author  berghofe 
Thu, 18 Feb 2010 17:27:18 +0100  
changeset 35210  6e45e4c94751 
parent 33049  c38f02fdf35d 
child 35408  b48ab741683b 
permissions  rwrr 
12784  1 
(* Title: Pure/pattern.ML 
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Author: Tobias Nipkow, Christine Heinzelmann, and Stefan Berghofer, TU Muenchen 
0  3 

4 
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  13 
infix aeconv; 
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0  15 
signature PATTERN = 
14787  16 
sig 
32738  17 
val trace_unify_fail: bool Unsynchronized.ref 
17203  18 
val aeconv: term * term > bool 
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val eta_long: typ list > term > term 

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val match: theory > term * term > Type.tyenv * Envir.tenv > Type.tyenv * Envir.tenv 
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val first_order_match: theory > term * term 
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> Type.tyenv * Envir.tenv > Type.tyenv * Envir.tenv 
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val matches: theory > term * term > bool 
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val matchess: theory > term list * term list > bool 
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val equiv: theory > term * term > bool 
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val matches_subterm: theory > term * term > bool 
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val unify: theory > term * term > Envir.env > Envir.env 
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val first_order: term > bool 
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val pattern: term > bool 

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val match_rew: theory > term > term * term > (term * term) option 
17203  31 
val rewrite_term: theory > (term * term) list > (term > term option) list > term > term 
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val rewrite_term_top: theory > (term * term) list > (term > term option) list > term > term 
0  33 
exception Unif 
34 
exception MATCH 

35 
exception Pattern 

14787  36 
end; 
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17203  38 
structure Pattern: PATTERN = 
0  39 
struct 
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41 
exception Unif; 

42 
exception Pattern; 

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val trace_unify_fail = Unsynchronized.ref false; 
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fun string_of_term thy env binders t = 
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Syntax.string_of_term_global thy 
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(Envir.norm_term env (subst_bounds (map Free binders, t))); 
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fun bname binders i = fst (nth binders i); 
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fun bnames binders is = space_implode " " (map (bname binders) is); 
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17203  53 
fun typ_clash thy (tye,T,U) = 
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if !trace_unify_fail 
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then let val t = Syntax.string_of_typ_global thy (Envir.norm_type tye T) 
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and u = Syntax.string_of_typ_global 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  74 
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 = Term.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 
19300  79 
val ys = bnames binders (subtract (op =) is (loose_bnos t)) 
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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  86 
fun ocheck_fail thy (F,t,binders,env) = 
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if !trace_unify_fail 
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then let val f = Term.string_of_vname F 
17203  89 
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  95 
fun occurs(F,t,env) = 
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let fun occ(Var (G, T)) = (case Envir.lookup (env, (G, T)) of 
15531  97 
SOME(t) => occ t 
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 NONE => F=G) 

0  99 
 occ(t1$t2) = occ t1 orelse occ t2 
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 occ(Abs(_,_,t)) = occ t 

101 
 occ _ = false 

102 
in occ t end; 

103 

104 

105 
fun mapbnd f = 

106 
let fun mpb d (Bound(i)) = if i < d then Bound(i) else Bound(f(id)+d) 

107 
 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; 
0  114 

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fun mkabs (binders,is,t) = 

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let fun mk(i::is) = let val (x,T) = nth binders i 
12784  117 
in Abs(x,T,mk is) end 
0  118 
 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) = 
0  125 
let val is = ints_of bs 
20672  126 
in if member (op =) is i then raise Pattern else i::is end 
0  127 
 ints_of _ = raise Pattern; 
128 

12232  129 
fun ints_of' env ts = ints_of (map (Envir.head_norm env) ts); 
130 

0  131 

132 
fun app (s,(i::is)) = app (s$Bound(i),is) 

133 
 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 (nth jn) t,is); 
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0  139 

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(* split_type ([T1,....,Tn]> T,n,[]) = ([Tn,...,T1],T) *) 

141 
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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32032  145 
fun type_of_G env (T, n, is) = 
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let 

147 
val tyenv = Envir.type_env env; 

148 
val (Ts, U) = split_type (Envir.norm_type tyenv T, n, []); 

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in map (nth Ts) is > U end; 
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fun mkhnf (binders,is,G,js) = mkabs (binders, is, app(G,js)); 

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153 
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; 
0  156 

157 

23222  158 
(*predicate: downto0 (is, n) <=> is = [n, n  1, ..., 0]*) 
159 
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n  1) 

160 
 downto0 ([], n) = n = ~1; 

161 

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(*mk_proj_list(is) = [ is  k  1 <= k <= is and is[k] >= 0 ]*) 

0  163 
fun mk_proj_list is = 
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let fun mk(i::is,j) = if is_some i then j :: mk(is,j1) else mk(is,j1) 
0  165 
 mk([],_) = [] 
166 
in mk(is,length is  1) end; 

167 

168 
fun proj(s,env,binders,is) = 

169 
let fun trans d i = if i<d then i else (idx is (id))+d; 

12232  170 
fun pr(s,env,d,binders) = (case Envir.head_norm env s of 
0  171 
Abs(a,T,t) => let val (t',env') = pr(t,env,d+1,((a,T)::binders)) 
172 
in (Abs(a,T,t'),env') end 

173 
 t => (case strip_comb t of 

174 
(c as Const _,ts) => 

175 
let val (ts',env') = prs(ts,env,d,binders) 

176 
in (list_comb(c,ts'),env') end 

177 
 (f as Free _,ts) => 

178 
let val (ts',env') = prs(ts,env,d,binders) 

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

180 
 (Bound(i),ts) => 

181 
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'; 
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val ls = map_filter I js' 
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val Hty = type_of_G env (Fty,length js,ks) 
0  190 
val (env',H) = Envir.genvar a (env,Hty) 
191 
val env'' = 

15797  192 
Envir.update (((F, Fty), mkhnf (binders, js, H, ks)), env') 
0  193 
in (app(H,ls),env'') end 
194 
 _ => raise Pattern)) 

195 
and prs(s::ss,env,d,binders) = 

196 
let val (s',env1) = pr(s,env,d,binders) 

197 
val (ss',env2) = prs(ss,env1,d,binders) 

198 
in (s'::ss',env2) end 

199 
 prs([],env,_,_) = ([],env) 

200 
in if downto0(is,length binders  1) then (s,env) 

201 
else pr(s,env,0,binders) 

202 
end; 

203 

204 

205 
(* mk_ff_list(is,js) = [ length(is)  k  1 <= k <= is and is[k] = js[k] ] *) 

12784  206 
fun mk_ff_list(is,js) = 
207 
let fun mk([],[],_) = [] 

16668  208 
 mk(i::is,j::js, k) = if (i:int) = j then k :: mk(is,js,k1) 
0  209 
else mk(is,js,k1) 
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 mk _ = error"mk_ff_list" 
0  211 
in mk(is,js,length is1) end; 
212 

213 
fun flexflex1(env,binders,F,Fty,is,js) = 

214 
if is=js then env 

215 
else let val ks = mk_ff_list(is,js) 

216 
in mknewhnf(env,binders,is,F,Fty,ks) end; 

217 

218 
fun flexflex2(env,binders,F,Fty,is,G,Gty,js) = 

219 
let fun ff(F,Fty,is,G as (a,_),Gty,js) = 

33038  220 
if subset (op =) (js, is) 
0  221 
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 = inter (op =) js is 
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val Hty = type_of_G env (Fty,length is,map (idx is) ks) 
0  225 
val (env',H) = Envir.genvar a (env,Hty) 
226 
fun lam(is) = mkabs(binders,is,app(H,map (idx is) ks)); 

15797  227 
in Envir.update (((G, Gty), lam js), Envir.update (((F, Fty), lam is), env')) 
0  228 
end; 
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in if TermOrd.indexname_ord (G,F) = LESS then ff(F,Fty,is,G,Gty,js) else ff(G,Gty,js,F,Fty,is) end 
0  230 

32032  231 
fun unify_types thy (T, U) (env as Envir.Envir {maxidx, tenv, tyenv}) = 
232 
if T = U then env 

233 
else 

234 
let val (tyenv', maxidx') = Sign.typ_unify thy (U, T) (tyenv, maxidx) 

235 
in Envir.Envir {maxidx = maxidx', tenv = tenv, tyenv = tyenv'} end 

236 
handle Type.TUNIFY => (typ_clash thy (tyenv, T, U); raise Unif); 

0  237 

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fun unif thy binders (s,t) env = case (Envir.head_norm env s, Envir.head_norm env t) of 
0  239 
(Abs(ns,Ts,ts),Abs(nt,Tt,tt)) => 
240 
let val name = if ns = "" then nt else ns 

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in unif thy ((name,Ts)::binders) (ts,tt) env end 
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 (Abs(ns,Ts,ts),t) => unif thy ((ns,Ts)::binders) (ts,(incr t)$Bound(0)) env 
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 (t,Abs(nt,Tt,tt)) => unif thy ((nt,Tt)::binders) ((incr t)$Bound(0),tt) env 
17203  244 
 p => cases thy (binders,env,p) 
0  245 

17203  246 
and cases thy (binders,env,(s,t)) = case (strip_comb s,strip_comb t) of 
12784  247 
((Var(F,Fty),ss),(Var(G,Gty),ts)) => 
12232  248 
if F = G then flexflex1(env,binders,F,Fty,ints_of' env ss,ints_of' env ts) 
249 
else flexflex2(env,binders,F,Fty,ints_of' env ss,G,Gty,ints_of' env ts) 

17203  250 
 ((Var(F,Fty),ss),_) => flexrigid thy (env,binders,F,Fty,ints_of' env ss,t) 
251 
 (_,(Var(F,Fty),ts)) => flexrigid thy (env,binders,F,Fty,ints_of' env ts,s) 

252 
 ((Const c,ss),(Const d,ts)) => rigidrigid thy (env,binders,c,d,ss,ts) 

253 
 ((Free(f),ss),(Free(g),ts)) => rigidrigid thy (env,binders,f,g,ss,ts) 

254 
 ((Bound(i),ss),(Bound(j),ts)) => rigidrigidB thy (env,binders,i,j,ss,ts) 

0  255 
 ((Abs(_),_),_) => raise Pattern 
256 
 (_,(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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259 
 ((Free(f,_),_),(Const(c,_),_)) => (clash f c; raise Unif) 
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260 
 ((Free(f,_),_),(Bound i,_)) => (clashB binders i f; raise Unif) 
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261 
 ((Bound i,_),(Const(c,_),_)) => (clashB binders i c; raise Unif) 
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262 
 ((Bound i,_),(Free(f,_),_)) => (clashB binders i f; raise Unif) 
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263 

0  264 

17203  265 
and rigidrigid thy (env,binders,(a,Ta),(b,Tb),ss,ts) = 
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if a<>b then (clash a b; raise Unif) 
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else env > unify_types thy (Ta,Tb) > fold (unif thy binders) (ss~~ts) 
0  268 

17203  269 
and rigidrigidB thy (env,binders,i,j,ss,ts) = 
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if i <> j then (clashBB binders i j; raise Unif) 
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else fold (unif thy binders) (ss~~ts) env 
0  272 

17203  273 
and flexrigid thy (params as (env,binders,F,Fty,is,t)) = 
274 
if occurs(F,t,env) then (ocheck_fail thy (F,t,binders,env); raise Unif) 

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else (let val (u,env') = proj(t,env,binders,is) 
15797  276 
in Envir.update (((F, Fty), mkabs (binders, is, u)), env') end 
17203  277 
handle Unif => (proj_fail thy params; raise Unif)); 
0  278 

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fun unify thy = unif thy []; 
0  280 

281 

13998  282 
(* put a term into eta long beta normal form *) 
283 
fun eta_long Ts (Abs (s, T, t)) = Abs (s, T, eta_long (T :: Ts) t) 

284 
 eta_long Ts t = (case strip_comb t of 

285 
(Abs _, _) => eta_long Ts (Envir.beta_norm t) 

14787  286 
 (u, ts) => 
13998  287 
let 
288 
val Us = binder_types (fastype_of1 (Ts, t)); 

289 
val i = length Us 

290 
in list_abs (map (pair "x") Us, 

291 
list_comb (incr_boundvars i u, map (eta_long (rev Us @ Ts)) 

292 
(map (incr_boundvars i) ts @ map Bound (i  1 downto 0)))) 

293 
end); 

294 

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295 

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(*Tests whether 2 terms are alpha/etaconvertible and have same type. 
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Note that Consts and Vars may have more than one type.*) 
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fun t aeconv u = t aconv u orelse 
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Envir.eta_contract t aconv Envir.eta_contract u; 
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300 

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301 

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302 
(*** Matching ***) 
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303 

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304 
exception MATCH; 
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305 

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fun typ_match thy TU tyenv = Sign.typ_match thy TU tyenv 
16939  307 
handle Type.TYPE_MATCH => raise MATCH; 
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308 

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309 
(*Firstorder matching; 
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310 
The pattern and object may have variables in common. 
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311 
Instantiation does not affect the object, so matching ?a with ?a+1 works. 
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312 
Object is etacontracted on the fly (by etaexpanding the pattern). 
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313 
Precondition: the pattern is already etacontracted! 
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314 
Types are matched on the fly*) 
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fun first_order_match thy = 
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let 
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fun mtch k (instsp as (tyinsts,insts)) = fn 
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(Var(ixn,T), t) => 
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319 
if k > 0 andalso loose_bvar(t,0) then raise MATCH 
16651  320 
else (case Envir.lookup' (insts, (ixn, T)) of 
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NONE => (typ_match thy (T, fastype_of t) tyinsts, 
17412  322 
Vartab.update_new (ixn, (T, t)) insts) 
15531  323 
 SOME u => if t aeconv u then instsp else raise MATCH) 
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 (Free (a,T), Free (b,U)) => 
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if a=b then (typ_match thy (T,U) tyinsts, insts) else raise MATCH 
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326 
 (Const (a,T), Const (b,U)) => 
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327 
if a=b then (typ_match thy (T,U) tyinsts, insts) else raise MATCH 
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328 
 (Bound i, Bound j) => if i=j then instsp else raise MATCH 
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 (Abs(_,T,t), Abs(_,U,u)) => 
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330 
mtch (k + 1) (typ_match thy (T,U) tyinsts, insts) (t,u) 
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331 
 (f$t, g$u) => mtch k (mtch k instsp (f,g)) (t, u) 
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332 
 (t, Abs(_,U,u)) => mtch (k + 1) instsp ((incr t)$(Bound 0), u) 
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333 
 _ => raise MATCH 
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in fn tu => fn env => mtch 0 env tu end; 
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335 

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336 

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337 
(* Matching of higherorder patterns *) 
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338 

15797  339 
fun match_bind(itms,binders,ixn,T,is,t) = 
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340 
let val js = loose_bnos t 
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341 
in if null is 
17412  342 
then if null js then Vartab.update_new (ixn, (T, t)) itms else raise MATCH 
33038  343 
else if subset (op =) (js, is) 
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344 
then let val t' = if downto0(is,length binders  1) then t 
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345 
else mapbnd (idx is) t 
17412  346 
in Vartab.update_new (ixn, (T, mkabs (binders, is, t'))) itms end 
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347 
else raise MATCH 
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348 
end; 
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349 

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350 
fun match thy (po as (pat,obj)) envir = 
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351 
let 
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352 
(* Pre: pat and obj have same type *) 
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353 
fun mtch binders (pat,obj) (env as (iTs,itms)) = 
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354 
case pat of 
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355 
Abs(ns,Ts,ts) => 
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356 
(case obj of 
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357 
Abs(nt,Tt,tt) => mtch ((nt,Tt)::binders) (ts,tt) env 
32035  358 
 _ => let val Tt = Envir.subst_type iTs Ts 
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359 
in mtch((ns,Tt)::binders) (ts,(incr obj)$Bound(0)) env end) 
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360 
 _ => (case obj of 
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361 
Abs(nt,Tt,tt) => 
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362 
mtch((nt,Tt)::binders) ((incr pat)$Bound(0),tt) env 
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363 
 _ => cases(binders,env,pat,obj)) 
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364 

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365 
and cases(binders,env as (iTs,itms),pat,obj) = 
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366 
let val (ph,pargs) = strip_comb pat 
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367 
fun rigrig1(iTs,oargs) = fold (mtch binders) (pargs~~oargs) (iTs,itms) 
16668  368 
fun rigrig2((a:string,Ta),(b,Tb),oargs) = 
369 
if a <> b then raise MATCH 

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370 
else rigrig1(typ_match thy (Ta,Tb) iTs, oargs) 
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371 
in case ph of 
15797  372 
Var(ixn,T) => 
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373 
let val is = ints_of pargs 
16651  374 
in case Envir.lookup' (itms, (ixn, T)) of 
15797  375 
NONE => (iTs,match_bind(itms,binders,ixn,T,is,obj)) 
15531  376 
 SOME u => if obj aeconv (red u is []) then env 
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377 
else raise MATCH 
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378 
end 
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379 
 _ => 
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380 
let val (oh,oargs) = strip_comb obj 
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381 
in case (ph,oh) of 
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382 
(Const c,Const d) => rigrig2(c,d,oargs) 
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383 
 (Free f,Free g) => rigrig2(f,g,oargs) 
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384 
 (Bound i,Bound j) => if i<>j then raise MATCH 
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385 
else rigrig1(iTs,oargs) 
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386 
 (Abs _, _) => raise Pattern 
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387 
 (_, Abs _) => raise Pattern 
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388 
 _ => raise MATCH 
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389 
end 
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390 
end; 
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391 

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392 
val pT = fastype_of pat 
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393 
and oT = fastype_of obj 
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394 
val envir' = apfst (typ_match thy (pT, oT)) envir; 
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395 
in mtch [] po envir' handle Pattern => first_order_match thy po envir' end; 
0  396 

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397 
fun matches thy po = (match thy po (Vartab.empty, Vartab.empty); true) handle MATCH => false; 
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398 

28348  399 
fun matchess thy pos = (fold (match thy) (op ~~ pos) (Vartab.empty, Vartab.empty); true) handle MATCH => false; 
400 

19880  401 
fun equiv thy (t, u) = matches thy (t, u) andalso matches thy (u, t); 
402 

0  403 

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404 
(* Does pat match a subterm of obj? *) 
22255  405 
fun matches_subterm thy (pat, obj) = 
406 
let 

407 
fun msub bounds obj = matches thy (pat, obj) orelse 

408 
(case obj of 

409 
Abs (x, T, t) => msub (bounds + 1) (snd (Term.dest_abs (Name.bound bounds, T, t))) 

410 
 t $ u => msub bounds t orelse msub bounds u 

411 
 _ => false) 

412 
in msub 0 obj end; 

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413 

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414 
fun first_order(Abs(_,_,t)) = first_order t 
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415 
 first_order(t $ u) = first_order t andalso first_order u andalso 
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416 
not(is_Var t) 
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417 
 first_order _ = true; 
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418 

20672  419 
fun pattern (Abs (_, _, t)) = pattern t 
420 
 pattern t = 

421 
let val (head, args) = strip_comb t in 

422 
if is_Var head then 

423 
forall is_Bound args andalso not (has_duplicates (op aconv) args) 

424 
else forall pattern args 

425 
end; 

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426 

12784  427 

428 
(* rewriting  simple but fast *) 

429 

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430 
fun match_rew thy tm (tm1, tm2) = 
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431 
let val rtm = the_default tm2 (Term.rename_abs tm1 tm tm2) in 
32035  432 
SOME (Envir.subst_term (match thy (tm1, tm) (Vartab.empty, Vartab.empty)) rtm, rtm) 
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433 
handle MATCH => NONE 
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434 
end; 
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435 

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436 
fun gen_rewrite_term bot thy rules procs tm = 
12784  437 
let 
13195  438 
val skel0 = Bound 0; 
439 

16939  440 
fun variant_absfree bounds (x, T, t) = 
12797  441 
let 
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442 
val (x', t') = Term.dest_abs (Name.bound bounds, T, t); 
16939  443 
fun abs u = Abs (x, T, abstract_over (Free (x', T), u)); 
444 
in (abs, t') end; 

12797  445 

15531  446 
fun rew (Abs (_, _, body) $ t) = SOME (subst_bound (t, body), skel0) 
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447 
 rew tm = 
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448 
(case get_first (match_rew thy tm) rules of 
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449 
NONE => Option.map (rpair skel0) (get_first (fn p => p tm) procs) 
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450 
 x => x); 
13195  451 

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452 
fun rew_sub r bounds skel (tm1 $ tm2) = (case tm1 of 
12784  453 
Abs (_, _, body) => 
454 
let val tm' = subst_bound (tm2, body) 

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455 
in SOME (the_default tm' (rew_sub r bounds skel0 tm')) end 
14787  456 
 _ => 
13195  457 
let val (skel1, skel2) = (case skel of 
458 
skel1 $ skel2 => (skel1, skel2) 

459 
 _ => (skel0, skel0)) 

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460 
in case r bounds skel1 tm1 of 
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461 
SOME tm1' => (case r bounds skel2 tm2 of 
15531  462 
SOME tm2' => SOME (tm1' $ tm2') 
463 
 NONE => SOME (tm1' $ tm2)) 

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464 
 NONE => (case r bounds skel2 tm2 of 
15531  465 
SOME tm2' => SOME (tm1 $ tm2') 
466 
 NONE => NONE) 

13195  467 
end) 
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468 
 rew_sub r bounds skel (Abs body) = 
13195  469 
let 
16939  470 
val (abs, tm') = variant_absfree bounds body; 
13195  471 
val skel' = (case skel of Abs (_, _, skel') => skel'  _ => skel0) 
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472 
in case r (bounds + 1) skel' tm' of 
15531  473 
SOME tm'' => SOME (abs tm'') 
474 
 NONE => NONE 

12797  475 
end 
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476 
 rew_sub _ _ _ _ = NONE; 
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477 

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478 
fun rew_bot bounds (Var _) _ = NONE 
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479 
 rew_bot bounds skel tm = (case rew_sub rew_bot bounds skel tm of 
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480 
SOME tm1 => (case rew tm1 of 
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481 
SOME (tm2, skel') => SOME (the_default tm2 (rew_bot bounds skel' tm2)) 
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482 
 NONE => SOME tm1) 
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483 
 NONE => (case rew tm of 
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484 
SOME (tm1, skel') => SOME (the_default tm1 (rew_bot bounds skel' tm1)) 
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485 
 NONE => NONE)); 
12784  486 

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487 
fun rew_top bounds _ tm = (case rew tm of 
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488 
SOME (tm1, _) => (case rew_sub rew_top bounds skel0 tm1 of 
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489 
SOME tm2 => SOME (the_default tm2 (rew_top bounds skel0 tm2)) 
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490 
 NONE => SOME tm1) 
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491 
 NONE => (case rew_sub rew_top bounds skel0 tm of 
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492 
SOME tm1 => SOME (the_default tm1 (rew_top bounds skel0 tm1)) 
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493 
 NONE => NONE)); 
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494 

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495 
in the_default tm ((if bot then rew_bot else rew_top) 0 skel0 tm) end; 
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496 

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497 
val rewrite_term = gen_rewrite_term true; 
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498 
val rewrite_term_top = gen_rewrite_term false; 
12784  499 

0  500 
end; 
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501 

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502 
val trace_unify_fail = Pattern.trace_unify_fail; 