31 lines
1.1 KiB
Text
31 lines
1.1 KiB
Text
class Semiring (α : Type) where add : α → α → α
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class Ring (α : Type) where add : α → α → α
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class AddCommMonoid (α : Type) where
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class AddCommGroup (α : Type) where
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class Module (α β : Type) [Semiring α] [AddCommMonoid β] where
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class NormedField (α : Type) where
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add : α → α → α
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add_comm : ∀ (x y : α), @Add.add _ ⟨add⟩ x y = @Add.add _ ⟨add⟩ y x
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class SemiNormedGroup (α : Type) where
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class SemiNormedSpace (α β : Type) [NormedField α] [SemiNormedGroup β] where
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instance SemiNormedGroup.toAddCommMonoid [SemiNormedGroup α] : AddCommMonoid α := {}
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instance Ring.toSemiring [instR : Ring α] : Semiring α := { add := instR.add }
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instance NormedField.toRing [instNF : NormedField α] : Ring α := { add := instNF.add }
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instance SemiNormedSpace.toModule [NormedField α] [SemiNormedGroup β] [SemiNormedSpace α β] : Module α β := {}
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opaque R : Type := Unit
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opaque foo (a b : R) : R := a
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instance R.NormedField : NormedField R := { add := foo, add_comm := sorry }
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instance R.Ring : Ring R := { add := foo }
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variable {E : Type} [instSNG : SemiNormedGroup E] [instSNS : SemiNormedSpace R E]
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#synth Module R E
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