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feat(frontends/lean): allow 'tactic hints' to be associated with 'holes'

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2013-12-06 14:42:49 -08:00
parent 2ddcc32c1d
commit 1df9d18891
11 changed files with 258 additions and 68 deletions
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2
src/frontends/lean/frontend_elaborator.cpp
View file

@ -123,7 +123,7 @@ class frontend_elaborator::imp {
virtual expr visit_constant(expr const & e, context const & ctx) {
if (is_placeholder(e)) {
expr m = m_ref.m_menv.mk_metavar(ctx);
expr m = m_ref.m_menv.mk_metavar(ctx, const_type(e));
m_ref.m_trace[m] = e;
return m;
} else {

180
src/frontends/lean/parser.cpp
View file

@ -134,6 +134,7 @@ class parser::imp {
typedef std::unordered_map<name, expr, name_hash, name_eq> builtins;
typedef std::pair<unsigned, unsigned> pos_info;
typedef expr_map<pos_info> expr_pos_info;
typedef expr_map<tactic> tactic_hints; // a mapping from placeholder to tactic
typedef buffer<std::tuple<pos_info, name, expr, bool>> bindings_buffer;
frontend & m_frontend;
scanner m_scanner;
@ -148,6 +149,7 @@ class parser::imp {
expr_pos_info m_expr_pos_info;
pos_info m_last_cmd_pos;
pos_info m_last_script_pos;
tactic_hints m_tactic_hints;
script_state * m_script_state;
@ -1122,6 +1124,72 @@ class parser::imp {
return save(mk_placeholder(), p);
}
/** \brief Parse a tactic expression, it can be
1) A Lua Script Block expression that returns a tactic
2) '(' expr ')' where expr is a proof term
3) identifier that is the name of a tactic or proof term.
*/
tactic parse_tactic_expr() {
auto p = pos();
tactic t;
if (curr() == scanner::token::ScriptBlock) {
parse_script_expr();
using_script([&](lua_State * L) {
try {
t = to_tactic_ext(L, -1);
} catch (...) {
throw parser_error("invalid script-block, it must return a tactic", p);
}
});
} else if (curr_is_lparen()) {
next();
expr pr = parse_expr();
check_rparen_next("invalid apply command, ')' expected");
expr pr_type = m_type_inferer(pr);
t = apply_tactic(pr, pr_type);
} else {
name n = check_identifier_next("invalid apply command, identifier, '(' expr ')', or 'script-block' expected");
object const & o = m_frontend.find_object(n);
if (o && (o.is_theorem() || o.is_axiom())) {
t = apply_tactic(n);
} else {
using_script([&](lua_State * L) {
lua_getglobal(L, n.to_string().c_str());
try {
t = to_tactic_ext(L, -1);
} catch (...) {
throw parser_error(sstream() << "unknown tactic '" << n << "'", p);
}
lua_pop(L, 1);
});
}
}
return t;
}
/** \brief Parse <tt>'show' expr 'by' tactic</tt> */
expr parse_show_expr() {
auto p = pos();
next();
expr t = parse_expr();
check_next(scanner::token::By, "invalid 'show _ by _' expression, 'by' expected");
tactic tac = parse_tactic_expr();
expr r = mk_placeholder(t);
m_tactic_hints[r] = tac;
return save(r, p);
}
/** \brief Parse <tt>'by' tactic</tt> */
expr parse_by_expr() {
auto p = pos();
next();
tactic tac = parse_tactic_expr();
expr r = mk_placeholder();
m_tactic_hints[r] = tac;
return save(r, p);
}
/**
\brief Auxiliary method used when processing the beginning of an expression.
*/
@ -1139,6 +1207,8 @@ class parser::imp {
case scanner::token::StringVal: return parse_string();
case scanner::token::Placeholder: return parse_placeholder();
case scanner::token::Type: return parse_type();
case scanner::token::Show: return parse_show_expr();
case scanner::token::By: return parse_by_expr();
default:
throw parser_error("invalid expression, unexpected token", pos());
}
@ -1260,7 +1330,7 @@ class parser::imp {
throw tactic_cmd_error("failed to backtrack", p, s);
}
void tactic_apply(proof_state_seq_stack & stack, proof_state & s, tactic const & t, pos_info const & tac_pos) {
void tactic_apply(proof_state_seq_stack & stack, proof_state & s, tactic const & t, pos_info const & p) {
proof_state_seq::maybe_pair r;
code_with_callbacks([&]() {
// t may have call-backs we should set ios in the script_state
@ -1271,46 +1341,20 @@ class parser::imp {
s = r->first;
stack.push_back(r->second);
} else {
throw tactic_cmd_error("tactic failed", tac_pos, s);
throw tactic_cmd_error("tactic failed", p, s);
}
}
proof_state tactic_apply(proof_state s, tactic const & t, pos_info const & p) {
proof_state_seq_stack stack;
tactic_apply(stack, s, t, p);
return s;
}
void tactic_apply(proof_state_seq_stack & stack, proof_state & s) {
auto tac_pos = pos();
next();
tactic t;
if (curr() == scanner::token::ScriptBlock) {
parse_script_expr();
using_script([&](lua_State * L) {
try {
t = to_tactic_ext(L, -1);
} catch (...) {
throw tactic_cmd_error(sstream() << "invalid script-block, it must return a tactic", tac_pos, s);
}
});
} else if (curr_is_lparen()) {
next();
expr pr = parse_expr();
check_rparen_next("invalid apply command, ')' expected");
expr pr_type = m_type_inferer(pr);
t = apply_tactic(pr, pr_type);
} else {
name n = check_identifier_next("invalid apply command, identifier, '(' expr ')', or 'script-block' expected");
object const & o = m_frontend.find_object(n);
if (o && (o.is_theorem() || o.is_axiom())) {
t = apply_tactic(n);
} else {
using_script([&](lua_State * L) {
lua_getglobal(L, n.to_string().c_str());
try {
t = to_tactic_ext(L, -1);
} catch (...) {
throw tactic_cmd_error(sstream() << "unknown tactic '" << n << "'", tac_pos, s);
}
lua_pop(L, 1);
});
}
}
tactic t = parse_tactic_expr();
tactic_apply(stack, s, t, tac_pos);
}
@ -1320,9 +1364,7 @@ class parser::imp {
tactic_apply(stack, s, assumption_tactic(), tac_pos);
}
expr tactic_done(proof_state const & s) {
auto p = pos();
next();
expr mk_proof_for(proof_state const & s, pos_info const & p) {
if (s.is_proof_final_state()) {
assignment a(s.get_menv());
proof_map m;
@ -1336,6 +1378,12 @@ class parser::imp {
}
}
expr tactic_done(proof_state const & s) {
auto p = pos();
next();
return mk_proof_for(s, p);
}
bool curr_is_tactic_cmd() {
if (curr_is_identifier()) {
name const & id = curr_name();
@ -1420,16 +1468,38 @@ class parser::imp {
}
}
expr parse_tactic(expr const & type, expr const & val, metavar_env & menv) {
/**
\brief Return a 'hint' tactic (if it exists) for the given metavariable.
If the metavariable is not associated with any hint, then return the
null tactic. The method also returns the position of the hint.
*/
std::pair<tactic, pos_info> get_tactic_tactic_for(expr const & mvar) {
expr placeholder = m_elaborator.get_original(mvar);
auto it = m_tactic_hints.find(placeholder);
if (it != m_tactic_hints.end()) {
return mk_pair(it->second, pos_of(placeholder, pos()));
} else {
return mk_pair(tactic(), pos_of(placeholder, pos()));
}
}
expr apply_tactics(expr const & type, expr const & val, metavar_env & menv) {
if (is_metavar(val)) {
// simple case
if (!m_type_inferer.is_proposition(type))
throw exception("failed to synthesize metavar, its type is not a proposition");
proof_state s = to_proof_state(m_frontend, context(), type);
display_proof_state_if_interactive(s);
show_tactic_prompt();
check_period_next("invalid theorem, '.' expected before tactical proof");
return parse_tactic(s);
std::pair<tactic, pos_info> hint_and_pos = get_tactic_tactic_for(val);
if (hint_and_pos.first) {
// metavariable has an associated tactic hint
s = tactic_apply(s, hint_and_pos.first, hint_and_pos.second);
return mk_proof_for(s, hint_and_pos.second);
} else {
display_proof_state_if_interactive(s);
show_tactic_prompt();
check_period_next("invalid theorem, '.' expected before tactical proof");
return parse_tactic(s);
}
} else {
buffer<expr> mvars;
for_each(val, [&](expr const & e, unsigned) {
@ -1453,14 +1523,21 @@ class parser::imp {
if (!m_type_inferer.is_proposition(mvar_type, mvar_ctx))
throw exception("failed to synthesize metavar, its type is not a proposition");
proof_state s = to_proof_state(m_frontend, mvar_ctx, mvar_type);
if (curr_is_period()) {
display_proof_state_if_interactive(s);
show_tactic_prompt();
next();
std::pair<tactic, pos_info> hint_and_pos = get_tactic_tactic_for(mvar);
if (hint_and_pos.first) {
// metavariable has an associated tactic hint
s = tactic_apply(s, hint_and_pos.first, hint_and_pos.second);
menv.assign(mvar, mk_proof_for(s, hint_and_pos.second));
} else {
if (curr_is_period()) {
display_proof_state_if_interactive(s);
show_tactic_prompt();
next();
}
expr mvar_val = parse_tactic(s);
if (mvar_val)
menv.assign(mvar, mvar_val);
}
expr mvar_val = parse_tactic(s);
if (mvar_val)
menv.assign(mvar, mvar_val);
}
return instantiate_metavars(val, menv);
}
@ -1507,7 +1584,7 @@ class parser::imp {
if (has_metavar(type))
throw exception("invalid definition, type still contains metavariables after elaboration");
if (!is_definition && has_metavar(val)) {
val = parse_tactic(type, val, menv);
val = apply_tactics(type, val, menv);
}
if (has_metavar(val))
throw exception("invalid definition, value still contains metavariables after elaboration");
@ -1915,6 +1992,7 @@ class parser::imp {
bool parse_command() {
m_elaborator.clear();
m_expr_pos_info.clear();
m_tactic_hints.clear();
m_last_cmd_pos = pos();
name const & cmd_id = curr_name();
if (cmd_id == g_definition_kwd) {

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

@ -28,6 +28,8 @@ static name g_forall_unicode("\u2200");
static name g_exists_name("exists");
static name g_exists_unicode("\u2203");
static name g_placeholder_name("_");
static name g_show_name("show");
static name g_by_name("by");
static char g_normalized[256];
@ -219,6 +221,10 @@ scanner::token scanner::read_a_symbol() {
return token::In;
else if (m_name_val == g_placeholder_name)
return token::Placeholder;
else if (m_name_val == g_show_name)
return token::Show;
else if (m_name_val == g_by_name)
return token::By;
else
return is_command(m_name_val) ? token::CommandId : token::Id;
}
@ -446,6 +452,8 @@ std::ostream & operator<<(std::ostream & out, scanner::token const & t) {
case scanner::token::Type: out << "Type"; break;
case scanner::token::Placeholder: out << "_"; break;
case scanner::token::ScriptBlock: out << "Script"; break;
case scanner::token::Show: out << "show"; break;
case scanner::token::By: out << "by"; break;
case scanner::token::Eof: out << "EOF"; break;
}
return out;

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

@ -21,7 +21,7 @@ public:
enum class token {
LeftParen, RightParen, LeftCurlyBracket, RightCurlyBracket, Colon, Comma, Period, Lambda, Pi, Arrow,
Let, In, Forall, Exists, Id, CommandId, NatVal, DecimalVal, StringVal, Eq, Assign, Type, Placeholder,
ScriptBlock, Eof
Show, By, ScriptBlock, Eof
};
protected:
int m_spos; // position in the current line of the stream

6
src/library/placeholder.cpp
View file

@ -12,8 +12,8 @@ Author: Leonardo de Moura
namespace lean {
static name g_placeholder_name("_");
expr mk_placeholder() {
return mk_constant(g_placeholder_name);
expr mk_placeholder(expr const & t) {
return mk_constant(g_placeholder_name, t);
}
bool is_placeholder(expr const & e) {
@ -30,7 +30,7 @@ class replace_placeholders_with_metavars_proc : public replace_visitor {
protected:
expr visit_constant(expr const & e, context const & c) {
if (is_placeholder(e)) {
return m_menv.mk_metavar(c);
return m_menv.mk_metavar(c, const_type(e));
} else {
return e;
}

7
src/library/placeholder.h
View file

@ -11,10 +11,11 @@ Author: Leonardo de Moura
namespace lean {
class metavar_env;
/**
\brief Return a new placeholder expression. To be able to track location,
a new constant for each placeholder.
\brief Return a new placeholder expression (with an optional
type). To be able to track location, a new constant for each
placeholder.
*/
expr mk_placeholder();
expr mk_placeholder(expr const & t = expr());
/**
\brief Return true iff the given expression is a placeholder.

4
tests/lean/interactive/t1.lean.expected.out
View file

@ -11,9 +11,7 @@ Proof state:
a : Bool, b : Bool ⊢ a ⇒ b ⇒ a ∧ b
## Proof state:
H : a, a : Bool, b : Bool ⊢ b ⇒ a ∧ b
## Error (line: 8, pos: 0) unknown tactic 'imp_tac2'
Proof state:
H : a, a : Bool, b : Bool ⊢ b ⇒ a ∧ b
## Error (line: 8, pos: 6) unknown tactic 'imp_tac2'
## Error (line: 9, pos: 0) invalid tactic command 'foo'
Proof state:
H : a, a : Bool, b : Bool ⊢ b ⇒ a ∧ b

4
tests/lean/interactive/t10.lean.expected.out
View file

@ -7,9 +7,7 @@ A : Bool, B : Bool, H : A ∧ B ⊢ A
no goals
## Proof state:
A : Bool, B : Bool, H : A ∧ B, H1 : A ⊢ B
## Error (line: 15, pos: 3) unknown tactic 'simple2_tac'
Proof state:
A : Bool, B : Bool, H : A ∧ B, H1 : A ⊢ B
## Error (line: 15, pos: 9) unknown tactic 'simple2_tac'
## Error (line: 15, pos: 22) invalid 'done' command, proof cannot be produced from this state
Proof state:
A : Bool, B : Bool, H : A ∧ B, H1 : A ⊢ B

58
tests/lean/interactive/t12.lean Normal file
View file

@ -0,0 +1,58 @@
(**
-- Define a simple tactic using Lua
auto = REPEAT(ORELSE(conj_hyp_tac, conj_tac, assumption_tac))
**)
(*
The (by [tactic]) expression is essentially creating a "hole" and associating a "hint" to it.
The "hint" is a tactic that should be used to fill the "hole".
In the following example, we use the tactic "auto" defined by the Lua code above.
The (show [expr] by [tactic]) expression is also creating a "hole" and associating a "hint" to it.
The expression [expr] after the shows is fixing the type of the "hole"
*)
Theorem T1 (A B : Bool) : A /\ B -> B /\ A :=
fun assumption : A /\ B,
let lemma1 : A := (by auto),
lemma2 : B := (by auto)
in (show B /\ A by auto)
(*
When hints are not provided, the user must fill the (remaining) holes using tactic command sequences.
Each hole must be filled with a tactic command sequence that terminates with the command 'done' and
successfully produces a proof term for filling the hole. Here is the same example without hints
This style is more convenient for interactive proofs
*)
Theorem T2 (A B : Bool) : A /\ B -> B /\ A :=
fun assumption : A /\ B,
let lemma1 : A := _, (* first hole *)
lemma2 : B := _ (* second hole *)
in _. (* third hole *)
apply auto. done. (* tactic command sequence for the first hole *)
apply auto. done. (* tactic command sequence for the second hole *)
apply auto. done. (* tactic command sequence for the third hole *)
(*
In the following example, instead of using the "auto" tactic, we apply a sequence of even simpler tactics.
*)
Theorem T3 (A B : Bool) : A /\ B -> B /\ A :=
fun assumption : A /\ B,
let lemma1 : A := _, (* first hole *)
lemma2 : B := _ (* second hole *)
in _. (* third hole *)
apply conj_hyp_tac. apply assumption_tac. done. (* tactic command sequence for the first hole *)
apply conj_hyp_tac. apply assumption_tac. done. (* tactic command sequence for the second hole *)
apply conj_tac. apply assumption_tac. done. (* tactic command sequence for the third hole *)
(*
We can also mix the two styles (hints and command sequences)
*)
Theorem T4 (A B : Bool) : A /\ B -> B /\ A :=
fun assumption : A /\ B,
let lemma1 : A := _, (* first hole *)
lemma2 : B := _ (* second hole *)
in (show B /\ A by auto).
apply conj_hyp_tac. apply assumption_tac. done. (* tactic command sequence for the first hole *)
apply conj_hyp_tac. apply assumption_tac. done. (* tactic command sequence for the second hole *)

51
tests/lean/interactive/t12.lean.expected.out Normal file
View file

@ -0,0 +1,51 @@
Type Ctrl-D or 'Exit.' to exit or 'Help.' for help.
# Set: pp::colors
Set: pp::unicode
Proved: T1
Proof state:
A : Bool, B : Bool, assumption : A ∧ B ⊢ A
## Proof state:
no goals
## Proof state:
A : Bool, B : Bool, assumption : A ∧ B, lemma1 : A ⊢ B
## Proof state:
no goals
## Proof state:
A : Bool, B : Bool, assumption : A ∧ B, lemma1 : A, lemma2 : B ⊢ B ∧ A
## Proof state:
no goals
## Proved: T2
# Proof state:
A : Bool, B : Bool, assumption : A ∧ B ⊢ A
## Proof state:
A : Bool, B : Bool, assumption::1 : A, assumption::2 : B ⊢ A
## Proof state:
no goals
## Proof state:
A : Bool, B : Bool, assumption : A ∧ B, lemma1 : A ⊢ B
## Proof state:
A : Bool, B : Bool, assumption::1 : A, assumption::2 : B, lemma1 : A ⊢ B
## Proof state:
no goals
## Proof state:
A : Bool, B : Bool, assumption : A ∧ B, lemma1 : A, lemma2 : B ⊢ B ∧ A
## Proof state:
A : Bool, B : Bool, assumption : A ∧ B, lemma1 : A, lemma2 : B ⊢ B
A : Bool, B : Bool, assumption : A ∧ B, lemma1 : A, lemma2 : B ⊢ A
## Proof state:
no goals
## Proved: T3
# Proof state:
A : Bool, B : Bool, assumption : A ∧ B ⊢ A
## Proof state:
A : Bool, B : Bool, assumption::1 : A, assumption::2 : B ⊢ A
## Proof state:
no goals
## Proof state:
A : Bool, B : Bool, assumption : A ∧ B, lemma1 : A ⊢ B
## Proof state:
A : Bool, B : Bool, assumption::1 : A, assumption::2 : B, lemma1 : A ⊢ B
## Proof state:
no goals
## Proved: T4
#

4
tests/lean/interactive/t2.lean.expected.out
View file

@ -5,9 +5,7 @@ Proof state:
a : Bool, b : Bool ⊢ a ⇒ b ⇒ a ∧ b
## Proof state:
H : a, a : Bool, b : Bool ⊢ b ⇒ a ∧ b
## Error (line: 6, pos: 0) unknown tactic 'imp_tac2'
Proof state:
H : a, a : Bool, b : Bool ⊢ b ⇒ a ∧ b
## Error (line: 6, pos: 6) unknown tactic 'imp_tac2'
## Error (line: 7, pos: 0) invalid tactic command 'foo'
Proof state:
H : a, a : Bool, b : Bool ⊢ b ⇒ a ∧ b