https://github.com/dmxlarchey/systemf

A clean and short proof of strong normalization for Curry-style System F
https://github.com/dmxlarchey/systemf

Last synced: about 1 month ago
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A clean and short proof of strong normalization for Curry-style System F

• Host: GitHub
• URL: https://github.com/dmxlarchey/systemf
• Owner: DmxLarchey
• License: mpl-2.0
• Created: 2023-11-27T08:26:20.000Z (about 1 year ago)
• Default Branch: main
• Last Pushed: 2024-01-27T09:49:21.000Z (about 1 year ago)
• Last Synced: 2024-11-06T07:44:17.677Z (3 months ago)
• Language: Coq
• Size: 98.6 KB
• Stars: 0
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# SystemF

A clean and short proof of strong normalization for Curry-style System F

```

Inductive term_beta : term → term → Prop :=

  | in_beta_redex u v :             (Ⲗu)@v -β-> u⌈v⌉

  | in_beta_lft u v w : u -β-> v   →   u@w -β-> v@w

  | in_beta_rt  u v w : u -β-> v   →   w@u -β-> w@v

  | in_beta_abs u v   : u -β-> v   →    Ⲗu -β-> Ⲗv

where  "x -β-> y" := (term_beta x y).

```

```

Inductive F_Typing_Judgement : (nat → type) → term → type → Prop :=

  | fty_var Γ x :                Γ ⊢ £x ∶ Γ x

  | fty_arr_intro Γ u A B  :   A∷Γ ⊢ u ∶ B 

                           →     Γ ⊢ Ⲗu ∶ A⇨B

  | fty_arr_elim Γ u v A B :     Γ ⊢ u ∶ A⇨B

                           →     Γ ⊢ v ∶ A

                           →     Γ ⊢ u@v ∶ B

  | fty_abs_intro Γ u A    :    ⇑Γ ⊢ u ∶ A

                           →     Γ ⊢ u ∶ ∇A

  | fty_abs_elim Γ u A B   :     Γ ⊢ u ∶ ∇A

                           →     Γ ⊢ u ∶ A⌈B⌉

where "Γ ⊢ u ∶ A" := (F_Typing_Judgement Γ u A).

```

```

Definition SN := Acc term_beta⁻¹.

Theorem FTJ_beta_sn Γ u A : Γ ⊢ u ∶ A → SN u.

```

To be able to implement such definitions, some infrastructure

is necessary.