author  wenzelm 
Thu, 01 Jul 1999 21:19:45 +0200  
changeset 6874  747f656e04ec 
parent 6566  7ed743d18af7 
child 7052  4c201f27c74e 
permissions  rwrr 
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(* Title: TFL/tfl 
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ID: $Id$ 
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Author: Konrad Slind, Cambridge University Computer Laboratory 
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Copyright 1997 University of Cambridge 
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Main module 
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*) 
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structure Prim : TFL_sig = 
2112  10 
struct 
11 

6498  12 
val trace = ref false; 
13 

2112  14 
(* Abbreviations *) 
15 
structure R = Rules; 

16 
structure S = USyntax; 

17 
structure U = S.Utils; 

18 

19 
val concl = #2 o R.dest_thm; 

20 
val hyp = #1 o R.dest_thm; 

21 

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val list_mk_type = U.end_itlist (curry(op >)); 
2112  23 

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fun enumerate l = 
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rev(#1(foldl (fn ((alist,i), x) => ((x,i)::alist, i+1)) (([],0), l))); 
2112  26 

27 
fun stringize [] = "" 

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 stringize [i] = Int.toString i 
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 stringize (h::t) = (Int.toString h^", "^stringize t); 
2112  30 

31 

32 
fun TFL_ERR{func,mesg} = U.ERR{module = "Tfl", func = func, mesg = mesg}; 

33 

34 

35 
(* 

6498  36 
handling of usersupplied congruence rules: lcp*) 
37 

38 
(*Convert conclusion from = to ==*) 

39 
val eq_reflect_list = map (fn th => (th RS eq_reflection) handle _ => th); 

40 

41 
(*default congruence rules include those for LET and IF*) 

42 
val default_congs = eq_reflect_list [Thms.LET_CONG, if_cong]; 

43 

44 
fun congs ths = default_congs @ eq_reflect_list ths; 

45 

46 
val default_simps = 

47 
[less_Suc_eq RS iffD2, lex_prod_def, measure_def, inv_image_def]; 

48 

49 

50 

51 

52 
(* 

2112  53 
* The next function is common to patternmatch translation and 
54 
* proof of completeness of cases for the induction theorem. 

55 
* 

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* The curried function "gvvariant" returns a function to generate distinct 
3405  57 
* variables that are guaranteed not to be in names. The names of 
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* the variables go u, v, ..., z, aa, ..., az, ... The returned 
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* function contains embedded refs! 
2112  60 
**) 
3405  61 
fun gvvariant names = 
62 
let val slist = ref names 

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val vname = ref "u" 
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fun new() = 
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if !vname mem_string (!slist) 
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then (vname := bump_string (!vname); new()) 
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else (slist := !vname :: !slist; !vname) 
2112  68 
in 
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fn ty => Free(new(), ty) 
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end; 
2112  71 

72 

73 
(* 

74 
* Used in induction theorem production. This is the simple case of 

75 
* partitioning up pattern rows by the leading constructor. 

76 
**) 

77 
fun ipartition gv (constructors,rows) = 

78 
let fun pfail s = raise TFL_ERR{func = "partition.part", mesg = s} 

79 
fun part {constrs = [], rows = [], A} = rev A 

80 
 part {constrs = [], rows = _::_, A} = pfail"extra cases in defn" 

81 
 part {constrs = _::_, rows = [], A} = pfail"cases missing in defn" 

82 
 part {constrs = c::crst, rows, A} = 

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let val (Name,Ty) = dest_Const c 
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val L = binder_types Ty 
2112  85 
val (in_group, not_in_group) = 
86 
U.itlist (fn (row as (p::rst, rhs)) => 

87 
fn (in_group,not_in_group) => 

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let val (pc,args) = S.strip_comb p 

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in if (#1(dest_Const pc) = Name) 
2112  90 
then ((args@rst, rhs)::in_group, not_in_group) 
91 
else (in_group, row::not_in_group) 

92 
end) rows ([],[]) 

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val col_types = U.take type_of (length L, #1(hd in_group)) 
2112  94 
in 
95 
part{constrs = crst, rows = not_in_group, 

96 
A = {constructor = c, 

97 
new_formals = map gv col_types, 

98 
group = in_group}::A} 

99 
end 

100 
in part{constrs = constructors, rows = rows, A = []} 

101 
end; 

102 

103 

104 

105 
(* 

106 
* This datatype carries some information about the origin of a 

107 
* clause in a function definition. 

108 
**) 

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datatype pattern = GIVEN of term * int 
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 OMITTED of term * int 
2112  111 

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fun pattern_map f (GIVEN (tm,i)) = GIVEN(f tm, i) 
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 pattern_map f (OMITTED (tm,i)) = OMITTED(f tm, i); 
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fun pattern_subst theta = pattern_map (subst_free theta); 
2112  116 

117 
fun dest_pattern (GIVEN (tm,i)) = ((GIVEN,i),tm) 

118 
 dest_pattern (OMITTED (tm,i)) = ((OMITTED,i),tm); 

119 

120 
val pat_of = #2 o dest_pattern; 

121 
val row_of_pat = #2 o #1 o dest_pattern; 

122 

123 
(* 

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* Produce an instance of a constructor, plus genvars for its arguments. 

125 
**) 

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fun fresh_constr ty_match colty gv c = 

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let val (_,Ty) = dest_Const c 
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val L = binder_types Ty 
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and ty = body_type Ty 
2112  130 
val ty_theta = ty_match ty colty 
131 
val c' = S.inst ty_theta c 

132 
val gvars = map (S.inst ty_theta o gv) L 

133 
in (c', gvars) 

134 
end; 

135 

136 

137 
(* 

138 
* Goes through a list of rows and picks out the ones beginning with a 

139 
* pattern with constructor = Name. 

140 
**) 

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fun mk_group Name rows = 

142 
U.itlist (fn (row as ((prefix, p::rst), rhs)) => 

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fn (in_group,not_in_group) => 

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let val (pc,args) = S.strip_comb p 

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in if ((#1(dest_Const pc) = Name) handle _ => false) 
2112  146 
then (((prefix,args@rst), rhs)::in_group, not_in_group) 
147 
else (in_group, row::not_in_group) end) 

148 
rows ([],[]); 

149 

150 
(* 

151 
* Partition the rows. Not efficient: we should use hashing. 

152 
**) 

153 
fun partition _ _ (_,_,_,[]) = raise TFL_ERR{func="partition", mesg="no rows"} 

154 
 partition gv ty_match 

155 
(constructors, colty, res_ty, rows as (((prefix,_),_)::_)) = 

156 
let val fresh = fresh_constr ty_match colty gv 

157 
fun part {constrs = [], rows, A} = rev A 

158 
 part {constrs = c::crst, rows, A} = 

159 
let val (c',gvars) = fresh c 

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val (Name,Ty) = dest_Const c' 
2112  161 
val (in_group, not_in_group) = mk_group Name rows 
162 
val in_group' = 

163 
if (null in_group) (* Constructor not given *) 

164 
then [((prefix, #2(fresh c)), OMITTED (S.ARB res_ty, ~1))] 

165 
else in_group 

166 
in 

167 
part{constrs = crst, 

168 
rows = not_in_group, 

169 
A = {constructor = c', 

170 
new_formals = gvars, 

171 
group = in_group'}::A} 

172 
end 

173 
in part{constrs=constructors, rows=rows, A=[]} 

174 
end; 

175 

176 
(* 

177 
* Misc. routines used in mk_case 

178 
**) 

179 

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fun mk_pat (c,l) = 
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let val L = length (binder_types (type_of c)) 
2112  182 
fun build (prefix,tag,plist) = 
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let val args = take (L,plist) 
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and plist' = drop(L,plist) 
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in (prefix,tag,list_comb(c,args)::plist') end 
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in map build l end; 
2112  187 

188 
fun v_to_prefix (prefix, v::pats) = (v::prefix,pats) 

189 
 v_to_prefix _ = raise TFL_ERR{func="mk_case", mesg="v_to_prefix"}; 

190 

191 
fun v_to_pats (v::prefix,tag, pats) = (prefix, tag, v::pats) 

192 
 v_to_pats _ = raise TFL_ERR{func="mk_case", mesg="v_to_pats"}; 

193 

194 

195 
(* 

196 
* Translation of pattern terms into nested case expressions. 

197 
* 

198 
* This performs the translation and also builds the full set of patterns. 

199 
* Thus it supports the construction of induction theorems even when an 

200 
* incomplete set of patterns is given. 

201 
**) 

202 

3405  203 
fun mk_case ty_info ty_match usednames range_ty = 
2112  204 
let 
205 
fun mk_case_fail s = raise TFL_ERR{func = "mk_case", mesg = s} 

3405  206 
val fresh_var = gvvariant usednames 
2112  207 
val divide = partition fresh_var ty_match 
208 
fun expand constructors ty ((_,[]), _) = mk_case_fail"expand_var_row" 

209 
 expand constructors ty (row as ((prefix, p::rst), rhs)) = 

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if (is_Free p) 
2112  211 
then let val fresh = fresh_constr ty_match ty fresh_var 
212 
fun expnd (c,gvs) = 

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let val capp = list_comb(c,gvs) 
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in ((prefix, capp::rst), pattern_subst[(p,capp)] rhs) 
2112  215 
end 
216 
in map expnd (map fresh constructors) end 

217 
else [row] 

218 
fun mk{rows=[],...} = mk_case_fail"no rows" 

219 
 mk{path=[], rows = ((prefix, []), rhs)::_} = (* Done *) 

220 
let val (tag,tm) = dest_pattern rhs 

221 
in ([(prefix,tag,[])], tm) 

222 
end 

223 
 mk{path=[], rows = _::_} = mk_case_fail"blunder" 

224 
 mk{path as u::rstp, rows as ((prefix, []), rhs)::rst} = 

225 
mk{path = path, 

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rows = ((prefix, [fresh_var(type_of u)]), rhs)::rst} 
2112  227 
 mk{path = u::rstp, rows as ((_, p::_), _)::_} = 
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let val (pat_rectangle,rights) = ListPair.unzip rows 
2112  229 
val col0 = map(hd o #2) pat_rectangle 
230 
in 

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if (forall is_Free col0) 
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then let val rights' = map (fn(v,e) => pattern_subst[(v,u)] e) 
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(ListPair.zip (col0, rights)) 
2112  234 
val pat_rectangle' = map v_to_prefix pat_rectangle 
235 
val (pref_patl,tm) = mk{path = rstp, 

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rows = ListPair.zip (pat_rectangle', 
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rights')} 
2112  238 
in (map v_to_pats pref_patl, tm) 
239 
end 

240 
else 

3944  241 
let val pty as Type (ty_name,_) = type_of p 
2112  242 
in 
243 
case (ty_info ty_name) 

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of None => mk_case_fail("Not a known datatype: "^ty_name) 
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 Some{case_const,constructors} => 
4221  246 
let open BasisLibrary (*restore original List*) 
4062  247 
val case_const_name = #1(dest_Const case_const) 
248 
val nrows = List.concat (map (expand constructors pty) rows) 

2112  249 
val subproblems = divide(constructors, pty, range_ty, nrows) 
250 
val groups = map #group subproblems 

251 
and new_formals = map #new_formals subproblems 

252 
and constructors' = map #constructor subproblems 

253 
val news = map (fn (nf,rows) => {path = nf@rstp, rows=rows}) 

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(ListPair.zip (new_formals, groups)) 
2112  255 
val rec_calls = map mk news 
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val (pat_rect,dtrees) = ListPair.unzip rec_calls 
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val case_functions = map S.list_mk_abs 
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(ListPair.zip (new_formals, dtrees)) 
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val types = map type_of (case_functions@[u]) @ [range_ty] 
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val case_const' = Const(case_const_name, list_mk_type types) 
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val tree = list_comb(case_const', case_functions@[u]) 
4062  262 
val pat_rect1 = List.concat 
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(ListPair.map mk_pat (constructors', pat_rect)) 
2112  264 
in (pat_rect1,tree) 
265 
end 

266 
end end 

267 
in mk 

268 
end; 

269 

270 

271 
(* Repeated variable occurrences in a pattern are not allowed. *) 

272 
fun FV_multiset tm = 

273 
case (S.dest_term tm) 

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of S.VAR{Name,Ty} => [Free(Name,Ty)] 
2112  275 
 S.CONST _ => [] 
276 
 S.COMB{Rator, Rand} => FV_multiset Rator @ FV_multiset Rand 

277 
 S.LAMB _ => raise TFL_ERR{func = "FV_multiset", mesg = "lambda"}; 

278 

279 
fun no_repeat_vars thy pat = 

280 
let fun check [] = true 

281 
 check (v::rst) = 

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if mem_term (v,rst) then 
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raise TFL_ERR{func = "no_repeat_vars", 
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mesg = quote(#1(dest_Free v)) ^ 
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" occurs repeatedly in the pattern " ^ 
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quote (string_of_cterm (Thry.typecheck thy pat))} 
2112  287 
else check rst 
288 
in check (FV_multiset pat) 

289 
end; 

290 

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local fun mk_functional_err s = raise TFL_ERR{func = "mk_functional", mesg=s} 
6566  292 
fun single [Free(a,_)] = 
293 
mk_functional_err (a ^ " has not been declared as a constant") 

294 
 single [f] = f 

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295 
 single fs = mk_functional_err (Int.toString (length fs) ^ 
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296 
" distinct function names!") 
2112  297 
in 
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298 
fun mk_functional thy clauses = 
6566  299 
let val (L,R) = ListPair.unzip (map HOLogic.dest_eq clauses) 
300 
handle _ => raise TFL_ERR 

301 
{func = "mk_functional", 

302 
mesg = "recursion equations must use the = relation"} 

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303 
val (funcs,pats) = ListPair.unzip (map (fn (t$u) =>(t,u)) L) 
3405  304 
val fcon as Const (fname, ftype) = single (gen_distinct (op aconv) funcs) 
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305 
val dummy = map (no_repeat_vars thy) pats 
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306 
val rows = ListPair.zip (map (fn x => ([],[x])) pats, 
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307 
map GIVEN (enumerate R)) 
3405  308 
val names = foldr add_term_names (R,[]) 
309 
val atype = type_of(hd pats) 

310 
and aname = variant names "a" 

311 
val a = Free(aname,atype) 

2112  312 
val ty_info = Thry.match_info thy 
313 
val ty_match = Thry.match_type thy 

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314 
val range_ty = type_of (hd R) 
3405  315 
val (patts, case_tm) = mk_case ty_info ty_match (aname::names) range_ty 
2112  316 
{path=[a], rows=rows} 
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317 
val patts1 = map (fn (_,(tag,i),[pat]) => tag (pat,i)) patts 
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318 
handle _ => mk_functional_err "error in patternmatch translation" 
2112  319 
val patts2 = U.sort(fn p1=>fn p2=> row_of_pat p1 < row_of_pat p2) patts1 
320 
val finals = map row_of_pat patts2 

321 
val originals = map (row_of_pat o #2) rows 

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322 
val dummy = case (originals\\finals) 
2112  323 
of [] => () 
324 
 L => mk_functional_err("The following rows (counting from zero)\ 

325 
\ are inaccessible: "^stringize L) 

3944  326 
in {functional = Abs(Sign.base_name fname, ftype, 
3405  327 
abstract_over (fcon, 
328 
absfree(aname,atype, case_tm))), 

2112  329 
pats = patts2} 
330 
end end; 

331 

332 

333 
(* 

334 
* 

335 
* PRINCIPLES OF DEFINITION 

336 
* 

337 
**) 

338 

339 

6498  340 
(*For Isabelle, the lhs of a definition must be a constant.*) 
341 
fun mk_const_def sign (Name, Ty, rhs) = 

342 
Sign.infer_types sign (K None) (K None) [] false 

343 
([Const("==",dummyT) $ Const(Name,Ty) $ rhs], propT) 

344 
> #1; 

345 

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346 
(*Make all TVars available for instantiation by adding a ? to the front*) 
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347 
fun poly_tvars (Type(a,Ts)) = Type(a, map (poly_tvars) Ts) 
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348 
 poly_tvars (TFree (a,sort)) = TVar (("?" ^ a, 0), sort) 
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349 
 poly_tvars (TVar ((a,i),sort)) = TVar (("?" ^ a, i+1), sort); 
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350 

3191  351 
local val f_eq_wfrec_R_M = 
352 
#ant(S.dest_imp(#2(S.strip_forall (concl Thms.WFREC_COROLLARY)))) 

353 
val {lhs=f, rhs} = S.dest_eq f_eq_wfrec_R_M 

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354 
val (fname,_) = dest_Free f 
3191  355 
val (wfrec,_) = S.strip_comb rhs 
356 
in 

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357 
fun wfrec_definition0 thy fid R (functional as Abs(Name, Ty, _)) = 
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358 
let val def_name = if Name<>fid then 
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359 
raise TFL_ERR{func = "wfrec_definition0", 
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360 
mesg = "Expected a definition of " ^ 
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361 
quote fid ^ " but found one of " ^ 
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362 
quote Name} 
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363 
else Name ^ "_def" 
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364 
val wfrec_R_M = map_term_types poly_tvars 
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365 
(wfrec $ map_term_types poly_tvars R) 
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366 
$ functional 
6498  367 
val def_term = mk_const_def (Theory.sign_of thy) (Name, Ty, wfrec_R_M) 
6092  368 
in PureThy.add_defs_i [Thm.no_attributes (def_name, def_term)] thy end 
3191  369 
end; 
2112  370 

371 

372 

373 
(* 

374 
* This structure keeps track of congruence rules that aren't derived 

375 
* from a datatype definition. 

376 
**) 

377 
fun extraction_thms thy = 

378 
let val {case_rewrites,case_congs} = Thry.extract_info thy 

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379 
in (case_rewrites, case_congs) 
2112  380 
end; 
381 

382 

383 
(* 

384 
* Pair patterns with termination conditions. The full list of patterns for 

385 
* a definition is merged with the TCs arising from the usergiven clauses. 

386 
* There can be fewer clauses than the full list, if the user omitted some 

387 
* cases. This routine is used to prepare input for mk_induction. 

388 
**) 

389 
fun merge full_pats TCs = 

390 
let fun insert (p,TCs) = 

391 
let fun insrt ((x as (h,[]))::rst) = 

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392 
if (p aconv h) then (p,TCs)::rst else x::insrt rst 
2112  393 
 insrt (x::rst) = x::insrt rst 
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394 
 insrt[] = raise TFL_ERR{func="merge.insert", 
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395 
mesg="pattern not found"} 
2112  396 
in insrt end 
397 
fun pass ([],ptcl_final) = ptcl_final 

398 
 pass (ptcs::tcl, ptcl) = pass(tcl, insert ptcs ptcl) 

399 
in 

400 
pass (TCs, map (fn p => (p,[])) full_pats) 

401 
end; 

402 

403 

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404 
fun givens [] = [] 
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changeset

405 
 givens (GIVEN(tm,_)::pats) = tm :: givens pats 
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diff
changeset

406 
 givens (OMITTED _::pats) = givens pats; 
2112  407 

6498  408 
(*called only by Tfl.simplify_defn*) 
409 
fun post_definition meta_tflCongs (theory, (def, pats)) = 

3191  410 
let val tych = Thry.typecheck theory 
411 
val f = #lhs(S.dest_eq(concl def)) 

412 
val corollary = R.MATCH_MP Thms.WFREC_COROLLARY def 

2112  413 
val given_pats = givens pats 
414 
val WFR = #ant(S.dest_imp(concl corollary)) 

3191  415 
val R = #Rand(S.dest_comb WFR) 
2112  416 
val corollary' = R.UNDISCH corollary (* put WF R on assums *) 
3391
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417 
val corollaries = map (fn pat => R.SPEC (tych pat) corollary') 
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418 
given_pats 
3191  419 
val (case_rewrites,context_congs) = extraction_thms theory 
3405  420 
val corollaries' = map(rewrite_rule case_rewrites) corollaries 
421 
val extract = R.CONTEXT_REWRITE_RULE 

6498  422 
(f, [R], cut_apply, meta_tflCongs@context_congs) 
3405  423 
val (rules, TCs) = ListPair.unzip (map extract corollaries') 
424 
val rules0 = map (rewrite_rule [Thms.CUT_DEF]) rules 

425 
val mk_cond_rule = R.FILTER_DISCH_ALL(not o curry (op aconv) WFR) 

2112  426 
val rules1 = R.LIST_CONJ(map mk_cond_rule rules0) 
427 
in 

428 
{theory = theory, (* holds def, if it's needed *) 

429 
rules = rules1, 

6498  430 
full_pats_TCs = merge (map pat_of pats) (ListPair.zip (given_pats, TCs)), 
2112  431 
TCs = TCs, 
432 
patterns = pats} 

433 
end; 

434 

6498  435 

2112  436 
(* 
437 
* Perform the extraction without making the definition. Definition and 

6498  438 
* extraction commute for the nonnested case. (Deferred recdefs) 
439 
**) 

440 
fun wfrec_eqns thy fid tflCongs eqns = 

441 
let val {functional as Abs(Name, Ty, _), pats} = mk_functional thy eqns 

2112  442 
val given_pats = givens pats 
6498  443 
val f = #1 (S.strip_comb(#lhs(S.dest_eq (hd eqns)))) 
444 
(* val f = Free(Name,Ty) *) 

445 
val Type("fun", [f_dty, f_rty]) = Ty 

446 
val dummy = if Name<>fid then 

447 
raise TFL_ERR{func = "lazyR_def", 

448 
mesg = "Expected a definition of " ^ 

449 
quote fid ^ " but found one of " ^ 

450 
quote Name} 

451 
else () 

452 
val SV = S.free_vars_lr functional (* schema variables *) 

2112  453 
val (case_rewrites,context_congs) = extraction_thms thy 
454 
val tych = Thry.typecheck thy 

455 
val WFREC_THM0 = R.ISPEC (tych functional) Thms.WFREC_COROLLARY 

3405  456 
val Const("All",_) $ Abs(Rname,Rtype,_) = concl WFREC_THM0 
457 
val R = Free (variant (foldr add_term_names (eqns,[])) Rname, 

458 
Rtype) 

2112  459 
val WFREC_THM = R.ISPECL [tych R, tych f] WFREC_THM0 
460 
val ([proto_def, WFR],_) = S.strip_imp(concl WFREC_THM) 

6498  461 
val dummy = 
462 
if !trace then 

463 
writeln ("ORIGINAL PROTO_DEF: " ^ 

464 
Sign.string_of_term (Theory.sign_of thy) proto_def) 

465 
else () 

2112  466 
val R1 = S.rand WFR 
467 
val corollary' = R.UNDISCH(R.UNDISCH WFREC_THM) 

3405  468 
val corollaries = map (fn pat => R.SPEC (tych pat) corollary') given_pats 
469 
val corollaries' = map (rewrite_rule case_rewrites) corollaries 

6498  470 
fun extract X = R.CONTEXT_REWRITE_RULE 
471 
(f, R1::SV, cut_apply, tflCongs@context_congs) X 

472 
in {proto_def = (*Use == rather than = for definitions*) 

473 
mk_const_def (Theory.sign_of thy) 

474 
(Name, Ty, S.rhs proto_def), 

475 
SV=SV, 

2112  476 
WFR=WFR, 
477 
pats=pats, 

478 
extracta = map extract corollaries'} 

479 
end; 

480 

481 

482 
(* 

483 
* Define the constant after extracting the termination conditions. The 

484 
* wellfounded relation used in the definition is computed by using the 

485 
* choice operator on the extracted conditions (plus the condition that 

486 
* such a relation must be wellfounded). 

6498  487 
**) 
488 
fun lazyR_def thy fid tflCongs eqns = 

489 
let val {proto_def,WFR,pats,extracta,SV} = 

490 
wfrec_eqns thy fid (congs tflCongs) eqns 

2112  491 
val R1 = S.rand WFR 
6498  492 
val f = #1 (Logic.dest_equals proto_def) 
3245
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Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

493 
val (extractants,TCl) = ListPair.unzip extracta 
6498  494 
val dummy = if !trace 
495 
then (writeln "Extractants = "; 

496 
prths extractants; 

497 
()) 

498 
else () 

3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

499 
val TCs = foldr (gen_union (op aconv)) (TCl, []) 
2112  500 
val full_rqt = WFR::TCs 
501 
val R' = S.mk_select{Bvar=R1, Body=S.list_mk_conj full_rqt} 

502 
val R'abs = S.rand R' 

6498  503 
val proto_def' = subst_free[(R1,R')] proto_def 
504 
val dummy = if !trace then writeln ("proto_def' = " ^ 

505 
Sign.string_of_term 

506 
(Theory.sign_of thy) proto_def') 

507 
else () 

4857  508 
val theory = 
509 
thy 

6498  510 
> PureThy.add_defs_i 
511 
[Thm.no_attributes (fid ^ "_def", proto_def')]; 

512 
val def = get_axiom theory (fid ^ "_def") RS meta_eq_to_obj_eq 

513 
val dummy = if !trace then writeln ("DEF = " ^ string_of_thm def) 

514 
else () 

2112  515 
val fconst = #lhs(S.dest_eq(concl def)) 
516 
val tych = Thry.typecheck theory 

6498  517 
val full_rqt_prop = map (Dcterm.mk_prop o tych) full_rqt 
518 
(*lcp: a lot of objectlogic inference to remove*) 

519 
val baz = R.DISCH_ALL 

520 
(U.itlist R.DISCH full_rqt_prop 

521 
(R.LIST_CONJ extractants)) 

522 
val dum = if !trace then writeln ("baz = " ^ string_of_thm baz) 

523 
else () 

524 
val f_free = Free (fid, fastype_of f) (*'cos f is a Const*) 

2112  525 
val def' = R.MP (R.SPEC (tych fconst) 
6498  526 
(R.SPEC (tych R') 
527 
(R.GENL[tych R1, tych f_free] baz))) 

2112  528 
def 
6498  529 
val body_th = R.LIST_CONJ (map R.ASSUME full_rqt_prop) 
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

530 
val bar = R.MP (R.ISPECL[tych R'abs, tych R1] Thms.SELECT_AX) 
3191  531 
body_th 
6498  532 
in {theory = theory, R=R1, SV=SV, 
2112  533 
rules = U.rev_itlist (U.C R.MP) (R.CONJUNCTS bar) def', 
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

534 
full_pats_TCs = merge (map pat_of pats) (ListPair.zip (givens pats, TCl)), 
2112  535 
patterns = pats} 
536 
end; 

537 

538 

539 

540 
(* 

541 
* 

542 
* INDUCTION THEOREM 

543 
* 

544 
**) 

545 

546 

547 
(* Miscellaneous function  

548 
* 

549 
* [x_1,...,x_n] ?v_1...v_n. M[v_1,...,v_n] 

550 
*  

551 
* ( M[x_1,...,x_n], [(x_i,?v_1...v_n. M[v_1,...,v_n]), 

552 
* ... 

553 
* (x_j,?v_n. M[x_1,...,x_(n1),v_n])] ) 

554 
* 

555 
* This function is totally ad hoc. Used in the production of the induction 

556 
* theorem. The nchotomy theorem can have clauses that look like 

557 
* 

558 
* ?v1..vn. z = C vn..v1 

559 
* 

560 
* in which the order of quantification is not the order of occurrence of the 

561 
* quantified variables as arguments to C. Since we have no control over this 

562 
* aspect of the nchotomy theorem, we make the correspondence explicit by 

563 
* pairing the incoming new variable with the term it gets betareduced into. 

564 
**) 

565 

3245
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Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

566 
fun alpha_ex_unroll (xlist, tm) = 
2112  567 
let val (qvars,body) = S.strip_exists tm 
568 
val vlist = #2(S.strip_comb (S.rhs body)) 

3245
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Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

569 
val plist = ListPair.zip (vlist, xlist) 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

570 
val args = map (fn qv => the (gen_assoc (op aconv) (plist, qv))) qvars 
4149  571 
handle OPTION => error 
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

572 
"TFL fault [alpha_ex_unroll]: no correspondence" 
3405  573 
fun build ex [] = [] 
574 
 build (_$rex) (v::rst) = 

575 
let val ex1 = betapply(rex, v) 

576 
in ex1 :: build ex1 rst 

2112  577 
end 
3245
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Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

578 
val (nex::exl) = rev (tm::build tm args) 
2112  579 
in 
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

580 
(nex, ListPair.zip (args, rev exl)) 
2112  581 
end; 
582 

583 

584 

585 
(* 

586 
* 

587 
* PROVING COMPLETENESS OF PATTERNS 

588 
* 

589 
**) 

590 

3405  591 
fun mk_case ty_info usednames thy = 
2112  592 
let 
3405  593 
val divide = ipartition (gvvariant usednames) 
2112  594 
val tych = Thry.typecheck thy 
3353
9112a2efb9a3
Removal of module Mask and datatype binding with its constructor >
paulson
parents:
3333
diff
changeset

595 
fun tych_binding(x,y) = (tych x, tych y) 
2112  596 
fun fail s = raise TFL_ERR{func = "mk_case", mesg = s} 
597 
fun mk{rows=[],...} = fail"no rows" 

598 
 mk{path=[], rows = [([], (thm, bindings))]} = 

599 
R.IT_EXISTS (map tych_binding bindings) thm 

600 
 mk{path = u::rstp, rows as (p::_, _)::_} = 

3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

601 
let val (pat_rectangle,rights) = ListPair.unzip rows 
2112  602 
val col0 = map hd pat_rectangle 
603 
val pat_rectangle' = map tl pat_rectangle 

604 
in 

3333
0bbf06e86c06
Now checks the name of the function being defined;
paulson
parents:
3301
diff
changeset

605 
if (forall is_Free col0) (* column 0 is all variables *) 
3353
9112a2efb9a3
Removal of module Mask and datatype binding with its constructor >
paulson
parents:
3333
diff
changeset

606 
then let val rights' = map (fn ((thm,theta),v) => (thm,theta@[(u,v)])) 
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

607 
(ListPair.zip (rights, col0)) 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

608 
in mk{path = rstp, rows = ListPair.zip (pat_rectangle', rights')} 
2112  609 
end 
610 
else (* column 0 is all constructors *) 

3944  611 
let val Type (ty_name,_) = type_of p 
2112  612 
in 
613 
case (ty_info ty_name) 

3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

614 
of None => fail("Not a known datatype: "^ty_name) 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

615 
 Some{constructors,nchotomy} => 
2112  616 
let val thm' = R.ISPEC (tych u) nchotomy 
617 
val disjuncts = S.strip_disj (concl thm') 

618 
val subproblems = divide(constructors, rows) 

619 
val groups = map #group subproblems 

620 
and new_formals = map #new_formals subproblems 

3245
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Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
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diff
changeset

621 
val existentials = ListPair.map alpha_ex_unroll 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

622 
(new_formals, disjuncts) 
2112  623 
val constraints = map #1 existentials 
624 
val vexl = map #2 existentials 

625 
fun expnd tm (pats,(th,b)) = (pats,(R.SUBS[R.ASSUME(tych tm)]th,b)) 

626 
val news = map (fn (nf,rows,c) => {path = nf@rstp, 

627 
rows = map (expnd c) rows}) 

628 
(U.zip3 new_formals groups constraints) 

629 
val recursive_thms = map mk news 

3245
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Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

630 
val build_exists = foldr 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
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diff
changeset

631 
(fn((x,t), th) => 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
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diff
changeset

632 
R.CHOOSE (tych x, R.ASSUME (tych t)) th) 
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Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

633 
val thms' = ListPair.map build_exists (vexl, recursive_thms) 
2112  634 
val same_concls = R.EVEN_ORS thms' 
635 
in R.DISJ_CASESL thm' same_concls 

636 
end 

637 
end end 

638 
in mk 

639 
end; 

640 

641 

642 
fun complete_cases thy = 

643 
let val tych = Thry.typecheck thy 

644 
val ty_info = Thry.induct_info thy 

645 
in fn pats => 

3405  646 
let val names = foldr add_term_names (pats,[]) 
3391
5e45dd3b64e9
More deHOLification: using Free, Const, etc. instead of mk_var, mk_const
paulson
parents:
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diff
changeset

647 
val T = type_of (hd pats) 
3405  648 
val aname = Term.variant names "a" 
649 
val vname = Term.variant (aname::names) "v" 

650 
val a = Free (aname, T) 

651 
val v = Free (vname, T) 

3245
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Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

652 
val a_eq_v = HOLogic.mk_eq(a,v) 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

653 
val ex_th0 = R.EXISTS (tych (S.mk_exists{Bvar=v,Body=a_eq_v}), tych a) 
2112  654 
(R.REFL (tych a)) 
655 
val th0 = R.ASSUME (tych a_eq_v) 

656 
val rows = map (fn x => ([x], (th0,[]))) pats 

657 
in 

658 
R.GEN (tych a) 

659 
(R.RIGHT_ASSOC 

660 
(R.CHOOSE(tych v, ex_th0) 

3405  661 
(mk_case ty_info (vname::aname::names) 
662 
thy {path=[v], rows=rows}))) 

2112  663 
end end; 
664 

665 

666 
(* 

667 
* Constructing induction hypotheses: one for each recursive call. 

668 
* 

669 
* Note. R will never occur as a variable in the ind_clause, because 

670 
* to do so, it would have to be from a nested definition, and we don't 

671 
* allow nested defns to have R variable. 

672 
* 

673 
* Note. When the context is empty, there can be no local variables. 

674 
**) 

6498  675 
(* 
3405  676 
local infix 5 ==> 
2112  677 
fun (tm1 ==> tm2) = S.mk_imp{ant = tm1, conseq = tm2} 
678 
in 

679 
fun build_ih f P (pat,TCs) = 

680 
let val globals = S.free_vars_lr pat 

3405  681 
fun nested tm = is_some (S.find_term (curry (op aconv) f) tm) 
2112  682 
fun dest_TC tm = 
683 
let val (cntxt,R_y_pat) = S.strip_imp(#2(S.strip_forall tm)) 

684 
val (R,y,_) = S.dest_relation R_y_pat 

3405  685 
val P_y = if (nested tm) then R_y_pat ==> P$y else P$y 
2112  686 
in case cntxt 
687 
of [] => (P_y, (tm,[])) 

688 
 _ => let 

689 
val imp = S.list_mk_conj cntxt ==> P_y 

3391
5e45dd3b64e9
More deHOLification: using Free, Const, etc. instead of mk_var, mk_const
paulson
parents:
3388
diff
changeset

690 
val lvs = gen_rems (op aconv) (S.free_vars_lr imp, globals) 
3405  691 
val locals = #2(U.pluck (curry (op aconv) P) lvs) handle _ => lvs 
2112  692 
in (S.list_mk_forall(locals,imp), (tm,locals)) end 
693 
end 

694 
in case TCs 

3405  695 
of [] => (S.list_mk_forall(globals, P$pat), []) 
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

696 
 _ => let val (ihs, TCs_locals) = ListPair.unzip(map dest_TC TCs) 
3405  697 
val ind_clause = S.list_mk_conj ihs ==> P$pat 
2112  698 
in (S.list_mk_forall(globals,ind_clause), TCs_locals) 
699 
end 

700 
end 

701 
end; 

6498  702 
*) 
2112  703 

6498  704 
local infix 5 ==> 
705 
fun (tm1 ==> tm2) = S.mk_imp{ant = tm1, conseq = tm2} 

706 
in 

707 
fun build_ih f (P,SV) (pat,TCs) = 

708 
let val pat_vars = S.free_vars_lr pat 

709 
val globals = pat_vars@SV 

710 
fun nested tm = is_some (S.find_term (curry (op aconv) f) tm) 

711 
fun dest_TC tm = 

712 
let val (cntxt,R_y_pat) = S.strip_imp(#2(S.strip_forall tm)) 

713 
val (R,y,_) = S.dest_relation R_y_pat 

714 
val P_y = if (nested tm) then R_y_pat ==> P$y else P$y 

715 
in case cntxt 

716 
of [] => (P_y, (tm,[])) 

717 
 _ => let 

718 
val imp = S.list_mk_conj cntxt ==> P_y 

719 
val lvs = gen_rems (op aconv) (S.free_vars_lr imp, globals) 

720 
val locals = #2(U.pluck (curry (op aconv) P) lvs) handle _ => lvs 

721 
in (S.list_mk_forall(locals,imp), (tm,locals)) end 

722 
end 

723 
in case TCs 

724 
of [] => (S.list_mk_forall(pat_vars, P$pat), []) 

725 
 _ => let val (ihs, TCs_locals) = ListPair.unzip(map dest_TC TCs) 

726 
val ind_clause = S.list_mk_conj ihs ==> P$pat 

727 
in (S.list_mk_forall(pat_vars,ind_clause), TCs_locals) 

728 
end 

729 
end 

730 
end; 

2112  731 

732 
(* 

6498  733 
* This function makes good on the promise made in "build_ih". 
2112  734 
* 
735 
* Input is tm = "(!y. R y pat ==> P y) ==> P pat", 

736 
* TCs = TC_1[pat] ... TC_n[pat] 

737 
* thm = ih1 /\ ... /\ ih_n  ih[pat] 

738 
**) 

739 
fun prove_case f thy (tm,TCs_locals,thm) = 

740 
let val tych = Thry.typecheck thy 

741 
val antc = tych(#ant(S.dest_imp tm)) 

742 
val thm' = R.SPEC_ALL thm 

3405  743 
fun nested tm = is_some (S.find_term (curry (op aconv) f) tm) 
2112  744 
fun get_cntxt TC = tych(#ant(S.dest_imp(#2(S.strip_forall(concl TC))))) 
745 
fun mk_ih ((TC,locals),th2,nested) = 

746 
R.GENL (map tych locals) 

747 
(if nested 

748 
then R.DISCH (get_cntxt TC) th2 handle _ => th2 

749 
else if S.is_imp(concl TC) 

750 
then R.IMP_TRANS TC th2 

751 
else R.MP th2 TC) 

752 
in 

753 
R.DISCH antc 

754 
(if S.is_imp(concl thm') (* recursive calls in this clause *) 

755 
then let val th1 = R.ASSUME antc 

756 
val TCs = map #1 TCs_locals 

757 
val ylist = map (#2 o S.dest_relation o #2 o S.strip_imp o 

758 
#2 o S.strip_forall) TCs 

759 
val TClist = map (fn(TC,lvs) => (R.SPEC_ALL(R.ASSUME(tych TC)),lvs)) 

760 
TCs_locals 

761 
val th2list = map (U.C R.SPEC th1 o tych) ylist 

762 
val nlist = map nested TCs 

763 
val triples = U.zip3 TClist th2list nlist 

764 
val Pylist = map mk_ih triples 

765 
in R.MP thm' (R.LIST_CONJ Pylist) end 

766 
else thm') 

767 
end; 

768 

769 

770 
(* 

771 
* 

772 
* x = (v1,...,vn)  M[x] 

773 
*  

774 
* ?v1 ... vn. x = (v1,...,vn)  M[x] 

775 
* 

776 
**) 

777 
fun LEFT_ABS_VSTRUCT tych thm = 

778 
let fun CHOOSER v (tm,thm) = 

779 
let val ex_tm = S.mk_exists{Bvar=v,Body=tm} 

780 
in (ex_tm, R.CHOOSE(tych v, R.ASSUME (tych ex_tm)) thm) 

781 
end 

3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

782 
val [veq] = filter (U.can S.dest_eq) (#1 (R.dest_thm thm)) 
2112  783 
val {lhs,rhs} = S.dest_eq veq 
784 
val L = S.free_vars_lr rhs 

3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

785 
in #2 (U.itlist CHOOSER L (veq,thm)) end; 
2112  786 

787 

788 
(* 

789 
* Input : f, R, and [(pat1,TCs1),..., (patn,TCsn)] 

790 
* 

791 
* Instantiates WF_INDUCTION_THM, getting Sinduct and then tries to prove 

792 
* recursion induction (Rinduct) by proving the antecedent of Sinduct from 

793 
* the antecedent of Rinduct. 

794 
**) 

6498  795 
fun mk_induction thy {fconst, R, SV, pat_TCs_list} = 
2112  796 
let val tych = Thry.typecheck thy 
797 
val Sinduction = R.UNDISCH (R.ISPEC (tych R) Thms.WF_INDUCTION_THM) 

3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

798 
val (pats,TCsl) = ListPair.unzip pat_TCs_list 
2112  799 
val case_thm = complete_cases thy pats 
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

800 
val domain = (type_of o hd) pats 
3405  801 
val Pname = Term.variant (foldr (foldr add_term_names) 
802 
(pats::TCsl, [])) "P" 

803 
val P = Free(Pname, domain > HOLogic.boolT) 

2112  804 
val Sinduct = R.SPEC (tych P) Sinduction 
805 
val Sinduct_assumf = S.rand ((#ant o S.dest_imp o concl) Sinduct) 

6498  806 
val Rassums_TCl' = map (build_ih fconst (P,SV)) pat_TCs_list 
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

807 
val (Rassums,TCl') = ListPair.unzip Rassums_TCl' 
2112  808 
val Rinduct_assum = R.ASSUME (tych (S.list_mk_conj Rassums)) 
3405  809 
val cases = map (fn pat => betapply (Sinduct_assumf, pat)) pats 
2112  810 
val tasks = U.zip3 cases TCl' (R.CONJUNCTS Rinduct_assum) 
6498  811 
val proved_cases = map (prove_case fconst thy) tasks 
3405  812 
val v = Free (variant (foldr add_term_names (map concl proved_cases, [])) 
813 
"v", 

814 
domain) 

2112  815 
val vtyped = tych v 
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

816 
val substs = map (R.SYM o R.ASSUME o tych o (curry HOLogic.mk_eq v)) pats 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

817 
val proved_cases1 = ListPair.map (fn (th,th') => R.SUBS[th]th') 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

818 
(substs, proved_cases) 
2112  819 
val abs_cases = map (LEFT_ABS_VSTRUCT tych) proved_cases1 
820 
val dant = R.GEN vtyped (R.DISJ_CASESL (R.ISPEC vtyped case_thm) abs_cases) 

821 
val dc = R.MP Sinduct dant 

3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

822 
val Parg_ty = type_of(#Bvar(S.dest_forall(concl dc))) 
3405  823 
val vars = map (gvvariant[Pname]) (S.strip_prod_type Parg_ty) 
2112  824 
val dc' = U.itlist (R.GEN o tych) vars 
825 
(R.SPEC (tych(S.mk_vstruct Parg_ty vars)) dc) 

826 
in 

827 
R.GEN (tych P) (R.DISCH (tych(concl Rinduct_assum)) dc') 

3391
5e45dd3b64e9
More deHOLification: using Free, Const, etc. instead of mk_var, mk_const
paulson
parents:
3388
diff
changeset

828 
end 
2112  829 
handle _ => raise TFL_ERR{func = "mk_induction", mesg = "failed derivation"}; 
830 

831 

832 

3391
5e45dd3b64e9
More deHOLification: using Free, Const, etc. instead of mk_var, mk_const
paulson
parents:
3388
diff
changeset

833 

2112  834 
(* 
835 
* 

836 
* POST PROCESSING 

837 
* 

838 
**) 

839 

840 

841 
fun simplify_induction thy hth ind = 

842 
let val tych = Thry.typecheck thy 

843 
val (asl,_) = R.dest_thm ind 

844 
val (_,tc_eq_tc') = R.dest_thm hth 

845 
val tc = S.lhs tc_eq_tc' 

846 
fun loop [] = ind 

847 
 loop (asm::rst) = 

848 
if (U.can (Thry.match_term thy asm) tc) 

849 
then R.UNDISCH 

850 
(R.MATCH_MP 

851 
(R.MATCH_MP Thms.simp_thm (R.DISCH (tych asm) ind)) 

852 
hth) 

853 
else loop rst 

854 
in loop asl 

855 
end; 

856 

857 

858 
(* 

859 
* The termination condition is an antecedent to the rule, and an 

860 
* assumption to the theorem. 

861 
**) 

862 
fun elim_tc tcthm (rule,induction) = 

863 
(R.MP rule tcthm, R.PROVE_HYP tcthm induction) 

864 

865 

866 
fun postprocess{WFtac, terminator, simplifier} theory {rules,induction,TCs} = 

867 
let val tych = Thry.typecheck theory 

868 

869 
(* 

870 
* Attempt to eliminate WF condition. It's the only assumption of rules 

871 
**) 

872 
val (rules1,induction1) = 

3405  873 
let val thm = R.prove(tych(HOLogic.mk_Trueprop 
874 
(hd(#1(R.dest_thm rules)))), 

875 
WFtac) 

2112  876 
in (R.PROVE_HYP thm rules, R.PROVE_HYP thm induction) 
877 
end handle _ => (rules,induction) 

878 

879 
(* 

880 
* The termination condition (tc) is simplified to  tc = tc' (there 

881 
* might not be a change!) and then 3 attempts are made: 

882 
* 

883 
* 1. if  tc = T, then eliminate it with eqT; otherwise, 

884 
* 2. apply the terminator to tc'. If  tc' = T then eliminate; else 

885 
* 3. replace tc by tc' in both the rules and the induction theorem. 

886 
**) 

6498  887 

888 
fun print_thms s L = 

889 
if !trace then writeln (cat_lines (s :: map string_of_thm L)) 

890 
else (); 

891 

892 
fun print_cterms s L = 

893 
if !trace then writeln (cat_lines (s :: map string_of_cterm L)) 

894 
else ();; 

895 

2112  896 
fun simplify_tc tc (r,ind) = 
6498  897 
let val tc1 = tych tc 
898 
val _ = print_cterms "TC before simplification: " [tc1] 

899 
val tc_eq = simplifier tc1 

900 
val _ = print_thms "result: " [tc_eq] 

2112  901 
in 
902 
elim_tc (R.MATCH_MP Thms.eqT tc_eq) (r,ind) 

903 
handle _ => 

904 
(elim_tc (R.MATCH_MP(R.MATCH_MP Thms.rev_eq_mp tc_eq) 

3405  905 
(R.prove(tych(HOLogic.mk_Trueprop(S.rhs(concl tc_eq))), 
906 
terminator))) 

2112  907 
(r,ind) 
908 
handle _ => 

909 
(R.UNDISCH(R.MATCH_MP (R.MATCH_MP Thms.simp_thm r) tc_eq), 

910 
simplify_induction theory tc_eq ind)) 

911 
end 

912 

913 
(* 

914 
* Nested termination conditions are harder to get at, since they are 

915 
* left embedded in the body of the function (and in induction 

916 
* theorem hypotheses). Our "solution" is to simplify them, and try to 

917 
* prove termination, but leave the application of the resulting theorem 

918 
* to a higher level. So things go much as in "simplify_tc": the 

919 
* termination condition (tc) is simplified to  tc = tc' (there might 

920 
* not be a change) and then 2 attempts are made: 

921 
* 

922 
* 1. if  tc = T, then return  tc; otherwise, 

923 
* 2. apply the terminator to tc'. If  tc' = T then return  tc; else 

924 
* 3. return  tc = tc' 

925 
**) 

926 
fun simplify_nested_tc tc = 

927 
let val tc_eq = simplifier (tych (#2 (S.strip_forall tc))) 

928 
in 

929 
R.GEN_ALL 

930 
(R.MATCH_MP Thms.eqT tc_eq 

931 
handle _ 

932 
=> (R.MATCH_MP(R.MATCH_MP Thms.rev_eq_mp tc_eq) 

3405  933 
(R.prove(tych(HOLogic.mk_Trueprop (S.rhs(concl tc_eq))), 
934 
terminator)) 

2112  935 
handle _ => tc_eq)) 
936 
end 

937 

938 
(* 

939 
* Attempt to simplify the termination conditions in each rule and 

940 
* in the induction theorem. 

941 
**) 

942 
fun strip_imp tm = if S.is_neg tm then ([],tm) else S.strip_imp tm 

943 
fun loop ([],extras,R,ind) = (rev R, ind, extras) 

944 
 loop ((r,ftcs)::rst, nthms, R, ind) = 

945 
let val tcs = #1(strip_imp (concl r)) 

3391
5e45dd3b64e9
More deHOLification: using Free, Const, etc. instead of mk_var, mk_const
paulson
parents:
3388
diff
changeset

946 
val extra_tcs = gen_rems (op aconv) (ftcs, tcs) 
2112  947 
val extra_tc_thms = map simplify_nested_tc extra_tcs 
948 
val (r1,ind1) = U.rev_itlist simplify_tc tcs (r,ind) 

949 
val r2 = R.FILTER_DISCH_ALL(not o S.is_WFR) r1 

950 
in loop(rst, nthms@extra_tc_thms, r2::R, ind1) 

951 
end 

3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

952 
val rules_tcs = ListPair.zip (R.CONJUNCTS rules1, TCs) 
2112  953 
val (rules2,ind2,extras) = loop(rules_tcs,[],[],induction1) 
954 
in 

955 
{induction = ind2, rules = R.LIST_CONJ rules2, nested_tcs = extras} 

956 
end; 

957 

958 
end; (* TFL *) 