b54a9ec9b9
We swap the arguments for `Membership.mem` so that when proceeded by a `SetLike` coercion, as is often the case in Mathlib, the resulting expression is recognized as eta expanded and reduce for many computations. The most beneficial outcome is that the discrimination tree keys for instances and simp lemmas concerning subsets become more robust resulting in more efficient searches. Closes `RFC` #4932 --------- Co-authored-by: Kim Morrison <kim@tqft.net> Co-authored-by: Henrik Böving <hargonix@gmail.com>
75 lines
1.3 KiB
Text
75 lines
1.3 KiB
Text
structure Foo where
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a : Nat
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b : Nat
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def bla (x : Foo) : IO Unit := do
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let { a, b } := x
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def Set (α : Type u) := α → Prop
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def setOf {α : Type u} (p : α → Prop) : Set α :=
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p
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namespace Set
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protected def mem (s : Set α) (a : α) :=
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s a
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instance : Membership α (Set α) :=
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⟨Set.mem⟩
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protected def subset (s₁ s₂ : Set α) :=
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∀ {a}, a ∈ s₁ → a ∈ s₂
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instance : EmptyCollection (Set α) :=
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⟨λ a => false⟩
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protected def insert (a : α) (s : Set α) : Set α :=
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fun b => b = a ∨ b ∈ s
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protected def singleton (a : α) : Set α :=
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fun b => b = a
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instance : Insert α (Set α) := ⟨Set.insert⟩
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instance : Singleton α (Set α) := ⟨Set.singleton⟩
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set_option pp.mvars false in
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/-- info: {1, 2} : ?_ -/
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#guard_msgs in
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#check { 1, 2 }
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end Set
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def f1 (a b : Nat) : Set Nat :=
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{ a, b }
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def f2 (a b : Nat) : Foo :=
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{ a, b }
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def f3 (a b : Nat) : Set Nat :=
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{ a, b }
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/-- info: f3 (a b : Nat) : Set Nat -/
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#guard_msgs in
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#check f3
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def f4 (a b : α) : Set α :=
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{ a, b }
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/-- info: @f4 : {α : Type u_1} → α → α → Set α -/
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#guard_msgs in
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#check @f4
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def f5 (a b : Nat) :=
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{ a, b : Foo }
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def boo1 (x : Foo) : IO Unit :=
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let { a, b } := x
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pure ()
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def boo2 (x : Foo) : IO Unit := do
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let { a, b } := x
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pure ()
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def boo3 (x : Nat → IO Foo) : IO Nat := do
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let { a, b } ← x 0
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return a + b
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