author | wenzelm |
Tue, 13 Mar 2012 20:04:24 +0100 | |
changeset 46909 | 3c73a121a387 |
parent 45403 | 7a0b8debef77 |
child 51717 | 9e7d1c139569 |
permissions | -rw-r--r-- |
31775 | 1 |
(* Title: HOL/Tools/Function/mutual.ML |
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Author: Alexander Krauss, TU Muenchen |
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Mutual recursive function definitions. |
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*) |
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signature FUNCTION_MUTUAL = |
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sig |
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val prepare_function_mutual : Function_Common.function_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 -> Function_Common.function_result) (* proof continuation *) |
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) * local_theory) |
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end |
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structure Function_Mutual: FUNCTION_MUTUAL = |
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struct |
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open Function_Lib |
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open Function_Common |
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type qgar = string * (string * typ) list * term list * term list * term |
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||
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datatype mutual_part = MutualPart of |
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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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datatype mutual_info = Mutual of |
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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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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 fqgars = map (split_def ctxt (K true)) 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, _)) 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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val rhs' = rhs |
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|> map_aterms (fn t as Free (n, _) => the_default t (AList.lookup (op =) rews n) | t => t) |
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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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Envir.beta_norm (SumTree.mk_inj RST n' i' rhs')) |
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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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Local_Theory.define |
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((Binding.name fname, mixfix), |
46909 | 137 |
((Binding.conceal (Binding.name (Thm.def_name fname)), []), |
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Term.subst_bound (fsum, f_def))) 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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144 |
|
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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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151 |
end |
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152 |
|
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fun in_context ctxt (f, pre_qs, pre_gs, pre_args, pre_rhs) F = |
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let |
42361 | 155 |
val thy = Proof_Context.theory_of ctxt |
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156 |
|
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val oqnames = map fst pre_qs |
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val (qs, _) = Variable.variant_fixes oqnames ctxt |
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|>> map2 (fn (_, T) => fn n => Free (n, T)) pre_qs |
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|
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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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165 |
|
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val cqs = map (cterm_of thy) qs |
36945 | 167 |
val ags = map (Thm.assume o cterm_of thy) gs |
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168 |
|
36945 | 169 |
val import = fold Thm.forall_elim cqs |
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#> fold Thm.elim_implies ags |
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171 |
|
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val export = fold_rev (Thm.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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176 |
end |
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177 |
|
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fun recover_mutual_psimp all_orig_fdefs parts ctxt (fname, _, _, args, rhs) |
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import (export : thm -> thm) sum_psimp_eq = |
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let |
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val (MutualPart {f=SOME f, ...}) = get_part fname parts |
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182 |
|
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val psimp = import sum_psimp_eq |
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val (simp, restore_cond) = |
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case cprems_of psimp of |
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[] => (psimp, I) |
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| [cond] => (Thm.implies_elim psimp (Thm.assume cond), Thm.implies_intr cond) |
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188 |
| _ => raise General.Fail "Too many conditions" |
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189 |
|
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190 |
in |
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191 |
Goal.prove ctxt [] [] |
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192 |
(HOLogic.Trueprop $ HOLogic.mk_eq (list_comb (f, args), rhs)) |
45403 | 193 |
(fn _ => |
194 |
Local_Defs.unfold_tac ctxt all_orig_fdefs |
|
195 |
THEN EqSubst.eqsubst_tac ctxt [0] [simp] 1 |
|
196 |
THEN (simp_tac (simpset_of ctxt)) 1) |
|
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|> restore_cond |
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|> export |
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199 |
end |
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200 |
|
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201 |
fun mk_applied_form ctxt caTs thm = |
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202 |
let |
42361 | 203 |
val thy = Proof_Context.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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205 |
in |
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fold (fn x => fn thm => Thm.combination thm (Thm.reflexive x)) xs thm |
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|> Conv.fconv_rule (Thm.beta_conversion true) |
36945 | 208 |
|> fold_rev Thm.forall_intr xs |
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|> Thm.forall_elim_vars 0 |
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210 |
end |
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211 |
|
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212 |
fun mutual_induct_rules lthy induct all_f_defs (Mutual {n, ST, parts, ...}) = |
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213 |
let |
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val cert = cterm_of (Proof_Context.theory_of lthy) |
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215 |
val newPs = |
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map2 (fn Pname => fn MutualPart {cargTs, ...} => |
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217 |
Free (Pname, cargTs ---> HOLogic.boolT)) |
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(mutual_induct_Pnames (length parts)) parts |
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219 |
|
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fun mk_P (MutualPart {cargTs, ...}) P = |
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221 |
let |
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val avars = map_index (fn (i,T) => Var (("a", i), T)) cargTs |
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val atup = foldr1 HOLogic.mk_prod avars |
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224 |
in |
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HOLogic.tupled_lambda atup (list_comb (P, avars)) |
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226 |
end |
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227 |
|
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228 |
val Ps = map2 mk_P parts newPs |
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229 |
val case_exp = SumTree.mk_sumcases HOLogic.boolT Ps |
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230 |
|
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231 |
val induct_inst = |
36945 | 232 |
Thm.forall_elim (cert case_exp) induct |
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233 |
|> full_simplify SumTree.sumcase_split_ss |
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234 |
|> full_simplify (HOL_basic_ss addsimps all_f_defs) |
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235 |
|
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236 |
fun project rule (MutualPart {cargTs, i, ...}) k = |
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237 |
let |
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238 |
val afs = map_index (fn (j,T) => Free ("a" ^ string_of_int (j + k), T)) cargTs (* FIXME! *) |
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239 |
val inj = SumTree.mk_inj ST n i (foldr1 HOLogic.mk_prod afs) |
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240 |
in |
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241 |
(rule |
36945 | 242 |
|> Thm.forall_elim (cert inj) |
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243 |
|> full_simplify SumTree.sumcase_split_ss |
36945 | 244 |
|> fold_rev (Thm.forall_intr o cert) (afs @ newPs), |
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245 |
k + length cargTs) |
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246 |
end |
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247 |
in |
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248 |
fst (fold_map (project induct_inst) parts 0) |
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249 |
end |
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250 |
|
22623 | 251 |
fun mk_partial_rules_mutual lthy inner_cont (m as Mutual {parts, fqgars, ...}) proof = |
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252 |
let |
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253 |
val result = inner_cont proof |
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254 |
val FunctionResult {G, R, cases, psimps, simple_pinducts=[simple_pinduct], |
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255 |
termination, domintros, ...} = result |
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256 |
|
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257 |
val (all_f_defs, fs) = |
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258 |
map (fn MutualPart {f_defthm = SOME f_def, f = SOME f, cargTs, ...} => |
36945 | 259 |
(mk_applied_form lthy cargTs (Thm.symmetric f_def), f)) |
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260 |
parts |
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261 |
|> split_list |
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262 |
|
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263 |
val all_orig_fdefs = |
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264 |
map (fn MutualPart {f_defthm = SOME f_def, ...} => f_def) parts |
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265 |
|
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266 |
fun mk_mpsimp fqgar sum_psimp = |
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267 |
in_context lthy fqgar (recover_mutual_psimp all_orig_fdefs parts) sum_psimp |
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268 |
|
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val rew_ss = HOL_basic_ss addsimps all_f_defs |
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val mpsimps = map2 mk_mpsimp fqgars psimps |
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val minducts = mutual_induct_rules lthy simple_pinduct all_f_defs m |
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val mtermination = full_simplify rew_ss termination |
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val mdomintros = Option.map (map (full_simplify rew_ss)) domintros |
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in |
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FunctionResult { fs=fs, G=G, R=R, |
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psimps=mpsimps, simple_pinducts=minducts, |
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cases=cases, termination=mtermination, |
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domintros=mdomintros} |
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end |
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|
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function package: more standard names for structures and files
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fun prepare_function_mutual config defname fixes eqss lthy = |
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let |
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val mutual as Mutual {fsum_var=(n, T), qglrs, ...} = |
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analyze_eqs lthy defname (map fst fixes) (map Envir.beta_eta_contract eqss) |
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|
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val ((fsum, goalstate, cont), lthy') = |
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Function_Core.prepare_function config defname [((n, T), NoSyn)] qglrs lthy |
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|
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val (mutual', lthy'') = define_projections fixes mutual fsum lthy' |
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val mutual_cont = mk_partial_rules_mutual lthy'' cont mutual' |
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in |
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((goalstate, mutual_cont), lthy'') |
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end |
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|
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end |