58 lines
1.3 KiB
Text
58 lines
1.3 KiB
Text
import logic
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namespace algebra
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inductive mul_struct (A : Type) : Type :=
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mk_mul_struct : (A → A → A) → mul_struct A
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definition mul [inline] {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 `*`:75 := mul
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end 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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variable mul : nat → nat → nat
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variable add : nat → nat → nat
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definition mul_struct [instance] : algebra.mul_struct nat
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:= algebra.mk_mul_struct mul
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end nat
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section
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using 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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using [notation] algebra
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using nat
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-- check mul_struct nat << This is an error, we are using 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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using nat
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-- check mul_struct nat << This is an error, we are using only the notation from algebra
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variables a b c : nat
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check #algebra a*b*c
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definition tst3 : nat := #algebra a*b*c
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end
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section
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using 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.mk_mul_struct add
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variables a b c : nat
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check #algebra a*b*c -- << is using add instead of mul
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definition tst4 : nat := #algebra a*b*c
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end
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