a993934839
With this, lean produces the following zoo of rewrite rules: ``` Option.map.eq_1 : Option.map f none = none Option.map.eq_2 : Option.map f (some x) = some (f x) Option.map.eq_def : Option.map f p = match o with | none => none | (some x) => some (f x) Option.map.eq_unfold : Option.map = fun f p => match o with | none => none | (some x) => some (f x) ``` The `f.eq_unfold` variant is especially useful to rewrite with `rw` under binders. This implements and fixes #5110
69 lines
1.6 KiB
Text
69 lines
1.6 KiB
Text
def Option_map (f : α → β) : Option α → Option β
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| none => none
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| some x => some (f x)
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/--
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info: equations:
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theorem Option_map.eq_1.{u_1, u_2} : ∀ {α : Type u_1} {β : Type u_2} (f : α → β), Option_map f none = none
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theorem Option_map.eq_2.{u_1, u_2} : ∀ {α : Type u_1} {β : Type u_2} (f : α → β) (x_1 : α),
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Option_map f (some x_1) = some (f x_1)
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-/
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#guard_msgs in
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#print equations Option_map
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/--
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info: Option_map.eq_def.{u_1, u_2} {α : Type u_1} {β : Type u_2} (f : α → β) :
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∀ (x : Option α),
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Option_map f x =
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match x with
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| none => none
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| some x => some (f x)
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-/
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#guard_msgs in
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#check Option_map.eq_def
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/--
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info: Option_map.eq_unfold.{u_1, u_2} :
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@Option_map = fun {α} {β} f x =>
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match x with
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| none => none
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| some x => some (f x)
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-/
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#guard_msgs in
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#check Option_map.eq_unfold
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def answer := 42
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/-- info: answer.eq_unfold : answer = 42 -/
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#guard_msgs in
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#check answer.eq_unfold
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-- structural recursion
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def List_map (f : α → β) : List α → List β
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| [] => []
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| x::xs => f x :: List_map f xs
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/--
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info: List_map.eq_unfold.{u_1, u_2} :
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@List_map = fun {α} {β} f x =>
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match x with
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| [] => []
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| x :: xs => f x :: List_map f xs
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-/
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#guard_msgs in
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#check List_map.eq_unfold
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-- wf recursion
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def List_map2 (f : α → β) : List α → List β
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| [] => []
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| x::xs => f x :: List_map2 f xs
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termination_by l => l
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/--
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info: List_map2.eq_unfold.{u_1, u_2} :
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@List_map2 = fun {α} {β} f x =>
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match x with
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| [] => []
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| x :: xs => f x :: List_map2 f xs
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-/
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#guard_msgs in
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#check List_map2.eq_unfold
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