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MLF: An extension of ML with first-class polymorphism and implicit instantiation

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Academic year: 2021

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Figure 1.1: Type equivalence under prefix Eq-Refl (Q) σ ≡ σ Eq-Freeα / ∈ ftv(σ 1 ) (Q) ∀ (α  σ) σ 1 ≡ σ 1 Eq-Comm α 1 ∈ ftv(σ/ 2 ) α 2 ∈ ftv(σ/ 1 ) α 1 6= α 2 (Q) ∀ (α 1  1 σ 1 ) ∀ (α 2  2 σ 2 ) σ ≡ ∀ (α 2  2 σ 2 ) ∀ (α 1  1 σ 1 ) σ Eq-Var (Q) ∀ (α 
Figure 1.2: The abstraction relation A-Equiv (Q) σ 1 ≡ σ 2 (Q) σ 1 @ − σ 2 A-Hyp(α1 = σ 1 ) ∈ Q(Q) σ1@− α1
Figure 1.3: Type instance I-Abstract (Q) σ 1 @ − σ 2 (Q) σ 1 v σ 2 I-Hyp(α1 ≥ σ 1 ) ∈ Q(Q) σ1v α1 I-Bot (Q) ⊥ v σ I-Rigid (Q) ∀ (α ≥ σ 1 ) σ v ∀ (α = σ 1 ) σ Properties 1.7.2
Figure 2.1: Frozen abstraction relation A-Equiv’ (Q) σ 1 ≡ σ 2 (Q) σ 1 @− α¯ σ 2 A-Hyp’ (α = σ) ∈ Q α / ∈ ¯α(Q) σ @−α¯α A-Up’ α 1 ∈ ftv(σ/ 0 ) (Q) ∀ (α = ∀ (α 1 = σ 1 ) σ) σ 0 @− α¯ ∀ (α 1 = σ 1 ) ∀ (α = σ) σ 0 A-Alias’ (Q) ∀ (α 1 = σ 1 ) ∀ (α 2 = σ 1 ) σ
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