statement stringlengths 1 1.02k | proof stringlengths 0 5.19k | type stringclasses 13
values | symbolic_name stringlengths 1 30 | library stringclasses 15
values | filename stringclasses 117
values | imports listlengths 0 16 | deps listlengths 0 16 | docstring stringclasses 50
values | source_url stringclasses 1
value | commit stringclasses 1
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|---|---|---|---|---|---|---|---|---|---|---|
"' pat <- c1 ;; c2" | :=
(@bind _ _ _ _ c1 (fun x => match x with pat => c2 end))
(at level 61, pat pattern, c1 at next level, right associativity) : monad_scope. | Notation | ' pat <- c1 ;; c2 | Structures | theories/Structures/Monad.v | [
"ExtLib.Structures.Functor",
"ExtLib.Structures.Applicative",
"MonadBaseNotation"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"'let*' p ':=' c1 'in' c2" | := (@bind _ _ _ _ c1 (fun p => c2))
(at level 61, p as pattern, c1 at next level, right associativity) : monad_scope. | Notation | 'let*' p ':=' c1 'in' c2 | Structures | theories/Structures/Monad.v | [
"ExtLib.Structures.Functor",
"ExtLib.Structures.Applicative",
"MonadBaseNotation"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Functor_Monad@{} : Functor m | :=
{ fmap := @liftM _ _ }. | Instance | Functor_Monad | Structures | theories/Structures/Monad.v | [
"ExtLib.Structures.Functor",
"ExtLib.Structures.Applicative",
"MonadBaseNotation"
] | [
"Functor",
"liftM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Applicative_Monad@{} : Applicative m | :=
{ pure := @ret _ _
; ap := @apM _ _
}. | Instance | Applicative_Monad | Structures | theories/Structures/Monad.v | [
"ExtLib.Structures.Functor",
"ExtLib.Structures.Applicative",
"MonadBaseNotation"
] | [
"Applicative",
"apM",
"pure"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Cont (m : Type -> Type) : Type | :=
{ callCC : forall a b, ((a -> m b) -> m a) -> m a }. | Class | Cont | Structures | theories/Structures/MonadCont.v | [
"ExtLib.Structures.Monad"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
MonadExc (E : Type) (m : Type -> Type) : Type | :=
{ raise : forall {T}, E -> m T
; catch : forall {T}, m T -> (E -> m T) -> m T
}. | Class | MonadExc | Structures | theories/Structures/MonadExc.v | [
"ExtLib.Structures.Monad"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
MonadFix (m : Type -> Type) : Type | :=
{ mfix : forall {T U}, ((T -> m U) -> T -> m U) -> T -> m U }. | Class | MonadFix | Structures | theories/Structures/MonadFix.v | [
"ExtLib.Structures.Monad"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
ftype (ls : list Type) (r : Type) : Type | :=
match ls with
| nil => r
| cons l ls => l -> ftype ls r
end. | Fixpoint | ftype | Structures | theories/Structures/MonadFix.v | [
"ExtLib.Structures.Monad"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
tuple (ls : list Type) : Type | :=
match ls with
| nil => unit
| cons l ls => l * tuple ls
end%type. | Fixpoint | tuple | Structures | theories/Structures/MonadFix.v | [
"ExtLib.Structures.Monad"
] | [
"type"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
wrap (ls : list Type) R {struct ls} : (tuple ls -> R) -> ftype ls R | :=
match ls as ls return (tuple ls -> R) -> ftype ls R with
| nil => fun f => f tt
| cons l ls => fun f => fun x => wrap ls (fun g => f (x,g))
end. | Fixpoint | wrap | Structures | theories/Structures/MonadFix.v | [
"ExtLib.Structures.Monad"
] | [
"ftype",
"tuple"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
apply (ls : list Type) R {struct ls} : ftype ls R -> tuple ls -> R | :=
match ls as ls return ftype ls R -> tuple ls -> R with
| nil => fun f _ => f
| cons l ls => fun f t => @apply ls R (f (fst t)) (snd t)
end. | Fixpoint | apply | Structures | theories/Structures/MonadFix.v | [
"ExtLib.Structures.Monad"
] | [
"ftype",
"tuple"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
mfix_multi (ls : list Type) (R : Type)
(f : ftype ls (m R) -> ftype ls (m R))
: ftype ls (m R) | :=
@wrap ls (m R) (@mfix _ MF (tuple ls) R
(fun packed => apply ls (m R) (f (wrap ls packed)))). | Definition | mfix_multi | Structures | theories/Structures/MonadFix.v | [
"ExtLib.Structures.Monad"
] | [
"apply",
"ftype",
"tuple",
"wrap"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
mfix2 A B C
(ff:(A -> B -> m C) -> (A -> B -> m C)) (a:A) (b:B) : m C | :=
let ff' fabp (abp:A*B) :=
let (a,b) := abp in
let fab a b := fabp (a,b) in
ff fab a b
in
mfix ff' (a,b). | Definition | mfix2 | Structures | theories/Structures/MonadFix.v | [
"ExtLib.Structures.Monad"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
mfix3 A B C D
(ff:(A -> B -> C -> m D) -> (A -> B -> C -> m D))
(a:A) (b:B) (c:C) : m D | :=
let ff' fabcp (abcp:A*B*C) :=
let (abp,c) := abcp in
let (a,b) := abp in
let fabc a b c := fabcp (a,b,c) in
ff fabc a b c
in
mfix ff' (a,b,c). | Definition | mfix3 | Structures | theories/Structures/MonadFix.v | [
"ExtLib.Structures.Monad"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
MonadLaws | :=
{ bind_of_return : forall {A B} (a : A) (f : A -> m B),
bind (ret a) f = f a
; return_of_bind : forall {A} (aM: m A),
bind aM ret = aM
; bind_associativity :
forall {A B C} (aM:m A) (f:A -> m B) (g:B -> m C),
bind (bind aM f) g = bind aM (fun a => bind (f a) g)
}. | Class | MonadLaws | Structures | theories/Structures/MonadLaws.v | [
"Setoid",
"Coq.Classes.Morphisms",
"ExtLib.Structures.Monads",
"ExtLib.Data.Fun",
"ExtLib.Data.Unit"
] | [] | This <= relation is a computational <= relation based on the ideas
of domain theory. It generalizes the usual equivalence relation by,
enabling the relation to talk about computations that are "more defined"
than others.
This generalization is done to support the fixpoint law.
* | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 |
MonadTLaws {n} (nM : Monad n) (MT : MonadT m n) | :=
{ lift_ret : forall {T} (x : T),
lift (ret x) = ret x
; lift_bind : forall {T U} (c : n T) (f : T -> n U),
lift (bind c f) = bind (lift c) (fun x => lift (f x))
}. | Class | MonadTLaws | Structures | theories/Structures/MonadLaws.v | [
"Setoid",
"Coq.Classes.Morphisms",
"ExtLib.Structures.Monads",
"ExtLib.Data.Fun",
"ExtLib.Data.Unit"
] | [
"Monad",
"MonadT"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
MonadStateLaws (MS : MonadState S m) | :=
{ get_put : bind get put = ret tt :> m unit
; put_get : forall x : S,
bind (put x) (fun _ => get) = bind (put x) (fun _ => ret x) :> m S
; put_put : forall {A} (x y : S) (f : unit -> m A),
bind (put x) (fun _ => bind (put y) f) = bind (put y) f
; get_get : forall {A} (f : S -> S -> m ... | Class | MonadStateLaws | Structures | theories/Structures/MonadLaws.v | [
"Setoid",
"Coq.Classes.Morphisms",
"ExtLib.Structures.Monads",
"ExtLib.Data.Fun",
"ExtLib.Data.Unit"
] | [
"MonadState",
"get",
"put"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
MonadReaderLaws (MR : MonadReader S m) | :=
{ ask_local : forall f : S -> S,
local f ask = bind ask (fun x => ret (f x))
; local_bind : forall {A B} (aM : m A) (f : S -> S) (g : A -> m B),
local f (bind aM g) = bind (local f aM) (fun x => local f (g x))
; local_ret : forall {A} (x : A) (f : S -> S),
local f (ret x) = ret ... | Class | MonadReaderLaws | Structures | theories/Structures/MonadLaws.v | [
"Setoid",
"Coq.Classes.Morphisms",
"ExtLib.Structures.Monads",
"ExtLib.Data.Fun",
"ExtLib.Data.Unit"
] | [
"MonadReader"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
MonadZeroLaws (MZ : MonadZero m) | :=
{ bind_zero : forall {A B} (f : A -> m B),
bind mzero f = mzero
}. | Class | MonadZeroLaws | Structures | theories/Structures/MonadLaws.v | [
"Setoid",
"Coq.Classes.Morphisms",
"ExtLib.Structures.Monads",
"ExtLib.Data.Fun",
"ExtLib.Data.Unit"
] | [
"MonadZero"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
MonadFixLaws (MF : MonadFix m) : Type | :=
{ mleq : forall {T}, relation T -> relation (m T)
; mfix_monotonic : forall {T U} (F : (T -> m U) -> T -> m U),
respectful eq (mleq eq) (mfix F) (F (mfix F))
}. | Class | MonadFixLaws | Structures | theories/Structures/MonadLaws.v | [
"Setoid",
"Coq.Classes.Morphisms",
"ExtLib.Structures.Monads",
"ExtLib.Data.Fun",
"ExtLib.Data.Unit"
] | [
"MonadFix"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
MonadPlus (m : Type -> Type) : Type | :=
{ mplus : forall {A B:Type}, m A -> m B -> m (A + B)%type }. | Class | MonadPlus | Structures | theories/Structures/MonadPlus.v | [
"ExtLib.Structures.Monad"
] | [
"type"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
mjoin {m : Type -> Type} {M : Monad m} {MP : MonadPlus m} {T} (a b : m T) : m T | :=
bind (mplus a b) (fun x =>
match x with
| inl x | inr x => ret x
end). | Definition | mjoin | Structures | theories/Structures/MonadPlus.v | [
"ExtLib.Structures.Monad"
] | [
"Monad",
"MonadPlus"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x <+> y" | := (@mplus _ _ _ _ x y) (at level 54, left associativity) : monad_scope. | Notation | x <+> y | Structures | theories/Structures/MonadPlus.v | [
"ExtLib.Structures.Monad"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
MonadReader@{d c} (T : Type@{d}) (m : Type@{d} -> Type@{c})
: Type | :=
{ local : forall {t : Type@{d}}, (T -> T) -> m t -> m t
; ask : m T
}. | Class | MonadReader | Structures | theories/Structures/MonadReader.v | [
"ExtLib.Structures.Monad"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
asks@{d c}
{m : Type@{d} -> Type@{c}}
{M : Monad m}
{T : Type@{d}}
{MR : MonadReader@{d c} T m}
{U : Type@{d}} (f : T -> U) : m U | :=
bind ask (fun x => ret (f x)). | Definition | asks | Structures | theories/Structures/MonadReader.v | [
"ExtLib.Structures.Monad"
] | [
"Monad",
"MonadReader"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
ReaderProd@{d c}
{m : Type@{d} -> Type@{c}}
{M : Monad m}
{T S : Type@{d}}
{MR : MonadReader T m}
(f : T -> S)
(g : S -> T -> T)
: MonadReader@{d c} S m | :=
{| ask := @asks m M T MR S f
; local := fun _T up (c : m _T) =>
@local T m MR _ (fun s => g (up (f s)) s) c
|}. | Definition | ReaderProd | Structures | theories/Structures/MonadReader.v | [
"ExtLib.Structures.Monad"
] | [
"Monad",
"MonadReader",
"asks"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
MonadState@{s d c} (T : Type@{s}) (m : Type@{d} -> Type@{c}) : Type | :=
{ get : m T
; put : T -> m unit
}. | Class | MonadState | Structures | theories/Structures/MonadState.v | [
"ExtLib.Structures.Monad"
] | [
"get",
"put"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
modify (f : T -> T) : m T | :=
bind get (fun x => bind (put (f x)) (fun _ => ret x)). | Definition | modify | Structures | theories/Structures/MonadState.v | [
"ExtLib.Structures.Monad"
] | [
"get",
"put"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
gets {U} (f : T -> U) : m U | :=
bind get (fun x => ret (f x)). | Definition | gets | Structures | theories/Structures/MonadState.v | [
"ExtLib.Structures.Monad"
] | [
"get"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
StateProd (f : T -> S) (g : S -> T -> T)
: MonadState S m | :=
{| get := @gets m M T MS S f
; put := fun x => bind get (fun s => put (g x s))
|}. | Definition | StateProd | Structures | theories/Structures/MonadState.v | [
"ExtLib.Structures.Monad"
] | [
"MonadState",
"get",
"gets",
"put"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
MonadT (m : Type -> Type) (mt : Type -> Type) : Type | :=
{ lift : forall {t}, mt t -> m t }. | Class | MonadT | Structures | theories/Structures/MonadTrans.v | [
"ExtLib.Structures.Monad"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
MonadWriter@{d c s} (T : Type@{s}) (M : Monoid T)
(m : Type@{d} -> Type@{c}) : Type | :=
{ tell : T -> m unit
; listen : forall {A : Type@{d}}, m A -> m (A * T)%type
; pass : forall {A : Type@{d}}, m (A * (T -> T))%type -> m A
}. | Class | MonadWriter | Structures | theories/Structures/MonadWriter.v | [
"ExtLib.Structures.Monad",
"ExtLib.Structures.Monoid"
] | [
"Monoid",
"type"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
listens@{d c s}
{m : Type@{d} -> Type@{c}}
{S : Type@{s}}
{Monad_m : Monad m}
{Monoid_S : Monoid S}
{Writer_m : MonadWriter Monoid_S m}
{A B : Type@{d}} (f : S -> B) (c : m A) : m (A * B)%type | :=
liftM (fun x => (fst x, f (snd x))) (listen c). | Definition | listens | Structures | theories/Structures/MonadWriter.v | [
"ExtLib.Structures.Monad",
"ExtLib.Structures.Monoid"
] | [
"Monad",
"MonadWriter",
"Monoid",
"liftM",
"type"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
censor@{d c s}
{m : Type@{d} -> Type@{c}}
{S : Type@{s}}
{Monad_m : Monad m}
{Monoid_S : Monoid S}
{Writer_m : MonadWriter Monoid_S m}
{A : Type@{d}} (f : S -> S) (c : m A) : m A | :=
pass (liftM (fun x => (x, f)) c). | Definition | censor | Structures | theories/Structures/MonadWriter.v | [
"ExtLib.Structures.Monad",
"ExtLib.Structures.Monoid"
] | [
"Monad",
"MonadWriter",
"Monoid",
"liftM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
MonadZero (m : Type -> Type) : Type | :=
{ mzero : forall {T}, m T }. | Class | MonadZero | Structures | theories/Structures/MonadZero.v | [
"ExtLib.Structures.Monad"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
assert (b : bool) : m unit | :=
if b then ret tt else mzero. | Definition | assert | Structures | theories/Structures/MonadZero.v | [
"ExtLib.Structures.Monad"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Monoid@{} : Type | :=
{ monoid_plus : S -> S -> S
; monoid_unit : S
}. | Record | Monoid | Structures | theories/Structures/Monoid.v | [
"ExtLib.Structures.BinOps"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
MonoidLaws@{} (M : Monoid) | :=
{ monoid_assoc : Associative M.(monoid_plus) eq
; monoid_lunit : LeftUnit M.(monoid_plus) M.(monoid_unit) eq
; monoid_runit : RightUnit M.(monoid_plus) M.(monoid_unit) eq
}. | Class | MonoidLaws | Structures | theories/Structures/Monoid.v | [
"ExtLib.Structures.BinOps"
] | [
"Associative",
"LeftUnit",
"Monoid",
"RightUnit"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Ident : Type | :=
lunit : forall a, equ (op u a) a. | Class | Ident | Structures | theories/Structures/Ops.v | [] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Reducible (T E : Type) : Type | :=
reduce : forall {A} (base : A) (single : E -> A) (join : A -> A -> A), T -> A. | Class | Reducible | Structures | theories/Structures/Reducible.v | [
"Coq.Classes.RelationClasses",
"ExtLib.Structures.BinOps",
"ExtLib.Structures.Monad"
] | [
"join",
"single"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Foldable (T E : Type) : Type | :=
fold : forall {A} (add : E -> A -> A) (base : A), T -> A. | Class | Foldable | Structures | theories/Structures/Reducible.v | [
"Coq.Classes.RelationClasses",
"ExtLib.Structures.BinOps",
"ExtLib.Structures.Monad"
] | [
"fold"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Reducible_from_Foldable (R : Foldable T E) : Reducible T E | 100 | :=
fun A base single join =>
@fold _ _ R A (fun x => join (single x)) base. | Instance | Reducible_from_Foldable | Structures | theories/Structures/Reducible.v | [
"Coq.Classes.RelationClasses",
"ExtLib.Structures.BinOps",
"ExtLib.Structures.Monad"
] | [
"Foldable",
"Reducible",
"fold",
"join",
"single"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
foldM {A} (add : E -> A -> m A) (base : m A) (t : T) : m A | :=
fold (fun x acc => bind acc (add x)) base t. | Definition | foldM | Structures | theories/Structures/Reducible.v | [
"Coq.Classes.RelationClasses",
"ExtLib.Structures.BinOps",
"ExtLib.Structures.Monad"
] | [
"fold"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
reduceM {A} (base : m A) (single : E -> m A) (join : A -> A -> m A) (t : T) : m A | :=
reduce base single (fun x y => bind x (fun x => bind y (fun y => join x y))) t. | Definition | reduceM | Structures | theories/Structures/Reducible.v | [
"Coq.Classes.RelationClasses",
"ExtLib.Structures.BinOps",
"ExtLib.Structures.Monad"
] | [
"join",
"single"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
iterM : T -> m unit | :=
reduce (ret tt) f (fun x y => bind x (fun _ => y)). | Definition | iterM | Structures | theories/Structures/Reducible.v | [
"Coq.Classes.RelationClasses",
"ExtLib.Structures.BinOps",
"ExtLib.Structures.Monad"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
DSet : Type | :=
{ contains : T -> S -> bool
; empty : S
; singleton : T -> S
; union : S -> S -> S
; filter : (T -> bool) -> S -> S
; intersect : S -> S -> S
; difference : S -> S -> S
; subset : S -> S -> bool
(** point-wise **)
; add : T -> S -> S
; remove : T -> S -> S
... | Class | DSet | Structures | theories/Structures/Sets.v | [
"ExtLib.Structures.Monoid"
] | [
"contains",
"empty",
"filter",
"remove",
"singleton"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
DSet_Laws : Type | :=
{ DSet_WF : S -> Prop
; empty_WF : DSet_WF empty
; singleton_WF : forall x, DSet_WF (singleton x)
; union_WF : forall s s', DSet_WF s -> DSet_WF s' -> DSet_WF (union s s')
; filter_WF : forall s f, DSet_WF s -> DSet_WF (filter f s)
; intersect_WF : forall s s', DSet_WF s -> DSet_WF s' -> DSet_WF (interse... | Class | DSet_Laws | Structures | theories/Structures/Sets.v | [
"ExtLib.Structures.Monoid"
] | [
"contains",
"empty",
"filter",
"remove",
"singleton"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Monoid_set_union : Monoid S | :=
{| monoid_plus := union
; monoid_unit := empty
|}. | Definition | Monoid_set_union | Structures | theories/Structures/Sets.v | [
"ExtLib.Structures.Monoid"
] | [
"Monoid",
"empty"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Traversable@{d r} (T : Type@{d} -> Type@{r}) : Type | :=
{ mapT : forall {F : Type@{d} -> Type@{r} }
{Ap:Applicative@{d r} F} {A B : Type@{d}},
(A -> F B) -> T A -> F (T B)
}. | Class | Traversable | Structures | theories/Structures/Traversable.v | [
"ExtLib.Structures.Applicative"
] | [
"Applicative"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
sequence@{d r}
{T : Type@{d} -> Type@{r}}
{Tr:Traversable T}
{F : Type@{d} -> Type@{r}} {Ap:Applicative F} {A : Type@{d}}
: T (F A) -> F (T A) | := mapT (@id (F A)). | Definition | sequence | Structures | theories/Structures/Traversable.v | [
"ExtLib.Structures.Applicative"
] | [
"Applicative",
"Traversable"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
forT@{d r}
{T : Type@{d} -> Type@{r}}
{Tr:Traversable T} {F : Type@{d} -> Type@{r}} {Ap:Applicative F}
{A B : Type@{d}} (aT:T A) (f:A -> F B) : F (T B) | := mapT f aT. | Definition | forT | Structures | theories/Structures/Traversable.v | [
"ExtLib.Structures.Applicative"
] | [
"Applicative",
"Traversable"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
negb_true : forall a, negb a = true -> a = false. | Proof.
destruct a; auto.
Qed. | Lemma | negb_true | Tactics | theories/Tactics/BoolTac.v | [
"Coq.Bool.Bool"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
negb_false : forall a, negb a = false -> a = true. | Proof.
destruct a; auto.
Qed. | Lemma | negb_false | Tactics | theories/Tactics/BoolTac.v | [
"Coq.Bool.Bool"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
do_bool' runner | :=
( autorewrite with bool_rw in * );
repeat match goal with
| [ H : negb _ = true |- _ ] => apply negb_true in H
| [ H : negb _ = false |- _ ] => apply negb_false in H
| [ H : andb _ _ = true |- _ ] =>
apply andb_true_iff in H; destruct H
| [ H : orb _ _ = f... | Ltac | do_bool' | Tactics | theories/Tactics/BoolTac.v | [
"Coq.Bool.Bool"
] | [
"apply",
"negb_false",
"negb_true"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
do_bool_case | :=
let t H := (destruct H) in do_bool' t. | Ltac | do_bool_case | Tactics | theories/Tactics/BoolTac.v | [
"Coq.Bool.Bool"
] | [
"do_bool'"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
do_bool | :=
let t _ := idtac in do_bool' t. | Ltac | do_bool | Tactics | theories/Tactics/BoolTac.v | [
"Coq.Bool.Bool"
] | [
"do_bool'"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
forward' dst sol | :=
let check X :=
match X with
| match _ with _ => _ end => fail 1
| if _ then _ else _ => fail 1
| _ => idtac
end
in
let go X :=
first [ (dst X; try solve [ sol ]); [ intros ]
| dst X; solve [ sol ] ]
in
repeat match goal with
| [ H : context [ match ?X with... | Ltac | forward' | Tactics | theories/Tactics/Cases.v | [
"ExtLib.Tactics.Consider"
] | [
"context"
] | This tactic will perform case splits on terms that
are matched on. It only does this on terms where only
one of the cases is non-trivial (i.e. by [intuition congruence]).
**
* | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 |
forward | :=
forward'
ltac:(fun x => consider x; intros)
ltac:(intuition congruence). | Ltac | forward | Tactics | theories/Tactics/Cases.v | [
"ExtLib.Tactics.Consider"
] | [
"consider",
"forward'"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
forward_unsafe' dst sol | :=
let check X :=
match X with
| match _ with _ => _ end => fail 1
| if _ then _ else _ => fail 1
| _ => idtac
end
in
let go X :=
dst X; try solve [ sol ]
in
repeat match goal with
| [ H : context [ match ?X with _ => _ end ] |- _ ] =>
go X
| ... | Ltac | forward_unsafe' | Tactics | theories/Tactics/Cases.v | [
"ExtLib.Tactics.Consider"
] | [
"context"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
forward_unsafe | :=
forward_unsafe'
ltac:(fun x => consider x; intros)
ltac:(intuition congruence). | Ltac | forward_unsafe | Tactics | theories/Tactics/Cases.v | [
"ExtLib.Tactics.Consider"
] | [
"consider",
"forward_unsafe'"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
change_rewrite H | :=
match type of H with
| ?X = _ =>
match goal with
| |- context [ ?Y ] =>
change Y with X ; rewrite H
end
end. | Ltac | change_rewrite | Tactics | theories/Tactics/Cases.v | [
"ExtLib.Tactics.Consider"
] | [
"context",
"type"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
change_rewrite_in H H' | :=
match type of H with
| ?X = _ =>
match type of H' with
| context [ ?Y ] =>
change Y with X in H' ; rewrite H in H'
end
end. | Ltac | change_rewrite_in | Tactics | theories/Tactics/Cases.v | [
"ExtLib.Tactics.Consider"
] | [
"context",
"type"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
rewrite_all_goal | :=
repeat match goal with
| [ H : _ |- _ ] =>
progress (erewrite H by eauto with typeclass_instances)
end. | Ltac | rewrite_all_goal | Tactics | theories/Tactics/Cases.v | [
"ExtLib.Tactics.Consider"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
rewrite_all_in H' | :=
repeat match goal with
| [ H : _ |- _ ] =>
progress (erewrite H in H' by eauto with typeclass_instances)
end. | Ltac | rewrite_all_in | Tactics | theories/Tactics/Cases.v | [
"ExtLib.Tactics.Consider"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
rewrite_all_star | :=
repeat match goal with
| [ H : _ |- _ ] =>
progress (erewrite H in * by eauto with typeclass_instances)
end. | Ltac | rewrite_all_star | Tactics | theories/Tactics/Cases.v | [
"ExtLib.Tactics.Consider"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
reflect (P Q : Prop) : bool -> Type | :=
| reflect_true : P -> reflect P Q true
| reflect_false : Q -> reflect P Q false. | Inductive | reflect | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [] | Two inductives to perform case-based reasonning | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 |
semi_reflect (P : Prop) : bool -> Type | :=
| semi_reflect_true : P -> semi_reflect P true
| semi_reflect_false : semi_reflect P false. | Inductive | semi_reflect | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
iff_to_reflect {A B} (P : A -> B -> Prop) (T : A -> B -> bool) :
(forall x y, T x y = true <-> P x y) ->
(forall x y, reflect (P x y) (~P x y) (T x y)). | Proof.
intros. case_eq (T x y); intros Hxy; constructor.
apply H. assumption.
intros Hf. apply H in Hf. congruence.
Qed. | Lemma | iff_to_reflect | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [
"apply",
"reflect"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
impl_to_semireflect {A B} (P : A -> B -> Prop) (T : A -> B -> bool) :
(forall x y, T x y = true -> P x y) ->
(forall x y, semi_reflect (P x y) (T x y)). | Proof.
intros. case_eq (T x y); intros Hxy; constructor.
apply H; auto.
Qed. | Lemma | impl_to_semireflect | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [
"apply",
"semi_reflect"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
reflect_true_inv P Q : reflect P Q true -> P. | Proof.
exact (fun x => match x in reflect _ _ b
return if b then P else ID
with | reflect_true _ _ H => H | reflect_false _ _ H => (fun _ x => x) end).
Qed. | Lemma | reflect_true_inv | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [
"ID",
"reflect"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
reflect_false_inv P Q : reflect P Q false -> Q. | Proof.
exact (fun x => match x in reflect _ _ b
return if b then ID else Q
with | reflect_true _ _ H => fun _ x => x | reflect_false _ _ H => H end).
Qed. | Lemma | reflect_false_inv | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [
"ID",
"reflect"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
semi_reflect_true_inv P : semi_reflect P true -> P. | Proof.
exact (fun x => match x in semi_reflect _ b
return if b then P else ID
with | semi_reflect_true _ H => H | semi_reflect_false _ => (fun _ x => x) end).
Qed. | Lemma | semi_reflect_true_inv | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [
"ID",
"semi_reflect"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Reflect (T : bool) (P Q : Prop) | := _Reflect : reflect P Q T. | Class | Reflect | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [
"reflect"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
SemiReflect (T : bool) (P : Prop) | := _SemiReflect : semi_reflect P T. | Class | SemiReflect | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [
"semi_reflect"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
t | :=
repeat match goal with
| H: Reflect true ?P ?Q |- _ => apply (reflect_true_inv P Q) in H
| H: Reflect false ?P ?Q |- _ => apply (reflect_false_inv P Q) in H
end. | Ltac | t | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [
"Reflect",
"apply",
"reflect_false_inv",
"reflect_true_inv"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Reflect_andb : Reflect (T1 && T2)%bool (P1 /\ P2) (Q1 \/ Q2). | Proof.
destruct T1; destruct T2; t; constructor; tauto.
Qed. | Instance | Reflect_andb | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [
"Reflect"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Reflect_orb : Reflect (T1 || T2)%bool (P1 \/ P2) (Q1 /\ Q2). | Proof.
destruct T1; destruct T2; t; constructor; tauto.
Qed. | Instance | Reflect_orb | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [
"Reflect"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Reflect_negb : Reflect (negb T1)%bool Q1 P1. | Proof.
destruct T1; t; constructor; tauto.
Qed. | Instance | Reflect_negb | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [
"Reflect"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Reflect_RelDecCorrect (a b : T)
: Reflect (rel_dec a b) (eqt a b) (~(eqt a b)). | Proof.
eapply iff_to_reflect.
eapply rel_dec_correct.
Qed. | Instance | Reflect_RelDecCorrect | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [
"Reflect",
"iff_to_reflect"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
consider f | :=
let rec clean :=
match goal with
| |- true = true -> _ => intros _ ; clean
| |- false = true -> _ => discriminate
| |- ?P1 -> ?P2 =>
let H := fresh in intros H ; clean; revert H
| |- _ => idtac
end
in
(repeat match goal with
| [ H : context [ f ] |- _ ] =>
... | Ltac | consider | Tactics | theories/Tactics/Consider.v | [
"ExtLib.Core.RelDec"
] | [
"Reflect",
"SemiReflect",
"context",
"type"
] | The main tactic. [consider f] will perform case-analysis (using
[case]) on the function symbol [f] using a reflection-lemma that is
inferred by type-class resolution. | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 |
UIP_refl : forall {x : A} (p1 : x = x), p1 = refl_equal _. | intros.
eapply Eqdep_dec.UIP_dec. apply equiv_dec.
Qed. | Theorem | UIP_refl | Tactics | theories/Tactics/EqDep.v | [
"Coq.Classes",
"EquivDec",
"ExtLib.Structures.EqDep",
"Coq.Logic",
"Eqdep_dec"
] | [
"apply"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
UIP_equal : forall {x y : A} (p1 p2 : x = y), p1 = p2. | eapply Eqdep_dec.UIP_dec. apply equiv_dec.
Qed. | Theorem | UIP_equal | Tactics | theories/Tactics/EqDep.v | [
"Coq.Classes",
"EquivDec",
"ExtLib.Structures.EqDep",
"Coq.Logic",
"Eqdep_dec"
] | [
"apply"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
notVar X | :=
match X with
| _ _ => idtac
| _ _ _ => idtac
| _ _ _ _ => idtac
| _ _ _ _ _ => idtac
| _ _ _ _ _ _ => idtac
| _ _ _ _ _ _ _ => idtac
| _ _ _ _ _ _ _ _ => idtac
| _ _ _ _ _ _ _ _ _ => idtac
| _ _ _ _ _ _ _ _ _ _ => idtac
| _ _ _ _ _ _ _ _ _ _ _ => idtac
| _ _ _ _ _ _ _ _ ... | Ltac | notVar | Tactics | theories/Tactics/EqDep.v | [
"Coq.Classes",
"EquivDec",
"ExtLib.Structures.EqDep",
"Coq.Logic",
"Eqdep_dec"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
gen_refl | :=
repeat match goal with
| H : context [ @eq_refl ?X ?Y ] |- _ =>
generalize dependent (@eq_refl X Y)
| |- context [ @eq_refl ?X ?Y ] =>
generalize dependent (@eq_refl X Y)
end. | Ltac | gen_refl | Tactics | theories/Tactics/EqDep.v | [
"Coq.Classes",
"EquivDec",
"ExtLib.Structures.EqDep",
"Coq.Logic",
"Eqdep_dec"
] | [
"context"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
uip_all | :=
repeat match goal with
| [ H : _ = _ |- _ ] => rewrite H
| [ |- context [ match ?X in _ = t return _ with
| refl_equal => _
end ] ] => notVar X; generalize X
| [ |- context [ eq_rect_r _ _ ?X ] ] => notVar X; generalize X
... | Ltac | uip_all | Tactics | theories/Tactics/EqDep.v | [
"Coq.Classes",
"EquivDec",
"ExtLib.Structures.EqDep",
"Coq.Logic",
"Eqdep_dec"
] | [
"UIP_refl",
"context",
"notVar"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
uip_all' | :=
repeat match goal with
| [ H : _ = _ |- _ ] => rewrite H
| [ |- context [ match ?X in _ = t return _ with
| refl_equal => _
end ] ] => notVar X; generalize X
| [ |- context [ eq_rect_r _ _ ?X ] ] => notVar X; generalize X
... | Ltac | uip_all' | Tactics | theories/Tactics/EqDep.v | [
"Coq.Classes",
"EquivDec",
"ExtLib.Structures.EqDep",
"Coq.Logic",
"Eqdep_dec"
] | [
"UIP_refl",
"context",
"notVar"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
eq_rw_goal | :=
autorewrite with eq_rw. | Ltac | eq_rw_goal | Tactics | theories/Tactics/Equality.v | [
"ExtLib.Data.Eq"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
eq_rw_hyp H | :=
autorewrite with eq_rw in H. | Ltac | eq_rw_hyp | Tactics | theories/Tactics/Equality.v | [
"ExtLib.Data.Eq"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
eq_rw_star | :=
autorewrite with eq_rw in *. | Ltac | eq_rw_star | Tactics | theories/Tactics/Equality.v | [
"ExtLib.Data.Eq"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
forward_reason | :=
repeat match goal with
| H : exists x, _ |- _ =>
destruct H
| H : _ /\ _ |- _ => destruct H
| H' : ?X , H : ?X -> ?Y |- _ =>
match type of X with
| Prop => specialize (H H')
end
| H : ?X -> ?Y |- _ =>
mat... | Ltac | forward_reason | Tactics | theories/Tactics/Forward.v | [] | [
"assert",
"type"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
rwHyps | :=
repeat match goal with
[ H: ?l = ?r |- _] =>
match r with
| context [l] => idtac
| _ => rewrite -> H
end
end. | Ltac | rwHyps | Tactics | theories/Tactics/Forward.v | [] | [
"context"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
rwHypsR | :=
repeat match goal with
[ H: _ = _ |- _] => rewrite <- H
end. | Ltac | rwHypsR | Tactics | theories/Tactics/Forward.v | [] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
rwHypsA | :=
repeat match goal with
[ H: _ = _ |- _] => rewrite -> H in *
end. | Ltac | rwHypsA | Tactics | theories/Tactics/Forward.v | [] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
rwHypsRA | :=
repeat match goal with
[ H: _ = _ |- _] => rewrite <- H in *
end. | Ltac | rwHypsRA | Tactics | theories/Tactics/Forward.v | [] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
clear_trivials | :=
repeat match goal with
| [ H : ?T = ?T |- _ ] => clear H
| [ H : ?T <-> ?T |- _ ] => clear H
| [ H : ?T -> ?T |- _ ] => clear H
| [ H1 : ?T, H2 : ?T |- _ ] => clear H2
| [ H : True |- _ ] => clear H
| [ H : not False |- _ ] => clear H
end. | Ltac | clear_trivials | Tactics | theories/Tactics/Forward.v | [] | [] | based on a tactic written by Vincent Rahli | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 |
Hidden (P:Type) : Prop | :=
| hidden (p:P): Hidden P. | Inductive | Hidden | Tactics | theories/Tactics/Hide.v | [] | [] | The names of the tactics here come from the 2013 distribution
of Software Foundations (SF). The implementations are different, though:
1) The hiding mechanism is SF was not fully reliable:
tactics that compute on hypotheses could unhide stuff
2) Hiding in SF was always reversible. Here, unhiding only works
when provi... | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 |
show_hyp H | :=
destruct H as [H]. | Ltac | show_hyp | Tactics | theories/Tactics/Hide.v | [] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
hide_hyp H | :=
apply hidden in H. | Ltac | hide_hyp | Tactics | theories/Tactics/Hide.v | [] | [
"apply"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
show_hyps | :=
repeat match goal with
H: Hidden _ |- _ => show_hyp H end. | Ltac | show_hyps | Tactics | theories/Tactics/Hide.v | [] | [
"Hidden",
"show_hyp"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Injective (P : Prop) : Type | :=
{ result : Prop
; injection : P -> result
}. | Class | Injective | Tactics | theories/Tactics/Injection.v | [] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 |
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