Featherweight Java: A Minimal Core Calculus for Java and GJ

• p. 13 Theorem 2.4.3

  containing (D)new C(ē) where C <: D

• p. 6 Section 2, informal soundness statement

  or stuck at a failing typecast

• p. 13 Theorem 2.4.3 statement

  or an expression containing (D)new C(ē) where C <: D.

• p. 13 Theorem 2.4.3

  containing (D)new C(¯e) where C <: D

Only the authors can say what is right here.

Judge's note: The page 13 image shows plain 'C <: D' with no negation slash. Rule R-CAST in Fig. 3 (p.12) has premise C <: D and reduces (D)(new C(ē)) to new C(ē). A normal form therefore cannot contain such a cast with C <: D, and the second alternative as printed can never occur. Counterexample checked: take class A extends Object. Then (A)new Object() is well typed by T-DCAST and is a normal form, because Object is not a subtype of A. It is not a value, and it contains no cast with C <: D, so it satisfies neither alternative as printed. The text on p.6 ('stuck at a failing typecast') and p.11 ('gets stuck at a downcast') states the intended negated condition.

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• p. 20 Theorem 3.4.3

  an expression containing (P)new N(ē) where ∅ ⊢ N <: P

• p. 20 Theorem 3.4.3 statement, alternative (2)

  or (2) an expression containing (P)new N(ē) where ∅ ⊢ N <: P.

• p. 20 Theorem 3.4.3

  an expression containing (P)new N(¯e) where ∅⊢N <: P.

Only the authors can say what is right here.

Judge's note: The page 20 image shows plain '∅ ⊢ N <: P' with no negation. GR-CAST reduces (P)new N(ē) whenever ∅ ⊢ N <: P, so alternative (2) as printed can never occur in a normal form. A failed downcast such as (A)new Object() would then satisfy neither alternative. This is the same slip as in Theorem 2.4.3 (C009), but it is in a separate theorem.

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• p. 15 Figure 4 caption

  Fig. 4. FJ: Syntax.

• p. 15 Section 3.1

  The abstract syntax of FGJ is given in Figure 4.

• p. 15 Fig. 4 caption

  FJ: Syntax.

Judge's note: The page 15 image shows a figure with generic syntax under the caption 'FJ: Syntax.'. Section 3.1 says the figure gives FGJ syntax. The caption should read 'FGJ: Syntax'.

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• p. 38 Proof of Lemma A.2.11, Case GT-INVK

  By the rule GT-METHOD, Δ; Γ ⊢ [d̄/x̄](e0.m<V̄>(ē)):[V̄/Ȳ]U′.

• p. 38 Lemma A.2.11, Case GT-INVK

  By the rule GT-METHOD, 1; 0 ⊢[¯d/¯x](e0.m<¯V>(¯e)):[¯V/¯Y]U′.

• p. 38 Lemma A.2.11 proof, Case GT-INVK

  By the rule GT-METHOD, Δ; Γ ⊢ [d/x](e0.m<V>(e)):[V/Y]U′.

Judge's note: Page 38 image. GT-Method concludes a method-declaration judgment (M OK IN C<...>), not an expression typing. The parallel step in Lemma A.2.10 (p.37) cites GT-Invk, so this is a wrong rule label.

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• p. 45 Proof of Theorem 4.5.1, second part

  By Lemma A.2.11,

• p. 45 Proof of Theorem 4.5.1, second part (method erasure)

  we have xi′ : Di ⊢ ei:|Ti|∆. By Lemma A.2.11,

Only the authors can say what is right here.

Judge's note: Page 45 image. The judgments here are FJ typings over the erased class table (|Γ|Δ, this:C ⊢FJ ...). Lemma A.2.11 (p.38) concerns FGJ judgments Δ;Γ ⊢ e:T. The FJ term-substitution lemma is A.1.2. Since |CT| is not assumed ok (p.43), the authors should say which substitution lemma, under which assumptions, justifies this step.

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• p. 47 Proof of Lemma A.4.2

  Case GT-METHOD. e = e0.m<V̄>(d̄)

• p. 47 Proof of Lemma A.4.2

  Case GT-METHOD. e = e0.m<¯V>(¯d)

Judge's note: Checked the page image of PDF p.47. The case analyses the invocation e0.m<V̄>(d̄) and lists GT-INVK's premises (mtype, Δ ⊢ V̄ ok, the argument typings, T = [V̄/Ȳ]U0). The analogous cases in the other lemma proofs are headed 'Case GT-INVK.' (layout lines 1801, 1905; text line 2443). The induction is on the expression-typing derivation, and GT-METHOD is the method-declaration rule, so the label is wrong. The authors also write 'GT-METHOD' loosely in a few other places (e.g. text line 2008), but the case heading here is still mislabelled.

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• p. 33 Proof of Thm 2.4.1, Case RC-CAST, Subcase T-SCAST

  Then, both C0′<:C and C ⊀: C0′ also hold

• p. 33 Proof of Theorem 2.4.1, Case RC-CAST, Subcase T-SCAST

  Then, both C0′<:C

• p. 33 A.1 proof, Case RC-CAST, Subcase T-SCAST

  Then, both C0′<:C and C </: C0′ also hold

Only the authors can say what is right here.

Judge's note: Page 33 image (and crop): the first relation is printed as plain <: and the second has the slash. Reworked the step: the subcase gives C ⊀: C0 and C0 ⊀: C (with D = C), and the IH gives C0′ <: C0. If C0′ <: C held as well, single inheritance would put C and C0 on the same superclass chain of C0′, so C <: C0 or C0 <: C, which contradicts the subcase. So the printed C0′ <: C is false here, and T-SCast needs C0′ ⊀: C. The fix is a slash and Theorem 2.4.1 is unaffected.

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• p. 37 Proof of Lemma A.2.10, Case GT-INVK, final step

  ([Ū/X̄]e0).m<[Ū/X̄]V̄>([Ū/X̄]d̄):S

• p. 37 Proof of Lemma A.2.10, Case GT-INVK (top of page)

  where S = [V̄/Ȳ]W0′, finishing the case.

Only the authors can say what is right here.

Judge's note: Pages 36–37 images. The case defines e = e0.m<V̄>(ē), but the conclusion uses d̄, and a comma separates the environment from Γ. Reworked the type: Lemma A.2.9 gives the method type <Ȳ◁[Ū/X̄]P̄>[Ū/X̄]W̄→W0′, and the invocation uses the type arguments [Ū/X̄]V̄. GT-Invk therefore gives the result type [[Ū/X̄]V̄/Ȳ]W0′. Lemma A.2.5 with that substitution gives [[Ū/X̄]V̄/Ȳ]W0′ <: [Ū/X̄][V̄/Ȳ]W0. The printed [V̄/Ȳ]W0′ can still contain X̄ when V̄ mentions X̄. The reviewer's instance (X ◁ Object, U = A, a method <Y> Y m(Y y)) gives X, which is not well formed after X has been substituted away. The step is faulty as printed; it is repairable and the lemma stands.

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• p. 38 Proof of Lemma A.2.10, Case GT-DCAST, final sentence

  Finally, by the rule GT-SCAST, Δ; Γ ⊢ [T̄/X̄]((N)e0):[T̄/X̄]N with stupid warning.

• p. 38 End of Case GT-DCAST in proof of Lemma A.2.10 (top of page)

  Finally, by the rule GT-SCAST, Δ; Γ ⊢ [T̄/X̄]((N)e0):[T̄/X̄]N with stupid warn-

• p. 38 Lemma A.2.10, end of Case GT-DCAST

  Finally, by the rule GT-SCAST, 1; 0 ⊢[¯T/¯X]((N)e0):[¯T/¯X]N with stupid warning.

Only the authors can say what is right here.

Judge's note: Images of p.37 (case header N = C<T̄>, Δ′ = Δ1,[Ū/X̄]Δ2) and p.38 (top line). This lemma substitutes Ū for X̄, and T̄ is bound to N's own type arguments. The other subcases and the following GT-SCast case correctly use Δ′ (or Δ1,[Ū/X̄]Δ2), [Ū/X̄]Γ and [Ū/X̄]. The judgment as printed is not what the lemma must deliver; it is repairable and the lemma stands.

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• p. 39 Proof of Lemma A.2.11, Case GT-DCAST, third subcase

  contradicting the assumption Δ ⊢ boundΔ(S0) <: N; thus, D ⋬ C.

• p. 39 Proof of Lemma A.2.11, Case GT-DCAST, third subcase (D ⊴ C branch)

  contradicting the assumption Δ ⊢ bound∆(S0) <: N; thus, D ⋬ C.

Only the authors can say what is right here.

Judge's note: Page 39 image: the relation is printed as plain <:, while the subcase header on the same page reads Δ ⊢ boundΔ(S0) ⊀: N. The parallel line on p.37 in Lemma A.2.10 has ⊀:. The proof has just derived bound(S0) <: C<V̄′> = N, which contradicts ⊀: but not <:. The step is faulty as printed; the fix is a slash and the lemma stands.

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• p. 46 Proof of Lemma A.4.2, Case GT-FIELD, first subcase

  |[Ū/X̄]e|Δ1,[Ū/X̄]Δ2,Γ′ = (|[Ū/X̄]Ti|...)s|[Ū/X̄]e|...fi

• p. 46 Proof of Lemma A.4.2, Case GT-FIELD, Subcase |Ti| ≠ Ci, final display

  |[Ū/X̄]e|Δ1,[Ū/X̄]Δ2,Γ′ = (|[Ū/X̄]Ti|Δ1,[Ū/X̄]Δ2)s|[Ū/X̄]e|Δ1,[Ū/X̄]Δ2,Γ′.fi

Only the authors can say what is right here.

Judge's note: Checked the page image of PDF p.46 and the layout text (line 2332), which both show |[Ū/X̄]e| on the right with no subscript 0. Reworking the step: here e = e0.fi, so [Ū/X̄]e = ([Ū/X̄]e0).fi. E-FIELD-CAST, as used a few lines up on the same page (|e|Δ,Γ = (|Ti|Δ)s|e0|Δ,Γ.fi), erases the receiver. So the right-hand side must be (...)s|[Ū/X̄]e0|....fi. That also matches the goal stated on the same page, '(D)s|[Ū/X̄]e0|....fi'. As printed the equation is circular. The parallel GT-INVK subcase on p.47 correctly writes |[Ū/X̄]e0|. The step can be repaired by changing e to e0, and the lemma's result stands.

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• p. 53 Proof of Lemma A.4.6, Subcase R-INVK, final display

  ⇒ (C)[ē/x̄, new D(d̄)/this]em′.

Only the authors can say what is right here.

Judge's note: Checked the page images of PDF pp.52-53. The preceding display on p.53 ends with '(|T|Δ)s[ē/x̄, new D(d̄)/this]em', with unprimed em and the synthetic s. The goal is d = (C)s d0 with d0 = [ē/x̄, new D(d̄)/this]em, where em is the FJ body from mbodyFJ(m,D) (p.52). The final display instead has em′, which is the FGJ body, and an unmarked cast (C). Combining C = |T|Δ with transitivity gives (C)s[...]em. The printed target is therefore not d, and it is not an FJ expansion. The step can be repaired and the result stands.

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