author | krauss |
Fri, 20 Apr 2007 10:06:11 +0200 | |
changeset 22733 | 0b14bb35be90 |
parent 22623 | 5fcee5b319a2 |
child 23189 | 4574ab8f3b21 |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/function_package/mutual.ML |
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ID: $Id$ |
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Author: Alexander Krauss, TU Muenchen |
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A package for general recursive function definitions. |
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Tools for mutual recursive definitions. |
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*) |
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signature FUNDEF_MUTUAL = |
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sig |
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val prepare_fundef_mutual : FundefCommon.fundef_config |
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-> string (* defname *) |
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-> ((string * typ) * mixfix) list |
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-> term list |
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-> string (* default, unparsed term *) |
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-> local_theory |
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-> ((thm (* goalstate *) |
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* (thm -> FundefCommon.fundef_result) (* proof continuation *) |
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* (thm list -> thm list list) (* sorting continuation *) |
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) * local_theory) |
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end |
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structure FundefMutual: FUNDEF_MUTUAL = |
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struct |
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open FundefLib |
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open FundefCommon |
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(* Theory dependencies *) |
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val sum_case_rules = thms "Sum_Type.sum_cases" |
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val split_apply = thm "Product_Type.split" |
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type qgar = string * (string * typ) list * term list * term list * term |
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fun name_of_fqgar (f, _, _, _, _) = f |
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datatype mutual_part = |
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MutualPart of |
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{ |
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fvar : string * typ, |
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cargTs: typ list, |
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pthA: SumTools.sum_path, |
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pthR: SumTools.sum_path, |
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f_def: term, |
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f: term option, |
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f_defthm : thm option |
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} |
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datatype mutual_info = |
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Mutual of |
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{ |
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fsum_var : string * typ, |
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||
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ST: typ, |
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RST: typ, |
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streeA: SumTools.sum_tree, |
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streeR: SumTools.sum_tree, |
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parts: mutual_part list, |
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fqgars: qgar list, |
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qglrs: ((string * typ) list * term list * term * term) list, |
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fsum : term option |
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} |
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fun mutual_induct_Pnames n = |
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if n < 5 then fst (chop n ["P","Q","R","S"]) |
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else map (fn i => "P" ^ string_of_int i) (1 upto n) |
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fun open_all_all (Const ("all", _) $ Abs (n, T, b)) = apfst (cons (n, T)) (open_all_all b) |
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| open_all_all t = ([], t) |
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(* Builds a curried clause description in abstracted form *) |
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fun split_def ctxt fnames geq arities = |
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let |
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fun input_error msg = cat_lines [msg, ProofContext.string_of_term ctxt geq] |
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val (qs, imp) = open_all_all geq |
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val gs = Logic.strip_imp_prems imp |
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val eq = Logic.strip_imp_concl imp |
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val (f_args, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop eq) |
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val (head, args) = strip_comb f_args |
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val invalid_head_msg = "Head symbol of left hand side must be " ^ plural "" "one out of " fnames ^ commas_quote fnames |
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val fname = fst (dest_Free head) |
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handle TERM _ => error (input_error invalid_head_msg) |
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val _ = fname mem fnames orelse error (input_error invalid_head_msg) |
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fun add_bvs t is = add_loose_bnos (t, 0, is) |
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val rvs = (add_bvs rhs [] \\ fold add_bvs args []) |
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|> map (fst o nth (rev qs)) |
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val _ = null rvs orelse error (input_error ("Variable" ^ plural " " "s " rvs ^ commas_quote rvs |
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^ " occur" ^ plural "s" "" rvs ^ " on right hand side only:")) |
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val _ = forall (forall_aterms (fn Free (n, _) => not (n mem fnames) | _ => true)) gs orelse |
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error (input_error "Recursive Calls not allowed in premises") |
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val k = length args |
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val arities' = case Symtab.lookup arities fname of |
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NONE => Symtab.update (fname, k) arities |
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| SOME i => (i = k orelse |
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error (input_error ("Function " ^ quote fname ^ " has different numbers of arguments in different equations")); |
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arities) |
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in |
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((fname, qs, gs, args, rhs), arities') |
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end |
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fun get_part fname = |
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the o find_first (fn (MutualPart {fvar=(n,_), ...}) => n = fname) |
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(* FIXME *) |
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fun mk_prod_abs e (t1, t2) = |
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let |
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val bTs = rev (map snd e) |
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val T1 = fastype_of1 (bTs, t1) |
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val T2 = fastype_of1 (bTs, t2) |
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in |
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HOLogic.pair_const T1 T2 $ t1 $ t2 |
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end; |
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fun analyze_eqs ctxt defname fs eqs = |
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let |
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val fnames = map fst fs |
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val (fqgars, arities) = fold_map (split_def ctxt fnames) eqs Symtab.empty |
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fun curried_types (fname, fT) = |
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let |
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val k = the_default 1 (Symtab.lookup arities fname) |
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val (caTs, uaTs) = chop k (binder_types fT) |
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in |
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(caTs, uaTs ---> body_type fT) |
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end |
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val (caTss, resultTs) = split_list (map curried_types fs) |
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val argTs = map (foldr1 HOLogic.mk_prodT) caTss |
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val (RST,streeR, pthsR) = SumTools.mk_tree_distinct resultTs |
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val (ST, streeA, pthsA) = SumTools.mk_tree argTs |
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val fsum_type = ST --> RST |
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val ([fsum_var_name], _) = Variable.add_fixes [ defname ^ "_sum" ] ctxt |
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val fsum_var = (fsum_var_name, fsum_type) |
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fun define (fvar as (n, T)) caTs pthA pthR = |
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let |
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val vars = map_index (fn (i,T) => Free ("x" ^ string_of_int i, T)) caTs (* FIXME: Bind xs properly *) |
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val f_exp = SumTools.mk_proj streeR pthR (Free fsum_var $ SumTools.mk_inj streeA pthA (foldr1 HOLogic.mk_prod vars)) |
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val def = Term.abstract_over (Free fsum_var, fold_rev lambda vars f_exp) |
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163 |
|
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164 |
val rew = (n, fold_rev lambda vars f_exp) |
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|
165 |
in |
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166 |
(MutualPart {fvar=fvar,cargTs=caTs,pthA=pthA,pthR=pthR,f_def=def,f=NONE,f_defthm=NONE}, rew) |
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167 |
end |
21237 | 168 |
|
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val (parts, rews) = split_list (map4 define fs caTss pthsA pthsR) |
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|
170 |
|
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fun convert_eqs (f, qs, gs, args, rhs) = |
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172 |
let |
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val MutualPart {pthA, pthR, ...} = get_part f parts |
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|
174 |
in |
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|
175 |
(qs, gs, SumTools.mk_inj streeA pthA (foldr1 (mk_prod_abs qs) args), |
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|
176 |
SumTools.mk_inj streeR pthR (replace_frees rews rhs) |
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177 |
|> Envir.norm_term (Envir.empty 0)) |
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178 |
end |
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|
179 |
|
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180 |
val qglrs = map convert_eqs fqgars |
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|
181 |
in |
22166 | 182 |
Mutual {fsum_var=fsum_var, ST=ST, RST=RST, streeA=streeA, streeR=streeR, |
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183 |
parts=parts, fqgars=fqgars, qglrs=qglrs, fsum=NONE} |
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|
184 |
end |
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|
185 |
|
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|
186 |
|
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|
187 |
|
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|
188 |
|
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|
189 |
fun define_projections fixes mutual fsum lthy = |
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190 |
let |
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191 |
fun def ((MutualPart {fvar=(fname, fT), cargTs, pthA, pthR, f_def, ...}), (_, mixfix)) lthy = |
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192 |
let |
21436 | 193 |
val ((f, (_, f_defthm)), lthy') = |
194 |
LocalTheory.def Thm.internalK ((fname, mixfix), |
|
195 |
((fname ^ "_def", []), Term.subst_bound (fsum, f_def))) |
|
196 |
lthy |
|
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197 |
in |
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|
198 |
(MutualPart {fvar=(fname, fT), cargTs=cargTs, pthA=pthA, pthR=pthR, f_def=f_def, |
21237 | 199 |
f=SOME f, f_defthm=SOME f_defthm }, |
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|
200 |
lthy') |
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|
201 |
end |
21237 | 202 |
|
22166 | 203 |
val Mutual { fsum_var, ST, RST, streeA, streeR, parts, fqgars, qglrs, ... } = mutual |
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|
204 |
val (parts', lthy') = fold_map def (parts ~~ fixes) lthy |
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|
205 |
in |
22166 | 206 |
(Mutual { fsum_var=fsum_var, ST=ST, RST=RST, streeA=streeA, streeR=streeR, parts=parts', |
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|
207 |
fqgars=fqgars, qglrs=qglrs, fsum=SOME fsum }, |
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|
208 |
lthy') |
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|
209 |
end |
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|
210 |
|
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|
211 |
|
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|
212 |
fun beta_reduce thm = Thm.equal_elim (Thm.beta_conversion true (cprop_of thm)) thm |
21237 | 213 |
|
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|
214 |
fun in_context ctxt (f, pre_qs, pre_gs, pre_args, pre_rhs) F = |
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|
215 |
let |
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|
216 |
val thy = ProofContext.theory_of ctxt |
21237 | 217 |
|
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218 |
val oqnames = map fst pre_qs |
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renamed Variable.invent_fixes to Variable.variant_fixes;
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|
219 |
val (qs, ctxt') = Variable.variant_fixes oqnames ctxt |
21237 | 220 |
|>> map2 (fn (_, T) => fn n => Free (n, T)) pre_qs |
221 |
||
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222 |
fun inst t = subst_bounds (rev qs, t) |
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|
223 |
val gs = map inst pre_gs |
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224 |
val args = map inst pre_args |
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225 |
val rhs = inst pre_rhs |
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|
226 |
|
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|
227 |
val cqs = map (cterm_of thy) qs |
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|
228 |
val ags = map (assume o cterm_of thy) gs |
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|
229 |
|
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|
230 |
val import = fold forall_elim cqs |
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|
231 |
#> fold implies_elim_swp ags |
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|
232 |
|
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|
233 |
val export = fold_rev (implies_intr o cprop_of) ags |
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|
234 |
#> fold_rev forall_intr_rename (oqnames ~~ cqs) |
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changeset
|
235 |
in |
22497
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|
236 |
F ctxt (f, qs, gs, args, rhs) import export |
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|
237 |
end |
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changeset
|
238 |
|
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changeset
|
239 |
fun recover_mutual_psimp all_orig_fdefs parts ctxt (fname, _, _, args, rhs) import (export : thm -> thm) sum_psimp_eq = |
20523
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|
240 |
let |
22497
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fixed problem with the construction of mutual simp rules
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changeset
|
241 |
val (MutualPart {f=SOME f, f_defthm=SOME f_def, pthR, ...}) = get_part fname parts |
1fe951654cee
fixed problem with the construction of mutual simp rules
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changeset
|
242 |
|
20523
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changeset
|
243 |
val psimp = import sum_psimp_eq |
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|
244 |
val (simp, restore_cond) = case cprems_of psimp of |
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|
245 |
[] => (psimp, I) |
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|
246 |
| [cond] => (implies_elim psimp (assume cond), implies_intr cond) |
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|
247 |
| _ => sys_error "Too many conditions" |
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|
248 |
in |
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|
249 |
Goal.prove ctxt [] [] |
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changeset
|
250 |
(HOLogic.Trueprop $ HOLogic.mk_eq (list_comb (f, args), rhs)) |
1fe951654cee
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|
251 |
(fn _ => SIMPSET (unfold_tac all_orig_fdefs) |
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|
252 |
THEN EqSubst.eqsubst_tac ctxt [0] [simp] 1 |
22622
25693088396b
Moving "FunDef" up in the HOL development graph, since it is independent from "Recdef" and "Datatype" now.
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diff
changeset
|
253 |
THEN SIMPSET' (fn ss => simp_tac (ss addsimps [SumTools.projl_inl, SumTools.projr_inr])) 1) |
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|
254 |
|> restore_cond |
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|
255 |
|> export |
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mk_partial_rules_mutual: expand result terms/thms;
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diff
changeset
|
256 |
end |
19770
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HOL/Tools/function_package: Added support for mutual recursive definitions.
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parents:
diff
changeset
|
257 |
|
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
diff
changeset
|
258 |
|
20523
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|
259 |
(* FIXME HACK *) |
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384c5bb713b2
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diff
changeset
|
260 |
fun mk_applied_form ctxt caTs thm = |
20523
36a59e5d0039
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changeset
|
261 |
let |
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Major update to function package, including new syntax and the (only theoretical)
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changeset
|
262 |
val thy = ProofContext.theory_of ctxt |
36a59e5d0039
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changeset
|
263 |
val xs = map_index (fn (i,T) => cterm_of thy (Free ("x" ^ string_of_int i, T))) caTs (* FIXME: Bind xs properly *) |
36a59e5d0039
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changeset
|
264 |
in |
36a59e5d0039
Major update to function package, including new syntax and the (only theoretical)
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changeset
|
265 |
fold (fn x => fn thm => combination thm (reflexive x)) xs thm |
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|
266 |
|> beta_reduce |
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|
267 |
|> fold_rev forall_intr xs |
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|
268 |
|> forall_elim_vars 0 |
36a59e5d0039
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changeset
|
269 |
end |
21237 | 270 |
|
20878
384c5bb713b2
mk_partial_rules_mutual: expand result terms/thms;
wenzelm
parents:
20851
diff
changeset
|
271 |
|
22623 | 272 |
fun mutual_induct_rules lthy induct all_f_defs (Mutual {RST, parts, streeA, ...}) = |
19770
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|
273 |
let |
22623 | 274 |
val cert = cterm_of (ProofContext.theory_of lthy) |
20949 | 275 |
val newPs = map2 (fn Pname => fn MutualPart {cargTs, ...} => |
21237 | 276 |
Free (Pname, cargTs ---> HOLogic.boolT)) |
20949 | 277 |
(mutual_induct_Pnames (length parts)) |
278 |
parts |
|
21237 | 279 |
|
280 |
fun mk_P (MutualPart {cargTs, ...}) P = |
|
281 |
let |
|
282 |
val avars = map_index (fn (i,T) => Var (("a", i), T)) cargTs |
|
283 |
val atup = foldr1 HOLogic.mk_prod avars |
|
284 |
in |
|
285 |
tupled_lambda atup (list_comb (P, avars)) |
|
286 |
end |
|
287 |
||
288 |
val Ps = map2 mk_P parts newPs |
|
289 |
val case_exp = SumTools.mk_sumcases streeA HOLogic.boolT Ps |
|
290 |
||
291 |
val induct_inst = |
|
22623 | 292 |
forall_elim (cert case_exp) induct |
21237 | 293 |
|> full_simplify (HOL_basic_ss addsimps (split_apply :: sum_case_rules)) |
294 |
|> full_simplify (HOL_basic_ss addsimps all_f_defs) |
|
295 |
||
296 |
fun mk_proj rule (MutualPart {cargTs, pthA, ...}) = |
|
297 |
let |
|
298 |
val afs = map_index (fn (i,T) => Free ("a" ^ string_of_int i, T)) cargTs |
|
299 |
val inj = SumTools.mk_inj streeA pthA (foldr1 HOLogic.mk_prod afs) |
|
300 |
in |
|
301 |
rule |
|
22623 | 302 |
|> forall_elim (cert inj) |
21237 | 303 |
|> full_simplify (HOL_basic_ss addsimps (split_apply :: sum_case_rules)) |
22623 | 304 |
|> fold_rev (forall_intr o cert) (afs @ newPs) |
21237 | 305 |
end |
306 |
||
19770
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
diff
changeset
|
307 |
in |
20523
36a59e5d0039
Major update to function package, including new syntax and the (only theoretical)
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parents:
19922
diff
changeset
|
308 |
map (mk_proj induct_inst) parts |
19770
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
diff
changeset
|
309 |
end |
21237 | 310 |
|
20878
384c5bb713b2
mk_partial_rules_mutual: expand result terms/thms;
wenzelm
parents:
20851
diff
changeset
|
311 |
|
22623 | 312 |
fun mk_partial_rules_mutual lthy inner_cont (m as Mutual {parts, fqgars, ...}) proof = |
19770
be5c23ebe1eb
HOL/Tools/function_package: Added support for mutual recursive definitions.
krauss
parents:
diff
changeset
|
313 |
let |
22166 | 314 |
val result = inner_cont proof |
22733
0b14bb35be90
definition lookup via terms, not names. Methods "relation" and "lexicographic_order"
krauss
parents:
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val FundefResult {fs=[f], G, R, cases, psimps, trsimps, subset_pinducts=[subset_pinduct],simple_pinducts=[simple_pinduct], |
22166 | 316 |
termination,domintros} = result |
21237 | 317 |
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val (all_f_defs, fs) = map (fn MutualPart {f_defthm = SOME f_def, f = SOME f, cargTs, ...} => |
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(mk_applied_form lthy cargTs (symmetric f_def), f)) |
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parts |
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|> split_list |
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fixed problem with the construction of mutual simp rules
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322 |
|
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fixed problem with the construction of mutual simp rules
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val all_orig_fdefs = map (fn MutualPart {f_defthm = SOME f_def, ...} => f_def) parts |
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|
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fun mk_mpsimp fqgar sum_psimp = |
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in_context lthy fqgar (recover_mutual_psimp all_orig_fdefs parts) sum_psimp |
21237 | 327 |
|
22166 | 328 |
val mpsimps = map2 mk_mpsimp fqgars psimps |
329 |
val mtrsimps = map_option (map2 mk_mpsimp fqgars) trsimps |
|
22623 | 330 |
val minducts = mutual_induct_rules lthy simple_pinduct all_f_defs m |
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val mtermination = full_simplify (HOL_basic_ss addsimps all_f_defs) termination |
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Major update to function package, including new syntax and the (only theoretical)
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332 |
in |
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FundefResult { fs=fs, G=G, R=R, |
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psimps=mpsimps, subset_pinducts=[subset_pinduct], simple_pinducts=minducts, |
335 |
cases=cases, termination=mtermination, |
|
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domintros=domintros, |
|
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trsimps=mtrsimps} |
|
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338 |
end |
21237 | 339 |
|
22166 | 340 |
|
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(* puts an object in the "right bucket" *) |
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fun store_grouped P x [] = [] |
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| store_grouped P x ((l, xs)::bs) = |
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if P (x, l) then ((l, x::xs)::bs) else ((l, xs)::store_grouped P x bs) |
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|
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fun sort_by_function (Mutual {fqgars, ...}) names xs = |
21237 | 347 |
fold_rev (store_grouped (eq_str o apfst fst)) (* fill *) |
348 |
(map name_of_fqgar fqgars ~~ xs) (* the name-thm pairs *) |
|
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(map (rpair []) names) (* in the empty buckets labeled with names *) |
|
350 |
||
351 |
|> map (snd #> map snd) (* and remove the labels afterwards *) |
|
22166 | 352 |
|
353 |
||
354 |
fun prepare_fundef_mutual config defname fixes eqss default lthy = |
|
355 |
let |
|
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beta_eta_contract specification befor processing. These normal forms avoid unpleasant surprises later on.
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val mutual = analyze_eqs lthy defname (map fst fixes) (map Envir.beta_eta_contract eqss) |
22166 | 357 |
val Mutual {fsum_var=(n, T), qglrs, ...} = mutual |
358 |
||
359 |
val ((fsum, goalstate, cont), lthy') = |
|
360 |
FundefCore.prepare_fundef config defname (n, T, NoSyn) qglrs default lthy |
|
361 |
||
362 |
val (mutual', lthy'') = define_projections fixes mutual fsum lthy' |
|
363 |
||
364 |
val mutual_cont = mk_partial_rules_mutual lthy'' cont mutual' |
|
365 |
val sort_cont = sort_by_function mutual' (map (fst o fst) fixes) |
|
366 |
in |
|
367 |
((goalstate, mutual_cont, sort_cont), lthy'') |
|
368 |
end |
|
369 |
||
21237 | 370 |
|
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HOL/Tools/function_package: Added support for mutual recursive definitions.
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|
371 |
end |