Verificación formal de los contratos inteligentes de Tezos

Siestamos de acuerdoen queelpropósito de los análisisesprobarpropiedades y ayudar a los usuarios de contratosinteligentes a comprenderlas,diría:

1. Valores:estudiar qué valorespuedetomar cadaelemento del almacenamientoen elfuturo.
2. Efectos:estudiar quéefectospueden ocurriren elfuturo:normalmente,quétransferenciaspueden ocurrir yen qué condiciones.
3. Propiedad: quiénpuede activar un cambioen quéparte del almacenamiento.

If we agree that the purpose of analyses is to both prove properties and help users of smart contracts to understand them, I would say:

1. Values: studying what values each element of the storage can take in the future.
2. Effects: studying what effects can occur in the future: typically what transfers can occur and on what conditions.
3. Ownership: who can trigger a change on what part of the storage.

Así queestaes unagranpregunta y creo que haymuchaspersonasmás calificadas que yo,pero ofreceré unaguíainicial.

En Software Foundations,un libro sobre Coq,se habla de un lenguajeimplícito llamado Imp. Imptiene una sintaxis como:

 Z ::= X;;
Y ::= 1;;
WHILE ~(Z = 0) DO
    Y ::= Y * Z;;
    Z ::= Z - 1
END
 

Lo que deberíaentendersefácilmente como una asignación y unbucle simple. ::=espara asignación,un ciclo while hasta que zes 0. En Pythonesto sería:

 def foo(x):
    z = x
    y = 1
    while z != 0:
        y = y * z
        z -= 1
 

A continuación,podemos definirparte de la lógica subyacente de los símbolos. Porejemplo,

 Fixpoint aeval (a : aexp) : nat :=
  match a with
  | ANum n ⇒ n
  | APlus a1 a2 ⇒ (aeval a1) + (aeval a2)
  | AMinus a1 a2 ⇒ (aeval a1) - (aeval a2)
  | AMult a1 a2 ⇒ (aeval a1) * (aeval a2)
  end.
 

Esto definirá las operaciones aritméticas.

Tambiénpuede analizarpalabras reservadas,como:

 Inductive com : Type :=
  | CSkip
  | CBreak (* <--- NEW *)
  | CAss (x : string) (a : aexp)
  | CSeq (c1 c2 : com)
  | CIf (b : bexp) (c1 c2 : com)
  | CWhile (b : bexp) (c : com).
 

Luego,podría asignarelprograma aestostipos definidosen Coq,como:

 CSeq (CAss Z X)
        (CSeq (CAss Y (S O))
              (CWhile (BNot (BEq Z O))
                      (CSeq (CAss Y (AMult Y Z))
                            (CAss Z (AMinus Z (S O))))))
 

Entoncespodemos hacer algunaspruebas sobre lasfunciones o declaraciones hechasen este lenguaje usando lógicaformal. Aquí hay unejemplo que demuestra que si znoes 4,entonces xnoes 2:

 Example ceval_example1:
  empty_st =[
     X ::= 2;;
     TEST X ≤ 1
       THEN Y ::= 3
       ELSE Z ::= 4
     FI
  ]⇒ (Z !-> 4 ; X !-> 2).
Proof.
  (* We must supply the intermediate state *)
  apply E_Seq with (X !-> 2).
  - (* assignment command *)
    apply E_Ass. reflexivity.
  - (* if command *)
    apply E_IfFalse.
    reflexivity.
    apply E_Ass. reflexivity.
Qed.
 

Por ahora,espero que la aplicación a un contratointeligente sea algoevidente. Sipudiera abstraerel contratointeligenteen Coq,podría usar Coqparaprobar rigurosamente algunos componentes de su contratointeligente. Tambiénexiste laposibilidad de describir las condiciones de un contratointeligenteen Coq y compilarlopara Michelson,peroesaes solo unaposibilidad yno he vistoningunaevidencia de su construcción.

ref: https://softwarefoundations.cis.upenn.edu/lf- current/Imp.html

So this is a huge question and I think there are many people more qualified than me, but I'll offer some initial guidance.

In Software Foundations, a book on Coq, they talk about an implied language called Imp. Imp has a syntax like:

Z ::= X;;
Y ::= 1;;
WHILE ~(Z = 0) DO
    Y ::= Y * Z;;
    Z ::= Z - 1
END

Which should be somewhat easily understood as assignment and some simple looping. ::= is for assignment, a while loop until z is 0. In python this would be:

def foo(x):
    z = x
    y = 1
    while z != 0:
        y = y * z
        z -= 1

We can then define some of the underlying logic for the symbols. For example,

Fixpoint aeval (a : aexp) : nat :=
  match a with
  | ANum n ⇒ n
  | APlus a1 a2 ⇒ (aeval a1) + (aeval a2)
  | AMinus a1 a2 ⇒ (aeval a1) - (aeval a2)
  | AMult a1 a2 ⇒ (aeval a1) * (aeval a2)
  end.

This will define arithmetic operations.

You could also parse out reserved words, like:

Inductive com : Type :=
  | CSkip
  | CBreak (* <--- NEW *)
  | CAss (x : string) (a : aexp)
  | CSeq (c1 c2 : com)
  | CIf (b : bexp) (c1 c2 : com)
  | CWhile (b : bexp) (c : com).

Then you could map the program to these defined types in Coq, like:

CSeq (CAss Z X)
        (CSeq (CAss Y (S O))
              (CWhile (BNot (BEq Z O))
                      (CSeq (CAss Y (AMult Y Z))
                            (CAss Z (AMinus Z (S O))))))

We can then make some proofs about the functions or statements made in this language using formal logic. Here is an example proving that if z is not 4, then x is not 2:

Example ceval_example1:
  empty_st =[
     X ::= 2;;
     TEST X ≤ 1
       THEN Y ::= 3
       ELSE Z ::= 4
     FI
  ]⇒ (Z !-> 4 ; X !-> 2).
Proof.
  (* We must supply the intermediate state *)
  apply E_Seq with (X !-> 2).
  - (* assignment command *)
    apply E_Ass. reflexivity.
  - (* if command *)
    apply E_IfFalse.
    reflexivity.
    apply E_Ass. reflexivity.
Qed.

By now I hope the application to a smart contract is somewhat apparent. If you could abstract the smart contract into Coq, you could use Coq to prove some components of your smart contract rigorously. There is also potential to outline conditions of a smart contract in Coq and compile it to Michelson, but that's just a possibility and I haven't seen any evidence of its construction.

ref: https://softwarefoundations.cis.upenn.edu/lf-current/Imp.html