90a79a0b06
Now, `universe` may declare many universes. The goal is to make it consistent with the `variable` command
69 lines
1.3 KiB
Text
69 lines
1.3 KiB
Text
/- Coercion pullback example from the paper "Hints in Unification" -/
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universe u
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structure Monoid where
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α : Type u
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op : α → α → α
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unit : α
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structure Group where
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α : Type u
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op : α → α → α
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unit : α
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inv : α → α
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structure Ring where
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α : Type u
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mul : α → α → α
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add : α → α → α
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neg : α → α
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one : α
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zero : α
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def Group.ofRing (r : Ring) : Group where
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α := r.α
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op := r.add
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inv := r.neg
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unit := r.zero
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def Monoid.ofRing (r : Ring) : Monoid where
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α := r.α
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op := r.mul
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unit := r.one
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instance : CoeSort Ring (Type u) where
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coe s := s.α
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instance : CoeSort Monoid (Type u) where
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coe s := s.α
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instance : CoeSort Group (Type u) where
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coe s := s.α
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def gop {s : Group} (a b : s) : s :=
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s.op a b
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def mop {s : Monoid} (a b : s) : s :=
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s.op a b
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infix:70 (priority := high) "*" => mop
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infix:65 (priority := high) "+" => gop
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unif_hint (r : Ring) (g : Group) where
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g =?= Group.ofRing r
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r.α =?= g.α
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unif_hint (r : Ring) (m : Monoid) where
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m =?= Monoid.ofRing r
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r.α =?= m.α
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def distrib {r : Ring} (a b c : r) := a * (b + c) = a * b + a * c
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theorem ex1 {r : Ring} (a b c : r) : distrib a b c = (a * (b + c) = a * b + a * c) :=
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rfl
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theorem ex2 {r : Ring} (a b c : r) : distrib a b c = (mop a (gop b c) = gop (mop a b) (mop a c)) :=
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rfl
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