feat(library/scoped_ext): force user to end a scope with an identifier matching the one used in beginning of scope, closes #30

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-08-07 16:59:08 -07:00
parent 2486c483cf
commit 1a67e69678
66 changed files with 156 additions and 173 deletions

View file

@ -16,7 +16,7 @@ definition transport {A : Type} {a b : A} {P : A → Type} (H1 : a = b) (H2 : P
namespace logic
notation p `*(`:75 u `)` := transport p u
end
end logic
using logic
definition symm {A : Type} {a b : A} (p : a = b) : b = a
@ -32,7 +32,7 @@ calc_trans trans
namespace logic
postfix `⁻¹`:100 := symm
infixr `⬝`:75 := trans
end
end logic
using logic
theorem trans_refl_right {A : Type} {x y : A} (p : x = y) : p = p ⬝ (refl y)
@ -115,7 +115,7 @@ abbreviation homotopy {A : Type} {P : A → Type} (f g : Π x, P x)
namespace logic
infix ``:50 := homotopy
end
end logic
using logic
notation `assume` binders `,` r:(scoped f, f) := r
@ -215,7 +215,7 @@ inductive sum (A : Type) (B : Type) : Type :=
namespace logic
infixr `+`:25 := sum
end
end logic
using logic
infixr ``:25 := sum

View file

@ -14,4 +14,4 @@ inductive pos_num : Type :=
inductive num : Type :=
| zero : num
| pos : pos_num → num
end
end num

View file

@ -10,4 +10,4 @@ inductive char : Type :=
inductive string : Type :=
| empty : string
| str : char → string → string
end
end string

View file

@ -51,4 +51,4 @@ notation `?` t:max := try t
definition repeat1 (t : tactic) : tactic := t ; !t
definition focus (t : tactic) : tactic := focus_at t 0
definition determ (t : tactic) : tactic := at_most t 1
end
end tactic

View file

@ -141,4 +141,4 @@ theorem bnot_false : !ff = tt := refl _
theorem bnot_true : !tt = ff := refl _
end
end bool

View file

@ -12,7 +12,7 @@ using decidable (hiding induction_on rec_on)
namespace helper_tactics
definition apply_refl := apply @refl
tactic_hint apply_refl
end
end helper_tactics
using helper_tactics

View file

@ -583,7 +583,4 @@ mul_eq_one_left ((mul_comm n m) ▸ H)
--- theorem mul_eq_one {n m : } (H : n * m = 1) : n = 1 ∧ m = 1
--- := and_intro (mul_eq_one_left H) (mul_eq_one_right H)
opaque_hint (hiding lt)
end -- namespace nat
end nat

View file

@ -508,6 +508,4 @@ or_elim (le_total k l)
(assume H : k ≤ l, dist_comm l k ▸ dist_comm _ _ ▸ aux l k H)
(assume H : l ≤ k, aux k l H)
opaque_hint (hiding dist)
end -- namespace nat
end nat

View file

@ -26,4 +26,4 @@ inhabited_intro one
theorem inhabited_num [instance] : inhabited num :=
inhabited_intro zero
end
end num

View file

@ -45,4 +45,4 @@ rec_on o₁
(take a₂ : A, decidable.rec_on (H a₁ a₂)
(assume Heq : a₁ = a₂, inl (Heq ▸ refl _))
(assume Hne : a₁ ≠ a₂, inr (assume Hn : some a₁ = some a₂, absurd (some_inj Hn) Hne))))
end
end option

View file

@ -10,7 +10,7 @@ namespace pair
inductive pair (A : Type) (B : Type) : Type :=
| mk_pair : A → B → pair A B
section
section thms
parameter {A : Type}
parameter {B : Type}
@ -34,7 +34,7 @@ section
... = mk_pair (fst p2) (snd p1) : {H1}
... = mk_pair (fst p2) (snd p2) : {H2}
... = p2 : pair_ext p2
end
end thms
instance pair_inhabited
@ -43,4 +43,4 @@ infixr × := pair
-- notation for n-ary tuples
notation `(` h `,` t:(foldl `,` (e r, mk_pair r e) h) `)` := t
end
end pair

View file

@ -61,4 +61,4 @@ theorem union_assoc (A B C : set T) : (A B) C = A (B C) :=
funext (λx, bor_assoc (A x) (B x) (C x))
end
end
end set

View file

@ -21,4 +21,4 @@ inhabited_intro (ascii ff ff ff ff ff ff ff ff)
theorem inhabited_string [instance] : inhabited string :=
inhabited_intro empty
end
end string

View file

@ -15,4 +15,4 @@ infixr `+`:25 := sum
theorem induction_on {A : Type} {B : Type} {C : Prop} (s : A + B) (H1 : A → C) (H2 : B → C) : C :=
sum_rec H1 H2 s
end
end sum

View file

@ -21,4 +21,4 @@ inhabited_intro ⋆
theorem decidable_eq [instance] (a b : unit) : decidable (a = b) :=
inl (unit_eq a b)
end
end unit

View file

@ -24,4 +24,5 @@ section
theorem compose_const_right (f : B → C) (b : B) : f ∘ (const A b) = const A (f b) :=
funext (take x, refl _)
end end
end
end function

View file

@ -87,4 +87,4 @@ rec_on Ha
theorem decidable_eq_equiv {a b : Prop} (Ha : decidable a) (H : a = b) : decidable b :=
decidable_iff_equiv Ha (eq_to_iff H)
end
end decidable

View file

@ -35,7 +35,7 @@ namespace eq_proofs
postfix `⁻¹`:100 := symm
infixr `⬝`:75 := trans
infixr `▸`:75 := subst
end
end eq_proofs
using eq_proofs
theorem congr1 {A : Type} {B : A → Type} {f g : Π x, B x} (H : f = g) (a : A) : f a = g a :=

View file

@ -52,4 +52,4 @@ notation f `-[` op `]-` g := combine f op g
-- Trick for using any binary function as infix operator
notation a `⟨` f `⟩` b := f a b
end
end function

View file

@ -36,4 +36,4 @@ section
... = a*(c*b) : {H_comm _ _}
... = (a*c)*b : (H_assoc _ _ _)⁻¹
end
end
end binary

View file

@ -27,4 +27,5 @@ equivalence_rec (λ r s t, s) H
theorem equivalence_transitive [instance] {A : Type} {p : A → A → Prop} (H : equivalence p) : transitive p :=
equivalence_rec (λ r s t, t) H
end
end equivalence

View file

@ -54,4 +54,4 @@ notation `?` t:max := try t
definition repeat1 (t : tactic) : tactic := t ; !t
definition focus (t : tactic) : tactic := focus_at t 0
definition determ (t : tactic) : tactic := at_most t 1
end
end tactic

View file

@ -63,8 +63,11 @@ environment print_cmd(parser & p) {
}
environment section_cmd(parser & p) {
name n;
if (p.curr_is_identifier())
n = p.check_atomic_id_next("invalid section, atomic identifier expected");
p.push_local_scope();
return push_scope(p.env(), p.ios());
return push_scope(p.env(), p.ios(), true, n);
}
environment namespace_cmd(parser & p) {
@ -72,14 +75,19 @@ environment namespace_cmd(parser & p) {
name n = p.check_atomic_id_next("invalid namespace declaration, atomic identifier expected");
if (is_root_namespace(n))
throw parser_error(sstream() << "invalid namespace name, '" << n << "' is reserved", pos);
return push_scope(p.env(), p.ios(), n);
return push_scope(p.env(), p.ios(), false, n);
}
environment end_scoped_cmd(parser & p) {
if (in_section(p.env()))
p.pop_local_scope();
if (p.curr_is_identifier()) {
name n = p.check_atomic_id_next("invalid end of scope, atomic identifier expected");
return pop_scope(p.env(), n);
} else {
return pop_scope(p.env());
}
}
environment check_cmd(parser & p) {
expr e = p.parse_expr();

View file

@ -7,6 +7,7 @@ Author: Leonardo de Moura
#include <vector>
#include <memory>
#include <string>
#include "util/sstream.h"
#include "library/scoped_ext.h"
#include "library/kernel_bindings.h"
@ -28,6 +29,7 @@ void register_scoped_ext(name const & c, using_namespace_fn use, push_scope_fn p
struct scope_mng_ext : public environment_extension {
name_set m_namespace_set; // all namespaces registered in the system
list<name> m_namespaces; // stack of namespaces/sections
list<name> m_headers; // namespace/section header
list<bool> m_in_section;
};
@ -80,10 +82,9 @@ optional<name> to_valid_namespace_name(environment const & env, name const & n)
}
static std::string g_new_namespace_key("nspace");
environment push_scope(environment const & env, io_state const & ios, name const & n) {
if (!n.is_anonymous() && in_section(env))
environment push_scope(environment const & env, io_state const & ios, bool add_sec, name const & n) {
if (!add_sec && in_section(env))
throw exception("invalid namespace declaration, a namespace cannot be declared inside a section");
bool in_section = n.is_anonymous();
name new_n = get_namespace(env) + n;
scope_mng_ext ext = get_extension(env);
bool save_ns = false;
@ -92,12 +93,13 @@ environment push_scope(environment const & env, io_state const & ios, name const
ext.m_namespace_set.insert(new_n);
}
ext.m_namespaces = cons(new_n, ext.m_namespaces);
ext.m_in_section = cons(n.is_anonymous(), ext.m_in_section);
ext.m_headers = cons(n, ext.m_headers);
ext.m_in_section = cons(add_sec, ext.m_in_section);
environment r = update(env, ext);
for (auto const & t : get_exts()) {
r = std::get<2>(t)(r, in_section);
r = std::get<2>(t)(r, add_sec);
}
if (!n.is_anonymous())
if (!add_sec)
r = using_namespace(r, ios, n);
if (save_ns)
r = module::add(r, g_new_namespace_key, [=](serializer & s) { s << new_n; });
@ -117,12 +119,15 @@ static void namespace_reader(deserializer & d, module_idx, shared_environment &,
}
register_module_object_reader_fn g_namespace_reader(g_new_namespace_key, namespace_reader);
environment pop_scope(environment const & env) {
environment pop_scope(environment const & env, name const & n) {
scope_mng_ext ext = get_extension(env);
if (is_nil(ext.m_namespaces))
throw exception("invalid end of scope, there are no open namespaces/sections");
if (n != head(ext.m_headers))
throw exception(sstream() << "invalid end of scope, begin/end mistmatch, scope starts with '" << head(ext.m_headers) << "', and ends with '" << n << "'");
bool in_section = head(ext.m_in_section);
ext.m_namespaces = tail(ext.m_namespaces);
ext.m_headers = tail(ext.m_headers);
ext.m_in_section = tail(ext.m_in_section);
environment r = update(env, ext);
for (auto const & t : get_exts()) {
@ -146,15 +151,21 @@ static int using_namespace_objects(lua_State * L) {
static int push_scope(lua_State * L) {
int nargs = lua_gettop(L);
if (nargs == 1)
return push_environment(L, push_scope(to_environment(L, 1), get_io_state(L)));
return push_environment(L, push_scope(to_environment(L, 1), get_io_state(L), true));
else if (nargs == 2)
return push_environment(L, push_scope(to_environment(L, 1), get_io_state(L), to_name_ext(L, 2)));
return push_environment(L, push_scope(to_environment(L, 1), get_io_state(L), false, to_name_ext(L, 2)));
else if (nargs == 3)
return push_environment(L, push_scope(to_environment(L, 1), get_io_state(L), lua_toboolean(L, 3), to_name_ext(L, 2)));
else
return push_environment(L, push_scope(to_environment(L, 1), to_io_state(L, 3), to_name_ext(L, 2)));
return push_environment(L, push_scope(to_environment(L, 1), to_io_state(L, 4), lua_toboolean(L, 3), to_name_ext(L, 2)));
}
static int pop_scope(lua_State * L) {
int nargs = lua_gettop(L);
if (nargs == 1)
return push_environment(L, pop_scope(to_environment(L, 1)));
else
return push_environment(L, pop_scope(to_environment(L, 1), to_name_ext(L, 2)));
}
void open_scoped_ext(lua_State * L) {

View file

@ -23,9 +23,9 @@ void register_scoped_ext(name const & n, using_namespace_fn use, push_scope_fn p
/** \brief Use objects defined in the namespace \c n, if \c c is not the anonymous name, then only object from "class" \c c are considered. */
environment using_namespace(environment const & env, io_state const & ios, name const & n, name const & c = name());
/** \brief Create a new scope, all scoped extensions are notified. */
environment push_scope(environment const & env, io_state const & ios, name const & n = name());
environment push_scope(environment const & env, io_state const & ios, bool section, name const & n = name());
/** \brief Delete the most recent scope, all scoped extensions are notified. */
environment pop_scope(environment const & env);
environment pop_scope(environment const & env, name const & n = name());
name const & get_namespace(environment const & env);
list<name> const & get_namespaces(environment const & env);

View file

@ -3,12 +3,12 @@ import logic
namespace N1
variable num : Type.{1}
variable foo : num → num → num
end
end N1
namespace N2
variable val : Type.{1}
variable foo : val → val → val
end
end N2
using N2
using N1

View file

@ -31,7 +31,7 @@ namespace algebra
:= add_struct_rec (fun f, f) s a b
infixl `+`:65 := add
end
end algebra
namespace nat
inductive nat : Type :=
@ -50,7 +50,7 @@ namespace nat
definition to_nat (n : num) : nat
:= #algebra
num_rec zero (λ n, pos_num_rec (succ zero) (λ n r, r + r) (λ n r, r + r + succ zero) n) n
end
end nat
namespace algebra
namespace semigroup
@ -74,7 +74,7 @@ namespace semigroup
definition is_semigroup [inline] [instance] (g : semigroup) : semigroup_struct (carrier g)
:= semigroup_rec (fun c s, s) g
end
end semigroup
namespace monoid
check semigroup.mul
@ -100,8 +100,8 @@ namespace monoid
definition is_monoid [inline] [instance] (m : monoid) : monoid_struct (carrier m)
:= monoid_rec (fun c s, s) m
end
end
end monoid
end algebra
section
using algebra algebra.semigroup algebra.monoid

View file

@ -3,12 +3,12 @@ import logic
namespace N1
variable num : Type.{1}
variable foo : num → num → num
end
end N1
namespace N2
variable val : Type.{1}
variable foo : val → val → val
end
end N2
using N1
using N2

View file

@ -3,12 +3,12 @@ import logic
namespace N1
variable num : Type.{1}
variable foo : num → num → num
end
end N1
namespace N2
variable val : Type.{1}
variable foo : val → val → val
end
end N2
using N2
using N1

View file

@ -10,7 +10,7 @@ namespace N1
check foo
end
check foo
end
end N1
check N1.foo
namespace N2
@ -22,5 +22,5 @@ namespace N2
check list
end
check list
end
end N2
check N2.list

View file

@ -60,7 +60,7 @@ section
end
check @foo.is_proj2.{1}
check @foo.is_proj3.{1 2}
end
end foo
namespace bla
section
@ -73,4 +73,4 @@ section
end
check @bla.is_proj2.{1 2}
check @bla.is_proj3.{1 2 3}
end
end bla

View file

@ -6,7 +6,7 @@ namespace foo
axiom le_trans {a b c : num} : le a b → le b c → le a c
calc_trans le_trans
infix `≤`:50 := le
end
end foo
namespace foo
theorem T {a b c d : num} : a ≤ b → b ≤ c → c ≤ d → a ≤ d
@ -14,4 +14,4 @@ namespace foo
calc a ≤ b : H1
... ≤ c : H2
... ≤ d : H3
end
end foo

View file

@ -6,7 +6,7 @@ set_option pp.coercion true
namespace foo
theorem trans {a b c : nat} (H1 : a = b) (H2 : b = c) : a = c :=
trans H1 H2
end
end foo
using foo

View file

@ -8,7 +8,7 @@ namespace algebra
:= mul_struct_rec (λ f, f) s a b
infixl `*`:75 := mul
end
end algebra
namespace nat
inductive nat : Type :=
@ -20,7 +20,7 @@ namespace nat
definition mul_struct [instance] : algebra.mul_struct nat
:= algebra.mk_mul_struct mul
end
end nat
section
using algebra nat

View file

@ -17,4 +17,4 @@ namespace setoid
inductive morphism (s1 s2 : setoid) : Type :=
| mk_morphism : Π (f : s1 → s2), (∀ x y, x ≈ y → f x ≈ f y) → morphism s1 s2
end
end setoid

View file

@ -27,4 +27,4 @@ namespace setoid
| mk_morphism2 : Π (f : s1 → s2), (∀ x y, x ≈ y → f x ≈ f y) → morphism2 s1 s2
check mk_morphism2
end
end setoid

View file

@ -31,4 +31,4 @@ namespace setoid
check morphism2
check mk_morphism2
end
end setoid

View file

@ -37,4 +37,4 @@ namespace setoid
check my_struct
definition tst2 : Type.{4} := my_struct.{1 2}
end
end setoid

View file

@ -44,4 +44,4 @@ theorem congr_and_comp [instance] {T : Type} {R : T → T → Prop} {f1 f2 : T
(C1 : struc R iff f1) (C2 : struc R iff f2) :
congr.struc R iff (λx, f1 x ∧ f2 x) := congr.compose21 congr_and C1 C2
end
end congr

View file

@ -5,7 +5,7 @@ namespace nat
variable nat : Type.{1}
variable add : nat → nat → nat
infixl + := add
end
end nat
namespace int
using nat (nat)
@ -14,7 +14,7 @@ namespace int
infixl + := add
variable of_nat : nat → int
coercion of_nat
end
end int
section
using nat

View file

@ -4,7 +4,7 @@ namespace nat
variable nat : Type.{1}
variable add : nat → nat → nat
infixl + := add
end
end nat
namespace int
using nat (nat)
@ -13,7 +13,7 @@ namespace int
infixl + := add
variable of_nat : nat → int
coercion of_nat
end
end int
section
-- Using "only" the notation and declarations from the namespaces nat and int

View file

@ -4,7 +4,7 @@ namespace nat
variable nat : Type.{1}
variable add : nat → nat → nat
infixl + := add
end
end nat
namespace int
using nat (nat)
@ -13,7 +13,7 @@ namespace int
infixl + := add
variable of_nat : nat → int
coercion of_nat
end
end int
variables n m : nat.nat
variables i j : int.int
@ -35,7 +35,7 @@ namespace int
definition add_in (a : int) (b : nat) := a + (of_nat b)
infixl + := add_ni
infixl + := add_in
end
end int
section
using [notation] nat

View file

@ -4,7 +4,7 @@ namespace nat
variable nat : Type.{1}
variable add : nat → nat → nat
infixl + := add
end
end nat
namespace int
using nat (nat)
@ -14,8 +14,8 @@ namespace int
variable of_nat : nat → int
namespace coercions
coercion of_nat
end
end
end coercions
end int
using nat
using int

View file

@ -5,7 +5,7 @@ namespace nat
variable nat : Type.{1}
variable add : nat → nat → nat
infixl + := add
end
end nat
namespace int
using nat (nat)
@ -14,7 +14,7 @@ namespace int
infixl + := add
variable of_nat : nat → int
coercion of_nat
end
end int
using int
using nat

View file

@ -5,7 +5,7 @@ namespace nat
variable nat : Type.{1}
variable add : nat → nat → nat
infixl + := add
end
end nat
namespace int
using nat (nat)
@ -14,7 +14,7 @@ namespace int
infixl + := add
variable of_nat : nat → int
coercion of_nat
end
end int
using nat
using int

View file

@ -4,7 +4,7 @@ namespace nat
variable nat : Type.{1}
variable add : nat → nat → nat
infixl + := add
end
end nat
namespace int
using nat (nat)
@ -13,7 +13,7 @@ namespace int
infixl + := add
variable of_nat : nat → int
coercion of_nat
end
end int
-- Using "only" the notation and declarations from the namespaces nat and int
using [notation] nat

View file

@ -4,7 +4,7 @@ namespace nat
variable nat : Type.{1}
variable add : nat → nat → nat
infixl + := add
end
end nat
namespace int
using nat (nat)
@ -12,11 +12,11 @@ namespace int
variable add : int → int → int
infixl + := add
variable of_nat : nat → int
end
end int
namespace int_coercions
coercion int.of_nat
end
end int_coercions
-- Using "only" the notation and declarations from the namespaces nat and int
using nat

View file

@ -6,4 +6,4 @@ namespace foo
check x
set_option pp.full_names true
check x
end
end foo

View file

@ -6,6 +6,6 @@ namespace list
check list.{1}
check cons.{1}
check list_rec.{1 1}
end
end list
check list.list.{1}

View file

@ -17,7 +17,7 @@ inductive tree (A : Type) : Type :=
with forest (A : Type) : Type :=
| nil : forest A
| cons : tree A → forest A → forest A
end
end Tree
inductive group_struct (A : Type) : Type :=
| mk_group_struct : (A → A → A) → A → group_struct A

View file

@ -5,13 +5,13 @@ namespace foo
variable a : N
variable f : N → N → N
infix + := f
end
end foo
namespace bla
variable b : N
variable f : N → N → N
infix + := f
end
end bla
variable g : N → N → N

View file

@ -3,8 +3,8 @@ import standard
namespace foo
namespace boo
theorem tst : true := trivial
end
end
end boo
end foo
using foo
check boo.tst

View file

@ -13,8 +13,8 @@ namespace N1
check N1.N2.foo
print raw foo
print raw _root_.foo
end
end
end N2
end N1

View file

@ -16,3 +16,5 @@ section
theorem mem_empty (x : T) : ¬ (x ∈ ∅)
:= not_intro (λH : x ∈ ∅, absurd H ff_ne_tt)
end
end set

View file

@ -1,7 +1,7 @@
namespace foo
definition f.{l} (A : Type.{l}) : Type.{l} := A
check f.{1}
end
end foo
variable N : Type.{1}
section

View file

@ -4,8 +4,8 @@ namespace foo
namespace tst
variable N : Type.{3}
print raw N
end
end
end tst
end foo
print raw N
namespace foo
print raw N
@ -15,5 +15,5 @@ namespace foo
variable N : Type.{4} -- Shadow previous ones.
print raw N
end
end
end
end tst
end foo

View file

@ -6,7 +6,7 @@ definition F (X : Type) : Type := (X → Prop) → Prop
hypothesis unfold.{l} : I.{l} → F I.{l}
hypothesis fold.{l} : F I.{l} → I.{l}
hypothesis iso1 : ∀x, fold (unfold x) = x
end
end S1
namespace S2
universe u
@ -15,7 +15,7 @@ definition F (X : Type) : Type := (X → Prop) → Prop
hypothesis unfold : I → F I
hypothesis fold : F I → I
hypothesis iso1 : ∀x, fold (unfold x) = x
end
end S2
namespace S3
@ -26,4 +26,4 @@ section
hypothesis fold : F I → I
hypothesis iso1 : ∀x, fold (unfold x) = x
end
end
end S3

View file

@ -24,3 +24,5 @@ simplifies_to_rec (λx, x) C
theorem simp_app [instance] (S T : Type) (f1 f2 : S → T) (s1 s2 : S)
(C1 : simplifies_to f1 f2) (C2 : simplifies_to s1 s2) : simplifies_to (f1 s1) (f2 s2) :=
mk (congr (get_eq C1) (get_eq C2))
end simp

View file

@ -188,46 +188,6 @@ list_induction_on l
append x (y :: l') = (y :: l') ++ [ x ] : append_eq_concat _ _
... = concat (reverse (reverse (y :: l'))) [ x ] : {symm (reverse_reverse _)}
... = reverse (x :: (reverse (y :: l'))) : refl _)
end
end list
exit
-- Head and tail
-- -------------
definition head (x0 : T) : list T → T := list_rec x0 (fun x l h, x)
theorem head_nil (x0 : T) : head x0 (@nil T) = x0 := refl _
theorem head_cons (x : T) (x0 : T) (t : list T) : head x0 (x :: t) = x := refl _
theorem head_concat (s t : list T) (x0 : T) : s ≠ nil → (head x0 (s ++ t) = head x0 s) :=
list_cases_on s
(take H : nil ≠ nil, absurd_elim (head x0 (concat nil t) = head x0 nil) (refl nil) H)
(take x s,
take H : cons x s ≠ nil,
calc
head x0 (concat (cons x s) t) = head x0 (cons x (concat s t)) : {cons_concat _ _ _}
... = x : {head_cons _ _ _}
... = head x0 (cons x s) : {symm ( head_cons x x0 s)})
definition tail : list T → list T := list_rec nil (fun x l b, l)
theorem tail_nil : tail (@nil T) = nil := refl _
theorem tail_cons (x : T) (l : list T) : tail (cons x l) = l := refl _
theorem cons_head_tail (x0 : T) (l : list T) : l ≠ nil → (head x0 l) :: (tail l) = l :=
list_cases_on l
(assume H : nil ≠ nil, absurd_elim _ (refl _) H)
(take x l, assume H : cons x l ≠ nil, refl _)
-- List membership
-- ---------------
definition mem (x : T) : list T → Prop := list_rec false (fun y l H, x = y H)
infix `∈` : 50 := mem
theorem mem_nil (x : T) : mem x nil ↔ false := iff_refl _
theorem mem_cons (x : T) (y : T) (l : list T) : mem x (cons y l) ↔ (x = y mem x l) := iff_refl _

View file

@ -23,7 +23,7 @@ definition to_nat [coercion] [inline] (n : num) :
namespace helper_tactics
definition apply_refl := apply @refl
tactic_hint apply_refl
end
end helper_tactics
using helper_tactics
theorem nat_rec_zero {P : → Type} (x : P 0) (f : ∀m, P m → P (succ m)) : nat_rec x f 0 = x
@ -1418,4 +1418,7 @@ theorem dist_eq_intro {n m k l : } (H : n + m = k + l) : dist n k = dist l m
dist n k = dist (n + m) (k + m) : symm (dist_add_right n m k)
... = dist (k + l) (k + m) : {H}
... = dist l m : dist_add_left k l m
end --namespace nat
end nat

View file

@ -4,7 +4,7 @@ namespace foo
variable a : A
variable x : A
variable c : A
end
end foo
section
using foo (renaming a->b x->y) (hiding c)
@ -34,7 +34,7 @@ end
namespace foo
variable f : A → A → A
infix `*`:75 := f
end
end foo
section
using foo

View file

@ -4,7 +4,7 @@ namespace tst
universe v
print raw Type.{v}
print raw Type.{tst.v}
end
end tst
print raw Type.{tst.v}
print raw Type.{v} -- Error: alias 'v' is not available anymore
section
@ -20,8 +20,8 @@ namespace tst
print raw Type.{u}
namespace foo
universe U
end
end
end foo
end tst
print raw Type.{tst.foo.U}
namespace tst.foo -- Error: we cannot use qualified names in declarations
universe full.name.U -- Error: we cannot use qualified names in declarations
@ -29,9 +29,9 @@ namespace tst
namespace foo
print raw Type.{v} -- Remark: alias 'v' for 'tst.v' is available again
print raw Type.{U} -- Remark: alias 'U' for 'tst.foo.U' is available again
end
end
end foo
end tst
namespace bla
universe u -- Error: we cannot shadow universe levels
end
end bla
print raw Type.{bla.u} -- Error: we failed to declare bla.u

View file

@ -34,17 +34,17 @@ namespace tst
variable M : Type.{2}
print raw N -- Two possible interpretations N and tst.N
print raw tst.N -- Only one interpretation
end
end tst
print raw N -- Only one interpretation
namespace foo
variable M : Type.{3}
print raw M -- Only one interpretation
end
end foo
check tst.M
check foo.M
namespace foo
check M
end
end foo
check M -- Error
print "ok"

View file

@ -8,6 +8,6 @@ namespace foo
check h
definition q [private] : N := f a
check q
end
end foo
check foo.h
check q -- Error q is now hidden

View file

@ -11,10 +11,10 @@ namespace foo
infixl + := add
infixl * := mul
check a+b*a
end
end foo
-- Notation is not avaiable outside the namespace
check a+b*a
namespace foo
-- Notation is restored
check a+b*a
end
end foo

View file

@ -42,7 +42,7 @@ function get_num_coercions(env)
end
for_each_coercion_user(env, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D) .. " : " .. tostring(f)) end)
assert(get_num_coercions(env) == 3)
env = pop_scope(env)
env = pop_scope(env, "tst")
print("---------")
for_each_coercion_user(env, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D) .. " : " .. tostring(f)) end)
assert(get_num_coercions(env) == 1)
@ -67,7 +67,7 @@ assert(get_num_coercions(env) == 6)
print("---------")
env = pop_scope(env)
assert(get_num_coercions(env) == 3)
env = pop_scope(env)
env = pop_scope(env, "tst")
for_each_coercion_user(env, function(C, D, f) print(tostring(C) .. " >-> " .. tostring(D) .. " : " .. tostring(f)) end)
assert(get_num_coercions(env) == 1)
env = push_scope(env, "tst")