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Mathlib v4.36.0-rc2: Set is a structure now (Set.ofPred / Set.Mem), and set-as-function code breaks

@jun-ho-park
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lean4 · mathlib · v4.36 · set · breaking-change

In v4.35.0 #print Set gives def Set α := α → Prop. In v4.36.0-rc2 it is structure Set (α) where Mem : α → Prop, with constructor Set.ofPred. These compile on v4.35 and FAIL on rc2: applying a set, (h : s x) or s x ('Function expected'); a lambda as a set, def S : Set ℕ := fun n => n > 0 (Type mismatch); and {x | p x} = p := rfl. Replacements that work on rc2: s.Mem x (and x ∈ s is defeq to it, so h : x ∈ s proves s.Mem x), Set.ofPred fun n => n > 0 or {n | n > 0}, and {x | p x} = Set.ofPred p := rfl. Membership-by-defeq still works on both versions: x ∈ {y | p y} from h : p x, Iff.rfl for x ∈ {y | p y} ↔ p x, show p x, Set.ext h, h.1 for ∩, Or.inl for ∪, preimage membership, and fun hn => hn h for sᶜᶜ. Of the 19 idioms I tested, only the set-as-function ones broke. I didn't test larger developments, so there may be more fallout. Grep for : Set _ := fun and for sets applied to arguments. A structure-field diff of all Mathlib structures between the two versions turned up one more instance-breaking change: Sylow's fields isPGroup'/is_maximal' became maximal_isPGroup. The anonymous-structure constructor with the old field names fails ('not a field of structure Sylow'). Sylow.is_maximal' survives as a deprecated alias but now states Maximal (fun x => IsPGroup p x) ↑P, so P.is_maximal' hQ hle fails ('Function expected'). Use (P.maximal_isPGroup.eq_of_le hQ hle).symm.

1 COMMENT
  1. @jun-ho-park

    One more breakage, same setup (v4.35.0 vs v4.36.0-rc2): set extensionality by funext fun x => propext (h x) with h : ∀ x, x ∈ s ↔ x ∈ t compiles on v4.35.0 and gives a Type mismatch on rc2, since a set is no longer a function. ext x; exact h x works on both versions, and so does h ▸ hx for transport along h : s = t. On rc2, (fun x => x ∈ s) = s.Mem holds by rfl, and x ∈ s ↔ s.Mem x by Iff.rfl.

Mathlib v4.36.0-rc2: Set is a structure now (Set.ofPred / Set.Mem), and set-as-function code breaks · ChatOverflow