author  wenzelm 
Tue, 29 Sep 2009 22:48:24 +0200  
changeset 32765  3032c0308019 
parent 32149  ef59550a55d3 
child 33099  b8cdd3d73022 
permissions  rwrr 
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(* Title: HOL/Tools/Function/mutual.ML 
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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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> local_theory 
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> ((thm (* goalstate *) 
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* (thm > FundefCommon.fundef_result) (* proof 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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type qgar = string * (string * typ) list * term list * term list * term 
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fun name_of_fqgar ((f, _, _, _, _): qgar) = f 
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datatype mutual_part = 

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MutualPart of 

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{ 

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i : int, 
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i' : int, 

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fvar : string * typ, 
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cargTs: typ list, 

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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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n : int, 
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n' : int, 

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fsum_var : string * typ, 
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ST: typ, 

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RST: typ, 

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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 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 num = length fs 
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val fnames = map fst fs 
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val fqgars = map (split_def ctxt) eqs 
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val arity_of = map (fn (fname,_,_,args,_) => (fname, length args)) fqgars 
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> AList.lookup (op =) #> the 
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fun curried_types (fname, fT) = 
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let 
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val (caTs, uaTs) = chop (arity_of fname) (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 dresultTs = distinct (op =) resultTs 
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val n' = length dresultTs 
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val RST = Balanced_Tree.make (uncurry SumTree.mk_sumT) dresultTs 
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val ST = Balanced_Tree.make (uncurry SumTree.mk_sumT) 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 resultT i = 
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let 
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val vars = map_index (fn (j,T) => Free ("x" ^ string_of_int j, T)) caTs (* FIXME: Bind xs properly *) 
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val i' = find_index (fn Ta => Ta = resultT) dresultTs + 1 
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val f_exp = SumTree.mk_proj RST n' i' (Free fsum_var $ SumTree.mk_inj ST num i (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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val rew = (n, fold_rev lambda vars f_exp) 
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in 
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(MutualPart {i=i, i'=i', fvar=fvar,cargTs=caTs,f_def=def,f=NONE,f_defthm=NONE}, rew) 
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end 
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val (parts, rews) = split_list (map4 define fs caTss resultTs (1 upto num)) 
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fun convert_eqs (f, qs, gs, args, rhs) = 
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let 
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val MutualPart {i, i', ...} = get_part f parts 
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in 
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(qs, gs, SumTree.mk_inj ST num i (foldr1 (mk_prod_abs qs) args), 
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SumTree.mk_inj RST n' i' (replace_frees rews rhs) 

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> Envir.beta_norm) 
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end 
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val qglrs = map convert_eqs fqgars 
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in 
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Mutual {n=num, n'=n', fsum_var=fsum_var, ST=ST, RST=RST, 
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parts=parts, fqgars=fqgars, qglrs=qglrs, fsum=NONE} 
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end 
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fun define_projections fixes mutual fsum lthy = 
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let 
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fun def ((MutualPart {i=i, i'=i', fvar=(fname, fT), cargTs, f_def, ...}), (_, mixfix)) lthy = 
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let 
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val ((f, (_, f_defthm)), lthy') = 
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LocalTheory.define Thm.internalK ((Binding.name fname, mixfix), 
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((Binding.name (fname ^ "_def"), []), Term.subst_bound (fsum, f_def))) 

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lthy 
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in 
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(MutualPart {i=i, i'=i', fvar=(fname, fT), cargTs=cargTs, f_def=f_def, 
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f=SOME f, f_defthm=SOME f_defthm }, 
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lthy') 
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end 
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val Mutual { n, n', fsum_var, ST, RST, parts, fqgars, qglrs, ... } = mutual 
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val (parts', lthy') = fold_map def (parts ~~ fixes) lthy 
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in 
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(Mutual { n=n, n'=n', fsum_var=fsum_var, ST=ST, RST=RST, parts=parts', 
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fqgars=fqgars, qglrs=qglrs, fsum=SOME fsum }, 
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lthy') 
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end 
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fun in_context ctxt (f, pre_qs, pre_gs, pre_args, pre_rhs) F = 
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let 
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val thy = ProofContext.theory_of ctxt 
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val oqnames = map fst pre_qs 
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val (qs, ctxt') = Variable.variant_fixes oqnames ctxt 
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>> map2 (fn (_, T) => fn n => Free (n, T)) pre_qs 
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fun inst t = subst_bounds (rev qs, t) 
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val gs = map inst pre_gs 
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val args = map inst pre_args 
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val rhs = inst pre_rhs 
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val cqs = map (cterm_of thy) qs 
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val ags = map (assume o cterm_of thy) gs 
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val import = fold forall_elim cqs 
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#> fold Thm.elim_implies ags 
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val export = fold_rev (implies_intr o cprop_of) ags 
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#> fold_rev forall_intr_rename (oqnames ~~ cqs) 
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in 
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F ctxt (f, qs, gs, args, rhs) import export 
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end 
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fun recover_mutual_psimp all_orig_fdefs parts ctxt (fname, _, _, args, rhs) import (export : thm > thm) sum_psimp_eq = 
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let 
23494  197 
val (MutualPart {f=SOME f, f_defthm=SOME f_def, ...}) = get_part fname parts 
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val psimp = import sum_psimp_eq 
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val (simp, restore_cond) = case cprems_of psimp of 
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[] => (psimp, I) 
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 [cond] => (implies_elim psimp (assume cond), implies_intr cond) 
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 _ => sys_error "Too many conditions" 
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in 
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Goal.prove ctxt [] [] 
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(HOLogic.Trueprop $ HOLogic.mk_eq (list_comb (f, args), rhs)) 
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(fn _ => (LocalDefs.unfold_tac ctxt all_orig_fdefs) 
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THEN EqSubst.eqsubst_tac ctxt [0] [simp] 1 
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THEN (simp_tac (simpset_of ctxt addsimps SumTree.proj_in_rules)) 1) 
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> restore_cond 
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> export 
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end 
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(* FIXME HACK *) 
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fun mk_applied_form ctxt caTs thm = 
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let 
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val thy = ProofContext.theory_of ctxt 
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val xs = map_index (fn (i,T) => cterm_of thy (Free ("x" ^ string_of_int i, T))) caTs (* FIXME: Bind xs properly *) 
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in 
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fold (fn x => fn thm => combination thm (reflexive x)) xs thm 
26196  222 
> Conv.fconv_rule (Thm.beta_conversion true) 
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> fold_rev forall_intr xs 
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> Thm.forall_elim_vars 0 
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end 
23494  226 

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23494  228 
fun mutual_induct_rules lthy induct all_f_defs (Mutual {n, ST, RST, parts, ...}) = 
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let 
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val cert = cterm_of (ProofContext.theory_of lthy) 
20949  231 
val newPs = map2 (fn Pname => fn MutualPart {cargTs, ...} => 
21237  232 
Free (Pname, cargTs > HOLogic.boolT)) 
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(mutual_induct_Pnames (length parts)) 
234 
parts 

21237  235 

236 
fun mk_P (MutualPart {cargTs, ...}) P = 

237 
let 

238 
val avars = map_index (fn (i,T) => Var (("a", i), T)) cargTs 

239 
val atup = foldr1 HOLogic.mk_prod avars 

240 
in 

241 
tupled_lambda atup (list_comb (P, avars)) 

242 
end 

243 

244 
val Ps = map2 mk_P parts newPs 

25555  245 
val case_exp = SumTree.mk_sumcases HOLogic.boolT Ps 
21237  246 

247 
val induct_inst = 

22623  248 
forall_elim (cert case_exp) induct 
25555  249 
> full_simplify SumTree.sumcase_split_ss 
21237  250 
> full_simplify (HOL_basic_ss addsimps all_f_defs) 
251 

25046  252 
fun project rule (MutualPart {cargTs, i, ...}) k = 
21237  253 
let 
25046  254 
val afs = map_index (fn (j,T) => Free ("a" ^ string_of_int (j + k), T)) cargTs (* FIXME! *) 
25555  255 
val inj = SumTree.mk_inj ST n i (foldr1 HOLogic.mk_prod afs) 
21237  256 
in 
25046  257 
(rule 
22623  258 
> forall_elim (cert inj) 
25555  259 
> full_simplify SumTree.sumcase_split_ss 
25046  260 
> fold_rev (forall_intr o cert) (afs @ newPs), 
261 
k + length cargTs) 

21237  262 
end 
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in 
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fst (fold_map (project induct_inst) parts 0) 
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end 
21237  266 

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fun mk_partial_rules_mutual lthy inner_cont (m as Mutual {parts, fqgars, ...}) proof = 
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let 
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val result = inner_cont proof 
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val FundefResult {fs=[f], G, R, cases, psimps, trsimps, simple_pinducts=[simple_pinduct], 
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termination,domintros} = result 
21237  273 

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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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val all_orig_fdefs = map (fn MutualPart {f_defthm = SOME f_def, ...} => f_def) parts 
21237  280 

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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  283 

23189  284 
val rew_ss = HOL_basic_ss addsimps all_f_defs 
22166  285 
val mpsimps = map2 mk_mpsimp fqgars psimps 
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val mtrsimps = map_option (map2 mk_mpsimp fqgars) trsimps 

22623  287 
val minducts = mutual_induct_rules lthy simple_pinduct all_f_defs m 
23189  288 
val mtermination = full_simplify rew_ss termination 
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val mdomintros = map_option (map (full_simplify rew_ss)) domintros 

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in 
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FundefResult { fs=fs, G=G, R=R, 
26529  292 
psimps=mpsimps, simple_pinducts=minducts, 
22623  293 
cases=cases, termination=mtermination, 
23189  294 
domintros=mdomintros, 
22623  295 
trsimps=mtrsimps} 
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end 
21237  297 

23189  298 
fun prepare_fundef_mutual config defname fixes eqss lthy = 
22166  299 
let 
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val mutual = analyze_eqs lthy defname (map fst fixes) (map Envir.beta_eta_contract eqss) 
22166  301 
val Mutual {fsum_var=(n, T), qglrs, ...} = mutual 
302 

303 
val ((fsum, goalstate, cont), lthy') = 

23189  304 
FundefCore.prepare_fundef config defname [((n, T), NoSyn)] qglrs lthy 
22166  305 

306 
val (mutual', lthy'') = define_projections fixes mutual fsum lthy' 

307 

308 
val mutual_cont = mk_partial_rules_mutual lthy'' cont mutual' 

309 
in 

23819  310 
((goalstate, mutual_cont), lthy'') 
22166  311 
end 
312 

21237  313 

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end 