46 lines
1.7 KiB
Text
46 lines
1.7 KiB
Text
inductive ty
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| base : string → ty
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| arr : ty → ty → ty
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namespace ty
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instance : decidable_eq ty := by tactic.mk_dec_eq_instance
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instance : inhabited ty := ⟨ty.base "o"⟩
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end ty
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@[reducible] def ctx := list ty
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inductive lamexp_core : ctx → ty → Type
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| var : Π {Γ : ctx} {t} (n : ℕ), list.nth Γ n = some t → lamexp_core Γ t
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| fv : Π {Γ}, string → Π t : ty, lamexp_core Γ t
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| con : Π {Γ}, string → Π t : ty, lamexp_core Γ t
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| app : Π {Γ} {t s}, lamexp_core Γ (ty.arr t s) → lamexp_core Γ t → lamexp_core Γ s
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| abs : Π {Γ : ctx} {t s}, lamexp_core (t::Γ) s → lamexp_core Γ (ty.arr t s)
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namespace lamexp_core
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-- instance {Γ t} : decidable_eq (lamexp_core Γ t) := by tactic.mk_dec_eq_instance
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instance {Γ t} : inhabited (lamexp_core Γ t) := ⟨lamexp_core.con "c" t⟩
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end lamexp_core
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@[reducible] def lamexp := lamexp_core []
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namespace lamexp
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lemma nth_append {α} {ys : list α} : Π {n xs}, list.nth xs n ≠ none → list.nth (xs ++ ys) n = list.nth xs n
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| 0 [] h := by contradiction
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| (n+1) [] h := by contradiction
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| 0 (x::xs) h := rfl
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| (n+1) (x::xs) h := @nth_append n xs h
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def weaken_core : ∀ {Γ Δ t}, lamexp_core Γ t → lamexp_core (Γ ++ Δ) t
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| Γ Δ .(t) (@lamexp_core.var .(Γ) t n h) := lamexp_core.var n $
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begin rw nth_append, assumption, rw h, intro, contradiction end
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| Γ Δ .(t) (lamexp_core.fv n t) := lamexp_core.fv n t
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| Γ Δ .(t) (lamexp_core.con n t) := lamexp_core.con n t
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| Γ Δ .(s) (@lamexp_core.app .(Γ) t s a b) := lamexp_core.app (weaken_core a) (weaken_core b)
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| Γ Δ (ty.arr .(t) .(s)) (@lamexp_core.abs .(Γ) t s a) :=
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lamexp_core.abs $ cast (by simp) (weaken_core a)
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def weaken {Γ t} : lamexp t → lamexp_core Γ t :=
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weaken_core
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end lamexp
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