97aca690d0
This PR fixes the bug that `collectAxioms` didn't collect axioms referenced by other axioms. One of the results of this bug is that axioms collected from a theorem proved by `native_decide` may not include `Lean.trustCompiler`. Closes #8840.
40 lines
1 KiB
Text
40 lines
1 KiB
Text
--
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/-
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This example demonstratea that when we are using `native_decide`,
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we are also trusting the correctness of `implemented_by` annotations,
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foreign functions (i.e., `[extern]` annotations), etc.
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-/
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def g (b : Bool) := false
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/-
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The following `implemented_by` is telling the compiler
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"trust me, `g` does implement `f`"
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which is clearly false in this example.
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-/
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@[implemented_by g]
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def f (b : Bool) := b
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theorem fConst (b : Bool) : f b = false :=
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match b with
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| true =>
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/- The following `native_decide` is going to use `g` to evaluate `f`
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because of the `implemented_by` directive. -/
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have : (f true) = false := by native_decide
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this
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| false => rfl
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theorem trueEqFalse : true = false :=
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have h₁ : f true = true := rfl;
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have h₂ : f true = false := fConst true;
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Eq.trans h₁.symm h₂
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/-
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We managed to prove `False` using the unsound annotation `implemented_by` above.
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-/
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theorem unsound : False :=
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Bool.noConfusion trueEqFalse
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/-- info: 'unsound' depends on axioms: [Lean.ofReduceBool, Lean.trustCompiler] -/
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#guard_msgs in
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#print axioms unsound
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