(*  Title:      HOLCF/Tools/holcf_library.ML

     Author:     Brian Huffman

 Functions for constructing HOLCF types and terms.

 *)

 structure HOLCF_Library =

 struct

 infixr 6 ->>;

 infixr -->>;

 infix 9 `;

 (*** Operations from Isabelle/HOL ***)

 val boolT = HOLogic.boolT;

 val natT = HOLogic.natT;

 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;

 val mk_imp = HOLogic.mk_imp;

 fun mk_ex (x, t) = HOLogic.exists_const (fastype_of x) $ Term.lambda x t;

 fun mk_all (x, t) = HOLogic.all_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_adm t =

   Const (@{const_name adm}, fastype_of t --> boolT) $ 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;

 fun mk_chain t =

   Const (@{const_name chain}, Term.fastype_of t --> boolT) $ t;

 fun mk_lub t =

   let

     val T = Term.range_type (Term.fastype_of t);

     val lub_const = Const (@{const_name lub}, (T --> boolT) --> T);

     val UNIV_const = @{term "UNIV :: nat set"};

     val image_type = (natT --> T) --> (natT --> boolT) --> T --> boolT;

     val image_const = Const (@{const_name image}, image_type);

   in

     lub_const $ (image_const $ t $ UNIV_const)

   end;

 (*** Continuous function space ***)

 fun mk_cfunT (T, U) = Type(@{type_name cfun}, [T, U]);

 val (op ->>) = mk_cfunT;

 val (op -->>) = Library.foldr mk_cfunT;

 fun dest_cfunT (Type(@{type_name cfun}, [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 cfun}, [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;

 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 strictify_const T = Const (@{const_name strictify}, T ->> T);

 fun mk_strictify t = strictify_const (fastype_of t) ` t;

 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 mk_fup t = fup_const (dest_cfunT (fastype_of t)) ` t;

 fun from_up T = fup_const (T, T) ` mk_ID T;

 (*** Lifted unit type ***)

 val oneT = @{typ "one"};

 fun one_case_const T = Const (@{const_name one_case}, T ->> oneT ->> T);

 fun mk_one_case t = one_case_const (fastype_of t) ` t;

 (*** Strict product type ***)

 fun mk_sprodT (T, U) = Type(@{type_name sprod}, [T, U]);

 fun dest_sprodT (Type(@{type_name sprod}, [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);

 fun ssplit_const (T, U, V) =

   Const (@{const_name ssplit}, (T ->> U ->> V) ->> mk_sprodT (T, U) ->> V);

 fun mk_ssplit t =

   let val (T, (U, V)) = apsnd dest_cfunT (dest_cfunT (fastype_of t));

   in ssplit_const (T, U, V) ` t end;

 (*** Strict sum type ***)

 fun mk_ssumT (T, U) = Type(@{type_name ssum}, [T, U]);

 fun dest_ssumT (Type(@{type_name ssum}, [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 [] = raise Fail "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 mk_sscase (t, u) =

   let val (T, V) = dest_cfunT (fastype_of t);

       val (U, V) = dest_cfunT (fastype_of u);

   in sscase_const (T, U, V) ` t ` u end;

 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 "match"}, [T]);

 fun dest_matchT (Type(@{type_name "match"}, [T])) = T

   | dest_matchT T = raise TYPE ("dest_matchT", [T], []);

 fun mk_fail T = Const (@{const_name "Fixrec.fail"}, mk_matchT T);

 fun succeed_const T = Const (@{const_name "Fixrec.succeed"}, T ->> mk_matchT T);

 fun mk_succeed t = succeed_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;

 fun iterate_const T =

   Const (@{const_name iterate}, natT --> (T ->> T) ->> (T ->> T));

 fun mk_iterate (n, f) =

   let val (T, _) = dest_cfunT (Term.fastype_of f);

   in (iterate_const T $ n) ` f ` mk_bottom T end;

 end;