author  wenzelm 
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permissions  rwrr 
12784  1 
(* Title: Pure/pattern.ML 
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ID: $Id$ 
12784  3 
Author: Tobias Nipkow, Christine Heinzelmann, and Stefan Berghofer 
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Unification of HigherOrder Patterns. 

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See also: 

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Tobias Nipkow. Functional Unification of HigherOrder Patterns. 

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In Proceedings of the 8th IEEE Symposium Logic in Computer Science, 1993. 

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TODO: optimize red by specialcasing it 
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*) 
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2751  14 
infix aeconv; 
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0  16 
signature PATTERN = 
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sig 
17203  18 
val trace_unify_fail: bool ref 
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val aeconv: term * term > bool 

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val eta_contract: term > term 

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val eta_long: typ list > term > term 

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val beta_eta_contract: term > term 

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val eta_contract_atom: term > term 

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val match: theory > term * term > Type.tyenv * Envir.tenv 

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val first_order_match: theory > term * term > Type.tyenv * Envir.tenv 

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val matches: theory > term * term > bool 

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val matches_subterm: theory > term * term > bool 

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val unify: theory * Envir.env * (term * term)list > Envir.env 

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val first_order: term > bool 

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val pattern: term > bool 

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val rewrite_term: theory > (term * term) list > (term > term option) list > term > term 

0  32 
exception Unif 
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exception MATCH 

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exception Pattern 

14787  35 
end; 
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17203  37 
structure Pattern: PATTERN = 
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struct 
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40 
exception Unif; 

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exception Pattern; 

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val trace_unify_fail = ref false; 
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fun string_of_term thy env binders t = Sign.string_of_term thy 
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(Envir.norm_term env (subst_bounds(map Free binders,t))); 
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fun bname binders i = fst(List.nth(binders,i)); 
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fun bnames binders is = space_implode " " (map (bname binders) is); 
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17203  51 
fun typ_clash thy (tye,T,U) = 
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if !trace_unify_fail 
17203  53 
then let val t = Sign.string_of_typ thy (Envir.norm_type tye T) 
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and u = Sign.string_of_typ thy (Envir.norm_type tye U) 

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in tracing("The following types do not unify:\n" ^ t ^ "\n" ^ u) end 
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else () 
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fun clash a b = 
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if !trace_unify_fail then tracing("Clash: " ^ a ^ " =/= " ^ b) else () 
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fun boundVar binders i = 
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"bound variable " ^ bname binders i ^ " (depth " ^ string_of_int i ^ ")"; 
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fun clashBB binders i j = 
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if !trace_unify_fail then clash (boundVar binders i) (boundVar binders j) 
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else () 
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fun clashB binders i s = 
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if !trace_unify_fail then clash (boundVar binders i) s 
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else () 
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17203  72 
fun proj_fail thy (env,binders,F,_,is,t) = 
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if !trace_unify_fail 
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then let val f = Syntax.string_of_vname F 
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val xs = bnames binders is 
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val u = string_of_term thy env binders t 
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val ys = bnames binders (loose_bnos t \\ is) 
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in tracing("Cannot unify variable " ^ f ^ 
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" (depending on bound variables " ^ xs ^ ")\nwith term " ^ u ^ 
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"\nTerm contains additional bound variable(s) " ^ ys) 
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end 
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else () 
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17203  84 
fun ocheck_fail thy (F,t,binders,env) = 
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if !trace_unify_fail 
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then let val f = Syntax.string_of_vname F 
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val u = string_of_term thy env binders t 
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in tracing("Variable " ^ f ^ " occurs in term\n" ^ u ^ 
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"\nCannot unify!\n") 
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end 
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else () 
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12784  93 
fun occurs(F,t,env) = 
15797  94 
let fun occ(Var (G, T)) = (case Envir.lookup (env, (G, T)) of 
15531  95 
SOME(t) => occ t 
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 NONE => F=G) 

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 occ(t1$t2) = occ t1 orelse occ t2 
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 occ(Abs(_,_,t)) = occ t 

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 occ _ = false 

100 
in occ t end; 

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102 

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fun mapbnd f = 

104 
let fun mpb d (Bound(i)) = if i < d then Bound(i) else Bound(f(id)+d) 

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 mpb d (Abs(s,T,t)) = Abs(s,T,mpb(d+1) t) 

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 mpb d ((u1 $ u2)) = (mpb d u1)$(mpb d u2) 
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 mpb _ atom = atom 
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in mpb 0 end; 
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fun idx [] j = raise Unif 
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 idx(i::is) j = if (i:int) =j then length is else idx is j; 
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15570  113 
fun at xs i = List.nth (xs,i); 
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115 
fun mkabs (binders,is,t) = 

15570  116 
let fun mk(i::is) = let val (x,T) = List.nth(binders,i) 
12784  117 
in Abs(x,T,mk is) end 
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 mk [] = t 
119 
in mk is end; 

120 

121 
val incr = mapbnd (fn i => i+1); 

122 

123 
fun ints_of [] = [] 

12784  124 
 ints_of (Bound i ::bs) = 
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let val is = ints_of bs 
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in if i mem_int is then raise Pattern else i::is end 
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 ints_of _ = raise Pattern; 
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12232  129 
fun ints_of' env ts = ints_of (map (Envir.head_norm env) ts); 
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0  131 

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fun app (s,(i::is)) = app (s$Bound(i),is) 

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 app (s,[]) = s; 

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fun red (Abs(_,_,s)) (i::is) js = red s is (i::js) 

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 red t [] [] = t 
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 red t is jn = app (mapbnd (at jn) t,is); 
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(* split_type ([T1,....,Tn]> T,n,[]) = ([Tn,...,T1],T) *) 

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fun split_type (T,0,Ts) = (Ts,T) 

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 split_type (Type ("fun",[T1,T2]),n,Ts) = split_type (T2,n1,T1::Ts) 

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 split_type _ = error("split_type"); 
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fun type_of_G (env as Envir.Envir {iTs, ...}) (T,n,is) = 
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let val (Ts, U) = split_type (Envir.norm_type iTs T, n, []) 
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in map (at Ts) is > U end; 
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fun mkhnf (binders,is,G,js) = mkabs (binders, is, app(G,js)); 

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fun mknewhnf(env,binders,is,F as (a,_),T,js) = 

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let val (env',G) = Envir.genvar a (env,type_of_G env (T,length is,js)) 
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in Envir.update (((F, T), mkhnf (binders, is, G, js)), env') end; 
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(* mk_proj_list(is) = [ is  k  1 <= k <= is and is[k] >= 0 ] *) 

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fun mk_proj_list is = 

15570  158 
let fun mk(i::is,j) = if isSome i then j :: mk(is,j1) else mk(is,j1) 
0  159 
 mk([],_) = [] 
160 
in mk(is,length is  1) end; 

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162 
fun proj(s,env,binders,is) = 

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let fun trans d i = if i<d then i else (idx is (id))+d; 

12232  164 
fun pr(s,env,d,binders) = (case Envir.head_norm env s of 
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Abs(a,T,t) => let val (t',env') = pr(t,env,d+1,((a,T)::binders)) 
166 
in (Abs(a,T,t'),env') end 

167 
 t => (case strip_comb t of 

168 
(c as Const _,ts) => 

169 
let val (ts',env') = prs(ts,env,d,binders) 

170 
in (list_comb(c,ts'),env') end 

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 (f as Free _,ts) => 

172 
let val (ts',env') = prs(ts,env,d,binders) 

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in (list_comb(f,ts'),env') end 

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 (Bound(i),ts) => 

175 
let val j = trans d i 

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val (ts',env') = prs(ts,env,d,binders) 
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in (list_comb(Bound j,ts'),env') end 
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 (Var(F as (a,_),Fty),ts) => 
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let val js = ints_of' env ts; 
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val js' = map (try (trans d)) js; 
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val ks = mk_proj_list js'; 
15570  182 
val ls = List.mapPartial I js' 
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val Hty = type_of_G env (Fty,length js,ks) 
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val (env',H) = Envir.genvar a (env,Hty) 
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val env'' = 

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Envir.update (((F, Fty), mkhnf (binders, js, H, ks)), env') 
0  187 
in (app(H,ls),env'') end 
188 
 _ => raise Pattern)) 

189 
and prs(s::ss,env,d,binders) = 

190 
let val (s',env1) = pr(s,env,d,binders) 

191 
val (ss',env2) = prs(ss,env1,d,binders) 

192 
in (s'::ss',env2) end 

193 
 prs([],env,_,_) = ([],env) 

194 
in if downto0(is,length binders  1) then (s,env) 

195 
else pr(s,env,0,binders) 

196 
end; 

197 

198 

199 
(* mk_ff_list(is,js) = [ length(is)  k  1 <= k <= is and is[k] = js[k] ] *) 

12784  200 
fun mk_ff_list(is,js) = 
201 
let fun mk([],[],_) = [] 

16668  202 
 mk(i::is,j::js, k) = if (i:int) = j then k :: mk(is,js,k1) 
0  203 
else mk(is,js,k1) 
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 mk _ = error"mk_ff_list" 
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in mk(is,js,length is1) end; 
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207 
fun flexflex1(env,binders,F,Fty,is,js) = 

208 
if is=js then env 

209 
else let val ks = mk_ff_list(is,js) 

210 
in mknewhnf(env,binders,is,F,Fty,ks) end; 

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212 
fun flexflex2(env,binders,F,Fty,is,G,Gty,js) = 

213 
let fun ff(F,Fty,is,G as (a,_),Gty,js) = 

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if js subset_int is 
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then let val t= mkabs(binders,is,app(Var(G,Gty),map (idx is) js)) 
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in Envir.update (((F, Fty), t), env) end 
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else let val ks = is inter_int js 
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val Hty = type_of_G env (Fty,length is,map (idx is) ks) 
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val (env',H) = Envir.genvar a (env,Hty) 
220 
fun lam(is) = mkabs(binders,is,app(H,map (idx is) ks)); 

15797  221 
in Envir.update (((G, Gty), lam js), Envir.update (((F, Fty), lam is), env')) 
0  222 
end; 
223 
in if xless(G,F) then ff(F,Fty,is,G,Gty,js) else ff(G,Gty,js,F,Fty,is) end 

224 

17203  225 
fun unify_types thy (T,U, env as Envir.Envir{asol,iTs,maxidx}) = 
0  226 
if T=U then env 
17203  227 
else let val (iTs',maxidx') = Sign.typ_unify thy (U, T) (iTs, maxidx) 
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in Envir.Envir{asol=asol,maxidx=maxidx',iTs=iTs'} end 
17203  229 
handle Type.TUNIFY => (typ_clash thy (iTs,T,U); raise Unif); 
0  230 

17203  231 
fun unif thy binders (env,(s,t)) = case (Envir.head_norm env s, Envir.head_norm env t) of 
0  232 
(Abs(ns,Ts,ts),Abs(nt,Tt,tt)) => 
233 
let val name = if ns = "" then nt else ns 

17203  234 
in unif thy ((name,Ts)::binders) (env,(ts,tt)) end 
235 
 (Abs(ns,Ts,ts),t) => unif thy ((ns,Ts)::binders) (env,(ts,(incr t)$Bound(0))) 

236 
 (t,Abs(nt,Tt,tt)) => unif thy ((nt,Tt)::binders) (env,((incr t)$Bound(0),tt)) 

237 
 p => cases thy (binders,env,p) 

0  238 

17203  239 
and cases thy (binders,env,(s,t)) = case (strip_comb s,strip_comb t) of 
12784  240 
((Var(F,Fty),ss),(Var(G,Gty),ts)) => 
12232  241 
if F = G then flexflex1(env,binders,F,Fty,ints_of' env ss,ints_of' env ts) 
242 
else flexflex2(env,binders,F,Fty,ints_of' env ss,G,Gty,ints_of' env ts) 

17203  243 
 ((Var(F,Fty),ss),_) => flexrigid thy (env,binders,F,Fty,ints_of' env ss,t) 
244 
 (_,(Var(F,Fty),ts)) => flexrigid thy (env,binders,F,Fty,ints_of' env ts,s) 

245 
 ((Const c,ss),(Const d,ts)) => rigidrigid thy (env,binders,c,d,ss,ts) 

246 
 ((Free(f),ss),(Free(g),ts)) => rigidrigid thy (env,binders,f,g,ss,ts) 

247 
 ((Bound(i),ss),(Bound(j),ts)) => rigidrigidB thy (env,binders,i,j,ss,ts) 

0  248 
 ((Abs(_),_),_) => raise Pattern 
249 
 (_,(Abs(_),_)) => raise Pattern 

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 ((Const(c,_),_),(Free(f,_),_)) => (clash c f; raise Unif) 
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 ((Const(c,_),_),(Bound i,_)) => (clashB binders i c; raise Unif) 
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 ((Free(f,_),_),(Const(c,_),_)) => (clash f c; raise Unif) 
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 ((Free(f,_),_),(Bound i,_)) => (clashB binders i f; raise Unif) 
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 ((Bound i,_),(Const(c,_),_)) => (clashB binders i c; raise Unif) 
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 ((Bound i,_),(Free(f,_),_)) => (clashB binders i f; raise Unif) 
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0  257 

17203  258 
and rigidrigid thy (env,binders,(a,Ta),(b,Tb),ss,ts) = 
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if a<>b then (clash a b; raise Unif) 
17203  260 
else Library.foldl (unif thy binders) (unify_types thy (Ta,Tb,env), ss~~ts) 
0  261 

17203  262 
and rigidrigidB thy (env,binders,i,j,ss,ts) = 
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if i <> j then (clashBB binders i j; raise Unif) 
17203  264 
else Library.foldl (unif thy binders) (env ,ss~~ts) 
0  265 

17203  266 
and flexrigid thy (params as (env,binders,F,Fty,is,t)) = 
267 
if occurs(F,t,env) then (ocheck_fail thy (F,t,binders,env); raise Unif) 

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268 
else (let val (u,env') = proj(t,env,binders,is) 
15797  269 
in Envir.update (((F, Fty), mkabs (binders, is, u)), env') end 
17203  270 
handle Unif => (proj_fail thy params; raise Unif)); 
0  271 

17203  272 
fun unify(thy,env,tus) = Library.foldl (unif thy []) (env,tus); 
0  273 

274 

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(*Etacontract a term (fully)*) 
2792  276 

12797  277 
fun eta_contract t = 
278 
let 

279 
exception SAME; 

14787  280 
fun eta (Abs (a, T, body)) = 
12797  281 
((case eta body of 
14787  282 
body' as (f $ Bound 0) => 
283 
if loose_bvar1 (f, 0) then Abs(a, T, body') 

284 
else incr_boundvars ~1 f 

12797  285 
 body' => Abs (a, T, body')) handle SAME => 
286 
(case body of 

14787  287 
(f $ Bound 0) => 
288 
if loose_bvar1 (f, 0) then raise SAME 

289 
else incr_boundvars ~1 f 

12797  290 
 _ => raise SAME)) 
291 
 eta (f $ t) = 

292 
(let val f' = eta f 

293 
in f' $ etah t end handle SAME => f $ eta t) 

294 
 eta _ = raise SAME 

295 
and etah t = (eta t handle SAME => t) 

296 
in etah t end; 

0  297 

12781  298 
val beta_eta_contract = eta_contract o Envir.beta_norm; 
299 

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300 
(*Etacontract a term from outside: just enough to reduce it to an atom 
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301 
DOESN'T QUITE WORK! 
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302 
*) 
12784  303 
fun eta_contract_atom (t0 as Abs(a, T, body)) = 
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304 
(case eta_contract2 body of 
12784  305 
body' as (f $ Bound 0) => 
306 
if loose_bvar1(f,0) then Abs(a,T,body') 

307 
else eta_contract_atom (incr_boundvars ~1 f) 

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308 
 _ => t0) 
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309 
 eta_contract_atom t = t 
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310 
and eta_contract2 (f$t) = f $ eta_contract_atom t 
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311 
 eta_contract2 t = eta_contract_atom t; 
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312 

13998  313 
(* put a term into eta long beta normal form *) 
314 
fun eta_long Ts (Abs (s, T, t)) = Abs (s, T, eta_long (T :: Ts) t) 

315 
 eta_long Ts t = (case strip_comb t of 

316 
(Abs _, _) => eta_long Ts (Envir.beta_norm t) 

14787  317 
 (u, ts) => 
13998  318 
let 
319 
val Us = binder_types (fastype_of1 (Ts, t)); 

320 
val i = length Us 

321 
in list_abs (map (pair "x") Us, 

322 
list_comb (incr_boundvars i u, map (eta_long (rev Us @ Ts)) 

323 
(map (incr_boundvars i) ts @ map Bound (i  1 downto 0)))) 

324 
end); 

325 

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326 

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327 
(*Tests whether 2 terms are alpha/etaconvertible and have same type. 
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328 
Note that Consts and Vars may have more than one type.*) 
2751  329 
fun t aeconv u = aconv_aux (eta_contract_atom t, eta_contract_atom u) 
330 
and aconv_aux (Const(a,T), Const(b,U)) = a=b andalso T=U 

331 
 aconv_aux (Free(a,T), Free(b,U)) = a=b andalso T=U 

332 
 aconv_aux (Var(v,T), Var(w,U)) = eq_ix(v,w) andalso T=U 

12784  333 
 aconv_aux (Bound i, Bound j) = i=j 
2751  334 
 aconv_aux (Abs(_,T,t), Abs(_,U,u)) = (t aeconv u) andalso T=U 
12784  335 
 aconv_aux (f$t, g$u) = (f aeconv g) andalso (t aeconv u) 
2751  336 
 aconv_aux _ = false; 
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337 

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338 

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339 
(*** Matching ***) 
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340 

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341 
exception MATCH; 
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342 

17203  343 
fun typ_match thy (tyenv, TU) = Sign.typ_match thy TU tyenv 
16939  344 
handle Type.TYPE_MATCH => raise MATCH; 
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345 

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346 
(*Firstorder matching; 
17203  347 
fomatch thy (pattern, object) returns a (tyvar,typ)list and (var,term)list. 
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348 
The pattern and object may have variables in common. 
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349 
Instantiation does not affect the object, so matching ?a with ?a+1 works. 
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350 
Object is etacontracted on the fly (by etaexpanding the pattern). 
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351 
Precondition: the pattern is already etacontracted! 
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352 
Note: types are matched on the fly *) 
17203  353 
fun fomatch thy = 
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354 
let 
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355 
fun mtch (instsp as (tyinsts,insts)) = fn 
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356 
(Var(ixn,T), t) => 
12784  357 
if loose_bvar(t,0) then raise MATCH 
16651  358 
else (case Envir.lookup' (insts, (ixn, T)) of 
17203  359 
NONE => (typ_match thy (tyinsts, (T, fastype_of t)), 
17412  360 
Vartab.update_new (ixn, (T, t)) insts) 
15531  361 
 SOME u => if t aeconv u then instsp else raise MATCH) 
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362 
 (Free (a,T), Free (b,U)) => 
17203  363 
if a=b then (typ_match thy (tyinsts,(T,U)), insts) else raise MATCH 
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364 
 (Const (a,T), Const (b,U)) => 
17203  365 
if a=b then (typ_match thy (tyinsts,(T,U)), insts) else raise MATCH 
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366 
 (Bound i, Bound j) => if i=j then instsp else raise MATCH 
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367 
 (Abs(_,T,t), Abs(_,U,u)) => 
17203  368 
mtch (typ_match thy (tyinsts,(T,U)),insts) (t,u) 
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369 
 (f$t, g$u) => mtch (mtch instsp (f,g)) (t, u) 
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370 
 (t, Abs(_,U,u)) => mtch instsp ((incr t)$(Bound 0), u) 
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371 
 _ => raise MATCH 
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372 
in mtch end; 
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373 

17203  374 
fun first_order_match thy = fomatch thy (Vartab.empty, Vartab.empty); 
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375 

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376 
(* Matching of higherorder patterns *) 
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377 

15797  378 
fun match_bind(itms,binders,ixn,T,is,t) = 
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379 
let val js = loose_bnos t 
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380 
in if null is 
17412  381 
then if null js then Vartab.update_new (ixn, (T, t)) itms else raise MATCH 
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382 
else if js subset_int is 
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383 
then let val t' = if downto0(is,length binders  1) then t 
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384 
else mapbnd (idx is) t 
17412  385 
in Vartab.update_new (ixn, (T, mkabs (binders, is, t'))) itms end 
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386 
else raise MATCH 
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387 
end; 
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388 

17203  389 
fun match thy (po as (pat,obj)) = 
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390 
let 
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391 
(* Pre: pat and obj have same type *) 
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392 
fun mtch binders (env as (iTs,itms),(pat,obj)) = 
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393 
case pat of 
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394 
Abs(ns,Ts,ts) => 
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395 
(case obj of 
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396 
Abs(nt,Tt,tt) => mtch ((nt,Tt)::binders) (env,(ts,tt)) 
15797  397 
 _ => let val Tt = Envir.typ_subst_TVars iTs Ts 
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398 
in mtch((ns,Tt)::binders)(env,(ts,(incr obj)$Bound(0))) end) 
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399 
 _ => (case obj of 
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400 
Abs(nt,Tt,tt) => 
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401 
mtch((nt,Tt)::binders)(env,((incr pat)$Bound(0),tt)) 
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402 
 _ => cases(binders,env,pat,obj)) 
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403 

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404 
and cases(binders,env as (iTs,itms),pat,obj) = 
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405 
let val (ph,pargs) = strip_comb pat 
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406 
fun rigrig1(iTs,oargs) = 
15570  407 
Library.foldl (mtch binders) ((iTs,itms), pargs~~oargs) 
16668  408 
fun rigrig2((a:string,Ta),(b,Tb),oargs) = 
409 
if a <> b then raise MATCH 

17203  410 
else rigrig1(typ_match thy (iTs,(Ta,Tb)), oargs) 
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411 
in case ph of 
15797  412 
Var(ixn,T) => 
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413 
let val is = ints_of pargs 
16651  414 
in case Envir.lookup' (itms, (ixn, T)) of 
15797  415 
NONE => (iTs,match_bind(itms,binders,ixn,T,is,obj)) 
15531  416 
 SOME u => if obj aeconv (red u is []) then env 
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417 
else raise MATCH 
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418 
end 
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419 
 _ => 
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420 
let val (oh,oargs) = strip_comb obj 
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421 
in case (ph,oh) of 
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422 
(Const c,Const d) => rigrig2(c,d,oargs) 
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423 
 (Free f,Free g) => rigrig2(f,g,oargs) 
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424 
 (Bound i,Bound j) => if i<>j then raise MATCH 
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425 
else rigrig1(iTs,oargs) 
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426 
 (Abs _, _) => raise Pattern 
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427 
 (_, Abs _) => raise Pattern 
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428 
 _ => raise MATCH 
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429 
end 
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430 
end; 
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431 

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432 
val pT = fastype_of pat 
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433 
and oT = fastype_of obj 
17203  434 
val iTs = typ_match thy (Vartab.empty, (pT,oT)) 
15797  435 
val insts2 = (iTs, Vartab.empty) 
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436 

15797  437 
in mtch [] (insts2, po) 
17203  438 
handle Pattern => fomatch thy insts2 po 
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439 
end; 
0  440 

441 
(*Predicate: does the pattern match the object?*) 

17203  442 
fun matches thy po = (match thy po; true) handle MATCH => false; 
0  443 

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444 
(* Does pat match a subterm of obj? *) 
17203  445 
fun matches_subterm thy (pat,obj) = 
446 
let fun msub(bounds,obj) = matches thy (pat,obj) orelse 

17756  447 
(case obj of 
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448 
Abs(x,T,t) => let val y = variant bounds x 
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449 
val f = Free(":" ^ y,T) 
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450 
in msub(x::bounds,subst_bound(f,t)) end 
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451 
 s$t => msub(bounds,s) orelse msub(bounds,t) 
17756  452 
 _ => false) 
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453 
in msub([],obj) end; 
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454 

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455 
fun first_order(Abs(_,_,t)) = first_order t 
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456 
 first_order(t $ u) = first_order t andalso first_order u andalso 
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457 
not(is_Var t) 
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458 
 first_order _ = true; 
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459 

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460 
fun pattern(Abs(_,_,t)) = pattern t 
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461 
 pattern(t) = let val (head,args) = strip_comb t 
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462 
in if is_Var head 
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463 
then let val _ = ints_of args in true end 
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464 
handle Pattern => false 
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465 
else forall pattern args 
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466 
end; 
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467 

12784  468 

469 
(* rewriting  simple but fast *) 

470 

17203  471 
fun rewrite_term thy rules procs tm = 
12784  472 
let 
13195  473 
val skel0 = Bound 0; 
474 

16939  475 
fun variant_absfree bounds (x, T, t) = 
12797  476 
let 
16986  477 
val (x', t') = Term.dest_abs (Term.bound bounds, T, t); 
16939  478 
fun abs u = Abs (x, T, abstract_over (Free (x', T), u)); 
479 
in (abs, t') end; 

12797  480 

12784  481 
fun match_rew tm (tm1, tm2) = 
16939  482 
let val rtm = if_none (Term.rename_abs tm1 tm tm2) tm2 in 
17203  483 
SOME (Envir.subst_vars (match thy (tm1, tm)) rtm, rtm) 
16939  484 
handle MATCH => NONE 
13195  485 
end; 
12784  486 

15531  487 
fun rew (Abs (_, _, body) $ t) = SOME (subst_bound (t, body), skel0) 
13195  488 
 rew tm = (case get_first (match_rew tm) rules of 
15570  489 
NONE => Option.map (rpair skel0) (get_first (fn p => p tm) procs) 
13195  490 
 x => x); 
491 

16939  492 
fun rew1 bounds (Var _) _ = NONE 
493 
 rew1 bounds skel tm = (case rew2 bounds skel tm of 

15531  494 
SOME tm1 => (case rew tm1 of 
16939  495 
SOME (tm2, skel') => SOME (if_none (rew1 bounds skel' tm2) tm2) 
15531  496 
 NONE => SOME tm1) 
497 
 NONE => (case rew tm of 

16939  498 
SOME (tm1, skel') => SOME (if_none (rew1 bounds skel' tm1) tm1) 
15531  499 
 NONE => NONE)) 
12784  500 

16939  501 
and rew2 bounds skel (tm1 $ tm2) = (case tm1 of 
12784  502 
Abs (_, _, body) => 
503 
let val tm' = subst_bound (tm2, body) 

16939  504 
in SOME (if_none (rew2 bounds skel0 tm') tm') end 
14787  505 
 _ => 
13195  506 
let val (skel1, skel2) = (case skel of 
507 
skel1 $ skel2 => (skel1, skel2) 

508 
 _ => (skel0, skel0)) 

16939  509 
in case rew1 bounds skel1 tm1 of 
510 
SOME tm1' => (case rew1 bounds skel2 tm2 of 

15531  511 
SOME tm2' => SOME (tm1' $ tm2') 
512 
 NONE => SOME (tm1' $ tm2)) 

16939  513 
 NONE => (case rew1 bounds skel2 tm2 of 
15531  514 
SOME tm2' => SOME (tm1 $ tm2') 
515 
 NONE => NONE) 

13195  516 
end) 
16939  517 
 rew2 bounds skel (Abs body) = 
13195  518 
let 
16939  519 
val (abs, tm') = variant_absfree bounds body; 
13195  520 
val skel' = (case skel of Abs (_, _, skel') => skel'  _ => skel0) 
16939  521 
in case rew1 (bounds + 1) skel' tm' of 
15531  522 
SOME tm'' => SOME (abs tm'') 
523 
 NONE => NONE 

12797  524 
end 
16939  525 
 rew2 _ _ _ = NONE; 
12784  526 

16939  527 
in if_none (rew1 0 skel0 tm) tm end; 
12784  528 

0  529 
end; 
13642
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530 

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531 
val trace_unify_fail = Pattern.trace_unify_fail; 