author | wenzelm |
Tue, 15 Apr 2008 16:12:05 +0200 | |
changeset 26653 | 60e0cf6bef89 |
parent 26529 | 03ad378ed5f0 |
child 28083 | 103d9282a946 |
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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-> 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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||
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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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||
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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 arities = mk_arities fqgars |
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fun curried_types (fname, fT) = |
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let |
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1. Function package accepts a parameter (default "some_term"), which specifies the functions
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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 dresultTs = distinct (Type.eq_type Vartab.empty) resultTs |
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val n' = length dresultTs |
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val RST = BalancedTree.make (uncurry SumTree.mk_sumT) dresultTs |
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val ST = BalancedTree.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 => Type.eq_type Vartab.empty (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') = |
25016 | 153 |
LocalTheory.define Thm.internalK ((fname, mixfix), |
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((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 |
21237 | 177 |
|>> map2 (fn (_, T) => fn n => Free (n, T)) pre_qs |
178 |
||
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fun inst t = subst_bounds (rev qs, t) |
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180 |
val gs = map inst pre_gs |
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181 |
val args = map inst pre_args |
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182 |
val rhs = inst pre_rhs |
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183 |
|
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184 |
val cqs = map (cterm_of thy) qs |
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val ags = map (assume o cterm_of thy) gs |
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186 |
|
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val import = fold forall_elim cqs |
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188 |
#> fold Thm.elim_implies ags |
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189 |
|
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190 |
val export = fold_rev (implies_intr o cprop_of) ags |
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191 |
#> fold_rev forall_intr_rename (oqnames ~~ cqs) |
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192 |
in |
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193 |
F ctxt (f, qs, gs, args, rhs) import export |
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194 |
end |
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|
195 |
|
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196 |
fun recover_mutual_psimp all_orig_fdefs parts ctxt (fname, _, _, args, rhs) import (export : thm -> thm) sum_psimp_eq = |
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197 |
let |
23494 | 198 |
val (MutualPart {f=SOME f, f_defthm=SOME f_def, ...}) = get_part fname parts |
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199 |
|
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200 |
val psimp = import sum_psimp_eq |
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201 |
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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204 |
| _ => sys_error "Too many conditions" |
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205 |
in |
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206 |
Goal.prove ctxt [] [] |
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207 |
(HOLogic.Trueprop $ HOLogic.mk_eq (list_comb (f, args), rhs)) |
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208 |
(fn _ => (LocalDefs.unfold_tac ctxt all_orig_fdefs) |
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209 |
THEN EqSubst.eqsubst_tac ctxt [0] [simp] 1 |
25555 | 210 |
THEN SIMPSET' (fn ss => simp_tac (ss addsimps SumTree.proj_in_rules)) 1) |
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211 |
|> restore_cond |
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212 |
|> export |
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213 |
end |
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|
214 |
|
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|
215 |
|
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|
216 |
(* FIXME HACK *) |
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|
217 |
fun mk_applied_form ctxt caTs thm = |
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218 |
let |
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219 |
val thy = ProofContext.theory_of ctxt |
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220 |
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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221 |
in |
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222 |
fold (fn x => fn thm => combination thm (reflexive x)) xs thm |
26196 | 223 |
|> Conv.fconv_rule (Thm.beta_conversion true) |
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224 |
|> fold_rev forall_intr xs |
26653 | 225 |
|> Thm.forall_elim_vars 0 |
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226 |
end |
23494 | 227 |
|
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228 |
|
23494 | 229 |
fun mutual_induct_rules lthy induct all_f_defs (Mutual {n, ST, RST, parts, ...}) = |
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230 |
let |
22623 | 231 |
val cert = cterm_of (ProofContext.theory_of lthy) |
20949 | 232 |
val newPs = map2 (fn Pname => fn MutualPart {cargTs, ...} => |
21237 | 233 |
Free (Pname, cargTs ---> HOLogic.boolT)) |
20949 | 234 |
(mutual_induct_Pnames (length parts)) |
235 |
parts |
|
21237 | 236 |
|
237 |
fun mk_P (MutualPart {cargTs, ...}) P = |
|
238 |
let |
|
239 |
val avars = map_index (fn (i,T) => Var (("a", i), T)) cargTs |
|
240 |
val atup = foldr1 HOLogic.mk_prod avars |
|
241 |
in |
|
242 |
tupled_lambda atup (list_comb (P, avars)) |
|
243 |
end |
|
244 |
||
245 |
val Ps = map2 mk_P parts newPs |
|
25555 | 246 |
val case_exp = SumTree.mk_sumcases HOLogic.boolT Ps |
21237 | 247 |
|
248 |
val induct_inst = |
|
22623 | 249 |
forall_elim (cert case_exp) induct |
25555 | 250 |
|> full_simplify SumTree.sumcase_split_ss |
21237 | 251 |
|> full_simplify (HOL_basic_ss addsimps all_f_defs) |
252 |
||
25046 | 253 |
fun project rule (MutualPart {cargTs, i, ...}) k = |
21237 | 254 |
let |
25046 | 255 |
val afs = map_index (fn (j,T) => Free ("a" ^ string_of_int (j + k), T)) cargTs (* FIXME! *) |
25555 | 256 |
val inj = SumTree.mk_inj ST n i (foldr1 HOLogic.mk_prod afs) |
21237 | 257 |
in |
25046 | 258 |
(rule |
22623 | 259 |
|> forall_elim (cert inj) |
25555 | 260 |
|> full_simplify SumTree.sumcase_split_ss |
25046 | 261 |
|> fold_rev (forall_intr o cert) (afs @ newPs), |
262 |
k + length cargTs) |
|
21237 | 263 |
end |
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|
264 |
in |
25046 | 265 |
fst (fold_map (project induct_inst) parts 0) |
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|
266 |
end |
21237 | 267 |
|
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|
268 |
|
22623 | 269 |
fun mk_partial_rules_mutual lthy inner_cont (m as Mutual {parts, fqgars, ...}) proof = |
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|
270 |
let |
22166 | 271 |
val result = inner_cont proof |
26529 | 272 |
val FundefResult {fs=[f], G, R, cases, psimps, trsimps, simple_pinducts=[simple_pinduct], |
22166 | 273 |
termination,domintros} = result |
21237 | 274 |
|
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|
275 |
val (all_f_defs, fs) = map (fn MutualPart {f_defthm = SOME f_def, f = SOME f, cargTs, ...} => |
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|
276 |
(mk_applied_form lthy cargTs (symmetric f_def), f)) |
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|
277 |
parts |
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|
278 |
|> split_list |
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|
279 |
|
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|
280 |
val all_orig_fdefs = map (fn MutualPart {f_defthm = SOME f_def, ...} => f_def) parts |
21237 | 281 |
|
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282 |
fun mk_mpsimp fqgar sum_psimp = |
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|
283 |
in_context lthy fqgar (recover_mutual_psimp all_orig_fdefs parts) sum_psimp |
21237 | 284 |
|
23189 | 285 |
val rew_ss = HOL_basic_ss addsimps all_f_defs |
22166 | 286 |
val mpsimps = map2 mk_mpsimp fqgars psimps |
287 |
val mtrsimps = map_option (map2 mk_mpsimp fqgars) trsimps |
|
22623 | 288 |
val minducts = mutual_induct_rules lthy simple_pinduct all_f_defs m |
23189 | 289 |
val mtermination = full_simplify rew_ss termination |
290 |
val mdomintros = map_option (map (full_simplify rew_ss)) domintros |
|
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|
291 |
in |
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|
292 |
FundefResult { fs=fs, G=G, R=R, |
26529 | 293 |
psimps=mpsimps, simple_pinducts=minducts, |
22623 | 294 |
cases=cases, termination=mtermination, |
23189 | 295 |
domintros=mdomintros, |
22623 | 296 |
trsimps=mtrsimps} |
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|
297 |
end |
21237 | 298 |
|
23189 | 299 |
fun prepare_fundef_mutual config defname fixes eqss lthy = |
22166 | 300 |
let |
22323
b8c227d8ca91
beta_eta_contract specification befor processing. These normal forms avoid unpleasant surprises later on.
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|
301 |
val mutual = analyze_eqs lthy defname (map fst fixes) (map Envir.beta_eta_contract eqss) |
22166 | 302 |
val Mutual {fsum_var=(n, T), qglrs, ...} = mutual |
303 |
||
304 |
val ((fsum, goalstate, cont), lthy') = |
|
23189 | 305 |
FundefCore.prepare_fundef config defname [((n, T), NoSyn)] qglrs lthy |
22166 | 306 |
|
307 |
val (mutual', lthy'') = define_projections fixes mutual fsum lthy' |
|
308 |
||
309 |
val mutual_cont = mk_partial_rules_mutual lthy'' cont mutual' |
|
310 |
in |
|
23819 | 311 |
((goalstate, mutual_cont), lthy'') |
22166 | 312 |
end |
313 |
||
21237 | 314 |
|
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changeset
|
315 |
end |