47 lines
1.4 KiB
Text
47 lines
1.4 KiB
Text
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open nat
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inductive type : Type :=
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| Nat : type
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| Func : type → type → type
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open type
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section var
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variable {var : type → Type}
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inductive term : type → Type :=
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| Var : ∀ {t}, var t → term t
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| Const : nat → term Nat
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| Plus : term Nat → term Nat → term Nat
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| Abs : ∀ {dom ran}, (var dom → term ran) → term (Func dom ran)
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| App : ∀ {dom ran}, term (Func dom ran) → term dom → term ran
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| Let : ∀ {t1 t2}, term t1 → (var t1 → term t2) → term t2
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end var
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open term
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definition Term t := Π (var : type → Type), @term var t
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open unit
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definition count_vars : Π {t : type}, @term (λ x, unit) t -> nat
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| count_vars (Var _) := 1
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| count_vars (Const _) := 0
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| count_vars (Plus e1 e2) := count_vars e1 + count_vars e2
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| count_vars (Abs e1) := count_vars (e1 star)
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| count_vars (App e1 e2) := count_vars e1 + count_vars e2
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| count_vars (Let e1 e2) := count_vars e1 + count_vars (e2 star)
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definition var (t : type) : @term (λ x, unit) t :=
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Var star
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example : count_vars (App (App (var (Func Nat (Func Nat Nat))) (var Nat)) (var Nat)) = 3 :=
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rfl
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definition count_vars2 : Π {t : type}, @term (λ x, unit) t -> nat
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| _ (Var _) := 1
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| _ (Const _) := 0
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| _ (Plus e1 e2) := count_vars2 e1 + count_vars2 e2
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| _ (Abs e1) := count_vars2 (e1 star)
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| _ (App e1 e2) := count_vars2 e1 + count_vars2 e2
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| _ (Let e1 e2) := count_vars2 e1 + count_vars2 (e2 star)
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