2663c9ab9f
add test/example that defines count_vars using tactics and recursors.
see #662 for original definition, and e3a0e62859 for the fix that
allows us to use recursive equations.
The recursive equations are compiled into recursors.
55 lines
1.4 KiB
Text
55 lines
1.4 KiB
Text
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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-- Define count_vars using tactics
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definition count_vars1 {t : type} (T : @term (λ x, unit) t) : nat :=
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begin
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induction T,
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{exact 1},
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{exact 0},
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{exact v_0 + v_1},
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{exact v_0 star},
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{exact v_0 + v_1},
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{exact v_0 + v_1 star},
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end
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-- Define count_vars using recursor
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definition count_vars2 {t : type} (T : @term (λ x, unit) t) : nat :=
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term.rec_on T
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(λ t u, 1)
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(λ n, 0)
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(λ T₁ T₂ n₁ n₂, n₁ + n₂)
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(λ d r f n, n star)
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(λ d r T₁ T₂ n₁ n₂, n₁ + n₂)
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(λ t₁ t₂ T₁ T₂ n₁ n₂, n₁ + n₂ 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_vars1 (App (App (var (Func Nat (Func Nat Nat))) (var Nat)) (var Nat)) = 3 :=
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rfl
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example : count_vars2 (App (App (var (Func Nat (Func Nat Nat))) (var Nat)) (var Nat)) = 3 :=
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rfl
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