Steve Dunham
63687499dc
Also clean up some comments. We now have types in constraints, but are still using values from context.
49 lines
1.3 KiB
Agda
49 lines
1.3 KiB
Agda
module Problem
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-- partial finished translation of "A correct-by-construction conversion from lambda calculus to combinatory logic", by Wouter Swierstra
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-- added as a test of impossible clauses (in `lookup` below)
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-- prj/menagerie/papers/combinatory
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data Unit : U where
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MkUnit : Unit
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infixr 7 _::_
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data List : U → U where
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Nil : {A : U} → List A
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_::_ : {A : U} → A → List A → List A
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infixr 6 _~>_
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data Type : U where
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ι : Type
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_~>_ : Type → Type → Type
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A : U
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A = Unit
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Val : Type → U
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Val ι = A
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Val (x ~> y) = Val x → Val y
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Ctx : U
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Ctx = List Type
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data Ref : Type → Ctx → U where
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Z : {σ : Type} {Γ : Ctx} → Ref σ (σ :: Γ)
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S : {σ τ : Type} {Γ : Ctx} → Ref σ Γ → Ref σ (τ :: Γ)
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data Term : Ctx → Type → U where
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App : {Γ : Ctx} {σ τ : Type} → Term Γ (σ ~> τ) → Term Γ σ → Term Γ τ
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Lam : {Γ : Ctx} {σ τ : Type} → Term (σ :: Γ) τ → Term Γ (σ ~> τ)
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Var : {Γ : Ctx} {σ : Type} → Ref σ Γ → Term Γ σ
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infixr 7 _:::_
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data Env : Ctx → U where
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ENil : Env Nil
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_:::_ : {Γ : Ctx} {σ : Type} → Val σ → Env Γ → Env (σ :: Γ)
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-- due to the order that we match constructors, we need the impossible clause here
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lookup : {σ : Type} {Γ : Ctx} → Ref σ Γ → Env Γ → Val σ
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lookup Z (x ::: y) = x
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lookup () ENil
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lookup (S i) (x ::: env) = lookup i env
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