38 lines
1,021 B
Text
38 lines
1,021 B
Text
new_frontend
|
|
|
|
/-
|
|
This example demonstratea that when we are using `nativeRefl!`,
|
|
we are also trusting the correctness of `implementedBy` annotations,
|
|
foreign functions (i.e., `[extern]` annotations), etc.
|
|
-/
|
|
def g (b : Bool) := false
|
|
|
|
/-
|
|
The following `implementedBy` is telling the compiler
|
|
"trust me, `g` does implement `f`"
|
|
which is clearly false in this example.
|
|
-/
|
|
@[implementedBy g]
|
|
def f (b : Bool) := b
|
|
|
|
theorem fConst (b : Bool) : f b = false :=
|
|
match b with
|
|
| true =>
|
|
/- The following `nativeRefl!` is going to use `g` to evaluate `f`
|
|
because of the `implementedBy` directive. -/
|
|
have (f true) = false from nativeRefl! (f true);
|
|
this
|
|
| false => rfl
|
|
|
|
theorem trueEqFalse : true = false :=
|
|
have h₁ : f true = true from rfl;
|
|
have h₂ : f true = false from fConst true;
|
|
Eq.trans h₁.symm h₂
|
|
|
|
/-
|
|
We managed to prove `False` using the unsound annotation `implementedBy` above.
|
|
-/
|
|
theorem unsound : False :=
|
|
Bool.noConfusion trueEqFalse
|
|
|
|
#print axioms unsound -- axiom 'Lean.ofReduceBool' is listed
|