src/HOL/Tools/Function/sum_tree.ML

centralized sum type matter in Sum_Type.thy

(*  Title:      HOL/Tools/Function/sum_tree.ML
    Author:     Alexander Krauss, TU Muenchen

Some common tools for working with sum types in balanced tree form.
*)

structure SumTree =
struct

(* Theory dependencies *)
val proj_in_rules = [@{thm Projl_Inl}, @{thm Projr_Inr}]
val sumcase_split_ss = HOL_basic_ss addsimps (@{thm Product_Type.split} :: @{thms sum.cases})

(* top-down access in balanced tree *)
fun access_top_down {left, right, init} len i =
    Balanced_Tree.access {left = (fn f => f o left), right = (fn f => f o right), init = I} len i init

(* Sum types *)
fun mk_sumT LT RT = Type ("+", [LT, RT])
fun mk_sumcase TL TR T l r = Const (@{const_name sum.sum_case}, (TL --> T) --> (TR --> T) --> mk_sumT TL TR --> T) $ l $ r

val App = curry op $

fun mk_inj ST n i = 
    access_top_down 
    { init = (ST, I : term -> term),
      left = (fn (T as Type ("+", [LT, RT]), inj) => (LT, inj o App (Const (@{const_name Inl}, LT --> T)))),
      right =(fn (T as Type ("+", [LT, RT]), inj) => (RT, inj o App (Const (@{const_name Inr}, RT --> T))))} n i 
    |> snd

fun mk_proj ST n i = 
    access_top_down 
    { init = (ST, I : term -> term),
      left = (fn (T as Type ("+", [LT, RT]), proj) => (LT, App (Const (@{const_name Sum_Type.Projl}, T --> LT)) o proj)),
      right =(fn (T as Type ("+", [LT, RT]), proj) => (RT, App (Const (@{const_name Sum_Type.Projr}, T --> RT)) o proj))} n i
    |> snd

fun mk_sumcases T fs =
      Balanced_Tree.make (fn ((f, fT), (g, gT)) => (mk_sumcase fT gT T f g, mk_sumT fT gT)) 
                        (map (fn f => (f, domain_type (fastype_of f))) fs)
      |> fst

end