dynamis-specs/TokenProof.tla at main · DynamisNetwork/dynamis-specs · GitHub

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----------------------------- MODULE TokenProof -----------------------------
(*
 * TLA+ Proof for Token Conservation of Funds
 * Uses TLAPS for machine-checked mathematical proof
 *)

EXTENDS Naturals, TLAPS

CONSTANTS Accounts  \* Set of account addresses

VARIABLES balances  \* Map: Account -> Natural

(***************************************************************************
 * Type Invariant
 ***************************************************************************)
TypeInvariant ==
    /\ balances \in [Accounts -> Nat]

(***************************************************************************
 * Total Supply - Sum of all balances
 ***************************************************************************)
TotalSupply ==
    \* Using bounded sum for finite Accounts
    LET Sum[S \in SUBSET Accounts] ==
        IF S = {} THEN 0
        ELSE LET a == CHOOSE x \in S : TRUE
             IN balances[a] + Sum[S \ {a}]
    IN Sum[Accounts]

(***************************************************************************
 * Conservation Invariant
 ***************************************************************************)
CONSTANT InitialSupply

Conservation == TotalSupply = InitialSupply

(***************************************************************************
 * Initial State
 ***************************************************************************)
InitAll ==
    /\ balances = [a \in Accounts |-> 0]

(***************************************************************************
 * Transfer Action
 ***************************************************************************)
Transfer(from, to, amount) ==
    /\ from \in Accounts
    /\ to \in Accounts
    /\ from # to
    /\ amount > 0
    /\ balances[from] >= amount
    /\ balances' = [balances EXCEPT
                    ![from] = @ - amount,
                    ![to] = @ + amount]

(***************************************************************************
 * THEOREM: Transfer Preserves Type Invariant
 ***************************************************************************)
THEOREM TransferPreservesType ==
    ASSUME TypeInvariant,
           NEW from \in Accounts,
           NEW to \in Accounts,
           NEW amount \in Nat,
           from # to,
           amount > 0,
           balances[from] >= amount
    PROVE  [balances EXCEPT ![from] = @ - amount, ![to] = @ + amount]
           \in [Accounts -> Nat]
PROOF
  <1>1. balances[from] - amount \in Nat
    BY SMT
  <1>2. balances[to] + amount \in Nat
    BY SMT
  <1>3. QED
    BY <1>1, <1>2

(***************************************************************************
 * THEOREM: Transfer Preserves Total (Conservation)
 * The key financial invariant: no tokens are created or destroyed
 ***************************************************************************)
THEOREM TransferPreservesTotal ==
    ASSUME TypeInvariant,
           NEW from \in Accounts,
           NEW to \in Accounts,
           NEW amount \in Nat,
           from # to,
           amount > 0,
           balances[from] >= amount
    PROVE  \A a \in Accounts :
           [balances EXCEPT ![from] = @ - amount, ![to] = @ + amount][a]
           = CASE a = from -> balances[from] - amount
               [] a = to   -> balances[to] + amount
               [] OTHER    -> balances[a]
PROOF OBVIOUS

=============================================================================
\* Generated by TLAPS for Dynamis blockchain verification