author  wenzelm 
Mon, 04 Oct 1999 21:41:09 +0200  
changeset 7697  cdaf7f18856d 
parent 7286  fcbf147e7b4c 
child 7906  0576dad973b1 
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 

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open BasisLibrary; (*restore original structures*) 
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2112  16 
(* Abbreviations *) 
17 
structure R = Rules; 

18 
structure S = USyntax; 

19 
structure U = S.Utils; 

20 

7262  21 
fun TFL_ERR{func,mesg} = U.ERR{module = "Tfl", func = func, mesg = mesg}; 
22 

2112  23 
val concl = #2 o R.dest_thm; 
24 
val hyp = #1 o R.dest_thm; 

25 

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val list_mk_type = U.end_itlist (curry(op >)); 
2112  27 

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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  30 

31 
fun stringize [] = "" 

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 stringize [i] = Int.toString i 
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 stringize (h::t) = (Int.toString h^", "^stringize t); 
2112  34 

7262  35 
fun front_last [] = raise TFL_ERR {func="front_last", mesg="empty list"} 
36 
 front_last [x] = ([],x) 

37 
 front_last (h::t) = 

38 
let val (pref,x) = front_last t 

39 
in 

40 
(h::pref,x) 

41 
end; 

2112  42 

43 

44 

45 
(* 

6498  46 
handling of usersupplied congruence rules: lcp*) 
47 

48 
(*Convert conclusion from = to ==*) 

49 
val eq_reflect_list = map (fn th => (th RS eq_reflection) handle _ => th); 

50 

51 
(*default congruence rules include those for LET and IF*) 

52 
val default_congs = eq_reflect_list [Thms.LET_CONG, if_cong]; 

53 

54 
fun congs ths = default_congs @ eq_reflect_list ths; 

55 

56 
val default_simps = 

57 
[less_Suc_eq RS iffD2, lex_prod_def, measure_def, inv_image_def]; 

58 

59 

60 

61 
(* 

2112  62 
* The next function is common to patternmatch translation and 
63 
* proof of completeness of cases for the induction theorem. 

64 
* 

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* The curried function "gvvariant" returns a function to generate distinct 
3405  66 
* 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  69 
**) 
3405  70 
fun gvvariant names = 
71 
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  77 
in 
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fn ty => Free(new(), ty) 
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end; 
2112  80 

81 

82 
(* 

83 
* Used in induction theorem production. This is the simple case of 

84 
* partitioning up pattern rows by the leading constructor. 

85 
**) 

86 
fun ipartition gv (constructors,rows) = 

87 
let fun pfail s = raise TFL_ERR{func = "partition.part", mesg = s} 

88 
fun part {constrs = [], rows = [], A} = rev A 

89 
 part {constrs = [], rows = _::_, A} = pfail"extra cases in defn" 

90 
 part {constrs = _::_, rows = [], A} = pfail"cases missing in defn" 

91 
 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  94 
val (in_group, not_in_group) = 
95 
U.itlist (fn (row as (p::rst, rhs)) => 

96 
fn (in_group,not_in_group) => 

97 
let val (pc,args) = S.strip_comb p 

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in if (#1(dest_Const pc) = Name) 
2112  99 
then ((args@rst, rhs)::in_group, not_in_group) 
100 
else (in_group, row::not_in_group) 

101 
end) rows ([],[]) 

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val col_types = U.take type_of (length L, #1(hd in_group)) 
2112  103 
in 
104 
part{constrs = crst, rows = not_in_group, 

105 
A = {constructor = c, 

106 
new_formals = map gv col_types, 

107 
group = in_group}::A} 

108 
end 

109 
in part{constrs = constructors, rows = rows, A = []} 

110 
end; 

111 

112 

113 

114 
(* 

115 
* This datatype carries some information about the origin of a 

116 
* clause in a function definition. 

117 
**) 

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datatype pattern = GIVEN of term * int 
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 OMITTED of term * int 
2112  120 

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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  125 

126 
fun dest_pattern (GIVEN (tm,i)) = ((GIVEN,i),tm) 

127 
 dest_pattern (OMITTED (tm,i)) = ((OMITTED,i),tm); 

128 

129 
val pat_of = #2 o dest_pattern; 

130 
val row_of_pat = #2 o #1 o dest_pattern; 

131 

132 
(* 

133 
* Produce an instance of a constructor, plus genvars for its arguments. 

134 
**) 

135 
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  139 
val ty_theta = ty_match ty colty 
140 
val c' = S.inst ty_theta c 

141 
val gvars = map (S.inst ty_theta o gv) L 

142 
in (c', gvars) 

143 
end; 

144 

145 

146 
(* 

147 
* Goes through a list of rows and picks out the ones beginning with a 

148 
* pattern with constructor = Name. 

149 
**) 

150 
fun mk_group Name rows = 

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U.itlist (fn (row as ((prfx, p::rst), rhs)) => 
2112  152 
fn (in_group,not_in_group) => 
153 
let val (pc,args) = S.strip_comb p 

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in if ((#1(dest_Const pc) = Name) handle _ => false) 
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then (((prfx,args@rst), rhs)::in_group, not_in_group) 
2112  156 
else (in_group, row::not_in_group) end) 
157 
rows ([],[]); 

158 

159 
(* 

160 
* Partition the rows. Not efficient: we should use hashing. 

161 
**) 

162 
fun partition _ _ (_,_,_,[]) = raise TFL_ERR{func="partition", mesg="no rows"} 

163 
 partition gv ty_match 

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(constructors, colty, res_ty, rows as (((prfx,_),_)::_)) = 
2112  165 
let val fresh = fresh_constr ty_match colty gv 
166 
fun part {constrs = [], rows, A} = rev A 

167 
 part {constrs = c::crst, rows, A} = 

168 
let val (c',gvars) = fresh c 

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val (Name,Ty) = dest_Const c' 
2112  170 
val (in_group, not_in_group) = mk_group Name rows 
171 
val in_group' = 

172 
if (null in_group) (* Constructor not given *) 

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then [((prfx, #2(fresh c)), OMITTED (S.ARB res_ty, ~1))] 
2112  174 
else in_group 
175 
in 

176 
part{constrs = crst, 

177 
rows = not_in_group, 

178 
A = {constructor = c', 

179 
new_formals = gvars, 

180 
group = in_group'}::A} 

181 
end 

182 
in part{constrs=constructors, rows=rows, A=[]} 

183 
end; 

184 

185 
(* 

186 
* Misc. routines used in mk_case 

187 
**) 

188 

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fun mk_pat (c,l) = 
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let val L = length (binder_types (type_of c)) 
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fun build (prfx,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 (prfx,tag,list_comb(c,args)::plist') end 
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in map build l end; 
2112  196 

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fun v_to_prfx (prfx, v::pats) = (v::prfx,pats) 
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 v_to_prfx _ = raise TFL_ERR{func="mk_case", mesg="v_to_prfx"}; 
2112  199 

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fun v_to_pats (v::prfx,tag, pats) = (prfx, tag, v::pats) 
2112  201 
 v_to_pats _ = raise TFL_ERR{func="mk_case", mesg="v_to_pats"}; 
202 

203 

204 
(* 

205 
* Translation of pattern terms into nested case expressions. 

206 
* 

207 
* This performs the translation and also builds the full set of patterns. 

208 
* Thus it supports the construction of induction theorems even when an 

209 
* incomplete set of patterns is given. 

210 
**) 

211 

3405  212 
fun mk_case ty_info ty_match usednames range_ty = 
2112  213 
let 
214 
fun mk_case_fail s = raise TFL_ERR{func = "mk_case", mesg = s} 

3405  215 
val fresh_var = gvvariant usednames 
2112  216 
val divide = partition fresh_var ty_match 
217 
fun expand constructors ty ((_,[]), _) = mk_case_fail"expand_var_row" 

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 expand constructors ty (row as ((prfx, p::rst), rhs)) = 
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if (is_Free p) 
2112  220 
then let val fresh = fresh_constr ty_match ty fresh_var 
221 
fun expnd (c,gvs) = 

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let val capp = list_comb(c,gvs) 
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in ((prfx, capp::rst), pattern_subst[(p,capp)] rhs) 
2112  224 
end 
225 
in map expnd (map fresh constructors) end 

226 
else [row] 

227 
fun mk{rows=[],...} = mk_case_fail"no rows" 

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 mk{path=[], rows = ((prfx, []), rhs)::_} = (* Done *) 
2112  229 
let val (tag,tm) = dest_pattern rhs 
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in ([(prfx,tag,[])], tm) 
2112  231 
end 
232 
 mk{path=[], rows = _::_} = mk_case_fail"blunder" 

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 mk{path as u::rstp, rows as ((prfx, []), rhs)::rst} = 
2112  234 
mk{path = path, 
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rows = ((prfx, [fresh_var(type_of u)]), rhs)::rst} 
2112  236 
 mk{path = u::rstp, rows as ((_, p::_), _)::_} = 
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let val (pat_rectangle,rights) = ListPair.unzip rows 
2112  238 
val col0 = map(hd o #2) pat_rectangle 
239 
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)) 
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val pat_rectangle' = map v_to_prfx pat_rectangle 
2112  244 
val (pref_patl,tm) = mk{path = rstp, 
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rows = ListPair.zip (pat_rectangle', 
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rights')} 
2112  247 
in (map v_to_pats pref_patl, tm) 
248 
end 

249 
else 

3944  250 
let val pty as Type (ty_name,_) = type_of p 
2112  251 
in 
252 
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} => 
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let 
4062  256 
val case_const_name = #1(dest_Const case_const) 
257 
val nrows = List.concat (map (expand constructors pty) rows) 

2112  258 
val subproblems = divide(constructors, pty, range_ty, nrows) 
259 
val groups = map #group subproblems 

260 
and new_formals = map #new_formals subproblems 

261 
and constructors' = map #constructor subproblems 

262 
val news = map (fn (nf,rows) => {path = nf@rstp, rows=rows}) 

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(ListPair.zip (new_formals, groups)) 
2112  264 
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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269 
val case_const' = Const(case_const_name, list_mk_type types) 
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270 
val tree = list_comb(case_const', case_functions@[u]) 
4062  271 
val pat_rect1 = List.concat 
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272 
(ListPair.map mk_pat (constructors', pat_rect)) 
2112  273 
in (pat_rect1,tree) 
274 
end 

275 
end end 

276 
in mk 

277 
end; 

278 

279 

280 
(* Repeated variable occurrences in a pattern are not allowed. *) 

281 
fun FV_multiset tm = 

282 
case (S.dest_term tm) 

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283 
of S.VAR{Name,Ty} => [Free(Name,Ty)] 
2112  284 
 S.CONST _ => [] 
285 
 S.COMB{Rator, Rand} => FV_multiset Rator @ FV_multiset Rand 

286 
 S.LAMB _ => raise TFL_ERR{func = "FV_multiset", mesg = "lambda"}; 

287 

288 
fun no_repeat_vars thy pat = 

289 
let fun check [] = true 

290 
 check (v::rst) = 

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291 
if mem_term (v,rst) then 
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292 
raise TFL_ERR{func = "no_repeat_vars", 
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293 
mesg = quote(#1(dest_Free v)) ^ 
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294 
" occurs repeatedly in the pattern " ^ 
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295 
quote (string_of_cterm (Thry.typecheck thy pat))} 
2112  296 
else check rst 
297 
in check (FV_multiset pat) 

298 
end; 

299 

7262  300 
fun dest_atom (Free p) = p 
301 
 dest_atom (Const p) = p 

302 
 dest_atom _ = raise TFL_ERR {func="dest_atom", 

303 
mesg="function name not an identifier"}; 

304 

305 

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306 
local fun mk_functional_err s = raise TFL_ERR{func = "mk_functional", mesg=s} 
7262  307 
fun single [_$_] = 
7052  308 
mk_functional_err "recdef does not allow currying" 
7262  309 
 single [f] = f 
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310 
 single fs = mk_functional_err (Int.toString (length fs) ^ 
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311 
" distinct function names!") 
2112  312 
in 
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313 
fun mk_functional thy clauses = 
6566  314 
let val (L,R) = ListPair.unzip (map HOLogic.dest_eq clauses) 
315 
handle _ => raise TFL_ERR 

316 
{func = "mk_functional", 

317 
mesg = "recursion equations must use the = relation"} 

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318 
val (funcs,pats) = ListPair.unzip (map (fn (t$u) =>(t,u)) L) 
7262  319 
val atom = single (gen_distinct (op aconv) funcs) 
320 
val (fname,ftype) = dest_atom atom 

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321 
val dummy = map (no_repeat_vars thy) pats 
7262  322 
val rows = ListPair.zip (map (fn x => ([]:term list,[x])) pats, 
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323 
map GIVEN (enumerate R)) 
3405  324 
val names = foldr add_term_names (R,[]) 
325 
val atype = type_of(hd pats) 

326 
and aname = variant names "a" 

327 
val a = Free(aname,atype) 

2112  328 
val ty_info = Thry.match_info thy 
329 
val ty_match = Thry.match_type thy 

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330 
val range_ty = type_of (hd R) 
3405  331 
val (patts, case_tm) = mk_case ty_info ty_match (aname::names) range_ty 
2112  332 
{path=[a], rows=rows} 
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333 
val patts1 = map (fn (_,(tag,i),[pat]) => tag (pat,i)) patts 
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334 
handle _ => mk_functional_err "error in patternmatch translation" 
2112  335 
val patts2 = U.sort(fn p1=>fn p2=> row_of_pat p1 < row_of_pat p2) patts1 
336 
val finals = map row_of_pat patts2 

337 
val originals = map (row_of_pat o #2) rows 

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338 
val dummy = case (originals\\finals) 
2112  339 
of [] => () 
340 
 L => mk_functional_err("The following rows (counting from zero)\ 

341 
\ are inaccessible: "^stringize L) 

3944  342 
in {functional = Abs(Sign.base_name fname, ftype, 
7262  343 
abstract_over (atom, 
344 
absfree(aname,atype, case_tm))), 

2112  345 
pats = patts2} 
346 
end end; 

347 

348 

349 
(* 

350 
* 

351 
* PRINCIPLES OF DEFINITION 

352 
* 

353 
**) 

354 

355 

6498  356 
(*For Isabelle, the lhs of a definition must be a constant.*) 
357 
fun mk_const_def sign (Name, Ty, rhs) = 

358 
Sign.infer_types sign (K None) (K None) [] false 

359 
([Const("==",dummyT) $ Const(Name,Ty) $ rhs], propT) 

360 
> #1; 

361 

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362 
(*Make all TVars available for instantiation by adding a ? to the front*) 
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363 
fun poly_tvars (Type(a,Ts)) = Type(a, map (poly_tvars) Ts) 
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364 
 poly_tvars (TFree (a,sort)) = TVar (("?" ^ a, 0), sort) 
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365 
 poly_tvars (TVar ((a,i),sort)) = TVar (("?" ^ a, i+1), sort); 
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366 

3191  367 
local val f_eq_wfrec_R_M = 
368 
#ant(S.dest_imp(#2(S.strip_forall (concl Thms.WFREC_COROLLARY)))) 

369 
val {lhs=f, rhs} = S.dest_eq f_eq_wfrec_R_M 

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370 
val (fname,_) = dest_Free f 
3191  371 
val (wfrec,_) = S.strip_comb rhs 
372 
in 

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373 
fun wfrec_definition0 thy fid R (functional as Abs(Name, Ty, _)) = 
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374 
let val def_name = if Name<>fid then 
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375 
raise TFL_ERR{func = "wfrec_definition0", 
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376 
mesg = "Expected a definition of " ^ 
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377 
quote fid ^ " but found one of " ^ 
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378 
quote Name} 
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379 
else Name ^ "_def" 
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380 
val wfrec_R_M = map_term_types poly_tvars 
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381 
(wfrec $ map_term_types poly_tvars R) 
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382 
$ functional 
6498  383 
val def_term = mk_const_def (Theory.sign_of thy) (Name, Ty, wfrec_R_M) 
6092  384 
in PureThy.add_defs_i [Thm.no_attributes (def_name, def_term)] thy end 
3191  385 
end; 
2112  386 

387 

388 

389 
(* 

390 
* This structure keeps track of congruence rules that aren't derived 

391 
* from a datatype definition. 

392 
**) 

393 
fun extraction_thms thy = 

394 
let val {case_rewrites,case_congs} = Thry.extract_info thy 

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395 
in (case_rewrites, case_congs) 
2112  396 
end; 
397 

398 

399 
(* 

400 
* Pair patterns with termination conditions. The full list of patterns for 

401 
* a definition is merged with the TCs arising from the usergiven clauses. 

402 
* There can be fewer clauses than the full list, if the user omitted some 

403 
* cases. This routine is used to prepare input for mk_induction. 

404 
**) 

405 
fun merge full_pats TCs = 

406 
let fun insert (p,TCs) = 

407 
let fun insrt ((x as (h,[]))::rst) = 

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408 
if (p aconv h) then (p,TCs)::rst else x::insrt rst 
2112  409 
 insrt (x::rst) = x::insrt rst 
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410 
 insrt[] = raise TFL_ERR{func="merge.insert", 
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411 
mesg="pattern not found"} 
2112  412 
in insrt end 
413 
fun pass ([],ptcl_final) = ptcl_final 

414 
 pass (ptcs::tcl, ptcl) = pass(tcl, insert ptcs ptcl) 

415 
in 

416 
pass (TCs, map (fn p => (p,[])) full_pats) 

417 
end; 

418 

419 

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420 
fun givens [] = [] 
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421 
 givens (GIVEN(tm,_)::pats) = tm :: givens pats 
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422 
 givens (OMITTED _::pats) = givens pats; 
2112  423 

6498  424 
(*called only by Tfl.simplify_defn*) 
425 
fun post_definition meta_tflCongs (theory, (def, pats)) = 

3191  426 
let val tych = Thry.typecheck theory 
427 
val f = #lhs(S.dest_eq(concl def)) 

428 
val corollary = R.MATCH_MP Thms.WFREC_COROLLARY def 

2112  429 
val given_pats = givens pats 
430 
val WFR = #ant(S.dest_imp(concl corollary)) 

3191  431 
val R = #Rand(S.dest_comb WFR) 
2112  432 
val corollary' = R.UNDISCH corollary (* put WF R on assums *) 
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433 
val corollaries = map (fn pat => R.SPEC (tych pat) corollary') 
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434 
given_pats 
3191  435 
val (case_rewrites,context_congs) = extraction_thms theory 
3405  436 
val corollaries' = map(rewrite_rule case_rewrites) corollaries 
437 
val extract = R.CONTEXT_REWRITE_RULE 

6498  438 
(f, [R], cut_apply, meta_tflCongs@context_congs) 
3405  439 
val (rules, TCs) = ListPair.unzip (map extract corollaries') 
440 
val rules0 = map (rewrite_rule [Thms.CUT_DEF]) rules 

441 
val mk_cond_rule = R.FILTER_DISCH_ALL(not o curry (op aconv) WFR) 

2112  442 
val rules1 = R.LIST_CONJ(map mk_cond_rule rules0) 
443 
in 

444 
{theory = theory, (* holds def, if it's needed *) 

445 
rules = rules1, 

6498  446 
full_pats_TCs = merge (map pat_of pats) (ListPair.zip (given_pats, TCs)), 
2112  447 
TCs = TCs, 
448 
patterns = pats} 

449 
end; 

450 

6498  451 

2112  452 
(* 
453 
* Perform the extraction without making the definition. Definition and 

6498  454 
* extraction commute for the nonnested case. (Deferred recdefs) 
7262  455 
* 
456 
* The purpose of wfrec_eqns is merely to instantiate the recursion theorem 

457 
* and extract termination conditions: no definition is made. 

6498  458 
**) 
7262  459 

6498  460 
fun wfrec_eqns thy fid tflCongs eqns = 
7262  461 
let val {lhs,rhs} = S.dest_eq (hd eqns) 
462 
val (f,args) = S.strip_comb lhs 

463 
val (fname,fty) = dest_atom f 

464 
val (SV,a) = front_last args (* SV = schematic variables *) 

465 
val g = list_comb(f,SV) 

466 
val h = Free(fname,type_of g) 

467 
val eqns1 = map (subst_free[(g,h)]) eqns 

468 
val {functional as Abs(Name, Ty, _), pats} = mk_functional thy eqns1 

2112  469 
val given_pats = givens pats 
6498  470 
(* val f = Free(Name,Ty) *) 
471 
val Type("fun", [f_dty, f_rty]) = Ty 

472 
val dummy = if Name<>fid then 

7262  473 
raise TFL_ERR{func = "wfrec_eqns", 
6498  474 
mesg = "Expected a definition of " ^ 
475 
quote fid ^ " but found one of " ^ 

476 
quote Name} 

477 
else () 

2112  478 
val (case_rewrites,context_congs) = extraction_thms thy 
479 
val tych = Thry.typecheck thy 

480 
val WFREC_THM0 = R.ISPEC (tych functional) Thms.WFREC_COROLLARY 

3405  481 
val Const("All",_) $ Abs(Rname,Rtype,_) = concl WFREC_THM0 
482 
val R = Free (variant (foldr add_term_names (eqns,[])) Rname, 

483 
Rtype) 

7262  484 
val WFREC_THM = R.ISPECL [tych R, tych g] WFREC_THM0 
2112  485 
val ([proto_def, WFR],_) = S.strip_imp(concl WFREC_THM) 
6498  486 
val dummy = 
487 
if !trace then 

488 
writeln ("ORIGINAL PROTO_DEF: " ^ 

489 
Sign.string_of_term (Theory.sign_of thy) proto_def) 

490 
else () 

2112  491 
val R1 = S.rand WFR 
492 
val corollary' = R.UNDISCH(R.UNDISCH WFREC_THM) 

3405  493 
val corollaries = map (fn pat => R.SPEC (tych pat) corollary') given_pats 
494 
val corollaries' = map (rewrite_rule case_rewrites) corollaries 

6498  495 
fun extract X = R.CONTEXT_REWRITE_RULE 
496 
(f, R1::SV, cut_apply, tflCongs@context_congs) X 

7262  497 
in {proto_def = proto_def, 
6498  498 
SV=SV, 
2112  499 
WFR=WFR, 
500 
pats=pats, 

501 
extracta = map extract corollaries'} 

502 
end; 

503 

504 

505 
(* 

506 
* Define the constant after extracting the termination conditions. The 

507 
* wellfounded relation used in the definition is computed by using the 

508 
* choice operator on the extracted conditions (plus the condition that 

509 
* such a relation must be wellfounded). 

6498  510 
**) 
7262  511 

6498  512 
fun lazyR_def thy fid tflCongs eqns = 
513 
let val {proto_def,WFR,pats,extracta,SV} = 

514 
wfrec_eqns thy fid (congs tflCongs) eqns 

2112  515 
val R1 = S.rand WFR 
7262  516 
val f = #lhs(S.dest_eq proto_def) 
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517 
val (extractants,TCl) = ListPair.unzip extracta 
6498  518 
val dummy = if !trace 
519 
then (writeln "Extractants = "; 

520 
prths extractants; 

521 
()) 

522 
else () 

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diff
changeset

523 
val TCs = foldr (gen_union (op aconv)) (TCl, []) 
2112  524 
val full_rqt = WFR::TCs 
525 
val R' = S.mk_select{Bvar=R1, Body=S.list_mk_conj full_rqt} 

526 
val R'abs = S.rand R' 

6498  527 
val proto_def' = subst_free[(R1,R')] proto_def 
528 
val dummy = if !trace then writeln ("proto_def' = " ^ 

529 
Sign.string_of_term 

530 
(Theory.sign_of thy) proto_def') 

531 
else () 

7262  532 
val {lhs,rhs} = S.dest_eq proto_def' 
533 
val (c,args) = S.strip_comb lhs 

534 
val (Name,Ty) = dest_atom c 

535 
val defn = mk_const_def (Theory.sign_of thy) 

536 
(Name, Ty, S.list_mk_abs (args,rhs)) 

537 
val theory = 

538 
thy 

539 
> PureThy.add_defs_i 

540 
[Thm.no_attributes (fid ^ "_def", defn)] 

541 
val def = freezeT (get_axiom theory (fid ^ "_def")) 

6498  542 
val dummy = if !trace then writeln ("DEF = " ^ string_of_thm def) 
543 
else () 

7262  544 
(* val fconst = #lhs(S.dest_eq(concl def)) *) 
2112  545 
val tych = Thry.typecheck theory 
6498  546 
val full_rqt_prop = map (Dcterm.mk_prop o tych) full_rqt 
547 
(*lcp: a lot of objectlogic inference to remove*) 

548 
val baz = R.DISCH_ALL 

549 
(U.itlist R.DISCH full_rqt_prop 

550 
(R.LIST_CONJ extractants)) 

551 
val dum = if !trace then writeln ("baz = " ^ string_of_thm baz) 

552 
else () 

553 
val f_free = Free (fid, fastype_of f) (*'cos f is a Const*) 

7262  554 
val SV' = map tych SV; 
555 
val SVrefls = map reflexive SV' 

556 
val def0 = (U.rev_itlist (fn x => fn th => R.rbeta(combination th x)) 

557 
SVrefls def) 

558 
RS meta_eq_to_obj_eq 

559 
val def' = R.MP (R.SPEC (tych R') (R.GEN (tych R1) baz)) def0 

6498  560 
val body_th = R.LIST_CONJ (map R.ASSUME full_rqt_prop) 
3245
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561 
val bar = R.MP (R.ISPECL[tych R'abs, tych R1] Thms.SELECT_AX) 
3191  562 
body_th 
6498  563 
in {theory = theory, R=R1, SV=SV, 
2112  564 
rules = U.rev_itlist (U.C R.MP) (R.CONJUNCTS bar) def', 
3245
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Removal of redundant code (unused or already present in Isabelle.
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changeset

565 
full_pats_TCs = merge (map pat_of pats) (ListPair.zip (givens pats, TCl)), 
2112  566 
patterns = pats} 
567 
end; 

568 

569 

570 

571 
(* 

572 
* 

573 
* INDUCTION THEOREM 

574 
* 

575 
**) 

576 

577 

578 
(* Miscellaneous function  

579 
* 

580 
* [x_1,...,x_n] ?v_1...v_n. M[v_1,...,v_n] 

581 
*  

582 
* ( M[x_1,...,x_n], [(x_i,?v_1...v_n. M[v_1,...,v_n]), 

583 
* ... 

584 
* (x_j,?v_n. M[x_1,...,x_(n1),v_n])] ) 

585 
* 

586 
* This function is totally ad hoc. Used in the production of the induction 

587 
* theorem. The nchotomy theorem can have clauses that look like 

588 
* 

589 
* ?v1..vn. z = C vn..v1 

590 
* 

591 
* in which the order of quantification is not the order of occurrence of the 

592 
* quantified variables as arguments to C. Since we have no control over this 

593 
* aspect of the nchotomy theorem, we make the correspondence explicit by 

594 
* pairing the incoming new variable with the term it gets betareduced into. 

595 
**) 

596 

3245
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changeset

597 
fun alpha_ex_unroll (xlist, tm) = 
2112  598 
let val (qvars,body) = S.strip_exists tm 
599 
val vlist = #2(S.strip_comb (S.rhs body)) 

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

600 
val plist = ListPair.zip (vlist, xlist) 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

601 
val args = map (fn qv => the (gen_assoc (op aconv) (plist, qv))) qvars 
4149  602 
handle OPTION => error 
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

603 
"TFL fault [alpha_ex_unroll]: no correspondence" 
3405  604 
fun build ex [] = [] 
605 
 build (_$rex) (v::rst) = 

606 
let val ex1 = betapply(rex, v) 

607 
in ex1 :: build ex1 rst 

2112  608 
end 
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

609 
val (nex::exl) = rev (tm::build tm args) 
2112  610 
in 
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

611 
(nex, ListPair.zip (args, rev exl)) 
2112  612 
end; 
613 

614 

615 

616 
(* 

617 
* 

618 
* PROVING COMPLETENESS OF PATTERNS 

619 
* 

620 
**) 

621 

3405  622 
fun mk_case ty_info usednames thy = 
2112  623 
let 
3405  624 
val divide = ipartition (gvvariant usednames) 
2112  625 
val tych = Thry.typecheck thy 
3353
9112a2efb9a3
Removal of module Mask and datatype binding with its constructor >
paulson
parents:
3333
diff
changeset

626 
fun tych_binding(x,y) = (tych x, tych y) 
2112  627 
fun fail s = raise TFL_ERR{func = "mk_case", mesg = s} 
628 
fun mk{rows=[],...} = fail"no rows" 

629 
 mk{path=[], rows = [([], (thm, bindings))]} = 

630 
R.IT_EXISTS (map tych_binding bindings) thm 

631 
 mk{path = u::rstp, rows as (p::_, _)::_} = 

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

632 
let val (pat_rectangle,rights) = ListPair.unzip rows 
2112  633 
val col0 = map hd pat_rectangle 
634 
val pat_rectangle' = map tl pat_rectangle 

635 
in 

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

636 
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

637 
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

638 
(ListPair.zip (rights, col0)) 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

639 
in mk{path = rstp, rows = ListPair.zip (pat_rectangle', rights')} 
2112  640 
end 
641 
else (* column 0 is all constructors *) 

3944  642 
let val Type (ty_name,_) = type_of p 
2112  643 
in 
644 
case (ty_info ty_name) 

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

645 
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

646 
 Some{constructors,nchotomy} => 
2112  647 
let val thm' = R.ISPEC (tych u) nchotomy 
648 
val disjuncts = S.strip_disj (concl thm') 

649 
val subproblems = divide(constructors, rows) 

650 
val groups = map #group subproblems 

651 
and new_formals = map #new_formals subproblems 

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

652 
val existentials = ListPair.map alpha_ex_unroll 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

653 
(new_formals, disjuncts) 
2112  654 
val constraints = map #1 existentials 
655 
val vexl = map #2 existentials 

656 
fun expnd tm (pats,(th,b)) = (pats,(R.SUBS[R.ASSUME(tych tm)]th,b)) 

657 
val news = map (fn (nf,rows,c) => {path = nf@rstp, 

658 
rows = map (expnd c) rows}) 

659 
(U.zip3 new_formals groups constraints) 

660 
val recursive_thms = map mk news 

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

661 
val build_exists = foldr 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

662 
(fn((x,t), th) => 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

663 
R.CHOOSE (tych x, R.ASSUME (tych t)) th) 
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

664 
val thms' = ListPair.map build_exists (vexl, recursive_thms) 
2112  665 
val same_concls = R.EVEN_ORS thms' 
666 
in R.DISJ_CASESL thm' same_concls 

667 
end 

668 
end end 

669 
in mk 

670 
end; 

671 

672 

673 
fun complete_cases thy = 

674 
let val tych = Thry.typecheck thy 

675 
val ty_info = Thry.induct_info thy 

676 
in fn pats => 

3405  677 
let val names = foldr add_term_names (pats,[]) 
3391
5e45dd3b64e9
More deHOLification: using Free, Const, etc. instead of mk_var, mk_const
paulson
parents:
3388
diff
changeset

678 
val T = type_of (hd pats) 
3405  679 
val aname = Term.variant names "a" 
680 
val vname = Term.variant (aname::names) "v" 

681 
val a = Free (aname, T) 

682 
val v = Free (vname, T) 

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

683 
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

684 
val ex_th0 = R.EXISTS (tych (S.mk_exists{Bvar=v,Body=a_eq_v}), tych a) 
2112  685 
(R.REFL (tych a)) 
686 
val th0 = R.ASSUME (tych a_eq_v) 

687 
val rows = map (fn x => ([x], (th0,[]))) pats 

688 
in 

689 
R.GEN (tych a) 

690 
(R.RIGHT_ASSOC 

691 
(R.CHOOSE(tych v, ex_th0) 

3405  692 
(mk_case ty_info (vname::aname::names) 
693 
thy {path=[v], rows=rows}))) 

2112  694 
end end; 
695 

696 

697 
(* 

698 
* Constructing induction hypotheses: one for each recursive call. 

699 
* 

700 
* Note. R will never occur as a variable in the ind_clause, because 

701 
* to do so, it would have to be from a nested definition, and we don't 

702 
* allow nested defns to have R variable. 

703 
* 

704 
* Note. When the context is empty, there can be no local variables. 

705 
**) 

6498  706 
(* 
3405  707 
local infix 5 ==> 
2112  708 
fun (tm1 ==> tm2) = S.mk_imp{ant = tm1, conseq = tm2} 
709 
in 

710 
fun build_ih f P (pat,TCs) = 

711 
let val globals = S.free_vars_lr pat 

3405  712 
fun nested tm = is_some (S.find_term (curry (op aconv) f) tm) 
2112  713 
fun dest_TC tm = 
714 
let val (cntxt,R_y_pat) = S.strip_imp(#2(S.strip_forall tm)) 

715 
val (R,y,_) = S.dest_relation R_y_pat 

3405  716 
val P_y = if (nested tm) then R_y_pat ==> P$y else P$y 
2112  717 
in case cntxt 
718 
of [] => (P_y, (tm,[])) 

719 
 _ => let 

720 
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

721 
val lvs = gen_rems (op aconv) (S.free_vars_lr imp, globals) 
3405  722 
val locals = #2(U.pluck (curry (op aconv) P) lvs) handle _ => lvs 
2112  723 
in (S.list_mk_forall(locals,imp), (tm,locals)) end 
724 
end 

725 
in case TCs 

3405  726 
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

727 
 _ => let val (ihs, TCs_locals) = ListPair.unzip(map dest_TC TCs) 
3405  728 
val ind_clause = S.list_mk_conj ihs ==> P$pat 
2112  729 
in (S.list_mk_forall(globals,ind_clause), TCs_locals) 
730 
end 

731 
end 

732 
end; 

6498  733 
*) 
2112  734 

6498  735 
local infix 5 ==> 
736 
fun (tm1 ==> tm2) = S.mk_imp{ant = tm1, conseq = tm2} 

737 
in 

738 
fun build_ih f (P,SV) (pat,TCs) = 

739 
let val pat_vars = S.free_vars_lr pat 

740 
val globals = pat_vars@SV 

741 
fun nested tm = is_some (S.find_term (curry (op aconv) f) tm) 

742 
fun dest_TC tm = 

743 
let val (cntxt,R_y_pat) = S.strip_imp(#2(S.strip_forall tm)) 

744 
val (R,y,_) = S.dest_relation R_y_pat 

745 
val P_y = if (nested tm) then R_y_pat ==> P$y else P$y 

746 
in case cntxt 

747 
of [] => (P_y, (tm,[])) 

748 
 _ => let 

749 
val imp = S.list_mk_conj cntxt ==> P_y 

750 
val lvs = gen_rems (op aconv) (S.free_vars_lr imp, globals) 

751 
val locals = #2(U.pluck (curry (op aconv) P) lvs) handle _ => lvs 

752 
in (S.list_mk_forall(locals,imp), (tm,locals)) end 

753 
end 

754 
in case TCs 

755 
of [] => (S.list_mk_forall(pat_vars, P$pat), []) 

756 
 _ => let val (ihs, TCs_locals) = ListPair.unzip(map dest_TC TCs) 

757 
val ind_clause = S.list_mk_conj ihs ==> P$pat 

758 
in (S.list_mk_forall(pat_vars,ind_clause), TCs_locals) 

759 
end 

760 
end 

761 
end; 

2112  762 

763 
(* 

6498  764 
* This function makes good on the promise made in "build_ih". 
2112  765 
* 
766 
* Input is tm = "(!y. R y pat ==> P y) ==> P pat", 

767 
* TCs = TC_1[pat] ... TC_n[pat] 

768 
* thm = ih1 /\ ... /\ ih_n  ih[pat] 

769 
**) 

770 
fun prove_case f thy (tm,TCs_locals,thm) = 

771 
let val tych = Thry.typecheck thy 

772 
val antc = tych(#ant(S.dest_imp tm)) 

773 
val thm' = R.SPEC_ALL thm 

3405  774 
fun nested tm = is_some (S.find_term (curry (op aconv) f) tm) 
2112  775 
fun get_cntxt TC = tych(#ant(S.dest_imp(#2(S.strip_forall(concl TC))))) 
776 
fun mk_ih ((TC,locals),th2,nested) = 

777 
R.GENL (map tych locals) 

778 
(if nested 

779 
then R.DISCH (get_cntxt TC) th2 handle _ => th2 

780 
else if S.is_imp(concl TC) 

781 
then R.IMP_TRANS TC th2 

782 
else R.MP th2 TC) 

783 
in 

784 
R.DISCH antc 

785 
(if S.is_imp(concl thm') (* recursive calls in this clause *) 

786 
then let val th1 = R.ASSUME antc 

787 
val TCs = map #1 TCs_locals 

788 
val ylist = map (#2 o S.dest_relation o #2 o S.strip_imp o 

789 
#2 o S.strip_forall) TCs 

790 
val TClist = map (fn(TC,lvs) => (R.SPEC_ALL(R.ASSUME(tych TC)),lvs)) 

791 
TCs_locals 

792 
val th2list = map (U.C R.SPEC th1 o tych) ylist 

793 
val nlist = map nested TCs 

794 
val triples = U.zip3 TClist th2list nlist 

795 
val Pylist = map mk_ih triples 

796 
in R.MP thm' (R.LIST_CONJ Pylist) end 

797 
else thm') 

798 
end; 

799 

800 

801 
(* 

802 
* 

803 
* x = (v1,...,vn)  M[x] 

804 
*  

805 
* ?v1 ... vn. x = (v1,...,vn)  M[x] 

806 
* 

807 
**) 

808 
fun LEFT_ABS_VSTRUCT tych thm = 

809 
let fun CHOOSER v (tm,thm) = 

810 
let val ex_tm = S.mk_exists{Bvar=v,Body=tm} 

811 
in (ex_tm, R.CHOOSE(tych v, R.ASSUME (tych ex_tm)) thm) 

812 
end 

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

813 
val [veq] = filter (U.can S.dest_eq) (#1 (R.dest_thm thm)) 
2112  814 
val {lhs,rhs} = S.dest_eq veq 
815 
val L = S.free_vars_lr rhs 

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

816 
in #2 (U.itlist CHOOSER L (veq,thm)) end; 
2112  817 

818 

819 
(* 

820 
* Input : f, R, and [(pat1,TCs1),..., (patn,TCsn)] 

821 
* 

822 
* Instantiates WF_INDUCTION_THM, getting Sinduct and then tries to prove 

823 
* recursion induction (Rinduct) by proving the antecedent of Sinduct from 

824 
* the antecedent of Rinduct. 

825 
**) 

6498  826 
fun mk_induction thy {fconst, R, SV, pat_TCs_list} = 
2112  827 
let val tych = Thry.typecheck thy 
828 
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

829 
val (pats,TCsl) = ListPair.unzip pat_TCs_list 
2112  830 
val case_thm = complete_cases thy pats 
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

831 
val domain = (type_of o hd) pats 
3405  832 
val Pname = Term.variant (foldr (foldr add_term_names) 
833 
(pats::TCsl, [])) "P" 

834 
val P = Free(Pname, domain > HOLogic.boolT) 

2112  835 
val Sinduct = R.SPEC (tych P) Sinduction 
836 
val Sinduct_assumf = S.rand ((#ant o S.dest_imp o concl) Sinduct) 

6498  837 
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

838 
val (Rassums,TCl') = ListPair.unzip Rassums_TCl' 
2112  839 
val Rinduct_assum = R.ASSUME (tych (S.list_mk_conj Rassums)) 
3405  840 
val cases = map (fn pat => betapply (Sinduct_assumf, pat)) pats 
2112  841 
val tasks = U.zip3 cases TCl' (R.CONJUNCTS Rinduct_assum) 
6498  842 
val proved_cases = map (prove_case fconst thy) tasks 
3405  843 
val v = Free (variant (foldr add_term_names (map concl proved_cases, [])) 
844 
"v", 

845 
domain) 

2112  846 
val vtyped = tych v 
3245
241838c01caf
Removal of redundant code (unused or already present in Isabelle.
paulson
parents:
3191
diff
changeset

847 
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

848 
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

849 
(substs, proved_cases) 
2112  850 
val abs_cases = map (LEFT_ABS_VSTRUCT tych) proved_cases1 
851 
val dant = R.GEN vtyped (R.DISJ_CASESL (R.ISPEC vtyped case_thm) abs_cases) 

852 
val dc = R.MP Sinduct dant 

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

853 
val Parg_ty = type_of(#Bvar(S.dest_forall(concl dc))) 
3405  854 
val vars = map (gvvariant[Pname]) (S.strip_prod_type Parg_ty) 
2112  855 
val dc' = U.itlist (R.GEN o tych) vars 
856 
(R.SPEC (tych(S.mk_vstruct Parg_ty vars)) dc) 

857 
in 

858 
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

859 
end 
2112  860 
handle _ => raise TFL_ERR{func = "mk_induction", mesg = "failed derivation"}; 
861 

862 

863 

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

864 

2112  865 
(* 
866 
* 

867 
* POST PROCESSING 

868 
* 

869 
**) 

870 

871 

872 
fun simplify_induction thy hth ind = 

873 
let val tych = Thry.typecheck thy 

874 
val (asl,_) = R.dest_thm ind 

875 
val (_,tc_eq_tc') = R.dest_thm hth 

876 
val tc = S.lhs tc_eq_tc' 

877 
fun loop [] = ind 

878 
 loop (asm::rst) = 

879 
if (U.can (Thry.match_term thy asm) tc) 

880 
then R.UNDISCH 

881 
(R.MATCH_MP 

882 
(R.MATCH_MP Thms.simp_thm (R.DISCH (tych asm) ind)) 

883 
hth) 

884 
else loop rst 

885 
in loop asl 

886 
end; 

887 

888 

889 
(* 

890 
* The termination condition is an antecedent to the rule, and an 

891 
* assumption to the theorem. 

892 
**) 

893 
fun elim_tc tcthm (rule,induction) = 

894 
(R.MP rule tcthm, R.PROVE_HYP tcthm induction) 

895 

896 

897 
fun postprocess{WFtac, terminator, simplifier} theory {rules,induction,TCs} = 

898 
let val tych = Thry.typecheck theory 

899 

900 
(* 

901 
* Attempt to eliminate WF condition. It's the only assumption of rules 

902 
**) 

903 
val (rules1,induction1) = 

3405  904 
let val thm = R.prove(tych(HOLogic.mk_Trueprop 
905 
(hd(#1(R.dest_thm rules)))), 

906 
WFtac) 

2112  907 
in (R.PROVE_HYP thm rules, R.PROVE_HYP thm induction) 
908 
end handle _ => (rules,induction) 

909 

910 
(* 

911 
* The termination condition (tc) is simplified to  tc = tc' (there 

912 
* might not be a change!) and then 3 attempts are made: 

913 
* 

914 
* 1. if  tc = T, then eliminate it with eqT; otherwise, 

915 
* 2. apply the terminator to tc'. If  tc' = T then eliminate; else 

916 
* 3. replace tc by tc' in both the rules and the induction theorem. 

917 
**) 

6498  918 

7262  919 
fun print_thms s L = 
920 
if !trace then writeln (cat_lines (s :: map string_of_thm L)) 

921 
else (); 

6498  922 

7262  923 
fun print_cterms s L = 
924 
if !trace then writeln (cat_lines (s :: map string_of_cterm L)) 

925 
else ();; 

6498  926 

2112  927 
fun simplify_tc tc (r,ind) = 
6498  928 
let val tc1 = tych tc 
929 
val _ = print_cterms "TC before simplification: " [tc1] 

930 
val tc_eq = simplifier tc1 

931 
val _ = print_thms "result: " [tc_eq] 

2112  932 
in 
933 
elim_tc (R.MATCH_MP Thms.eqT tc_eq) (r,ind) 

934 
handle _ => 

935 
(elim_tc (R.MATCH_MP(R.MATCH_MP Thms.rev_eq_mp tc_eq) 

3405  936 
(R.prove(tych(HOLogic.mk_Trueprop(S.rhs(concl tc_eq))), 
937 
terminator))) 

2112  938 
(r,ind) 
939 
handle _ => 

940 
(R.UNDISCH(R.MATCH_MP (R.MATCH_MP Thms.simp_thm r) tc_eq), 

941 
simplify_induction theory tc_eq ind)) 

942 
end 

943 

944 
(* 

945 
* Nested termination conditions are harder to get at, since they are 

946 
* left embedded in the body of the function (and in induction 

947 
* theorem hypotheses). Our "solution" is to simplify them, and try to 

948 
* prove termination, but leave the application of the resulting theorem 

949 
* to a higher level. So things go much as in "simplify_tc": the 

950 
* termination condition (tc) is simplified to  tc = tc' (there might 

951 
* not be a change) and then 2 attempts are made: 

952 
* 

953 
* 1. if  tc = T, then return  tc; otherwise, 

954 
* 2. apply the terminator to tc'. If  tc' = T then return  tc; else 

955 
* 3. return  tc = tc' 

956 
**) 

957 
fun simplify_nested_tc tc = 

958 
let val tc_eq = simplifier (tych (#2 (S.strip_forall tc))) 

959 
in 

960 
R.GEN_ALL 

961 
(R.MATCH_MP Thms.eqT tc_eq 

962 
handle _ 

963 
=> (R.MATCH_MP(R.MATCH_MP Thms.rev_eq_mp tc_eq) 

3405  964 
(R.prove(tych(HOLogic.mk_Trueprop (S.rhs(concl tc_eq))), 
965 
terminator)) 

2112  966 
handle _ => tc_eq)) 
967 
end 

968 

969 
(* 

970 
* Attempt to simplify the termination conditions in each rule and 

971 
* in the induction theorem. 

972 
**) 

973 
fun strip_imp tm = if S.is_neg tm then ([],tm) else S.strip_imp tm 

974 
fun loop ([],extras,R,ind) = (rev R, ind, extras) 

975 
 loop ((r,ftcs)::rst, nthms, R, ind) = 

976 
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

977 
val extra_tcs = gen_rems (op aconv) (ftcs, tcs) 
2112  978 
val extra_tc_thms = map simplify_nested_tc extra_tcs 
979 
val (r1,ind1) = U.rev_itlist simplify_tc tcs (r,ind) 

980 
val r2 = R.FILTER_DISCH_ALL(not o S.is_WFR) r1 

981 
in loop(rst, nthms@extra_tc_thms, r2::R, ind1) 

982 
end 

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

983 
val rules_tcs = ListPair.zip (R.CONJUNCTS rules1, TCs) 
2112  984 
val (rules2,ind2,extras) = loop(rules_tcs,[],[],induction1) 
985 
in 

986 
{induction = ind2, rules = R.LIST_CONJ rules2, nested_tcs = extras} 

987 
end; 

988 

989 
end; (* TFL *) 