src/HOL/Library/Old_SMT/smt_datatypes.ML

+(*  Title:      HOL/Library/Old_SMT/smt_datatypes.ML
+    Author:     Sascha Boehme, TU Muenchen
+
+Collector functions for common type declarations and their representation
+as algebraic datatypes.
+*)
+
+signature SMT_DATATYPES =
+sig
+  val add_decls: typ ->
+    (typ * (term * term list) list) list list * Proof.context ->
+    (typ * (term * term list) list) list list * Proof.context
+end
+
+structure SMT_Datatypes: SMT_DATATYPES =
+struct
+
+fun mk_selectors T Ts =
+  Variable.variant_fixes (replicate (length Ts) "select")
+  #>> map2 (fn U => fn n => Free (n, T --> U)) Ts
+
+
+(* free constructor type declarations *)
+
+fun get_ctr_sugar_decl ({ctrs, ...} : Ctr_Sugar.ctr_sugar) T Ts ctxt =
+  let
+    fun mk_constr ctr0 =
+      let val ctr = Ctr_Sugar.mk_ctr Ts ctr0 in
+        mk_selectors T (binder_types (fastype_of ctr)) #>> pair ctr
+      end
+  in
+    fold_map mk_constr ctrs ctxt
+    |>> (pair T #> single)
+  end
+
+
+(* typedef declarations *)
+
+fun get_typedef_decl (({Abs_name, Rep_name, abs_type, rep_type, ...}, {Abs_inverse, ...})
+    : Typedef.info) T Ts =
+  if can (curry (op RS) @{thm UNIV_I}) Abs_inverse then
+    let
+      val env = snd (Term.dest_Type abs_type) ~~ Ts
+      val instT = Term.map_atyps (perhaps (AList.lookup (op =) env))
+
+      val constr = Const (Abs_name, instT (rep_type --> abs_type))
+      val select = Const (Rep_name, instT (abs_type --> rep_type))
+    in [(T, [(constr, [select])])] end
+  else
+    []
+
+
+(* collection of declarations *)
+
+fun declared declss T = exists (exists (equal T o fst)) declss
+fun declared' dss T = exists (exists (equal T o fst) o snd) dss
+
+fun get_decls T n Ts ctxt =
+  (case Ctr_Sugar.ctr_sugar_of ctxt n of
+    SOME ctr_sugar => get_ctr_sugar_decl ctr_sugar T Ts ctxt
+  | NONE =>
+      (case Typedef.get_info ctxt n of
+        [] => ([], ctxt)
+      | info :: _ => (get_typedef_decl info T Ts, ctxt)))
+
+fun add_decls T (declss, ctxt) =
+  let
+    fun depends Ts ds = exists (member (op =) (map fst ds)) Ts
+
+    fun add (TFree _) = I
+      | add (TVar _) = I
+      | add (T as Type (@{type_name fun}, _)) =
+          fold add (Term.body_type T :: Term.binder_types T)
+      | add @{typ bool} = I
+      | add (T as Type (n, Ts)) = (fn (dss, ctxt1) =>
+          if declared declss T orelse declared' dss T then (dss, ctxt1)
+          else if SMT_Builtin.is_builtin_typ_ext ctxt1 T then (dss, ctxt1)
+          else
+            (case get_decls T n Ts ctxt1 of
+              ([], _) => (dss, ctxt1)
+            | (ds, ctxt2) =>
+                let
+                  val constrTs =
+                    maps (map (snd o Term.dest_Const o fst) o snd) ds
+                  val Us = fold (union (op =) o Term.binder_types) constrTs []
+
+                  fun ins [] = [(Us, ds)]
+                    | ins ((Uds as (Us', _)) :: Udss) =
+                        if depends Us' ds then (Us, ds) :: Uds :: Udss
+                        else Uds :: ins Udss
+            in fold add Us (ins dss, ctxt2) end))
+  in add T ([], ctxt) |>> append declss o map snd end
+
+end