src/Pure/pattern.ML

extend: cleaned up, adapted for new Syntax.extend;
extend, merge: improved roots (logical_types) handling;

(*  Title: 	pattern
    ID:         $Id$
    Author: 	Tobias Nipkow and Christine Heinzelmann, TU Muenchen
    Copyright   1993  TU Muenchen

Unification of Higher-Order Patterns.

See also:
Tobias Nipkow. Functional Unification of Higher-Order Patterns.
In Proceedings of the 8th IEEE Symposium Logic in Computer Science, 1993.
*)

signature PATTERN =
sig
  type type_sig
  type sg
  type env
  val eta_contract: term -> term
  val match: type_sig -> term * term
        -> (indexname*typ)list * (indexname*term)list
  val eta_matches: type_sig -> term * term -> bool
  val unify: sg * env * (term * term)list -> env
  exception Unif
  exception MATCH
  exception Pattern
end;

functor PatternFun(structure Sign:SIGN and Envir:ENVIR): PATTERN =
struct

structure Type = Sign.Type;

type type_sig = Type.type_sig
type sg = Sign.sg
type env = Envir.env

exception Unif;
exception Pattern;

fun occurs(F,t,env) = 
    let fun occ(Var(G,_))   = (case Envir.lookup(env,G) of
                                 Some(t) => occ t
                               | None    => F=G)
          | occ(t1$t2)      = occ t1 orelse occ t2
          | occ(Abs(_,_,t)) = occ t
          | occ _           = false
    in occ t end;

(* Something's wrong *)
fun ill_formed s = error ("Ill-formed argument in "^s);


fun mapbnd f =
    let fun mpb d (Bound(i))     = if i < d then Bound(i) else Bound(f(i-d)+d)
          | mpb d (Free(c,T))    = Free(c,T)
          | mpb d (Const(c,T))   = Const(c,T)
          | mpb d (Var(iname,T)) = Var(iname,T)
          | mpb d (Abs(s,T,t))   = Abs(s,T,mpb(d+1) t)
          | mpb d ((u1 $ u2))    = mpb d (u1)$ mpb d (u2)
    in mpb 0 end;

fun idx [] j     = ~10000
  | idx(i::is) j = if i=j then length is else idx is j;

val nth_type = snd o nth_elem;

fun at xs i = nth_elem (i,xs);

fun mkabs (binders,is,t)  =
    let fun mk(i::is) = let val (x,T) = nth_elem(i,binders)
                        in Abs(x,T,mk is) end 
          | mk []     = t
    in mk is end;

val incr = mapbnd (fn i => i+1);

(* termlist --> intlist *)
fun ints_of []             = []
  | ints_of (Bound i ::bs) = 
      let val is = ints_of bs
      in if i mem is then raise Pattern else i::is end
  | ints_of _              = raise Pattern;


fun app (s,(i::is)) = app (s$Bound(i),is)
  | app (s,[])      = s;

fun red (Abs(_,_,s)) (i::is) js = red s is (i::js)
  | red s            is      jn = app (mapbnd (at jn) s,is);

(* split_type ([T1,....,Tn]---> T,n,[]) = ([Tn,...,T1],T) *)
fun split_type (T,0,Ts)                    = (Ts,T)
  | split_type (Type ("fun",[T1,T2]),n,Ts) = split_type (T2,n-1,T1::Ts)
  | split_type _                           = ill_formed("split_type");

fun type_of_G (T,n,is) =
  let val (Ts,U) = split_type(T,n,[]) in map(at Ts)is ---> U end;

fun mkhnf (binders,is,G,js) = mkabs (binders, is, app(G,js));

fun mknewhnf(env,binders,is,F as (a,_),T,js) =
  let val (env',G) = Envir.genvar a (env,type_of_G(T,length is,js))
  in Envir.update((F,mkhnf(binders,is,G,js)),env') end;


fun devar env t = case strip_comb t of
        (Var(F,_),ys) =>
            (case Envir.lookup(env,F) of
               Some(t) => devar env (red t (ints_of  ys) []) 
             | None    => t)
      |  _            => t;


(* mk_proj_list(is) = [ |is| - k | 1 <= k <= |is| and is[k] >= 0 ] *)
fun mk_proj_list is =
    let fun mk(i::is,j) = if i >= 0 then j :: mk(is,j-1) else mk(is,j-1)
          | mk([],_)    = []
    in mk(is,length is - 1) end;

fun proj(s,env,binders,is) =
    let fun trans d i = if i<d then i else (idx is (i-d))+d;
        fun pr(s,env,d,binders) = (case devar env s of
              Abs(a,T,t) => let val (t',env') = pr(t,env,d+1,((a,T)::binders))
                            in (Abs(a,T,t'),env') end
            | t => (case strip_comb t of
                (c as Const _,ts) =>
                         let val (ts',env') = prs(ts,env,d,binders)
                         in (list_comb(c,ts'),env') end
                 | (f as Free _,ts) =>
                         let val (ts',env') = prs(ts,env,d,binders)
                         in (list_comb(f,ts'),env') end
                 | (Bound(i),ts) =>
                         let val j = trans d i
                         in if j < 0 then raise Unif
                            else let val (ts',env') = prs(ts,env,d,binders)
                                 in (list_comb(Bound j,ts'),env') end
                         end
                 | (Var(F as (a,_),Fty),ts) =>
                      let val js = ints_of ts;
                          val js' = map (trans d) js;
                          val ks = mk_proj_list js';
                          val ls = filter (fn i => i >= 0) js'
                          val Hty = type_of_G(Fty,length js,ks)
                          val (env',H) = Envir.genvar a (env,Hty)
                          val env'' =
                                Envir.update((F,mkhnf(binders,js,H,ks)),env')
                      in (app(H,ls),env'') end
                 | _  => raise Pattern))
        and prs(s::ss,env,d,binders) =
              let val (s',env1) = pr(s,env,d,binders)
                  val (ss',env2) = prs(ss,env1,d,binders)
              in (s'::ss',env2) end
          | prs([],env,_,_) = ([],env)
   in if downto0(is,length binders - 1) then (s,env)
      else pr(s,env,0,binders)
   end;


(* mk_ff_list(is,js) = [ length(is) - k | 1 <= k <= |is| and is[k] = js[k] ] *)
fun mk_ff_list(is,js) = 
    let fun mk([],[],_)        = [] 
          | mk(i::is,j::js, k) = if i=j then k :: mk(is,js,k-1)
                                        else mk(is,js,k-1)
          | mk _               = ill_formed"mk_ff_list"
    in mk(is,js,length is-1) end;

fun flexflex1(env,binders,F,Fty,is,js) =
  if is=js then env
  else let val ks = mk_ff_list(is,js)
       in mknewhnf(env,binders,is,F,Fty,ks) end;

fun flexflex2(env,binders,F,Fty,is,G,Gty,js) =
  let fun ff(F,Fty,is,G as (a,_),Gty,js) =
            if js subset is
            then let val t= mkabs(binders,is,app(Var(G,Gty),map (idx is) js))
                 in Envir.update((F,t),env) end
            else let val ks = is inter js
                     val Hty = type_of_G(Fty,length is,map (idx is) ks)
                     val (env',H) = Envir.genvar a (env,Hty)
                     fun lam(is) = mkabs(binders,is,app(H,map (idx is) ks));
                 in Envir.update((G,lam js), Envir.update((F,lam is),env'))
                 end;
  in if xless(G,F) then ff(F,Fty,is,G,Gty,js) else ff(G,Gty,js,F,Fty,is) end

val tsgr = ref(Type.tsig0);

fun unify_types(T,U, env as Envir.Envir{asol,iTs,maxidx}) =
  if T=U then env
  else let val iTs' = Type.unify (!tsgr) ((U,T),iTs)
       in Envir.Envir{asol=asol,maxidx=maxidx,iTs=iTs'} end
       handle Type.TUNIFY => raise Unif;

fun unif binders (env,(s,t)) = case (devar env s,devar env t) of
      (Abs(ns,Ts,ts),Abs(nt,Tt,tt)) =>
         let val name = if ns = "" then nt else ns
         in unif ((name,Ts)::binders) (env,(ts,tt)) end
    | (Abs(ns,Ts,ts),t) => unif ((ns,Ts)::binders) (env,(ts,(incr t)$Bound(0)))
    | (t,Abs(nt,Tt,tt)) => unif ((nt,Tt)::binders) (env,((incr t)$Bound(0),tt))
    | p => cases(binders,env,p)

and cases(binders,env,(s,t)) = case (strip_comb s,strip_comb t) of
       ((Var(F,Fty),ss),(Var(G,Gty),ts)) => 
         if F = G then flexflex1(env,binders,F,Fty,ints_of ss,ints_of ts)
                  else flexflex2(env,binders,F,Fty,ints_of ss,G,Gty,ints_of ts)
      | ((Var(F,_),ss),_)             => flexrigid(env,binders,F,ints_of ss,t)
      | (_,(Var(F,_),ts))             => flexrigid(env,binders,F,ints_of ts,s)
      | ((Const c,ss),(Const d,ts))   => rigidrigid(env,binders,c,d,ss,ts)
      | ((Free(f),ss),(Free(g),ts))   => rigidrigid(env,binders,f,g,ss,ts)
      | ((Bound(i),ss),(Bound(j),ts)) => rigidrigidB (env,binders,i,j,ss,ts) 
      | ((Abs(_),_),_)                => raise Pattern
      | (_,(Abs(_),_))                => raise Pattern
      | _                             => raise Unif

and rigidrigid (env,binders,(a,Ta),(b,Tb),ss,ts) =
      if a<>b then raise Unif
      else foldl (unif binders) (unify_types(Ta,Tb,env), ss~~ts)

and rigidrigidB (env,binders,i,j,ss,ts) =
     if i <> j then raise Unif else foldl (unif binders) (env ,ss~~ts)

and flexrigid (env,binders,F,is,t) =
      if occurs(F,t,env) then raise Unif
      else let val (u,env') = proj(t,env,binders,is)
           in Envir.update((F,mkabs(binders,is,u)),env') end;

fun unify(sg,env,tus) = (tsgr := #tsig(Sign.rep_sg sg);
                         foldl (unif []) (env,tus));


(*Perform eta-contractions upon a term*)
fun eta_contract (Abs(a,T,body)) = 
      (case eta_contract body  of
        body' as (f $ Bound i) => 
	  if i=0 andalso not (0 mem loose_bnos f) then incr_boundvars ~1 f 
	  else Abs(a,T,body')
      | body' => Abs(a,T,body'))
  | eta_contract(f$t) = eta_contract f $ eta_contract t
  | eta_contract t = t;


(* Pattern matching. Raises MATCH if non-pattern *)
exception MATCH;
(* something wron with types, esp in abstractions
fun typ_match args = Type.typ_match (!tsgr) args
                     handle Type.TYPE_MATCH => raise MATCH;

fun match_bind(itms,binders,ixn,is,t) =
  let val js = loose_bnos t
  in if null is
     then if null js then (ixn,t)::itms else raise MATCH
     else if js subset is
          then let val t' = if downto0(is,length binders - 1) then t
                            else mapbnd (idx is) t
               in (ixn, eta_contract(mkabs(binders,is,t'))) :: itms end
          else raise MATCH
  end;

fun match_rr (iTs,(a,Ta),(b,Tb)) =
      if a<>b then raise MATCH else typ_match (iTs,(Ta,Tb))

(* Pre: pat and obj have same type *)
fun mtch(binders,env as (iTs,itms),pat,obj) = case pat of
      Var(ixn,_) => (case assoc(itms,ixn) of
                       None => (iTs,match_bind(itms,binders,ixn,[],obj))
                     | Some u => if obj aconv u then env else raise MATCH)
    | Abs(ns,Ts,ts) =>
        (case obj of
           Abs(nt,Tt,tt) => mtch((nt,Tt)::binders,env,ts,tt)
         | _ => let val Tt = typ_subst_TVars iTs Ts
                in  mtch((ns,Tt)::binders,env,ts,(incr obj)$Bound(0)) end)
    | _ => (case obj of
              Abs(nt,Tt,tt) =>
                mtch((nt,Tt)::binders,env,(incr pat)$Bound(0),tt)
            | _ => cases(binders,env,pat,obj))

and cases(binders,env as (iTs,itms),pat,obj) =
  let fun structural() = case (pat,obj) of
            (Const c,Const d) => (match_rr(iTs,c,d),itms)
          | (Free f,Free g)   => (match_rr(iTs,f,g),itms)
          | (Bound i,Bound j) => if i=j then env else raise MATCH
          | (f$t,g$u)         => mtch(binders,mtch(binders,env,t,u),f,g)
          | _                 => raise MATCH
  in case strip_comb pat of
       (Var(ixn,_),bs) =>
         (let val is = ints_of bs
          in case assoc(itms,ixn) of
               None => (iTs,match_bind(itms,binders,ixn,is,obj))
             | Some u => if obj aconv (red u is []) then env else raise MATCH
          end (* if ints_of fails: *) handle Pattern => structural())
     | _ => structural()
  end;

fun match tsg = (tsgr := tsg;
                 fn (pat,obj) => 
                   let val pT = fastype_of pat
                       and oT = fastype_of obj
                       val iTs = typ_match ([],(pT,oT))
                   in mtch([], (iTs,[]), pat, eta_contract obj)
                      handle Pattern => raise MATCH
                   end)

(*Predicate: does the pattern match the object?*)
fun matches tsig args = (match tsig args; true)
                        handle MATCH => false;
*)

(*First-order matching;  term_match tsig (pattern, object)
    returns a (tyvar,typ)list and (var,term)list.
  The pattern and object may have variables in common.
  Instantiation does not affect the object, so matching ?a with ?a+1 works.
  A Const does not match a Free of the same name! 
  Does not notice eta-equality, thus f does not match %(x)f(x)  *)
fun match tsig (pat,obj) =
  let fun typ_match args = (Type.typ_match tsig args)
			   handle Type.TYPE_MATCH => raise MATCH;
      fun mtch (tyinsts,insts) = fn
	(Var(ixn,T), t)  =>
	  if null (loose_bnos t)
	  then case assoc(insts,ixn) of
		  None => (typ_match (tyinsts, (T, fastype_of t)), 
			   (ixn,t)::insts)
		| Some u => if t aconv u then (tyinsts,insts) else raise MATCH
	  else raise MATCH
      | (Free (a,T), Free (b,U)) =>
	  if  a=b  then (typ_match (tyinsts,(T,U)), insts)  else raise MATCH
      | (Const (a,T), Const (b,U))  =>
	  if  a=b  then (typ_match (tyinsts,(T,U)), insts)  else raise MATCH
      | (Bound i, Bound j)  =>
          if  i=j  then  (tyinsts,insts)  else raise MATCH
      | (Abs(_,T,t), Abs(_,U,u))  =>
	  mtch (typ_match (tyinsts,(T,U)),insts) (t,u)
      | (f$t, g$u) => mtch (mtch (tyinsts,insts) (f,g)) (t, u)
      | _ => raise MATCH
  in mtch([],[]) (pat,obj) end;

(*Predicate: does the pattern match the object?*)
fun eta_matches tsig (pat,obj) =
      (match tsig (eta_contract pat,eta_contract obj); true)
      handle MATCH => false;

end;