotheses

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This commit is contained in:
Leonardo de Moura 2015-07-20 21:43:47 -07:00
parent 18dd57978d
commit b9451549d1
10 changed files with 136 additions and 31 deletions
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50
library/theories/number_theory/primes.lean
View file

@ -65,10 +65,10 @@ assume h d, obtain h₁ h₂, from h, h₂ m d
lemma gt_one_of_pos_of_prime_dvd {i p : nat} : prime p → 0 < i → i mod p = 0 → 1 < i :=
assume ipp pos h,
have h₁ : p ≥ 2, from ge_two_of_prime ipp,
have p ∣ i, from dvd_of_mod_eq_zero h,
have p ≤ i, from le_of_dvd pos this,
lt_of_succ_le (le.trans h₁ this)
have p ≥ 2, from ge_two_of_prime ipp,
have p ∣ i, from dvd_of_mod_eq_zero h,
have p ≤ i, from le_of_dvd pos this,
lt_of_succ_le (le.trans `2 ≤ p` this)
definition sub_dvd_of_not_prime {n : nat} : n ≥ 2 → ¬ prime n → {m | m ∣ n ∧ m ≠ 1 ∧ m ≠ n} :=
assume h₁ h₂,
@ -124,30 +124,30 @@ definition infinite_primes (n : nat) : {p | p ≥ n ∧ prime p} :=
let m := fact (n + 1) in
have m ≥ 1, from le_of_lt_succ (succ_lt_succ (fact_pos _)),
have m + 1 ≥ 2, from succ_le_succ this,
obtain p (prime_p : prime p) (p_dvd_m1 : p ∣ m + 1), from sub_prime_and_dvd this,
have p_ge_2 : p ≥ 2, from ge_two_of_prime prime_p,
have p_gt_0 : p > 0, from lt_of_succ_lt (lt_of_succ_le p_ge_2),
obtain p (pp : prime p) (pd : p ∣ m + 1), from sub_prime_and_dvd this,
have p ≥ 2, from ge_two_of_prime `prime p`,
have p > 0, from lt_of_succ_lt (lt_of_succ_le `p ≥ 2`),
have p ≥ n, from by_contradiction
(suppose ¬ p ≥ n,
have p < n, from lt_of_not_ge this,
have p ≤ n + 1, from le_of_lt (lt.step this),
have p ∣ m, from dvd_fact p_gt_0 this,
have p ∣ 1, from dvd_of_dvd_add_right (!add.comm ▸ p_dvd_m1) this,
have p ∣ m, from dvd_fact `p > 0` this,
have p ∣ 1, from dvd_of_dvd_add_right (!add.comm ▸ `p ∣ m + 1`) this,
have p ≤ 1, from le_of_dvd zero_lt_one this,
absurd (le.trans p_ge_2 this) dec_trivial),
subtype.tag p (and.intro this prime_p)
absurd (le.trans `2 ≤ p` `p ≤ 1`) dec_trivial),
subtype.tag p (and.intro this `prime p`)
lemma ex_infinite_primes (n : nat) : ∃ p, p ≥ n ∧ prime p :=
ex_of_sub (infinite_primes n)
lemma odd_of_prime {p : nat} : prime p → p > 2 → odd p :=
λ pp p_gt_2, by_contradiction (λ hn,
have even_p : even p, from even_of_not_odd hn,
obtain k (hk : p = 2*k), from exists_of_even even_p,
assert two_div_p : 2 ∣ p, by rewrite [hk]; apply dvd_mul_right,
or.elim (eq_one_or_eq_self_of_prime_of_dvd pp two_div_p)
(λ h : 2 = 1, absurd h dec_trivial)
(λ h : 2 = p, by subst h; exact absurd p_gt_2 !lt.irrefl))
have even p, from even_of_not_odd hn,
obtain k (hk : p = 2*k), from exists_of_even this,
assert 2 ∣ p, by rewrite [hk]; apply dvd_mul_right,
or.elim (eq_one_or_eq_self_of_prime_of_dvd pp this)
(suppose 2 = 1, absurd this dec_trivial)
(suppose 2 = p, by subst this; exact absurd p_gt_2 !lt.irrefl))
theorem dvd_of_prime_of_not_coprime {p n : ℕ} (primep : prime p) (nc : ¬ coprime p n) : p ∣ n :=
have H : gcd p n = 1 ∨ gcd p n = p, from eq_one_or_eq_self_of_prime_of_dvd primep !gcd_dvd_left,
@ -195,8 +195,8 @@ lemma dvd_of_prime_of_dvd_pow {p m : nat} : ∀ {n}, prime p → p ∣ m^n → p
| (succ n) hp hd :=
have p ∣ (m^n)*m, by rewrite [pow_succ at hd]; exact hd,
or.elim (dvd_or_dvd_of_prime_of_dvd_mul hp this)
(λ h : p ∣ m^n, dvd_of_prime_of_dvd_pow hp h)
(λ h : p ∣ m, h)
(suppose p ∣ m^n, dvd_of_prime_of_dvd_pow hp this)
(suppose p ∣ m, this)
lemma coprime_pow_of_prime_of_not_dvd {p m a : nat} : prime p → ¬ p ∣ a → coprime a (p^m) :=
λ h₁ h₂, coprime_pow_right m (coprime_swap (coprime_of_prime_of_not_dvd h₁ h₂))
@ -205,21 +205,21 @@ lemma coprime_primes {p q : nat} : prime p → prime q → p ≠ q → coprime p
λ hp hq hn,
assert gcd p q ∣ p, from !gcd_dvd_left,
or.elim (eq_one_or_eq_self_of_prime_of_dvd hp this)
(λ h : gcd p q = 1, h)
(λ h : gcd p q = p,
(suppose gcd p q = 1, this)
(assume h : gcd p q = p,
assert gcd p q ∣ q, from !gcd_dvd_right,
have p ∣ q, by rewrite -h; exact this,
or.elim (eq_one_or_eq_self_of_prime_of_dvd hq this)
(λ h₁ : p = 1, by subst p; exact absurd hp not_prime_one)
(λ he : p = q, by contradiction))
(suppose p = 1, by subst p; exact absurd hp not_prime_one)
(suppose p = q, by contradiction))
lemma coprime_pow_primes {p q : nat} (n m : nat) : prime p → prime q → p ≠ q → coprime (p^n) (q^m) :=
λ hp hq hn, coprime_pow_right m (coprime_pow_left n (coprime_primes hp hq hn))
lemma coprime_or_dvd_of_prime {p} (Pp : prime p) (i : nat) : coprime p i ∨ p ∣ i :=
by_cases
(λ h : p ∣ i, or.inr h)
(λ h : ¬ p ∣ i, or.inl (coprime_of_prime_of_not_dvd Pp h))
(suppose p ∣ i, or.inr this)
(suppose ¬ p ∣ i, or.inl (coprime_of_prime_of_not_dvd Pp this))
lemma eq_one_or_dvd_of_dvd_prime_pow {p : nat} : ∀ {m i : nat}, prime p → i ∣ (p^m) → i = 1 ∨ p ∣ i
| 0 := take i, assume Pp, begin rewrite [pow_zero], intro Pdvd, apply or.inl (eq_one_of_dvd_one Pdvd) end

10
src/frontends/lean/notation_cmd.cpp
View file

@ -813,6 +813,7 @@ static environment dispatch_notation_cmd(parser & p, bool overload, notation_ent
}
environment local_notation_cmd(parser & p) {
parser::in_notation_ctx ctx(p);
bool overload = false; // REMARK: local notation override global one
notation_entry_group grp = notation_entry_group::Main;
bool persistent = false;
@ -820,6 +821,7 @@ environment local_notation_cmd(parser & p) {
}
static environment reserve_cmd(parser & p) {
parser::in_notation_ctx ctx(p);
bool overload = false;
notation_entry_group grp = notation_entry_group::Reserve;
bool persistent = true;
@ -849,4 +851,12 @@ void register_notation_cmds(cmd_table & r) {
add_cmd(r, cmd_info("tactic_notation", "declare a new tacitc notation", tactic_notation_cmd));
add_cmd(r, cmd_info("reserve", "reserve notation", reserve_cmd));
}
bool is_notation_cmd(name const & n) {
return
n == get_infix_tk() || n == get_infixl_tk() || n == get_infixr_tk() || n == get_postfix_tk() ||
n == get_prefix_tk() || n == get_notation_tk() || n == get_precedence_tk() ||
n == get_tactic_infix_tk() || n == get_tactic_infixl_tk() || n == get_tactic_infixr_tk() || n == get_tactic_postfix_tk() ||
n == get_tactic_prefix_tk() || n == get_tactic_notation_tk();
}
}

2
src/frontends/lean/notation_cmd.h
View file

@ -21,4 +21,6 @@ notation_entry parse_notation(parser & p, bool overload, buffer<token_entry> & n
environment local_notation_cmd(parser & p);
void register_notation_cmds(cmd_table & r);
bool is_notation_cmd(name const & cmd_name);
}

34
src/frontends/lean/parser.cpp
View file

@ -31,6 +31,7 @@ Author: Leonardo de Moura
#include "library/module.h"
#include "library/scoped_ext.h"
#include "library/explicit.h"
#include "library/typed_expr.h"
#include "library/let.h"
#include "library/num.h"
#include "library/string.h"
@ -111,7 +112,8 @@ parser::parser(environment const & env, io_state const & ios,
m_theorem_queue(*this, num_threads > 1 ? num_threads - 1 : 0),
m_snapshot_vector(sv), m_info_manager(im), m_cache(nullptr), m_index(nullptr) {
m_local_decls_size_at_beg_cmd = 0;
m_profile = ios.get_options().get_bool("profile", false);
m_in_backtick = false;
m_profile = ios.get_options().get_bool("profile", false);
if (num_threads > 1 && m_profile)
throw exception("option --profile cannot be used when theorems are compiled in parallel");
m_has_params = false;
@ -961,6 +963,7 @@ local_environment parser::parse_binders(buffer<expr> & r, buffer<notation_entry>
bool parser::parse_local_notation_decl(buffer<notation_entry> * nentries) {
if (curr_is_notation_decl(*this)) {
parser::in_notation_ctx ctx(*this);
buffer<token_entry> new_tokens;
bool overload = false;
bool allow_local = true;
@ -1327,6 +1330,19 @@ expr parser::parse_string_expr() {
return from_string(v);
}
expr parser::parse_backtick_expr() {
auto p = pos();
next();
flet<bool> set(m_in_backtick, true);
expr type = parse_expr();
if (curr() != scanner::token_kind::Backtick) {
throw parser_error("invalid expression, '`' expected", pos());
}
next();
expr assump = mk_by_plus(save_pos(mk_constant(get_tactic_assumption_name()), p), p);
return save_pos(mk_typed_expr(type, assump), p);
}
expr parser::parse_nud() {
switch (curr()) {
case scanner::token_kind::Keyword: return parse_nud_notation();
@ -1334,6 +1350,7 @@ expr parser::parse_nud() {
case scanner::token_kind::Numeral: return parse_numeral_expr();
case scanner::token_kind::Decimal: return parse_decimal_expr();
case scanner::token_kind::String: return parse_string_expr();
case scanner::token_kind::Backtick: return parse_backtick_expr();
default: throw parser_error("invalid expression, unexpected token", pos());
}
}
@ -1355,6 +1372,8 @@ unsigned parser::curr_lbp_core(bool as_tactic) const {
case scanner::token_kind::CommandKeyword: case scanner::token_kind::Eof:
case scanner::token_kind::ScriptBlock: case scanner::token_kind::QuotedSymbol:
return 0;
case scanner::token_kind::Backtick:
return m_in_backtick ? 0 : get_max_prec();
case scanner::token_kind::Identifier: case scanner::token_kind::Numeral:
case scanner::token_kind::Decimal: case scanner::token_kind::String:
return get_max_prec();
@ -1636,9 +1655,16 @@ void parser::parse_command() {
name const & cmd_name = get_token_info().value();
m_cmd_token = get_token_info().token();
if (auto it = cmds().find(cmd_name)) {
next();
m_local_decls_size_at_beg_cmd = m_local_decls.size();
m_env = it->get_fn()(*this);
if (is_notation_cmd(cmd_name)) {
in_notation_ctx ctx(*this);
next();
m_local_decls_size_at_beg_cmd = m_local_decls.size();
m_env = it->get_fn()(*this);
} else {
next();
m_local_decls_size_at_beg_cmd = m_local_decls.size();
m_env = it->get_fn()(*this);
}
} else {
auto p = pos();
next();

9
src/frontends/lean/parser.h
View file

@ -233,6 +233,9 @@ class parser {
elaborator_context mk_elaborator_context(environment const & env, pos_info_provider const & pp);
elaborator_context mk_elaborator_context(environment const & env, local_level_decls const & lls, pos_info_provider const & pp);
bool m_in_backtick; // true if parser `expr` notation
expr parse_backtick_expr();
optional<expr> is_tactic_command(name & id);
expr parse_tactic_option_num();
expr parse_tactic_led(expr left);
@ -511,6 +514,12 @@ public:
/** parse all commands in the input stream */
bool operator()() { return parse_commands(); }
class in_notation_ctx {
scanner::in_notation_ctx m_ctx;
public:
in_notation_ctx(parser & p):m_ctx(p.m_scanner) {}
};
};
bool parse_commands(environment & env, io_state & ios, std::istream & in, char const * strm_name,

8
src/frontends/lean/scanner.cpp
View file

@ -437,7 +437,12 @@ auto scanner::scan(environment const & env) -> token_kind {
case '\"':
return read_string();
case '`':
return read_quoted_symbol();
if (m_in_notation) {
return read_quoted_symbol();
} else {
next();
return token_kind::Backtick;
}
case -1:
return token_kind::Eof;
default:
@ -471,6 +476,7 @@ scanner::scanner(std::istream & strm, char const * strm_name, unsigned line):
m_line = line;
m_spos = 0;
m_upos = 0;
m_in_notation = false;
if (std::getline(m_stream, m_curr_line)) {
m_last_line = false;
m_curr_line.push_back('\n');

12
src/frontends/lean/scanner.h
View file

@ -8,6 +8,7 @@ Author: Leonardo de Moura
#include <string>
#include <iostream>
#include "util/name.h"
#include "util/flet.h"
#include "util/numerics/mpq.h"
#include "kernel/environment.h"
#include "frontends/lean/token_table.h"
@ -22,7 +23,7 @@ namespace lean {
*/
class scanner {
public:
enum class token_kind {Keyword, CommandKeyword, ScriptBlock, Identifier, Numeral, Decimal, String, QuotedSymbol, Eof};
enum class token_kind {Keyword, CommandKeyword, ScriptBlock, Identifier, Numeral, Decimal, String, QuotedSymbol, Backtick, Eof};
protected:
token_table const * m_tokens;
std::istream & m_stream;
@ -45,6 +46,9 @@ protected:
std::string m_buffer;
std::string m_aux_buffer;
bool m_in_notation;
[[ noreturn ]] void throw_exception(char const * msg);
void next();
char curr() const { return m_curr; }
@ -80,6 +84,12 @@ public:
token_info const & get_token_info() const { return m_token_info; }
std::string const & get_stream_name() const { return m_stream_name; }
class in_notation_ctx {
flet<bool> m_in_notation;
public:
in_notation_ctx(scanner & s):m_in_notation(s.m_in_notation, true) {}
};
};
std::ostream & operator<<(std::ostream & out, scanner::token_kind k);
void initialize_scanner();

28
src/frontends/lean/tokens.cpp
View file

@ -126,12 +126,19 @@ static name const * g_foldr_tk = nullptr;
static name const * g_foldl_tk = nullptr;
static name const * g_binder_tk = nullptr;
static name const * g_binders_tk = nullptr;
static name const * g_precedence_tk = nullptr;
static name const * g_infix_tk = nullptr;
static name const * g_infixl_tk = nullptr;
static name const * g_infixr_tk = nullptr;
static name const * g_postfix_tk = nullptr;
static name const * g_prefix_tk = nullptr;
static name const * g_notation_tk = nullptr;
static name const * g_tactic_infix_tk = nullptr;
static name const * g_tactic_infixl_tk = nullptr;
static name const * g_tactic_infixr_tk = nullptr;
static name const * g_tactic_postfix_tk = nullptr;
static name const * g_tactic_prefix_tk = nullptr;
static name const * g_tactic_notation_tk = nullptr;
static name const * g_call_tk = nullptr;
static name const * g_calc_tk = nullptr;
static name const * g_obtain_tk = nullptr;
@ -266,12 +273,19 @@ void initialize_tokens() {
g_foldl_tk = new name{"foldl"};
g_binder_tk = new name{"binder"};
g_binders_tk = new name{"binders"};
g_precedence_tk = new name{"precedence"};
g_infix_tk = new name{"infix"};
g_infixl_tk = new name{"infixl"};
g_infixr_tk = new name{"infixr"};
g_postfix_tk = new name{"postfix"};
g_prefix_tk = new name{"prefix"};
g_notation_tk = new name{"notation"};
g_tactic_infix_tk = new name{"tactic_infix"};
g_tactic_infixl_tk = new name{"tactic_infixl"};
g_tactic_infixr_tk = new name{"tactic_infixr"};
g_tactic_postfix_tk = new name{"tactic_postfix"};
g_tactic_prefix_tk = new name{"tactic_prefix"};
g_tactic_notation_tk = new name{"tactic_notation"};
g_call_tk = new name{"call"};
g_calc_tk = new name{"calc"};
g_obtain_tk = new name{"obtain"};
@ -407,12 +421,19 @@ void finalize_tokens() {
delete g_foldl_tk;
delete g_binder_tk;
delete g_binders_tk;
delete g_precedence_tk;
delete g_infix_tk;
delete g_infixl_tk;
delete g_infixr_tk;
delete g_postfix_tk;
delete g_prefix_tk;
delete g_notation_tk;
delete g_tactic_infix_tk;
delete g_tactic_infixl_tk;
delete g_tactic_infixr_tk;
delete g_tactic_postfix_tk;
delete g_tactic_prefix_tk;
delete g_tactic_notation_tk;
delete g_call_tk;
delete g_calc_tk;
delete g_obtain_tk;
@ -547,12 +568,19 @@ name const & get_foldr_tk() { return *g_foldr_tk; }
name const & get_foldl_tk() { return *g_foldl_tk; }
name const & get_binder_tk() { return *g_binder_tk; }
name const & get_binders_tk() { return *g_binders_tk; }
name const & get_precedence_tk() { return *g_precedence_tk; }
name const & get_infix_tk() { return *g_infix_tk; }
name const & get_infixl_tk() { return *g_infixl_tk; }
name const & get_infixr_tk() { return *g_infixr_tk; }
name const & get_postfix_tk() { return *g_postfix_tk; }
name const & get_prefix_tk() { return *g_prefix_tk; }
name const & get_notation_tk() { return *g_notation_tk; }
name const & get_tactic_infix_tk() { return *g_tactic_infix_tk; }
name const & get_tactic_infixl_tk() { return *g_tactic_infixl_tk; }
name const & get_tactic_infixr_tk() { return *g_tactic_infixr_tk; }
name const & get_tactic_postfix_tk() { return *g_tactic_postfix_tk; }
name const & get_tactic_prefix_tk() { return *g_tactic_prefix_tk; }
name const & get_tactic_notation_tk() { return *g_tactic_notation_tk; }
name const & get_call_tk() { return *g_call_tk; }
name const & get_calc_tk() { return *g_calc_tk; }
name const & get_obtain_tk() { return *g_obtain_tk; }

7
src/frontends/lean/tokens.h
View file

@ -128,12 +128,19 @@ name const & get_foldr_tk();
name const & get_foldl_tk();
name const & get_binder_tk();
name const & get_binders_tk();
name const & get_precedence_tk();
name const & get_infix_tk();
name const & get_infixl_tk();
name const & get_infixr_tk();
name const & get_postfix_tk();
name const & get_prefix_tk();
name const & get_notation_tk();
name const & get_tactic_infix_tk();
name const & get_tactic_infixl_tk();
name const & get_tactic_infixr_tk();
name const & get_tactic_postfix_tk();
name const & get_tactic_prefix_tk();
name const & get_tactic_notation_tk();
name const & get_call_tk();
name const & get_calc_tk();
name const & get_obtain_tk();

7
src/frontends/lean/tokens.txt
View file

@ -121,12 +121,19 @@ foldr foldr
foldl foldl
binder binder
binders binders
precedence precedence
infix infix
infixl infixl
infixr infixr
postfix postfix
prefix prefix
notation notation
tactic_infix tactic_infix
tactic_infixl tactic_infixl
tactic_infixr tactic_infixr
tactic_postfix tactic_postfix
tactic_prefix tactic_prefix
tactic_notation tactic_notation
call call
calc calc
obtain obtain