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fix: add grind annotations and a lemma #435

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fix: add grind annotations and a lemma #435

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ab08403
add grind annotations and coe instance
Shreyas4991 Mar 17, 2026
7b4ea35
Readd lemmas
Shreyas4991 Mar 17, 2026
32741ca
Remove unnecessary type annotation
Shreyas4991 Mar 17, 2026
7935144
remove Coe as advised
Shreyas4991 Mar 17, 2026
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15 changes: 11 additions & 4 deletions Cslib/Foundations/Control/Monad/Free.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -96,7 +96,7 @@ variable {F : Type u → Type v} {ι : Type u} {α : Type w} {β : Type w'} {γ

instance : Pure (FreeM F) where pure := .pure

@[simp]
@[simp, grind =]
theorem pure_eq_pure : (pure : α → FreeM F α) = FreeM.pure := rfl

/-- Bind operation for the `FreeM` monad. -/
Expand All @@ -115,7 +115,7 @@ protected theorem bind_assoc (x : FreeM F α) (f : α → FreeM F β) (g : β

instance : Bind (FreeM F) where bind := .bind

@[simp]
@[simp, grind =]
theorem bind_eq_bind {α β : Type w} : Bind.bind = (FreeM.bind : FreeM F α → _ → FreeM F β) := rfl

/-- Map a function over a `FreeM` monad. -/
Expand Down Expand Up @@ -154,14 +154,21 @@ lemma map_lift (f : ι → α) (op : F ι) :
map f (lift op : FreeM F ι) = liftBind op (fun z => (.pure (f z) : FreeM F α)) := rfl

/-- `.pure a` followed by `bind` collapses immediately. -/
@[simp]
@[simp, grind =]
lemma pure_bind (a : α) (f : α → FreeM F β) : (.pure a : FreeM F α).bind f = f a := rfl

@[simp]
@[simp, grind =]
lemma pure_bind' {α β} (a : α) (f : α → FreeM F β) : (.pure a : FreeM F α) >>= f = f a :=
pure_bind a f
Comment on lines +160 to +162
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@eric-wieser eric-wieser Mar 17, 2026

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Maybe @kim-em can comment on why the simpNF linter does not reject this due to bind_eq_bind simplifying the LHS?


@[simp, grind =]
lemma bind_pure : ∀ x : FreeM F α, x.bind (.pure) = x
| .pure a => rfl
| liftBind op k => by simp [FreeM.bind, bind_pure]

@[simp, grind =]
lemma bind_pure' : ∀ x : FreeM F α, x >>= .pure = x := bind_pure

@[simp]
lemma bind_pure_comp (f : α → β) : ∀ x : FreeM F α, x.bind (.pure ∘ f) = map f x
| .pure a => rfl
Expand Down
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