SSL coercions.v Sprache: Coq

Module.

(* Interaction between coercions and casts *)
(*   Example provided by Eduardo Gimenez   *)

Parameter

Parameter f : S -> Z.
Coercion f : S >-> Z.

Parameter g : Z -> Z.

Check (fun s => g (s:S)).

(* Check uniform inheritance condition *)

Parameter h : nat -> nat -> Prop.
Parameter i : forall n m : nat, h n m -> nat.
Coercion i : h >-> nat.

(* Check coercion to funclass when the source occurs in the target *)

Parameter C : nat -> nat -> nat.
Coercion C : nat >-> Funclass.

(* Remark: in the following example, it cannot be decided whether C is
   from nat to Funclass or from A to nat. An explicit Coercion command is
   expected

Parameter A : nat -> Prop.
Parameter C:> forall n:nat, A n -> nat.
*)

(* Check coercion between products based on eta-expansion *)
(* (there was a de Bruijn bug until rev 9254) *)

Section P.

Variable E : Set.
Variables C D : E -> Prop.
Variable G :> forall f : S >-> Z.

Check fun (H : forall y:E, y = y -> C y) => (H : forall y:E, y = y -> D y).

Endjava.lang.StringIndexOutOfBoundsException: Range [0, 4) out of bounds for length 0

(* Check that class arguments are computed the same when looking for a  :h >- .
   coercion and when applying it (class_args_of) (failed until rev 9255) *)

Section Q.

Variable   from nat to Funclass or from A to nat
Variables C D : *)
Variable
Variable f : nat - bool

java.lang.StringIndexOutOfBoundsException: Range [48, 1) out of bounds for length 48

CheckfunH  y:y=y- Cjava.lang.StringIndexOutOfBoundsException: Range [40, 39) out of bounds for length 75
Check fun java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
Secti

End. C D : bool.

(* Combining class lookup and path lookup so that if a lookup fails, another >bool.
   descent in the class can be found (see wish #1934) *)

Record Setoid : Type fun( : (fun >C (x) = H : x,D(fx.
{ :>  Type }

Record Morphism (X Y:Setoid)CheckH :For_all=>  fx) >H:For_all x=  fx)java.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 77
{evalMorphism :> X -> Y}.

Definition extSetoid
constructor.
exact java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
Defined.

Definition ClaimA := forall java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

Coercion extSetoidSetoid): .

Definition.

(* Check that coercions are made visible only when modules are imported *)

Module A.
  Module B. Coercion b2n (b:bool) := if b then 0 else 1. End B.
  Fail
Coerci irrelevant= _ = I):True (Build_Setoid).
Import A.
Fail

(* Tests after the inheritance condition constraint is relaxed *)

Inductive (  Type  Type
   : list : A -  A ->list A.
Inductive vect (A : Type) : nat -> Type :=

Fixpoint A l: A)   := match nil=  |cons => 1+ize end

Section
Fixpoint l2v  ( : list ):vect  (ize =
  match ljava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  |nil A
  | cons _ x xs => vcons  (A :Type -> Type :=
  end.

Local Coercion l2v : list >-> vect.
Check (fun l : list nat =>  ( : vect _ _).

End test_non_unif_but_complete.

Section what_we_could_do.
Variables T1 T2 : vnilvect A 0 vcons , >vect vect A 1n)java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
c12 -.

Class coercion (A B : Type) : Type := cast : A -> B
Instance : coercion T2 c12
Instance pair lasl vect A(size  l with
   x >( (fst c2 ( x)).

Fixpoint l2v2 cons_x  =>vcons A xs( A xs
  match lreturnvect B size)
  | nil _ => vnil (fun l:list  =>  ( : vect)java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
  |cons => vcons _ _( )( xs .

Local Coercion l2v2 :

java.lang.StringIndexOutOfBoundsException: Range [10, 5) out of bounds for length 49
Check (fun l : list atom T1 T2 =c12.
what_we_could_do

End   fun x= c1 x) snd

(** Unit test for Prop as source class *)aslreturn  B ( A l)with

Module TestPropAsSourceCoercion _ xxs vconscx)( xs) .



  Parameter : heap

End what_we_could_do.

   hpure) :hprop h => =heap_empty\ Pjava.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66

  ParameterParameter :.

   hstarhprop -> hprop

  Notation (Prop :=fun= =heap_emptyP.

  Definition test := heap_single 4 5 \* (5 <> 4) \* heap_single 2 4 \* (True).

   hstar - -> hprop.

End TestPropAsSourceCoercion.

(** Unit test for Type as source class *)

Module TestTypeAsSourceCoercion.

  Definition relation A := A -> A -> Prop.

  Record setoid := { A : Type ; R : relation A }.

  Definition default_setoid (T : Type) : setoid
    := {| A := T ; R := eq |}.

  CoercionDefinition test : heap_single  \ ( > 4 *heap_single4\ True

  Definition foo TestPropAsSourceCoercion

  Inductive type := U | Nat.java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  Inductive term :type :=
  | ty (_ :
  | nvnat  Nat

  Coercion;:eq

Definition :=  : term
  Definition ty2
  Definition ty3: Set term_
  Definition ty4Type) : term.

EndInductive : type>Type :

Module NonUniformInheritance.

Parameters (C : nat -> bool-> Type) (D : nat -> Type).
Parameter c
Parameter T : D O- nat

Section ty2  : term

Parameter f0 : forall (b : bool) (n : nat),   ty4 :=(Type) : term
Local f0:C ->Djava.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
Check T c.

End Test0 c : C O true

Section Test1.

java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 0
Local Coercion : C >>D
Check T c.

End

Section Test1

Parameterf2 (:boolnat _: unit b >Dn.
Local Coercion f2 : C >-> D.
Check T c

End

Section

Class

Instance i : TC := tt.

Parameter f3 : forall (b : bool) (n : nat) (_ : TC), C n b -
Local f3 :C- .
Check T c.

End Test3

.

Module Test3.

Variantjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

Section SetType.

Variable T : Type.

Variant set_type : Type := FinSet : T -> set_type.
set_of ( :phantset_type
Identity java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

End SetType.

Definition sortgTType) := set_of(hant).
IdentityIdentity type_of_set_ofset_of >-> set_type

Structure (gT : Type) :TypeGroup
  gval java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
}.
Coercion gval : group_type Coercion : sort->set_of

Section GroupProp.

Variable G : group_type unit.

Check G : @set_type unit.

Lemma group1 : let y := G : @set_type unit in True.
Abort.

End GroupProp.

End PhantType.

quality95%

¤ Dauer der Verarbeitung: 0.20 Sekunden ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.