# HG changeset patch
# User huffman
# Date 1267399844 28800
# Node ID 979019ab92eb9a03b18f5c8cd1fce9d2f0f1266b
# Parent  7675a41e755a1108d8993407763d88710db9d82f
move common functions into new file holcf_library.ML

diff -r 7675a41e755a -r 979019ab92eb src/HOLCF/IsaMakefile
--- a/src/HOLCF/IsaMakefile	Sun Feb 28 15:09:09 2010 -0800
+++ b/src/HOLCF/IsaMakefile	Sun Feb 28 15:30:44 2010 -0800
@@ -64,6 +64,7 @@
   Tools/adm_tac.ML \
   Tools/cont_consts.ML \
   Tools/cont_proc.ML \
+  Tools/holcf_library.ML \
   Tools/Domain/domain_extender.ML \
   Tools/Domain/domain_axioms.ML \
   Tools/Domain/domain_constructors.ML \
diff -r 7675a41e755a -r 979019ab92eb src/HOLCF/Representable.thy
--- a/src/HOLCF/Representable.thy	Sun Feb 28 15:09:09 2010 -0800
+++ b/src/HOLCF/Representable.thy	Sun Feb 28 15:30:44 2010 -0800
@@ -8,6 +8,7 @@
 imports Algebraic Universal Ssum Sprod One Fixrec
 uses
   ("Tools/repdef.ML")
+  ("Tools/holcf_library.ML")
   ("Tools/Domain/domain_isomorphism.ML")
 begin
 
@@ -749,6 +750,7 @@
 
 subsection {* Constructing Domain Isomorphisms *}
 
+use "Tools/holcf_library.ML"
 use "Tools/Domain/domain_isomorphism.ML"
 
 setup {*
diff -r 7675a41e755a -r 979019ab92eb src/HOLCF/Tools/Domain/domain_constructors.ML
--- a/src/HOLCF/Tools/Domain/domain_constructors.ML	Sun Feb 28 15:09:09 2010 -0800
+++ b/src/HOLCF/Tools/Domain/domain_constructors.ML	Sun Feb 28 15:30:44 2010 -0800
@@ -36,256 +36,7 @@
 structure Domain_Constructors :> DOMAIN_CONSTRUCTORS =
 struct
 
-(******************************************************************************)
-(************************** building types and terms **************************)
-(******************************************************************************)
-
-
-(*** Operations from Isabelle/HOL ***)
-
-val boolT = HOLogic.boolT;
-
-val mk_equals = Logic.mk_equals;
-val mk_eq = HOLogic.mk_eq;
-val mk_trp = HOLogic.mk_Trueprop;
-val mk_fst = HOLogic.mk_fst;
-val mk_snd = HOLogic.mk_snd;
-val mk_not = HOLogic.mk_not;
-val mk_conj = HOLogic.mk_conj;
-val mk_disj = HOLogic.mk_disj;
-
-fun mk_ex (x, t) = HOLogic.exists_const (fastype_of x) $ Term.lambda x t;
-
-(*** Basic HOLCF concepts ***)
-
-fun mk_bottom T = Const (@{const_name UU}, T);
-
-fun below_const T = Const (@{const_name below}, [T, T] ---> boolT);
-fun mk_below (t, u) = below_const (fastype_of t) $ t $ u;
-
-fun mk_undef t = mk_eq (t, mk_bottom (fastype_of t));
-
-fun mk_defined t = mk_not (mk_undef t);
-
-fun mk_compact t =
-  Const (@{const_name compact}, fastype_of t --> boolT) $ t;
-
-fun mk_cont t =
-  Const (@{const_name cont}, fastype_of t --> boolT) $ t;
-
-
-(*** Continuous function space ***)
-
-(* ->> is taken from holcf_logic.ML *)
-fun mk_cfunT (T, U) = Type(@{type_name "->"}, [T, U]);
-
-infixr 6 ->>; val (op ->>) = mk_cfunT;
-infix -->>; val (op -->>) = Library.foldr mk_cfunT;
-
-fun dest_cfunT (Type(@{type_name "->"}, [T, U])) = (T, U)
-  | dest_cfunT T = raise TYPE ("dest_cfunT", [T], []);
-
-fun capply_const (S, T) =
-  Const(@{const_name Rep_CFun}, (S ->> T) --> (S --> T));
-
-fun cabs_const (S, T) =
-  Const(@{const_name Abs_CFun}, (S --> T) --> (S ->> T));
-
-fun mk_cabs t =
-  let val T = fastype_of t
-  in cabs_const (Term.domain_type T, Term.range_type T) $ t end
-
-(* builds the expression (% v1 v2 .. vn. rhs) *)
-fun lambdas [] rhs = rhs
-  | lambdas (v::vs) rhs = Term.lambda v (lambdas vs rhs);
-
-(* builds the expression (LAM v. rhs) *)
-fun big_lambda v rhs =
-  cabs_const (fastype_of v, fastype_of rhs) $ Term.lambda v rhs;
-
-(* builds the expression (LAM v1 v2 .. vn. rhs) *)
-fun big_lambdas [] rhs = rhs
-  | big_lambdas (v::vs) rhs = big_lambda v (big_lambdas vs rhs);
-
-fun mk_capply (t, u) =
-  let val (S, T) =
-    case fastype_of t of
-        Type(@{type_name "->"}, [S, T]) => (S, T)
-      | _ => raise TERM ("mk_capply " ^ ML_Syntax.print_list ML_Syntax.print_term [t, u], [t, u]);
-  in capply_const (S, T) $ t $ u end;
-
-infix 9 ` ; val (op `) = mk_capply;
-
-val list_ccomb : term * term list -> term = Library.foldl mk_capply;
-
-fun mk_ID T = Const (@{const_name ID}, T ->> T);
-
-fun cfcomp_const (T, U, V) =
-  Const (@{const_name cfcomp}, (U ->> V) ->> (T ->> U) ->> (T ->> V));
-
-fun mk_cfcomp (f, g) =
-  let
-    val (U, V) = dest_cfunT (fastype_of f);
-    val (T, U') = dest_cfunT (fastype_of g);
-  in
-    if U = U'
-    then mk_capply (mk_capply (cfcomp_const (T, U, V), f), g)
-    else raise TYPE ("mk_cfcomp", [U, U'], [f, g])
-  end;
-
-
-(*** Product type ***)
-
-val mk_prodT = HOLogic.mk_prodT
-
-fun mk_tupleT [] = HOLogic.unitT
-  | mk_tupleT [T] = T
-  | mk_tupleT (T :: Ts) = mk_prodT (T, mk_tupleT Ts);
-
-(* builds the expression (v1,v2,..,vn) *)
-fun mk_tuple [] = HOLogic.unit
-  | mk_tuple (t::[]) = t
-  | mk_tuple (t::ts) = HOLogic.mk_prod (t, mk_tuple ts);
-
-(* builds the expression (%(v1,v2,..,vn). rhs) *)
-fun lambda_tuple [] rhs = Term.lambda (Free("unit", HOLogic.unitT)) rhs
-  | lambda_tuple (v::[]) rhs = Term.lambda v rhs
-  | lambda_tuple (v::vs) rhs =
-      HOLogic.mk_split (Term.lambda v (lambda_tuple vs rhs));
-
-
-(*** Lifted cpo type ***)
-
-fun mk_upT T = Type(@{type_name "u"}, [T]);
-
-fun dest_upT (Type(@{type_name "u"}, [T])) = T
-  | dest_upT T = raise TYPE ("dest_upT", [T], []);
-
-fun up_const T = Const(@{const_name up}, T ->> mk_upT T);
-
-fun mk_up t = up_const (fastype_of t) ` t;
-
-fun fup_const (T, U) =
-  Const(@{const_name fup}, (T ->> U) ->> mk_upT T ->> U);
-
-fun from_up T = fup_const (T, T) ` mk_ID T;
-
-
-(*** Strict product type ***)
-
-val oneT = @{typ "one"};
-
-fun mk_sprodT (T, U) = Type(@{type_name "**"}, [T, U]);
-
-fun dest_sprodT (Type(@{type_name "**"}, [T, U])) = (T, U)
-  | dest_sprodT T = raise TYPE ("dest_sprodT", [T], []);
-
-fun spair_const (T, U) =
-  Const(@{const_name spair}, T ->> U ->> mk_sprodT (T, U));
-
-(* builds the expression (:t, u:) *)
-fun mk_spair (t, u) =
-  spair_const (fastype_of t, fastype_of u) ` t ` u;
-
-(* builds the expression (:t1,t2,..,tn:) *)
-fun mk_stuple [] = @{term "ONE"}
-  | mk_stuple (t::[]) = t
-  | mk_stuple (t::ts) = mk_spair (t, mk_stuple ts);
-
-fun sfst_const (T, U) =
-  Const(@{const_name sfst}, mk_sprodT (T, U) ->> T);
-
-fun ssnd_const (T, U) =
-  Const(@{const_name ssnd}, mk_sprodT (T, U) ->> U);
-
-
-(*** Strict sum type ***)
-
-fun mk_ssumT (T, U) = Type(@{type_name "++"}, [T, U]);
-
-fun dest_ssumT (Type(@{type_name "++"}, [T, U])) = (T, U)
-  | dest_ssumT T = raise TYPE ("dest_ssumT", [T], []);
-
-fun sinl_const (T, U) = Const(@{const_name sinl}, T ->> mk_ssumT (T, U));
-fun sinr_const (T, U) = Const(@{const_name sinr}, U ->> mk_ssumT (T, U));
-
-(* builds the list [sinl(t1), sinl(sinr(t2)), ... sinr(...sinr(tn))] *)
-fun mk_sinjects ts =
-  let
-    val Ts = map fastype_of ts;
-    fun combine (t, T) (us, U) =
-      let
-        val v = sinl_const (T, U) ` t;
-        val vs = map (fn u => sinr_const (T, U) ` u) us;
-      in
-        (v::vs, mk_ssumT (T, U))
-      end
-    fun inj [] = error "mk_sinjects: empty list"
-      | inj ((t, T)::[]) = ([t], T)
-      | inj ((t, T)::ts) = combine (t, T) (inj ts);
-  in
-    fst (inj (ts ~~ Ts))
-  end;
-
-fun sscase_const (T, U, V) =
-  Const(@{const_name sscase},
-    (T ->> V) ->> (U ->> V) ->> mk_ssumT (T, U) ->> V);
-
-fun from_sinl (T, U) =
-  sscase_const (T, U, T) ` mk_ID T ` mk_bottom (U ->> T);
-
-fun from_sinr (T, U) =
-  sscase_const (T, U, U) ` mk_bottom (T ->> U) ` mk_ID U;
-
-
-(*** pattern match monad type ***)
-
-fun mk_matchT T = Type (@{type_name "maybe"}, [T]);
-
-fun dest_matchT (Type(@{type_name "maybe"}, [T])) = T
-  | dest_matchT T = raise TYPE ("dest_matchT", [T], []);
-
-fun mk_fail T = Const (@{const_name "Fixrec.fail"}, mk_matchT T);
-
-fun return_const T = Const (@{const_name "Fixrec.return"}, T ->> mk_matchT T);
-fun mk_return t = return_const (fastype_of t) ` t;
-
-
-(*** miscellaneous constructions ***)
-
-val trT = @{typ "tr"};
-
-val deflT = @{typ "udom alg_defl"};
-
-fun mapT T =
-  let
-    fun argTs (Type (_, Ts)) = Ts | argTs _ = [];
-    fun auto T = T ->> T;
-  in
-    map auto (argTs T) -->> auto T
-  end;
-
-fun mk_strict t =
-  let val (T, U) = dest_cfunT (fastype_of t);
-  in mk_eq (t ` mk_bottom T, mk_bottom U) end;
-
-fun mk_fix t =
-  let val (T, _) = dest_cfunT (fastype_of t)
-  in mk_capply (Const(@{const_name fix}, (T ->> T) ->> T), t) end;
-
-fun mk_Rep_of T =
-  Const (@{const_name Rep_of}, Term.itselfT T --> deflT) $ Logic.mk_type T;
-
-fun coerce_const T = Const (@{const_name coerce}, T);
-
-fun isodefl_const T =
-  Const (@{const_name isodefl}, (T ->> T) --> deflT --> boolT);
-
-(* splits a cterm into the right and lefthand sides of equality *)
-fun dest_eqs t = HOLogic.dest_eq (HOLogic.dest_Trueprop t);
-
-fun mk_eqs (t, u) = HOLogic.mk_Trueprop (HOLogic.mk_eq (t, u));
-
+open HOLCF_Library;
 
 (************************** miscellaneous functions ***************************)
 
diff -r 7675a41e755a -r 979019ab92eb src/HOLCF/Tools/Domain/domain_isomorphism.ML
--- a/src/HOLCF/Tools/Domain/domain_isomorphism.ML	Sun Feb 28 15:09:09 2010 -0800
+++ b/src/HOLCF/Tools/Domain/domain_isomorphism.ML	Sun Feb 28 15:30:44 2010 -0800
@@ -94,99 +94,20 @@
 
 
 (******************************************************************************)
-(******************************* building types *******************************)
+(************************** building types and terms **************************)
 (******************************************************************************)
 
-(* ->> is taken from holcf_logic.ML *)
-fun cfunT (T, U) = Type(@{type_name "->"}, [T, U]);
-
-infixr 6 ->>; val (op ->>) = cfunT;
+open HOLCF_Library;
 
-fun dest_cfunT (Type(@{type_name "->"}, [T, U])) = (T, U)
-  | dest_cfunT T = raise TYPE ("dest_cfunT", [T], []);
-
-fun tupleT [] = HOLogic.unitT
-  | tupleT [T] = T
-  | tupleT (T :: Ts) = HOLogic.mk_prodT (T, tupleT Ts);
+infixr 6 ->>;
+infix -->>;
 
 val deflT = @{typ "udom alg_defl"};
 
 fun mapT (T as Type (_, Ts)) =
-    Library.foldr cfunT (map (fn T => T ->> T) Ts, T ->> T)
+    (map (fn T => T ->> T) Ts) -->> (T ->> T)
   | mapT T = T ->> T;
 
-(******************************************************************************)
-(******************************* building terms *******************************)
-(******************************************************************************)
-
-(* builds the expression (v1,v2,..,vn) *)
-fun mk_tuple [] = HOLogic.unit
-|   mk_tuple (t::[]) = t
-|   mk_tuple (t::ts) = HOLogic.mk_prod (t, mk_tuple ts);
-
-(* builds the expression (%(v1,v2,..,vn). rhs) *)
-fun lambda_tuple [] rhs = Term.lambda (Free("unit", HOLogic.unitT)) rhs
-  | lambda_tuple (v::[]) rhs = Term.lambda v rhs
-  | lambda_tuple (v::vs) rhs =
-      HOLogic.mk_split (Term.lambda v (lambda_tuple vs rhs));
-
-(* continuous application and abstraction *)
-
-fun capply_const (S, T) =
-  Const(@{const_name Rep_CFun}, (S ->> T) --> (S --> T));
-
-fun cabs_const (S, T) =
-  Const(@{const_name Abs_CFun}, (S --> T) --> (S ->> T));
-
-fun mk_cabs t =
-  let val T = Term.fastype_of t
-  in cabs_const (Term.domain_type T, Term.range_type T) $ t end
-
-(* builds the expression (LAM v. rhs) *)
-fun big_lambda v rhs =
-  cabs_const (Term.fastype_of v, Term.fastype_of rhs) $ Term.lambda v rhs;
-
-(* builds the expression (LAM v1 v2 .. vn. rhs) *)
-fun big_lambdas [] rhs = rhs
-  | big_lambdas (v::vs) rhs = big_lambda v (big_lambdas vs rhs);
-
-fun mk_capply (t, u) =
-  let val (S, T) =
-    case Term.fastype_of t of
-        Type(@{type_name "->"}, [S, T]) => (S, T)
-      | _ => raise TERM ("mk_capply " ^ ML_Syntax.print_list ML_Syntax.print_term [t, u], [t, u]);
-  in capply_const (S, T) $ t $ u end;
-
-(* miscellaneous term constructions *)
-
-val mk_trp = HOLogic.mk_Trueprop;
-
-val mk_fst = HOLogic.mk_fst;
-val mk_snd = HOLogic.mk_snd;
-
-fun mk_cont t =
-  let val T = Term.fastype_of t
-  in Const(@{const_name cont}, T --> HOLogic.boolT) $ t end;
-
-fun mk_fix t =
-  let val (T, _) = dest_cfunT (Term.fastype_of t)
-  in mk_capply (Const(@{const_name fix}, (T ->> T) ->> T), t) end;
-
-fun ID_const T = Const (@{const_name ID}, cfunT (T, T));
-
-fun cfcomp_const (T, U, V) =
-  Const (@{const_name cfcomp}, (U ->> V) ->> (T ->> U) ->> (T ->> V));
-
-fun mk_cfcomp (f, g) =
-  let
-    val (U, V) = dest_cfunT (Term.fastype_of f);
-    val (T, U') = dest_cfunT (Term.fastype_of g);
-  in
-    if U = U'
-    then mk_capply (mk_capply (cfcomp_const (T, U, V), f), g)
-    else raise TYPE ("mk_cfcomp", [U, U'], [f, g])
-  end;
-
 fun mk_Rep_of T =
   Const (@{const_name Rep_of}, Term.itselfT T --> deflT) $ Logic.mk_type T;
 
@@ -301,7 +222,7 @@
         case Symtab.lookup tab c of
           SOME t => Library.foldl mk_capply (Const (t, mapT T), map map_of Ts)
         | NONE => if is_closed_typ T
-                  then ID_const T
+                  then mk_ID T
                   else error ("map_of_typ: type variable under unsupported type constructor " ^ c);
   in map_of T end;
 
@@ -383,7 +304,7 @@
     (* declare deflation combinator constants *)
     fun declare_defl_const (vs, tbind, mx, rhs, morphs) thy =
       let
-        val defl_type = Library.foldr cfunT (map (K deflT) vs, deflT);
+        val defl_type = map (K deflT) vs -->> deflT;
         val defl_bind = Binding.suffix_name "_defl" tbind;
       in
         Sign.declare_const ((defl_bind, defl_type), NoSyn) thy
@@ -442,8 +363,8 @@
     (* define rep/abs functions *)
     fun mk_rep_abs ((tbind, morphs), (lhsT, rhsT)) thy =
       let
-        val rep_type = cfunT (lhsT, rhsT);
-        val abs_type = cfunT (rhsT, lhsT);
+        val rep_type = lhsT ->> rhsT;
+        val abs_type = rhsT ->> lhsT;
         val rep_bind = Binding.suffix_name "_rep" tbind;
         val abs_bind = Binding.suffix_name "_abs" tbind;
         val (rep_bind, abs_bind) = the_default (rep_bind, abs_bind) morphs;
@@ -594,8 +515,8 @@
         (((map_const, (lhsT, _)), REP_thm), isodefl_thm) =
       let
         val Ts = snd (dest_Type lhsT);
-        val lhs = Library.foldl mk_capply (map_const, map ID_const Ts);
-        val goal = mk_eqs (lhs, ID_const lhsT);
+        val lhs = Library.foldl mk_capply (map_const, map mk_ID Ts);
+        val goal = mk_eqs (lhs, mk_ID lhsT);
         val tac = EVERY
           [rtac @{thm isodefl_REP_imp_ID} 1,
            stac REP_thm 1,
@@ -616,7 +537,7 @@
     (* define copy combinators *)
     val new_dts =
       map (apsnd (map (fst o dest_TFree)) o dest_Type o fst) dom_eqns;
-    val copy_arg_type = tupleT (map (fn (T, _) => T ->> T) dom_eqns);
+    val copy_arg_type = mk_tupleT (map (fn (T, _) => T ->> T) dom_eqns);
     val copy_arg = Free ("f", copy_arg_type);
     val copy_args =
       let fun mk_copy_args [] t = []
@@ -627,16 +548,16 @@
     fun copy_of_dtyp (T, dt) =
         if Datatype_Aux.is_rec_type dt
         then copy_of_dtyp' (T, dt)
-        else ID_const T
+        else mk_ID T
     and copy_of_dtyp' (T, Datatype_Aux.DtRec i) = nth copy_args i
-      | copy_of_dtyp' (T, Datatype_Aux.DtTFree a) = ID_const T
+      | copy_of_dtyp' (T, Datatype_Aux.DtTFree a) = mk_ID T
       | copy_of_dtyp' (T, Datatype_Aux.DtType (c, ds)) =
         case Symtab.lookup map_tab' c of
           SOME f =>
           Library.foldl mk_capply
             (Const (f, mapT T), map copy_of_dtyp (snd (dest_Type T) ~~ ds))
         | NONE =>
-          (warning ("copy_of_dtyp: unknown type constructor " ^ c); ID_const T);
+          (warning ("copy_of_dtyp: unknown type constructor " ^ c); mk_ID T);
     fun define_copy ((tbind, (rep_const, abs_const)), (lhsT, rhsT)) thy =
       let
         val copy_type = copy_arg_type ->> (lhsT ->> lhsT);
@@ -686,7 +607,7 @@
     val fix_copy_lemma =
       let
         fun mk_map_ID (map_const, (T, rhsT)) =
-          Library.foldl mk_capply (map_const, map ID_const (snd (dest_Type T)));
+          Library.foldl mk_capply (map_const, map mk_ID (snd (dest_Type T)));
         val rhs = mk_tuple (map mk_map_ID (map_consts ~~ dom_eqns));
         val goal = mk_eqs (mk_fix c_const, rhs);
         val rules =
diff -r 7675a41e755a -r 979019ab92eb src/HOLCF/Tools/holcf_library.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Tools/holcf_library.ML	Sun Feb 28 15:30:44 2010 -0800
@@ -0,0 +1,237 @@
+(*  Title:      HOLCF/Tools/holcf_library.ML
+    Author:     Brian Huffman
+
+Functions for constructing HOLCF types and terms.
+*)
+
+structure HOLCF_Library =
+struct
+
+(*** Operations from Isabelle/HOL ***)
+
+val boolT = HOLogic.boolT;
+
+val mk_equals = Logic.mk_equals;
+val mk_eq = HOLogic.mk_eq;
+val mk_trp = HOLogic.mk_Trueprop;
+val mk_fst = HOLogic.mk_fst;
+val mk_snd = HOLogic.mk_snd;
+val mk_not = HOLogic.mk_not;
+val mk_conj = HOLogic.mk_conj;
+val mk_disj = HOLogic.mk_disj;
+
+fun mk_ex (x, t) = HOLogic.exists_const (fastype_of x) $ Term.lambda x t;
+
+
+(*** Basic HOLCF concepts ***)
+
+fun mk_bottom T = Const (@{const_name UU}, T);
+
+fun below_const T = Const (@{const_name below}, [T, T] ---> boolT);
+fun mk_below (t, u) = below_const (fastype_of t) $ t $ u;
+
+fun mk_undef t = mk_eq (t, mk_bottom (fastype_of t));
+
+fun mk_defined t = mk_not (mk_undef t);
+
+fun mk_compact t =
+  Const (@{const_name compact}, fastype_of t --> boolT) $ t;
+
+fun mk_cont t =
+  Const (@{const_name cont}, fastype_of t --> boolT) $ t;
+
+
+(*** Continuous function space ***)
+
+(* ->> is taken from holcf_logic.ML *)
+fun mk_cfunT (T, U) = Type(@{type_name "->"}, [T, U]);
+
+infixr 6 ->>; val (op ->>) = mk_cfunT;
+infix -->>; val (op -->>) = Library.foldr mk_cfunT;
+
+fun dest_cfunT (Type(@{type_name "->"}, [T, U])) = (T, U)
+  | dest_cfunT T = raise TYPE ("dest_cfunT", [T], []);
+
+fun capply_const (S, T) =
+  Const(@{const_name Rep_CFun}, (S ->> T) --> (S --> T));
+
+fun cabs_const (S, T) =
+  Const(@{const_name Abs_CFun}, (S --> T) --> (S ->> T));
+
+fun mk_cabs t =
+  let val T = fastype_of t
+  in cabs_const (Term.domain_type T, Term.range_type T) $ t end
+
+(* builds the expression (% v1 v2 .. vn. rhs) *)
+fun lambdas [] rhs = rhs
+  | lambdas (v::vs) rhs = Term.lambda v (lambdas vs rhs);
+
+(* builds the expression (LAM v. rhs) *)
+fun big_lambda v rhs =
+  cabs_const (fastype_of v, fastype_of rhs) $ Term.lambda v rhs;
+
+(* builds the expression (LAM v1 v2 .. vn. rhs) *)
+fun big_lambdas [] rhs = rhs
+  | big_lambdas (v::vs) rhs = big_lambda v (big_lambdas vs rhs);
+
+fun mk_capply (t, u) =
+  let val (S, T) =
+    case fastype_of t of
+        Type(@{type_name "->"}, [S, T]) => (S, T)
+      | _ => raise TERM ("mk_capply " ^ ML_Syntax.print_list ML_Syntax.print_term [t, u], [t, u]);
+  in capply_const (S, T) $ t $ u end;
+
+infix 9 ` ; val (op `) = mk_capply;
+
+val list_ccomb : term * term list -> term = Library.foldl mk_capply;
+
+fun mk_ID T = Const (@{const_name ID}, T ->> T);
+
+fun cfcomp_const (T, U, V) =
+  Const (@{const_name cfcomp}, (U ->> V) ->> (T ->> U) ->> (T ->> V));
+
+fun mk_cfcomp (f, g) =
+  let
+    val (U, V) = dest_cfunT (fastype_of f);
+    val (T, U') = dest_cfunT (fastype_of g);
+  in
+    if U = U'
+    then mk_capply (mk_capply (cfcomp_const (T, U, V), f), g)
+    else raise TYPE ("mk_cfcomp", [U, U'], [f, g])
+  end;
+
+fun mk_strict t =
+  let val (T, U) = dest_cfunT (fastype_of t);
+  in mk_eq (t ` mk_bottom T, mk_bottom U) end;
+
+
+(*** Product type ***)
+
+val mk_prodT = HOLogic.mk_prodT
+
+fun mk_tupleT [] = HOLogic.unitT
+  | mk_tupleT [T] = T
+  | mk_tupleT (T :: Ts) = mk_prodT (T, mk_tupleT Ts);
+
+(* builds the expression (v1,v2,..,vn) *)
+fun mk_tuple [] = HOLogic.unit
+  | mk_tuple (t::[]) = t
+  | mk_tuple (t::ts) = HOLogic.mk_prod (t, mk_tuple ts);
+
+(* builds the expression (%(v1,v2,..,vn). rhs) *)
+fun lambda_tuple [] rhs = Term.lambda (Free("unit", HOLogic.unitT)) rhs
+  | lambda_tuple (v::[]) rhs = Term.lambda v rhs
+  | lambda_tuple (v::vs) rhs =
+      HOLogic.mk_split (Term.lambda v (lambda_tuple vs rhs));
+
+
+(*** Lifted cpo type ***)
+
+fun mk_upT T = Type(@{type_name "u"}, [T]);
+
+fun dest_upT (Type(@{type_name "u"}, [T])) = T
+  | dest_upT T = raise TYPE ("dest_upT", [T], []);
+
+fun up_const T = Const(@{const_name up}, T ->> mk_upT T);
+
+fun mk_up t = up_const (fastype_of t) ` t;
+
+fun fup_const (T, U) =
+  Const(@{const_name fup}, (T ->> U) ->> mk_upT T ->> U);
+
+fun from_up T = fup_const (T, T) ` mk_ID T;
+
+
+(*** Strict product type ***)
+
+val oneT = @{typ "one"};
+
+fun mk_sprodT (T, U) = Type(@{type_name "**"}, [T, U]);
+
+fun dest_sprodT (Type(@{type_name "**"}, [T, U])) = (T, U)
+  | dest_sprodT T = raise TYPE ("dest_sprodT", [T], []);
+
+fun spair_const (T, U) =
+  Const(@{const_name spair}, T ->> U ->> mk_sprodT (T, U));
+
+(* builds the expression (:t, u:) *)
+fun mk_spair (t, u) =
+  spair_const (fastype_of t, fastype_of u) ` t ` u;
+
+(* builds the expression (:t1,t2,..,tn:) *)
+fun mk_stuple [] = @{term "ONE"}
+  | mk_stuple (t::[]) = t
+  | mk_stuple (t::ts) = mk_spair (t, mk_stuple ts);
+
+fun sfst_const (T, U) =
+  Const(@{const_name sfst}, mk_sprodT (T, U) ->> T);
+
+fun ssnd_const (T, U) =
+  Const(@{const_name ssnd}, mk_sprodT (T, U) ->> U);
+
+
+(*** Strict sum type ***)
+
+fun mk_ssumT (T, U) = Type(@{type_name "++"}, [T, U]);
+
+fun dest_ssumT (Type(@{type_name "++"}, [T, U])) = (T, U)
+  | dest_ssumT T = raise TYPE ("dest_ssumT", [T], []);
+
+fun sinl_const (T, U) = Const(@{const_name sinl}, T ->> mk_ssumT (T, U));
+fun sinr_const (T, U) = Const(@{const_name sinr}, U ->> mk_ssumT (T, U));
+
+(* builds the list [sinl(t1), sinl(sinr(t2)), ... sinr(...sinr(tn))] *)
+fun mk_sinjects ts =
+  let
+    val Ts = map fastype_of ts;
+    fun combine (t, T) (us, U) =
+      let
+        val v = sinl_const (T, U) ` t;
+        val vs = map (fn u => sinr_const (T, U) ` u) us;
+      in
+        (v::vs, mk_ssumT (T, U))
+      end
+    fun inj [] = error "mk_sinjects: empty list"
+      | inj ((t, T)::[]) = ([t], T)
+      | inj ((t, T)::ts) = combine (t, T) (inj ts);
+  in
+    fst (inj (ts ~~ Ts))
+  end;
+
+fun sscase_const (T, U, V) =
+  Const(@{const_name sscase},
+    (T ->> V) ->> (U ->> V) ->> mk_ssumT (T, U) ->> V);
+
+fun from_sinl (T, U) =
+  sscase_const (T, U, T) ` mk_ID T ` mk_bottom (U ->> T);
+
+fun from_sinr (T, U) =
+  sscase_const (T, U, U) ` mk_bottom (T ->> U) ` mk_ID U;
+
+
+(*** pattern match monad type ***)
+
+fun mk_matchT T = Type (@{type_name "maybe"}, [T]);
+
+fun dest_matchT (Type(@{type_name "maybe"}, [T])) = T
+  | dest_matchT T = raise TYPE ("dest_matchT", [T], []);
+
+fun mk_fail T = Const (@{const_name "Fixrec.fail"}, mk_matchT T);
+
+fun return_const T = Const (@{const_name "Fixrec.return"}, T ->> mk_matchT T);
+fun mk_return t = return_const (fastype_of t) ` t;
+
+
+(*** lifted boolean type ***)
+
+val trT = @{typ "tr"};
+
+
+(*** theory of fixed points ***)
+
+fun mk_fix t =
+  let val (T, _) = dest_cfunT (fastype_of t)
+  in mk_capply (Const(@{const_name fix}, (T ->> T) ->> T), t) end;
+
+
+end;