src/HOLCF/Tools/domain/domain_library.ML
author huffman
Tue, 12 May 2009 12:01:25 -0700
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child 31228 bcacfd816d28
permissions -rw-r--r--
add cpo_type function
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(*  Title:      HOLCF/Tools/domain/domain_library.ML
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    Author:     David von Oheimb
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Library for domain command.
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*)
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(* ----- general support ---------------------------------------------------- *)
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fun mapn f n []      = []
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|   mapn f n (x::xs) = (f n x) :: mapn f (n+1) xs;
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fun foldr'' f (l,f2) = let fun itr []  = raise Fail "foldr''"
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			     | itr [a] = f2 a
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			     | itr (a::l) = f(a, itr l)
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in  itr l  end;
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fun map_cumulr f start xs = List.foldr (fn (x,(ys,res))=>case f(x,res) of (y,res2) =>
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						  (y::ys,res2)) ([],start) xs;
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fun first  (x,_,_) = x; fun second (_,x,_) = x; fun third  (_,_,x) = x;
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fun upd_first  f (x,y,z) = (f x,   y,   z);
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fun upd_second f (x,y,z) = (  x, f y,   z);
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fun upd_third  f (x,y,z) = (  x,   y, f z);
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fun atomize ctxt thm = let val r_inst = read_instantiate ctxt;
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    fun at  thm = case concl_of thm of
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      _$(Const("op &",_)$_$_)       => at(thm RS conjunct1)@at(thm RS conjunct2)
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    | _$(Const("All" ,_)$Abs(s,_,_))=> at(thm RS (r_inst [(("x", 0), "?" ^ s)] spec))
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    | _				    => [thm];
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in map zero_var_indexes (at thm) end;
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(* infix syntax *)
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infixr 5 -->;
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infixr 6 ->>;
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infixr 0 ===>;
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infixr 0 ==>;
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infix 0 ==;
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infix 1 ===;
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infix 1 ~=;
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infix 1 <<;
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infix 1 ~<<;
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infix 9 `  ;
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infix 9 `% ;
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infix 9 `%%;
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(* ----- specific support for domain ---------------------------------------- *)
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signature DOMAIN_LIBRARY =
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sig
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  val Imposs : string -> 'a;
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  val cpo_type : theory -> typ -> bool;
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  val pcpo_type : theory -> typ -> bool;
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  val string_of_typ : theory -> typ -> string;
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  (* Creating HOLCF types *)
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  val mk_cfunT : typ * typ -> typ;
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  val ->> : typ * typ -> typ;
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  val mk_ssumT : typ * typ -> typ;
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  val mk_sprodT : typ * typ -> typ;
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  val mk_uT : typ -> typ;
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  val oneT : typ;
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  val trT : typ;
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  val mk_maybeT : typ -> typ;
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  val mk_ctupleT : typ list -> typ;
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  val mk_TFree : string -> typ;
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  val pcpoS : sort;
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  (* Creating HOLCF terms *)
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  val %: : string -> term;
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  val %%: : string -> term;
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  val ` : term * term -> term;
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  val `% : term * string -> term;
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  val /\ : string -> term -> term;
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  val UU : term;
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  val TT : term;
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  val FF : term;
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  val mk_up : term -> term;
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  val mk_sinl : term -> term;
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  val mk_sinr : term -> term;
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  val mk_stuple : term list -> term;
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  val mk_ctuple : term list -> term;
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  val mk_fix : term -> term;
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  val mk_iterate : term * term * term -> term;
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  val mk_fail : term;
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  val mk_return : term -> term;
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  val cproj : term -> 'a list -> int -> term;
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  val list_ccomb : term * term list -> term;
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  val con_app : string -> ('a * 'b * string) list -> term;
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  val con_app2 : string -> ('a -> term) -> 'a list -> term;
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  val proj : term -> 'a list -> int -> term;
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  val prj : ('a -> 'b -> 'a) -> ('a -> 'b -> 'a) -> 'a -> 'b list -> int -> 'a;
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  val mk_ctuple_pat : term list -> term;
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  val mk_branch : term -> term;
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  (* Creating propositions *)
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  val mk_conj : term * term -> term;
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  val mk_disj : term * term -> term;
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  val mk_imp : term * term -> term;
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  val mk_lam : string * term -> term;
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  val mk_all : string * term -> term;
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  val mk_ex : string * term -> term;
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  val mk_constrain : typ * term -> term;
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  val mk_constrainall : string * typ * term -> term;
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  val === : term * term -> term;
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  val << : term * term -> term;
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  val ~<< : term * term -> term;
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  val strict : term -> term;
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  val defined : term -> term;
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  val mk_adm : term -> term;
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  val mk_compact : term -> term;
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  val lift : ('a -> term) -> 'a list * term -> term;
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  val lift_defined : ('a -> term) -> 'a list * term -> term;
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  (* Creating meta-propositions *)
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  val mk_trp : term -> term; (* HOLogic.mk_Trueprop *)
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  val == : term * term -> term;
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  val ===> : term * term -> term;
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  val ==> : term * term -> term;
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  val mk_All : string * term -> term;
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  (* Domain specifications *)
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  type arg = (bool * int * DatatypeAux.dtyp) * string option * string;
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  type cons = string * arg list;
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  type eq = (string * typ list) * cons list;
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  val is_lazy : arg -> bool;
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  val rec_of : arg -> int;
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  val sel_of : arg -> string option;
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  val vname : arg -> string;
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  val upd_vname : (string -> string) -> arg -> arg;
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  val is_rec : arg -> bool;
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  val is_nonlazy_rec : arg -> bool;
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  val nonlazy : arg list -> string list;
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  val nonlazy_rec : arg list -> string list;
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  val %# : arg -> term;
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  val /\# : arg * term -> term;
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  val when_body : cons list -> (int * int -> term) -> term;
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  val when_funs : 'a list -> string list;
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  val bound_arg : ''a list -> ''a -> term; (* ''a = arg or string *)
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  val idx_name : 'a list -> string -> int -> string;
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  val app_rec_arg : (int -> term) -> arg -> term;
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  (* Name mangling *)
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  val strip_esc : string -> string;
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  val extern_name : string -> string;
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  val dis_name : string -> string;
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  val mat_name : string -> string;
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  val pat_name : string -> string;
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  val mk_var_names : string list -> string list;
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end;
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structure Domain_Library :> DOMAIN_LIBRARY =
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struct
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exception Impossible of string;
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fun Imposs msg = raise Impossible ("Domain:"^msg);
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(* ----- name handling ----- *)
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val strip_esc = let fun strip ("'" :: c :: cs) = c :: strip cs
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		    |   strip ["'"] = []
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		    |   strip (c :: cs) = c :: strip cs
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		    |   strip [] = [];
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in implode o strip o Symbol.explode end;
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fun extern_name con = case Symbol.explode con of 
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		   ("o"::"p"::" "::rest) => implode rest
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		   | _ => con;
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fun dis_name  con = "is_"^ (extern_name con);
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fun dis_name_ con = "is_"^ (strip_esc   con);
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fun mat_name  con = "match_"^ (extern_name con);
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fun mat_name_ con = "match_"^ (strip_esc   con);
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fun pat_name  con = (extern_name con) ^ "_pat";
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fun pat_name_ con = (strip_esc   con) ^ "_pat";
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(* make distinct names out of the type list, 
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   forbidding "o","n..","x..","f..","P.." as names *)
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(* a number string is added if necessary *)
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fun mk_var_names ids : string list = let
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    fun nonreserved s = if s mem ["n","x","f","P"] then s^"'" else s;
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    fun index_vnames(vn::vns,occupied) =
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          (case AList.lookup (op =) occupied vn of
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             NONE => if vn mem vns
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                     then (vn^"1") :: index_vnames(vns,(vn,1)  ::occupied)
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                     else  vn      :: index_vnames(vns,          occupied)
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           | SOME(i) => (vn^(string_of_int (i+1)))
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				   :: index_vnames(vns,(vn,i+1)::occupied))
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      | index_vnames([],occupied) = [];
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in index_vnames(map nonreserved ids, [("O",0),("o",0)]) end;
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fun cpo_type sg t = Sign.of_sort sg (Sign.certify_typ sg t, @{sort cpo});
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fun pcpo_type sg t = Sign.of_sort sg (Sign.certify_typ sg t, @{sort pcpo});
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fun string_of_typ sg = Syntax.string_of_typ_global sg o Sign.certify_typ sg;
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(* ----- constructor list handling ----- *)
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type arg =
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  (bool * int * DatatypeAux.dtyp) *	(*  (lazy,recursive element or ~1) *)
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  string option *			(*   selector name    *)
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  string;				(*   argument name    *)
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type cons =
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  string *				(* operator name of constr *)
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  arg list;				(* argument list      *)
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type eq =
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  (string *		(* name      of abstracted type *)
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   typ list) *		(* arguments of abstracted type *)
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  cons list;		(* represented type, as a constructor list *)
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fun rec_of arg  = second (first arg);
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fun is_lazy arg = first (first arg);
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val sel_of    =       second;
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val     vname =       third;
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val upd_vname =   upd_third;
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fun is_rec         arg = rec_of arg >=0;
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fun is_nonlazy_rec arg = is_rec arg andalso not (is_lazy arg);
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fun nonlazy     args   = map vname (filter_out is_lazy    args);
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fun nonlazy_rec args   = map vname (List.filter is_nonlazy_rec args);
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(* ----- support for type and mixfix expressions ----- *)
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fun mk_uT T = Type(@{type_name "u"}, [T]);
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fun mk_cfunT (T, U) = Type(@{type_name "->"}, [T, U]);
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fun mk_sprodT (T, U) = Type(@{type_name "**"}, [T, U]);
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fun mk_ssumT (T, U) = Type(@{type_name "++"}, [T, U]);
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val oneT = @{typ one};
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val trT = @{typ tr};
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val op ->> = mk_cfunT;
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fun mk_TFree s = TFree ("'" ^ s, @{sort pcpo});
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(* ----- support for term expressions ----- *)
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fun %: s = Free(s,dummyT);
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fun %# arg = %:(vname arg);
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fun %%: s = Const(s,dummyT);
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local open HOLogic in
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val mk_trp = mk_Trueprop;
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fun mk_conj (S,T) = conj $ S $ T;
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fun mk_disj (S,T) = disj $ S $ T;
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fun mk_imp  (S,T) = imp  $ S $ T;
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fun mk_lam  (x,T) = Abs(x,dummyT,T);
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fun mk_all  (x,P) = HOLogic.mk_all (x,dummyT,P);
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fun mk_ex   (x,P) = mk_exists (x,dummyT,P);
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val mk_constrain = uncurry TypeInfer.constrain;
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fun mk_constrainall (x,typ,P) = %%:"All" $ (TypeInfer.constrain (typ --> boolT) (mk_lam(x,P)));
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end
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fun mk_All  (x,P) = %%:"all" $ mk_lam(x,P); (* meta universal quantification *)
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infixr 0 ===>;  fun S ===> T = %%:"==>" $ S $ T;
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infixr 0 ==>;   fun S ==> T = mk_trp S ===> mk_trp T;
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infix 0 ==;     fun S ==  T = %%:"==" $ S $ T;
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infix 1 ===;    fun S === T = %%:"op =" $ S $ T;
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infix 1 ~=;     fun S ~=  T = HOLogic.mk_not (S === T);
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infix 1 <<;     fun S <<  T = %%: @{const_name Porder.below} $ S $ T;
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infix 1 ~<<;    fun S ~<< T = HOLogic.mk_not (S << T);
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infix 9 `  ; fun f ` x = %%: @{const_name Rep_CFun} $ f $ x;
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infix 9 `% ; fun f`% s = f` %: s;
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infix 9 `%%; fun f`%%s = f` %%:s;
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fun mk_adm t = %%: @{const_name adm} $ t;
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fun mk_compact t = %%: @{const_name compact} $ t;
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val ID = %%: @{const_name ID};
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fun mk_strictify t = %%: @{const_name strictify}`t;
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fun mk_cfst t = %%: @{const_name cfst}`t;
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fun mk_csnd t = %%: @{const_name csnd}`t;
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(*val csplitN    = "Cprod.csplit";*)
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(*val sfstN      = "Sprod.sfst";*)
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(*val ssndN      = "Sprod.ssnd";*)
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fun mk_ssplit t = %%: @{const_name ssplit}`t;
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fun mk_sinl t = %%: @{const_name sinl}`t;
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fun mk_sinr t = %%: @{const_name sinr}`t;
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fun mk_sscase (x, y) = %%: @{const_name sscase}`x`y;
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fun mk_up t = %%: @{const_name up}`t;
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fun mk_fup (t,u) = %%: @{const_name fup} ` t ` u;
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val ONE = @{term ONE};
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val TT = @{term TT};
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val FF = @{term FF};
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fun mk_iterate (n,f,z) = %%: @{const_name iterate} $ n ` f ` z;
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fun mk_fix t = %%: @{const_name fix}`t;
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fun mk_return t = %%: @{const_name Fixrec.return}`t;
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val mk_fail = %%: @{const_name Fixrec.fail};
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fun mk_branch t = %%: @{const_name Fixrec.branch} $ t;
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val pcpoS = @{sort pcpo};
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val list_ccomb = Library.foldl (op `); (* continuous version of list_comb *)
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fun con_app2 con f args = list_ccomb(%%:con,map f args);
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fun con_app con = con_app2 con %#;
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fun if_rec  arg f y   = if is_rec arg then f (rec_of arg) else y;
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fun app_rec_arg p arg = if_rec arg (fn n => fn x => (p n)`x) I (%# arg);
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fun prj _  _  x (   _::[]) _ = x
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|   prj f1 _  x (_::y::ys) 0 = f1 x y
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|   prj f1 f2 x (y::   ys) j = prj f1 f2 (f2 x y) ys (j-1);
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fun  proj x      = prj (fn S => K(%%:"fst" $S)) (fn S => K(%%:"snd" $S)) x;
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fun cproj x      = prj (fn S => K(mk_cfst S)) (fn S => K(mk_csnd S)) x;
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fun lift tfn = Library.foldr (fn (x,t)=> (mk_trp(tfn x) ===> t));
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fun /\ v T = %%: @{const_name Abs_CFun} $ mk_lam(v,T);
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fun /\# (arg,T) = /\ (vname arg) T;
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infixr 9 oo; fun S oo T = %%: @{const_name cfcomp}`S`T;
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val UU = %%: @{const_name UU};
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fun strict f = f`UU === UU;
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fun defined t = t ~= UU;
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fun cpair (t,u) = %%: @{const_name cpair}`t`u;
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fun spair (t,u) = %%: @{const_name spair}`t`u;
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fun mk_ctuple [] = HOLogic.unit (* used in match_defs *)
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|   mk_ctuple ts = foldr1 cpair ts;
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fun mk_stuple [] = ONE
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|   mk_stuple ts = foldr1 spair ts;
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fun mk_ctupleT [] = HOLogic.unitT   (* used in match_defs *)
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|   mk_ctupleT Ts = foldr1 HOLogic.mk_prodT Ts;
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fun mk_maybeT T = Type ("Fixrec.maybe",[T]);
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fun cpair_pat (p1,p2) = %%: @{const_name cpair_pat} $ p1 $ p2;
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val mk_ctuple_pat = foldr1 cpair_pat;
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fun lift_defined f = lift (fn x => defined (f x));
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fun bound_arg vns v = Bound(length vns -find_index_eq v vns -1);
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fun cont_eta_contract (Const("Cfun.Abs_CFun",TT) $ Abs(a,T,body)) = 
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      (case cont_eta_contract body  of
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        body' as (Const("Cfun.Rep_CFun",Ta) $ f $ Bound 0) => 
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	  if not (0 mem loose_bnos f) then incr_boundvars ~1 f 
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	  else   Const("Cfun.Abs_CFun",TT) $ Abs(a,T,body')
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      | body' => Const("Cfun.Abs_CFun",TT) $ Abs(a,T,body'))
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|   cont_eta_contract(f$t) = cont_eta_contract f $ cont_eta_contract t
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|   cont_eta_contract t    = t;
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fun idx_name dnames s n = s^(if length dnames = 1 then "" else string_of_int n);
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fun when_funs cons = if length cons = 1 then ["f"] 
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                     else mapn (fn n => K("f"^(string_of_int n))) 1 cons;
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fun when_body cons funarg = let
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	fun one_fun n (_,[]  ) = /\ "dummy" (funarg(1,n))
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	|   one_fun n (_,args) = let
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		val l2 = length args;
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		fun idxs m arg = (if is_lazy arg then (fn t => mk_fup (ID, t))
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					         else I) (Bound(l2-m));
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		in cont_eta_contract (foldr'' 
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			(fn (a,t) => mk_ssplit (/\# (a,t)))
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			(args,
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			fn a=> /\#(a,(list_ccomb(funarg(l2,n),mapn idxs 1 args))))
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			) end;
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in (if length cons = 1 andalso length(snd(hd cons)) <= 1
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    then mk_strictify else I)
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     (foldr1 mk_sscase (mapn one_fun 1 cons)) end;
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end; (* struct *)