IndGroupInfo.lean

/-
Copyright (c) 2024 Lean FRO. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joachim Breitner
-/
prelude
import Lean.Meta.InferType

/-!
This module contains the types
* `IndGroupInfo`, a variant of `InductiveVal` with information that
   applies to a whole group of mutual inductives and
* `IndGroupInst` which extends `IndGroupInfo` with levels and parameters
   to indicate a instantiation of the group.

One purpose of this abstraction is to make it clear when a fuction operates on a group as
a whole, rather than a specific inductive within the group.
-/

namespace Lean.Elab.Structural
open Lean Meta

/--
A mutually inductive group, identified by the `all` array of the `InductiveVal` of its
constituents.
-/
structure IndGroupInfo where
  all       : Array Name
  numNested : Nat
deriving BEq, Inhabited

def IndGroupInfo.ofInductiveVal (indInfo : InductiveVal) : IndGroupInfo where
  all       := indInfo.all.toArray
  numNested := indInfo.numNested

def IndGroupInfo.numMotives (group : IndGroupInfo) : Nat :=
  group.all.size + group.numNested

/--
An instance of an mutually inductive group of inductives, identified by the `all` array
and the level and expressions parameters.

For example this distinguishes between `List α` and `List β` so that we will not even attempt
mutual structural recursion on such incompatible types.
-/
structure IndGroupInst extends IndGroupInfo where
  levels    : List Level
  params    : Array Expr
deriving Inhabited

def IndGroupInst.toMessageData (igi : IndGroupInst) : MessageData :=
  mkAppN (.const igi.all[0]! igi.levels) igi.params

instance : ToMessageData IndGroupInst where
  toMessageData := IndGroupInst.toMessageData

def IndGroupInst.isDefEq (igi1 igi2 : IndGroupInst) : MetaM Bool := do
  unless igi1.toIndGroupInfo == igi2.toIndGroupInfo do return false
  unless igi1.levels.length = igi2.levels.length do return false
  unless (igi1.levels.zip igi2.levels).all (fun (l₁, l₂) => Level.isEquiv l₁ l₂) do return false
  unless igi1.params.size = igi2.params.size do return false
  unless (← (igi1.params.zip igi2.params).allM (fun (e₁, e₂) => Meta.isDefEqGuarded e₁ e₂)) do return false
  return true

end Lean.Elab.Structural