## Dafny compilation to Boogie

### {:opaque} attribute

During verification in Boogie, all functions are given an extra first parameter, which is the fuel (represented in Boogie by unary numbers, e.g. $LS($LS($LZ)) is a fuel of two). To unroll a function, axioms ensure that a recursive call is provided with the current fuel minus 1, so that we don’t unroll undefinitely. Normal behavior: When verifying a method or a function, Dafny will look at every assert. If it finds one, every function call inside it will use a fuel argument of at least 2 ($LS($LS($LZ))), meaning the verifier will be able to unroll the function’s body twice for this assertion. When this assertion is proven, Dafny provides an assume about the result, but in this case the functions are provided a fuel of only 1 ($LS($LZ)), meaning it unrolls the body only once.

Opaque behavior: When Dafny sees an {:opaque} attribute on a function foo, Dafny declares to Boogie two unknown constants StartFuel_f and StartFuelAssert_f. It uses StartFuelAssert_f in lieu of the default fuel ($LS($LS($LZ))) in the context of assert statements or expressions, and StartFuel_f in lieu of the default fuel ($LS($LZ)) in the context of the assume that immediately follows the assert. These two constants don’t have any axioms so, by default, the verifier is unable to unroll the functions and they behave like uninterpreted functions. Reveal lemma: Every statement (or part of expression) reveal foo(), bar(); is translated to calls to lemmas reveal_foo(); reveal_bar();. Such lemmas are defined in Dafny and with special attribute provide the postcondition that 1) StartFuel_f is $LS(MoreFuel_f) (where MoreFuel_f is an declared constant without axiom), and StartFuelAssert_f is $LS($LS(MoreFuel_f)). This makes the call to a function the same as if it was not opaque.

  lemma {:axiom} {:opaque_reveal} {:auto_generated} {:fuel foo,1,2} reveal_foo()


The {:fuel foo,1,2} annotation in Dafny corresponds to the Boogie equivalent of:

ensures StartFuel_f = $LS(MoreFuel_f) ensures StartFuelAssert_f =$LS(\$LS(MoreFuel_f))