TFL/usyntax.sml

new distributive laws

(*  Title:      TFL/usyntax
    ID:         $Id$
    Author:     Konrad Slind, Cambridge University Computer Laboratory
    Copyright   1997  University of Cambridge

Emulation of HOL's abstract syntax functions
*)

structure USyntax : USyntax_sig =
struct

structure Utils = Utils;
open Utils;

infix 4 ##;

fun USYN_ERR{func,mesg} = Utils.ERR{module = "USyntax", func = func, mesg = mesg};


(*---------------------------------------------------------------------------
 *
 *                            Types 
 *
 *---------------------------------------------------------------------------*)
val mk_prim_vartype = TVar;
fun mk_vartype s = mk_prim_vartype((s,0),["term"]);

(* But internally, it's useful *)
fun dest_vtype (TVar x) = x
  | dest_vtype _ = raise USYN_ERR{func = "dest_vtype", 
                             mesg = "not a flexible type variable"};

val is_vartype = Utils.can dest_vtype;

val type_vars  = map mk_prim_vartype o typ_tvars
fun type_varsl L = distinct (Utils.rev_itlist (curry op @ o type_vars) L []);

val alpha  = mk_vartype "'a"
val beta   = mk_vartype "'b"

fun strip_prod_type (Type("*", [ty1,ty2])) =
	strip_prod_type ty1 @ strip_prod_type ty2
  | strip_prod_type ty = [ty];



(*---------------------------------------------------------------------------
 *
 *                              Terms 
 *
 *---------------------------------------------------------------------------*)

(* Free variables, in order of occurrence, from left to right in the 
 * syntax tree. *)
fun free_vars_lr tm = 
  let fun memb x = let fun m[] = false | m(y::rst) = (x=y)orelse m rst in m end
      fun add (t, frees) = case t of
            Free   _ => if (memb t frees) then frees else t::frees
          | Abs (_,_,body) => add(body,frees)
          | f$t =>  add(t, add(f, frees))
          | _ => frees
  in rev(add(tm,[]))
  end;



val type_vars_in_term = map mk_prim_vartype o term_tvars;



(* Prelogic *)
fun dest_tybinding (v,ty) = (#1(dest_vtype v),ty)
fun inst theta = subst_vars (map dest_tybinding theta,[])


(* Construction routines *)

fun mk_abs{Bvar as Var((s,_),ty),Body}  = Abs(s,ty,abstract_over(Bvar,Body))
  | mk_abs{Bvar as Free(s,ty),Body}  = Abs(s,ty,abstract_over(Bvar,Body))
  | mk_abs _ = raise USYN_ERR{func = "mk_abs", mesg = "Bvar is not a variable"};


fun mk_imp{ant,conseq} = 
   let val c = Const("op -->",HOLogic.boolT --> HOLogic.boolT --> HOLogic.boolT)
   in list_comb(c,[ant,conseq])
   end;

fun mk_select (r as {Bvar,Body}) = 
  let val ty = type_of Bvar
      val c = Const("Eps",(ty --> HOLogic.boolT) --> ty)
  in list_comb(c,[mk_abs r])
  end;

fun mk_forall (r as {Bvar,Body}) = 
  let val ty = type_of Bvar
      val c = Const("All",(ty --> HOLogic.boolT) --> HOLogic.boolT)
  in list_comb(c,[mk_abs r])
  end;

fun mk_exists (r as {Bvar,Body}) = 
  let val ty = type_of Bvar 
      val c = Const("Ex",(ty --> HOLogic.boolT) --> HOLogic.boolT)
  in list_comb(c,[mk_abs r])
  end;


fun mk_conj{conj1,conj2} =
   let val c = Const("op &",HOLogic.boolT --> HOLogic.boolT --> HOLogic.boolT)
   in list_comb(c,[conj1,conj2])
   end;

fun mk_disj{disj1,disj2} =
   let val c = Const("op |",HOLogic.boolT --> HOLogic.boolT --> HOLogic.boolT)
   in list_comb(c,[disj1,disj2])
   end;

fun prod_ty ty1 ty2 = Type("*", [ty1,ty2]);

local
fun mk_uncurry(xt,yt,zt) =
    Const("split",(xt --> yt --> zt) --> prod_ty xt yt --> zt)
fun dest_pair(Const("Pair",_) $ M $ N) = {fst=M, snd=N}
  | dest_pair _ = raise USYN_ERR{func = "dest_pair", mesg = "not a pair"}
fun is_var(Var(_)) = true | is_var (Free _) = true | is_var _ = false
in
fun mk_pabs{varstruct,body} = 
 let fun mpa(varstruct,body) =
       if (is_var varstruct)
       then mk_abs{Bvar = varstruct, Body = body}
       else let val {fst,snd} = dest_pair varstruct
            in mk_uncurry(type_of fst,type_of snd,type_of body) $
	       mpa(fst,mpa(snd,body))
            end
 in mpa(varstruct,body)
 end
 handle _ => raise USYN_ERR{func = "mk_pabs", mesg = ""};
end;

(* Destruction routines *)

datatype lambda = VAR   of {Name : string, Ty : typ}
                | CONST of {Name : string, Ty : typ}
                | COMB  of {Rator: term, Rand : term}
                | LAMB  of {Bvar : term, Body : term};


fun dest_term(Var((s,i),ty)) = VAR{Name = s, Ty = ty}
  | dest_term(Free(s,ty))    = VAR{Name = s, Ty = ty}
  | dest_term(Const(s,ty))   = CONST{Name = s, Ty = ty}
  | dest_term(M$N)           = COMB{Rator=M,Rand=N}
  | dest_term(Abs(s,ty,M))   = let  val v = Free(s,ty)
                               in LAMB{Bvar = v, Body = betapply (M,v)}
                               end
  | dest_term(Bound _)       = raise USYN_ERR{func = "dest_term",mesg = "Bound"};

fun dest_const(Const(s,ty)) = {Name = s, Ty = ty}
  | dest_const _ = raise USYN_ERR{func = "dest_const", mesg = "not a constant"};

fun dest_comb(t1 $ t2) = {Rator = t1, Rand = t2}
  | dest_comb _ =  raise USYN_ERR{func = "dest_comb", mesg = "not a comb"};

fun dest_abs(a as Abs(s,ty,M)) = 
     let val v = Free(s,ty)
     in {Bvar = v, Body = betapply (a,v)}
     end
  | dest_abs _ =  raise USYN_ERR{func = "dest_abs", mesg = "not an abstraction"};

fun dest_eq(Const("op =",_) $ M $ N) = {lhs=M, rhs=N}
  | dest_eq _ = raise USYN_ERR{func = "dest_eq", mesg = "not an equality"};

fun dest_imp(Const("op -->",_) $ M $ N) = {ant=M, conseq=N}
  | dest_imp _ = raise USYN_ERR{func = "dest_imp", mesg = "not an implication"};

fun dest_forall(Const("All",_) $ (a as Abs _)) = dest_abs a
  | dest_forall _ = raise USYN_ERR{func = "dest_forall", mesg = "not a forall"};

fun dest_exists(Const("Ex",_) $ (a as Abs _)) = dest_abs a
  | dest_exists _ = raise USYN_ERR{func = "dest_exists", mesg="not an existential"};

fun dest_neg(Const("not",_) $ M) = M
  | dest_neg _ = raise USYN_ERR{func = "dest_neg", mesg = "not a negation"};

fun dest_conj(Const("op &",_) $ M $ N) = {conj1=M, conj2=N}
  | dest_conj _ = raise USYN_ERR{func = "dest_conj", mesg = "not a conjunction"};

fun dest_disj(Const("op |",_) $ M $ N) = {disj1=M, disj2=N}
  | dest_disj _ = raise USYN_ERR{func = "dest_disj", mesg = "not a disjunction"};

fun mk_pair{fst,snd} = 
   let val ty1 = type_of fst
       val ty2 = type_of snd
       val c = Const("Pair",ty1 --> ty2 --> prod_ty ty1 ty2)
   in list_comb(c,[fst,snd])
   end;

fun dest_pair(Const("Pair",_) $ M $ N) = {fst=M, snd=N}
  | dest_pair _ = raise USYN_ERR{func = "dest_pair", mesg = "not a pair"};


local  fun ucheck t = (if #Name(dest_const t) = "split" then t
                       else raise Match)
in
fun dest_pabs tm =
   let val {Bvar,Body} = dest_abs tm
   in {varstruct = Bvar, body = Body}
   end 
    handle 
     _ => let val {Rator,Rand} = dest_comb tm
              val _ = ucheck Rator
              val {varstruct = lv,body} = dest_pabs Rand
              val {varstruct = rv,body} = dest_pabs body
          in {varstruct = mk_pair{fst = lv, snd = rv}, body = body}
          end
end;


val lhs   = #lhs o dest_eq
val rhs   = #rhs o dest_eq
val rand  = #Rand o dest_comb
  

(* Query routines *)
val is_imp    = can dest_imp
val is_forall = can dest_forall
val is_exists = can dest_exists
val is_neg    = can dest_neg
val is_conj   = can dest_conj
val is_disj   = can dest_disj
val is_pair   = can dest_pair
val is_pabs   = can dest_pabs


(* Construction of a cterm from a list of Terms *)

fun list_mk_abs(L,tm) = itlist (fn v => fn M => mk_abs{Bvar=v, Body=M}) L tm;

(* These others are almost never used *)
fun list_mk_imp(A,c) = itlist(fn a => fn tm => mk_imp{ant=a,conseq=tm}) A c;
fun list_mk_forall(V,t) = itlist(fn v => fn b => mk_forall{Bvar=v, Body=b})V t;
val list_mk_conj = end_itlist(fn c1 => fn tm => mk_conj{conj1=c1, conj2=tm})


(* Need to reverse? *)
fun gen_all tm = list_mk_forall(term_frees tm, tm);

(* Destructing a cterm to a list of Terms *)
fun strip_comb tm = 
   let fun dest(M$N, A) = dest(M, N::A)
         | dest x = x
   in dest(tm,[])
   end;

fun strip_abs(tm as Abs _) =
       let val {Bvar,Body} = dest_abs tm
           val (bvs, core) = strip_abs Body
       in (Bvar::bvs, core)
       end
  | strip_abs M = ([],M);


fun strip_imp fm =
   if (is_imp fm)
   then let val {ant,conseq} = dest_imp fm
            val (was,wb) = strip_imp conseq
        in ((ant::was), wb)
        end
   else ([],fm);

fun strip_forall fm =
   if (is_forall fm)
   then let val {Bvar,Body} = dest_forall fm
            val (bvs,core) = strip_forall Body
        in ((Bvar::bvs), core)
        end
   else ([],fm);


fun strip_exists fm =
   if (is_exists fm)
   then let val {Bvar, Body} = dest_exists fm 
            val (bvs,core) = strip_exists Body
        in (Bvar::bvs, core)
        end
   else ([],fm);

fun strip_disj w =
   if (is_disj w)
   then let val {disj1,disj2} = dest_disj w 
        in (strip_disj disj1@strip_disj disj2)
        end
   else [w];


(* Miscellaneous *)

fun mk_vstruct ty V =
  let fun follow_prod_type (Type("*",[ty1,ty2])) vs =
	      let val (ltm,vs1) = follow_prod_type ty1 vs
		  val (rtm,vs2) = follow_prod_type ty2 vs1
	      in (mk_pair{fst=ltm, snd=rtm}, vs2) end
	| follow_prod_type _ (v::vs) = (v,vs)
  in #1 (follow_prod_type ty V)  end;


(* Search a term for a sub-term satisfying the predicate p. *)
fun find_term p =
   let fun find tm =
      if (p tm) then Some tm 
      else case tm of
	  Abs(_,_,body) => find body
	| (t$u)         => (Some (the (find t)) handle _ => find u)
	| _             => None
   in find
   end;

fun dest_relation tm =
   if (type_of tm = HOLogic.boolT)
   then let val (Const("op :",_) $ (Const("Pair",_)$y$x) $ R) = tm
        in (R,y,x)
        end handle _ => raise USYN_ERR{func="dest_relation",
                                  mesg="unexpected term structure"}
   else raise USYN_ERR{func="dest_relation",mesg="not a boolean term"};

fun is_WFR (Const("wf",_)$_) = true
  | is_WFR _                 = false;

fun ARB ty = mk_select{Bvar=Free("v",ty),
                       Body=Const("True",HOLogic.boolT)};

end; (* Syntax *)