feat: add KMP frontend for lists

Batteries/Data/List.lean

@@ -3,6 +3,7 @@ import Batteries.Data.List.Count
 import Batteries.Data.List.EraseIdx
 import Batteries.Data.List.Init.Lemmas
 import Batteries.Data.List.Lemmas
+import Batteries.Data.List.Matcher
 import Batteries.Data.List.Monadic
 import Batteries.Data.List.OfFn
 import Batteries.Data.List.Pairwise

Batteries/Data/List/Matcher.lean

@@ -0,0 +1,58 @@
+/-
+Copyright (c) 2024 François G. Dorais. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: François G. Dorais
+-/
+import Batteries.Data.Array.Match
+import Batteries.Data.String.Basic
+
+namespace List
+
+/-- Knuth-Morris-Pratt matcher type
+
+This type is used to keep data for running the Knuth-Morris-Pratt (KMP) list matching algorithm.
+KMP is a linear time algorithm to locate all sublists of a list that match a given pattern.
+Generating the algorithm data is also linear in the length of the pattern but the data can be
+re-used to match the same pattern over multiple lists.
+
+The KMP data for a pattern can be generated using `Matcher.ofList`. Then `Matcher.find?` and
+`Matcher.findAll` can be used to run the algorithm on an input list.
+```
+def m := Matcher.ofList [0,1,1,0]
+
+#eval Option.isSome <| m.find? [2,1,1,0,1,1,2] -- false
+#eval Option.isSome <| m.find? [0,0,1,1,0,0] -- true
+
+#eval Array.size <| m.findAll [0,1,1,0,1,1,0] -- 2
+#eval Array.size <| m.findAll [0,1,1,0,1,1,0,1,1,0] -- 3
+```
+-/
+structure Matcher (α : Type _) extends Array.Matcher α where
+  /-- The pattern for the matcher -/
+  pattern : List α
+
+/-- Make KMP matcher from list pattern. -/
+@[inline] def Matcher.ofList [BEq α] (pattern : List α) : Matcher α where
+  toMatcher := Array.Matcher.ofStream pattern
+  pattern := pattern
+
+local instance (α) : Stream (List α × Nat) α where
+  next?
+  | ([], _) => none
+  | (x::xs, n) => (x, xs, n+1)
+
+/-- Find all start and end positions of all sublists of `l` matching `m.pattern`. -/
+partial def Matcher.findAll [BEq α] (m : Matcher α) (l : List α) : Array (Nat × Nat) :=
+  loop (l, 0) m.toMatcher #[]
+where
+  /-- Accumulator loop for `List.Matcher.findAll` -/
+  loop (l : List α × Nat) (am : Array.Matcher α) (occs : Array (Nat × Nat)) : Array (Nat × Nat) :=
+    match am.next? l with
+    | none => occs
+    | some (l, am) => loop l am (occs.push (l.snd - m.table.size, l.snd))
+
+/-- Find the start and end positions of the first sublist of `l` matching `m.pattern`, or `none`. -/
+def Matcher.find? [BEq α] (m : Matcher α) (l : List α) : Option (Nat × Nat) :=
+  match m.next? (l, 0) with
+  | none => none
+  | some (l, _) => some (l.snd - m.table.size, l.snd)

BatteriesTest/kmp_matcher.lean

@@ -1,6 +1,9 @@
 import Batteries.Data.String.Matcher
+import Batteries.Data.List.Matcher
 
-/-! Tests for Knuth-Morris-Pratt matching algorithm -/
+/-! # Tests for the Knuth-Morris-Pratt (KMP) matching algorithm -/
+
+/-! ### String API -/
 
 /-- Matcher for pattern "abba" -/
 def m := String.Matcher.ofString "abba"
@@ -24,3 +27,15 @@ def m := String.Matcher.ofString "abba"
 #guard Array.size ("xyxyyxxyx".findAllSubstr "xyx") = 2
 
 #guard Array.size ("xyxyxyyxxyxyx".findAllSubstr "xyx") = 4
+
+/-! ### List API -/
+
+def lm := List.Matcher.ofList [0,1,1,0]
+
+#guard lm.find? [2,1,1,0,1,1,2] == none
+
+#guard lm.find? [0,0,1,1,0,0] == some (1, 5)
+
+#guard (lm.findAll [0,1,1,0,1,1,0]).size == 2
+
+#guard (lm.findAll [0,1,1,0,1,1,0,1,1,0]).size == 3