60 lines
1.3 KiB
Text
60 lines
1.3 KiB
Text
import logic
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namespace experiment
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namespace algebra
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inductive mul_struct [class] (A : Type) : Type :=
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mk : (A → A → A) → mul_struct A
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definition mul {A : Type} [s : mul_struct A] (a b : A)
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:= mul_struct.rec (λ f, f) s a b
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infixl `*` := mul
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end algebra
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open algebra
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namespace nat
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inductive nat : Type :=
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zero : nat,
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succ : nat → nat
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constant mul : nat → nat → nat
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constant add : nat → nat → nat
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definition mul_struct [instance] : algebra.mul_struct nat
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:= algebra.mul_struct.mk mul
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end nat
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section
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open algebra nat
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variables a b c : nat
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check a * b * c
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definition tst1 : nat := a * b * c
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end
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section
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open [notations] algebra
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open nat
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-- check mul_struct nat << This is an error, we opened only the notation from algebra
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variables a b c : nat
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check a * b * c
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definition tst2 : nat := a * b * c
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end
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section
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open nat
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-- check mul_struct nat << This is an error, we opened only the notation from algebra
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variables a b c : nat
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check a*b*c
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definition tst3 : nat := #nat a*b*c
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end
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section
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open nat
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set_option pp.implicit true
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definition add_struct [instance] : algebra.mul_struct nat
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:= algebra.mul_struct.mk add
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variables a b c : nat
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check #experiment.algebra a*b*c -- << is open add instead of mul
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definition tst4 : nat := #experiment.algebra a*b*c
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end
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end experiment
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