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
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neg_eqv {T} {E:Eqv T} (x:T) (y:T) : Prop | := not (eqv x y). | Definition | neg_eqv | Programming | theories/Programming/Eqv.v | [
"Equivalence",
"ExtLib.Core.RelDec",
"EqvNotation"
] | [
"Eqv"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
EqvWF T | :=
{ eqvWFEqv : Eqv T
; eqvWFEquivalence : Equivalence eqv
}. | Class | EqvWF | Programming | theories/Programming/Eqv.v | [
"Equivalence",
"ExtLib.Core.RelDec",
"EqvNotation"
] | [
"Eqv"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
EqvWF_Build {T} {E:Eqv T} {EV:Equivalence eqv} : EqvWF T | :=
{ eqvWFEqv := E ; eqvWFEquivalence := EV }. | Instance | EqvWF_Build | Programming | theories/Programming/Eqv.v | [
"Equivalence",
"ExtLib.Core.RelDec",
"EqvNotation"
] | [
"Eqv",
"EqvWF"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
eqv_dec {T} {E:Eqv T} {R:RelDec eqv} | := rel_dec. | Definition | eqv_dec | Programming | theories/Programming/Eqv.v | [
"Equivalence",
"ExtLib.Core.RelDec",
"EqvNotation"
] | [
"Eqv",
"RelDec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
neg_eqv_dec {T} {E:Eqv T} {R:RelDec eqv} x y | := negb (rel_dec x y). | Definition | neg_eqv_dec | Programming | theories/Programming/Eqv.v | [
"Equivalence",
"ExtLib.Core.RelDec",
"EqvNotation"
] | [
"Eqv",
"RelDec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
eqv_dec_p (x:T) (y:T) : {eqv x y} + {~eqv x y} | := rel_dec_p x y. | Definition | eqv_dec_p | Programming | theories/Programming/Eqv.v | [
"Equivalence",
"ExtLib.Core.RelDec",
"EqvNotation"
] | [
"rel_dec_p"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
neg_eqv_dec_p (x:T) (y:T) : {~eqv x y} + {eqv x y} | := neg_rel_dec_p x y. | Definition | neg_eqv_dec_p | Programming | theories/Programming/Eqv.v | [
"Equivalence",
"ExtLib.Core.RelDec",
"EqvNotation"
] | [
"neg_rel_dec_p"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
injection_eqv_equivalence : Equivalence (eqv (T:=U)). | Proof. repeat constructor ;
unfold Reflexive ; unfold Symmetric ; unfold Transitive ; intros.
apply injResp. reflexivity.
apply injResp. apply injResp in H. symmetry. auto.
apply injResp. apply injResp in H. apply injResp in H0.
transitivity (inj y) ; auto.
Qed. | Definition | injection_eqv_equivalence | Programming | theories/Programming/Eqv.v | [
"Equivalence",
"ExtLib.Core.RelDec",
"EqvNotation"
] | [
"apply"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"f $ x" | := (f x)
(at level 99, x at level 99, right associativity, only parsing). | Notation | f $ x | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"'begin' e1 'end'" | := ((e1))
(at level 0, only parsing). | Notation | 'begin' e1 'end' | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
deprecated_uncurry A B C (f:A -> B -> C) (x:A * B) : C | := let (a,b) := x in f a b. | Definition | deprecated_uncurry | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
uncurry | := deprecated_uncurry. | Notation | uncurry | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [
"deprecated_uncurry"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
deprecated_curry {A B C} (f : A * B -> C) (a : A) (b : B) : C | := f (a, b). | Definition | deprecated_curry | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
curry | := deprecated_curry. | Notation | curry | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [
"deprecated_curry"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
deprecated_uncurry_curry : forall A B C (f : A -> B -> C) a b,
curry (uncurry f) a b = f a b. | Proof.
unfold curry, uncurry.
reflexivity.
Qed. | Lemma | deprecated_uncurry_curry | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [
"curry",
"uncurry"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
uncurry_curry | := deprecated_uncurry_curry. | Notation | uncurry_curry | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [
"deprecated_uncurry_curry"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
deprecated_curry_uncurry : forall A B C (f : A * B -> C) ab,
uncurry (curry f) ab = f ab. | Proof.
unfold uncurry, curry.
destruct ab.
reflexivity.
Qed. | Lemma | deprecated_curry_uncurry | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [
"curry",
"uncurry"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
curry_uncurry | := deprecated_curry_uncurry. | Notation | curry_uncurry | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [
"deprecated_curry_uncurry"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
deprecated_zip A B (xs:list A) (ys:list B) : list (A * B) | :=
match xs, ys with
| [], _ => []
| _, [] => []
| x::xs, y::ys => (x,y)::deprecated_zip xs ys
end
. | Fixpoint | deprecated_zip | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
zip | := deprecated_zip. | Notation | zip | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [
"deprecated_zip"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
deprecated_unzip A B (xys:list (A * B)) : list A * list B | :=
match xys with
| [] => ([], [])
| (x,y)::xys => let (xs,ys) := deprecated_unzip xys in (x::xs,y::ys)
end. | Fixpoint | deprecated_unzip | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
unzip | := deprecated_unzip. | Notation | unzip | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [
"deprecated_unzip"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
sum_tot {A} (x:A + A) : A | := match x with inl a => a | inr a => a end. | Definition | sum_tot | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
forEach A B (xs:list A) (f:A -> B) : list B | := map f xs. | Definition | forEach | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
lsingleton {A} (x:A) : list A | := [x]. | Definition | lsingleton | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
firstf {A B C} (f:A->C) (xy:A*B) : C*B | :=
let (x,y) := xy in (f x, y). | Definition | firstf | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
secondf {A B C} (f:B->C) (xy:A*B) : A*C | :=
let (x,y) := xy in (x, f y). | Definition | secondf | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
update {K V} {kRealDec:RelDec (@eq K)} x v l : list (K * V) | :=
match l with
| [] => [(x,v)]
| (y,w)::l' => if eq_dec x y then (x,v)::l' else (y,w)::update x v l'
end. | Fixpoint | update | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [
"RelDec",
"eq_dec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
updateMany {K V} {kRealDec:RelDec (@eq K)}
(ups:list (K * V)) (init:list (K * V)) : list (K * V) | :=
fold_right (uncurry update) init ups. | Definition | updateMany | Programming | theories/Programming/Extras.v | [
"List",
"String",
"ExtLib.Structures.Monads",
"ExtLib.Core.RelDec",
"MonadNotation",
"ListNotations",
"FunNotation"
] | [
"RelDec",
"fold_right",
"uncurry",
"update"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Injection (x : Type) (t : Type) | := inject : x -> t. | Class | Injection | Programming | theories/Programming/Injection.v | [
"Coq.Strings.Ascii",
"Coq.Strings.String"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Injection_refl {T : Type} : Injection T T | :=
{ inject := @id T }. | Instance | Injection_refl | Programming | theories/Programming/Injection.v | [
"Coq.Strings.Ascii",
"Coq.Strings.String"
] | [
"Injection"
] | Class Projection x t := { project : t -> x ; pmodify : (x -> x) -> (t -> t) }. | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 |
Injection_ascii_string : Injection ascii string | :=
{ inject a := String a EmptyString }. | Instance | Injection_ascii_string | Programming | theories/Programming/Injection.v | [
"Coq.Strings.Ascii",
"Coq.Strings.String"
] | [
"Injection"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Injection_ascii_string_cons : Injection ascii (string -> string) | :=
{ inject := String }. | Instance | Injection_ascii_string_cons | Programming | theories/Programming/Injection.v | [
"Coq.Strings.Ascii",
"Coq.Strings.String"
] | [
"Injection"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Lte T | := { lte : T -> T -> Prop }. | Class | Lte | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
neg_lte {T} {L:Lte T} (x:T) (y:T) : Prop | := not (lte x y). | Definition | neg_lte | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"Lte"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
lt {T} {L:Lte T} x y | := lte x y /\ ~lte y x. | Definition | lt | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"Lte"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
neg_lt {T} {L:Lte T} x y | := not (lt x y). | Definition | neg_lt | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"Lte",
"lt"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
lt_RelDec {T} {L:Lte T} {RD:RelDec lte} : RelDec lt | :=
{ rel_dec x y := (rel_dec x y && negb (rel_dec y x))%bool }. | Instance | lt_RelDec | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"Lte",
"RelDec",
"lt"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
lt_RelDecCorrect {T} {L:Lte T} {RD:RelDec lte} {RDC:RelDec_Correct RD}
: RelDec_Correct lt_RelDec. | Proof. constructor.
intros ; constructor ; intros.
unfold rel_dec in H. simpl in H. apply andb_true_iff in H. destruct H.
unfold lt. constructor. apply rel_dec_correct. auto.
apply neg_rel_dec_correct. simpl in H0.
apply negb_true_iff in H0. auto.
unfold lt in H. destruct H. unfold rel_dec. simpl. app... | Instance | lt_RelDecCorrect | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"Lte",
"RelDec",
"RelDec_Correct",
"apply",
"lt",
"lt_RelDec",
"neg_rel_dec_correct"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
LteWF T | :=
{ lteWFLte : Lte T
; lteWFPreOrder : PreOrder lte
}. | Class | LteWF | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"Lte"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
LteWF_Build {T} {L:Lte T} {PO:PreOrder lte} : LteWF T | :=
{ lteWFLte := L ; lteWFPreOrder := PO }. | Instance | LteWF_Build | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"Lte",
"LteWF"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
lte_dec {T} {L:Lte T} {R:RelDec lte} | := rel_dec. | Definition | lte_dec | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"Lte",
"RelDec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
neg_lte_dec {T} {L:Lte T} {R:RelDec lte} x y | := negb (lte_dec x y). | Definition | neg_lte_dec | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"Lte",
"RelDec",
"lte_dec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
lt_dec {T} {L:Lte T} {R:RelDec lte} | := rel_dec. | Definition | lt_dec | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"Lte",
"RelDec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
neg_lt_dec {T} {L:Lte T} {R:RelDec lte} x y | := negb (lt_dec x y). | Definition | neg_lt_dec | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"Lte",
"RelDec",
"lt_dec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
lte_dec_p (x:T) (y:T) : {lte x y} + {~lte x y} | := rel_dec_p x y. | Definition | lte_dec_p | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"rel_dec_p"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
neg_lte_dec_p (x:T) (y:T) : {~lte x y} + {lte x y} | := neg_rel_dec_p x y. | Definition | neg_lte_dec_p | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"neg_rel_dec_p"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
lt_dec_p (x:T) (y:T) : {lt x y} + {~lt x y} | := rel_dec_p x y. | Definition | lt_dec_p | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lt",
"rel_dec_p"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
neg_lt_dec_p (x:T) (y:T) : {~lt x y} + {lt x y} | := neg_rel_dec_p x y. | Definition | neg_lt_dec_p | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lt",
"neg_rel_dec_p"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x <=! y" | := (lte_dec x y)
(at level 35, no associativity). | Notation | x <=! y | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lte_dec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x <=! y <=! z" | := (lte_dec x y /\ lte_dec y z)
(at level 35, y at next level, no associativity). | Notation | x <=! y <=! z | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lte_dec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x >=! y" | := (lte_dec y x)
(at level 35, no associativity, only parsing). | Notation | x >=! y | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lte_dec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x >=! y >=! z" | := (lte_dec z y /\ lte_dec y x)
(at level 35, y at next level, no associativity). | Notation | x >=! y >=! z | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lte_dec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x <! y" | := (lt_dec x y)
(at level 35, no associativity). | Notation | x <! y | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lt_dec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x <! y <! z" | := (lt_dec x y /\ lt_dec y z)
(at level 35, y at next level, no associativity). | Notation | x <! y <! z | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lt_dec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x >! y" | := (lt_dec y x)
(at level 35, no associativity, only parsing). | Notation | x >! y | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lt_dec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x >! y >! z" | := (lt_dec z y /\ lt_dec y x)
(at level 35, y at next level, no associativity). | Notation | x >! y >! z | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lt_dec"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x <=? y" | := (lte_dec_p y x)
(at level 35, no associativity). | Notation | x <=? y | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lte_dec_p"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x <=? y <=? z" | := (lte_dec_p x y /\ lte_dec_p y z)
(at level 35, y at next level, no associativity). | Notation | x <=? y <=? z | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lte_dec_p"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x >=? y" | := (lte_dec_p y x)
(at level 35, no associativity, only parsing). | Notation | x >=? y | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lte_dec_p"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x >=? y >=? z" | := (lte_dec_p z y /\ lte_dec_p y x)
(at level 35, y at next level, no associativity, only parsing). | Notation | x >=? y >=? z | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lte_dec_p"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x <? y" | := (lt_dec_p y x)
(at level 35, no associativity). | Notation | x <? y | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lt_dec_p"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x <? y <? z" | := (lt_dec_p x y /\ lt_dec_p y z)
(at level 35, y at next level, no associativity). | Notation | x <? y <? z | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lt_dec_p"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x >? y" | := (lt_dec_p y x)
(at level 35, no associativity, only parsing). | Notation | x >? y | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lt_dec_p"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x >? y >? z" | := (lt_dec_p z y /\ lt_dec_p y x)
(at level 35, y at next level, no associativity, only parsing). | Notation | x >? y >? z | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lt_dec_p"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x <=. y" | := (lte x y)
(at level 70, no associativity). | Notation | x <=. y | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x <=. y <=. z" | := (lte x y /\ lte y z)
(at level 70, y at next level, no associativity). | Notation | x <=. y <=. z | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x >=. y" | := (lte y x)
(at level 70, no associativity, only parsing). | Notation | x >=. y | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x >=. y >=. z" | := (lte z y /\ lte y x)
(at level 70, y at next level, no associativity, only parsing). | Notation | x >=. y >=. z | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x <. y" | := (lt x y)
(at level 70, no associativity). | Notation | x <. y | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lt"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x <. y <. z" | := (lt x y /\ lt y z)
(at level 70, y at next level, no associativity). | Notation | x <. y <. z | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lt"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x >. y" | := (lt y x)
(at level 70, no associativity, only parsing). | Notation | x >. y | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lt"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x >. y >. z" | := (lt z y /\ lt y x)
(at level 70, y at next level, no associativity, only parsing). | Notation | x >. y >. z | Programming | theories/Programming/Le.v | [
"Coq.Bool.Bool",
"Equivalence",
"ExtLib.Core.RelDec"
] | [
"lt"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
showM@{T} : Type@{Ushow} | :=
forall m : Type@{T}, Injection ascii m -> Monoid m -> m. | Definition | showM | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"Injection",
"Monoid"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
ShowScheme@{t} (T : Type@{t}) : Type | :=
{ show_mon : Monoid@{t} T
; show_inj : Injection ascii T
}. | Class | ShowScheme | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"Injection",
"Monoid"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
ShowScheme_string : ShowScheme string | :=
{ show_mon := Monoid_string_append
; show_inj := fun x => String x EmptyString
}. | Instance | ShowScheme_string | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"Monoid_string_append",
"ShowScheme"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
ShowScheme_string_compose : ShowScheme (string -> string) | :=
{ show_mon := Monoid_compose string
; show_inj := String
}. | Instance | ShowScheme_string_compose | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"Monoid_compose",
"ShowScheme"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
runShow {T} {M : ShowScheme T} (m : showM) : T | :=
m _ show_inj show_mon. | Definition | runShow | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"ShowScheme",
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Show@{t m} (T : Type@{t}) : Type | :=
show : T -> showM@{m}. | Class | Show | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
to_string {T} {M : Show T} (v : T) : string | :=
runShow (show v) ""%string. | Definition | to_string | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"Show",
"runShow"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
empty : showM | :=
fun _ _ m => monoid_unit m. | Definition | empty | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
cat (a b : showM) : showM | :=
fun _ i m => monoid_plus m (a _ i m) (b _ i m). | Definition | cat | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
Injection_ascii_showM : Injection ascii showM | :=
fun v => fun _ i _ => i v. | Instance | Injection_ascii_showM | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"Injection",
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
show_exact (s : string) : showM | :=
match s with
| EmptyString => empty
| String a s' => cat (inject a) (show_exact s')
end. | Fixpoint | show_exact | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"cat",
"empty",
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
"x << y" | := (cat x%show y%show) (at level 100) : show_scope. | Notation | x << y | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"cat"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
show_exact : string >-> showM. | Coercion | show_exact | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | ||
_inject_char : ascii -> showM | := inject. | Definition | _inject_char | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
_inject_char : ascii >-> showM. | Coercion | _inject_char | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | ||
indent (indent : showM) (v : showM) : showM | :=
let nl := Ascii.ascii_of_nat 10 in
fun _ inj mon =>
v _ (fun a => if eq_dec a nl
then monoid_plus mon (inj a) (indent _ inj mon)
else inj a) mon. | Definition | indent | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"eq_dec",
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
sepBy {T : Type}
{F : Foldable T showM} (sep : showM) (ls : T) : showM | :=
match
fold (fun s acc =>
match acc with
| None => Some s
| Some x => Some (x << sep << s)
end) None ls
with
| None => empty
| Some s => s
end. | Definition | sepBy | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"Foldable",
"empty",
"fold",
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
sepBy_f (sep : showM) (ls : T) : showM | :=
match
fold (fun s acc =>
match acc with
| None => Some (f s)
| Some x => Some (x << sep << f s)
end) None ls
with
| None => empty
| Some s => s
end. | Definition | sepBy_f | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"empty",
"fold",
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
wrap (before after : showM) (x : showM) : showM | :=
cat before (cat x after). | Definition | wrap | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"cat",
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
sum_Show@{a m}
{A : Type@{a}} {B : Type@{a}} {AS:Show@{a m} A} {BS:Show@{a m} B}
: Show@{a m} (A+B) | :=
fun s =>
let (tag, payload) :=
match s with
| inl a => (show_exact "inl"%string, show a)
| inr b => (show_exact "inr"%string, show b)
end
in
"("%char <<
tag <<
" "%char <<
payload <<
")"%char. | Definition | sum_Show | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"Show",
"show_exact"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
foldable_Show : Show B | :=
{ show s := sepBy_f show (show_exact ", "%string) s }. | Instance | foldable_Show | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"Show",
"sepBy_f",
"show_exact"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
iter_show (ss : list showM) : showM | :=
match ss with
| nil => empty
| cons s ss => cat s (iter_show ss)
end. | Fixpoint | iter_show | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"cat",
"empty",
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
unit_Show : Show unit | :=
{ show u := "tt"%string }. | Instance | unit_Show | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"Show"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
bool_Show : Show bool | :=
{ show b := if b then "true"%string else "false"%string }. | Instance | bool_Show | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"Show"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
ascii_Show : Show ascii | :=
fun a => "'"%char << a << "'"%char. | Instance | ascii_Show | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"Show"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
string_Show : Show string | :=
{ show s := """"%char << s << """"%char }. | Instance | string_Show | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"Show"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 | |
nat_show (n:nat) {measure n} : showM :=
if Compare_dec.le_gt_dec n 9 then
inject (Char.digit2ascii n)
else
let n' := Nat.div n 10 in
(@nat_show n' _) << (inject (Char.digit2ascii (n - 10 * n'))). | Next Obligation.
assert (Nat.div n 10 < n) ; eauto.
eapply Nat.div_lt.
match goal with [ H : n > _ |- _ ] => inversion H end; apply Nat.lt_0_succ.
repeat constructor.
Defined. | Fixpoint | nat_show | Programming | theories/Programming/Show.v | [
"Coq",
"Ascii",
"String",
"Coq.Program",
"Wf",
"BinPos",
"ZArith",
"ExtLib.Structures.Monoid",
"ExtLib.Structures.Reducible",
"ExtLib.Programming.Injection",
"ExtLib.Data.Char",
"ExtLib.Data.String",
"ExtLib.Data.Fun",
"ExtLib.Core.RelDec",
"ShowNotation"
] | [
"apply",
"assert",
"digit2ascii",
"showM"
] | https://github.com/coq-community/coq-ext-lib | ddd03d257f6b85a93bfaa0ed4d03658e0ddf5075 |
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