author | wenzelm |
Wed, 20 Oct 2021 18:13:17 +0200 | |
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parent 74282 | c2ee8d993d6a |
child 77879 | dd222e2af01a |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/semiring_normalizer.ML |
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Author: Amine Chaieb, TU Muenchen |
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Normalization of expressions in semirings. |
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*) |
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||
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signature SEMIRING_NORMALIZER = |
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sig |
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type entry |
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val match: Proof.context -> cterm -> entry option |
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val the_semiring: Proof.context -> thm -> cterm list * thm list |
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val the_ring: Proof.context -> thm -> cterm list * thm list |
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val the_field: Proof.context -> thm -> cterm list * thm list |
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val the_idom: Proof.context -> thm -> thm list |
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val the_ideal: Proof.context -> thm -> thm list |
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val declare: thm -> {semiring: term list * thm list, ring: term list * thm list, |
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field: term list * thm list, idom: thm list, ideal: thm list} -> |
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local_theory -> local_theory |
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val semiring_normalize_conv: Proof.context -> conv |
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val semiring_normalize_ord_conv: Proof.context -> cterm ord -> conv |
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val semiring_normalize_wrapper: Proof.context -> entry -> conv |
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val semiring_normalize_ord_wrapper: Proof.context -> entry -> cterm ord -> conv |
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val semiring_normalizers_conv: cterm list -> cterm list * thm list |
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-> cterm list * thm list -> cterm list * thm list -> |
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(cterm -> bool) * conv * conv * conv -> cterm ord -> |
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{add: Proof.context -> conv, |
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mul: Proof.context -> conv, |
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neg: Proof.context -> conv, |
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main: Proof.context -> conv, |
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pow: Proof.context -> conv, |
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sub: Proof.context -> conv} |
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val semiring_normalizers_ord_wrapper: Proof.context -> entry -> cterm ord -> |
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{add: Proof.context -> conv, |
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mul: Proof.context -> conv, |
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neg: Proof.context -> conv, |
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main: Proof.context -> conv, |
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pow: Proof.context -> conv, |
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sub: Proof.context -> conv} |
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end |
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||
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structure Semiring_Normalizer: SEMIRING_NORMALIZER = |
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struct |
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(** data **) |
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type entry = |
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{vars: cterm list, |
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semiring: cterm list * thm list, |
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ring: cterm list * thm list, |
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field: cterm list * thm list, |
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idom: thm list, |
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ideal: thm list} * |
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{is_const: cterm -> bool, |
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dest_const: cterm -> Rat.rat, |
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mk_const: ctyp -> Rat.rat -> cterm, |
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conv: Proof.context -> cterm -> thm}; |
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structure Data = Generic_Data |
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( |
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type T = (thm * entry) list; |
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val empty = []; |
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fun merge data = AList.merge Thm.eq_thm (K true) data; |
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); |
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fun the_rules ctxt = fst o the o AList.lookup Thm.eq_thm (Data.get (Context.Proof ctxt)) |
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val the_semiring = #semiring oo the_rules |
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val the_ring = #ring oo the_rules |
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val the_field = #field oo the_rules |
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val the_idom = #idom oo the_rules |
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val the_ideal = #ideal oo the_rules |
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fun match ctxt tm = |
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let |
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fun match_inst |
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({vars, semiring = (sr_ops, sr_rules), |
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ring = (r_ops, r_rules), field = (f_ops, f_rules), idom, ideal}, |
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fns) pat = |
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let |
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fun h instT = |
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let |
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val substT = Thm.instantiate (instT, Vars.empty); |
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val substT_cterm = Drule.cterm_rule substT; |
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val vars' = map substT_cterm vars; |
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val semiring' = (map substT_cterm sr_ops, map substT sr_rules); |
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val ring' = (map substT_cterm r_ops, map substT r_rules); |
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val field' = (map substT_cterm f_ops, map substT f_rules); |
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val idom' = map substT idom; |
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val ideal' = map substT ideal; |
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val result = ({vars = vars', semiring = semiring', |
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ring = ring', field = field', idom = idom', ideal = ideal'}, fns); |
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in SOME result end |
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in (case try Thm.match (pat, tm) of |
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NONE => NONE |
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| SOME (instT, _) => h instT) |
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end; |
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fun match_struct (_, |
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entry as ({semiring = (sr_ops, _), ring = (r_ops, _), field = (f_ops, _), ...}, _): entry) = |
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get_first (match_inst entry) (sr_ops @ r_ops @ f_ops); |
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in get_first match_struct (Data.get (Context.Proof ctxt)) end; |
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(* extra-logical functions *) |
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val semiring_norm_ss = |
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simpset_of (put_simpset HOL_basic_ss \<^context> addsimps @{thms semiring_norm}); |
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val semiring_funs = |
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{is_const = can HOLogic.dest_number o Thm.term_of, |
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dest_const = (fn ct => |
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Rat.of_int (snd |
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(HOLogic.dest_number (Thm.term_of ct) |
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handle TERM _ => error "ring_dest_const"))), |
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mk_const = (fn cT => fn x => Numeral.mk_cnumber cT |
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(case Rat.dest x of (i, 1) => i | _ => error "int_of_rat: bad int")), |
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conv = (fn ctxt => |
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Simplifier.rewrite (put_simpset semiring_norm_ss ctxt) |
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then_conv Simplifier.rewrite (put_simpset HOL_basic_ss ctxt addsimps @{thms numeral_One}))}; |
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val divide_const = Thm.cterm_of \<^context> (Logic.varify_global \<^term>\<open>(/)\<close>); |
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val [divide_tvar] = Term.add_tvars (Thm.term_of divide_const) []; |
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val field_funs = |
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let |
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fun numeral_is_const ct = |
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case Thm.term_of ct of |
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Const (\<^const_name>\<open>Rings.divide\<close>,_) $ a $ b => |
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can HOLogic.dest_number a andalso can HOLogic.dest_number b |
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| Const (\<^const_name>\<open>Fields.inverse\<close>,_)$t => can HOLogic.dest_number t |
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| t => can HOLogic.dest_number t |
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fun dest_const ct = ((case Thm.term_of ct of |
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Const (\<^const_name>\<open>Rings.divide\<close>,_) $ a $ b=> |
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Rat.make (snd (HOLogic.dest_number a), snd (HOLogic.dest_number b)) |
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| Const (\<^const_name>\<open>Fields.inverse\<close>,_)$t => |
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Rat.inv (Rat.of_int (snd (HOLogic.dest_number t))) |
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| t => Rat.of_int (snd (HOLogic.dest_number t))) |
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handle TERM _ => error "ring_dest_const") |
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fun mk_const cT x = |
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let val (a, b) = Rat.dest x |
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in if b = 1 then Numeral.mk_cnumber cT a |
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else Thm.apply |
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(Thm.apply |
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(Thm.instantiate_cterm (TVars.make [(divide_tvar, cT)], Vars.empty) divide_const) |
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(Numeral.mk_cnumber cT a)) |
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(Numeral.mk_cnumber cT b) |
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end |
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in |
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{is_const = numeral_is_const, |
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dest_const = dest_const, |
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mk_const = mk_const, |
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conv = Numeral_Simprocs.field_comp_conv} |
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end; |
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(* logical content *) |
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val semiringN = "semiring"; |
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val ringN = "ring"; |
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val fieldN = "field"; |
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val idomN = "idom"; |
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fun declare raw_key |
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{semiring = raw_semiring0, ring = raw_ring0, field = raw_field0, idom = raw_idom, ideal = raw_ideal} |
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lthy = |
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let |
70308 | 170 |
val ctxt' = fold Proof_Context.augment (fst raw_semiring0 @ fst raw_ring0 @ fst raw_field0) lthy; |
61153 | 171 |
val prepare_ops = apfst (Variable.export_terms ctxt' lthy #> map (Thm.cterm_of lthy)); |
172 |
val raw_semiring = prepare_ops raw_semiring0; |
|
173 |
val raw_ring = prepare_ops raw_ring0; |
|
174 |
val raw_field = prepare_ops raw_field0; |
|
175 |
in |
|
176 |
lthy |> Local_Theory.declaration {syntax = false, pervasive = false} (fn phi => fn context => |
|
177 |
let |
|
178 |
val ctxt = Context.proof_of context; |
|
179 |
val key = Morphism.thm phi raw_key; |
|
180 |
fun transform_ops_rules (ops, rules) = |
|
181 |
(map (Morphism.cterm phi) ops, Morphism.fact phi rules); |
|
182 |
val (sr_ops, sr_rules) = transform_ops_rules raw_semiring; |
|
183 |
val (r_ops, r_rules) = transform_ops_rules raw_ring; |
|
184 |
val (f_ops, f_rules) = transform_ops_rules raw_field; |
|
185 |
val idom = Morphism.fact phi raw_idom; |
|
186 |
val ideal = Morphism.fact phi raw_ideal; |
|
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parents:
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diff
changeset
|
187 |
|
61153 | 188 |
fun check kind name xs n = |
189 |
null xs orelse length xs = n orelse |
|
190 |
error ("Expected " ^ string_of_int n ^ " " ^ kind ^ " for " ^ name); |
|
191 |
val check_ops = check "operations"; |
|
192 |
val check_rules = check "rules"; |
|
193 |
val _ = |
|
194 |
check_ops semiringN sr_ops 5 andalso |
|
195 |
check_rules semiringN sr_rules 36 andalso |
|
196 |
check_ops ringN r_ops 2 andalso |
|
197 |
check_rules ringN r_rules 2 andalso |
|
198 |
check_ops fieldN f_ops 2 andalso |
|
199 |
check_rules fieldN f_rules 2 andalso |
|
200 |
check_rules idomN idom 2; |
|
201 |
||
202 |
val mk_meta = Local_Defs.meta_rewrite_rule ctxt; |
|
203 |
val sr_rules' = map mk_meta sr_rules; |
|
204 |
val r_rules' = map mk_meta r_rules; |
|
205 |
val f_rules' = map mk_meta f_rules; |
|
206 |
||
207 |
fun rule i = nth sr_rules' (i - 1); |
|
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haftmann
parents:
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diff
changeset
|
208 |
|
61153 | 209 |
val (cx, cy) = Thm.dest_binop (hd sr_ops); |
210 |
val cz = rule 34 |> Thm.rhs_of |> Thm.dest_arg |> Thm.dest_arg; |
|
211 |
val cn = rule 36 |> Thm.rhs_of |> Thm.dest_arg |> Thm.dest_arg; |
|
212 |
val ((clx, crx), (cly, cry)) = |
|
213 |
rule 13 |> Thm.rhs_of |> Thm.dest_binop |> apply2 Thm.dest_binop; |
|
214 |
val ((ca, cb), (cc, cd)) = |
|
215 |
rule 20 |> Thm.lhs_of |> Thm.dest_binop |> apply2 Thm.dest_binop; |
|
216 |
val cm = rule 1 |> Thm.rhs_of |> Thm.dest_arg; |
|
217 |
val (cp, cq) = rule 26 |> Thm.lhs_of |> Thm.dest_binop |> apply2 Thm.dest_arg; |
|
218 |
||
219 |
val vars = [ca, cb, cc, cd, cm, cn, cp, cq, cx, cy, cz, clx, crx, cly, cry]; |
|
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haftmann
parents:
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diff
changeset
|
220 |
|
61153 | 221 |
val semiring = (sr_ops, sr_rules'); |
222 |
val ring = (r_ops, r_rules'); |
|
223 |
val field = (f_ops, f_rules'); |
|
224 |
val ideal' = map (Thm.symmetric o mk_meta) ideal |
|
225 |
in |
|
226 |
context |
|
227 |
|> Data.map (AList.update Thm.eq_thm (key, |
|
228 |
({vars = vars, semiring = semiring, ring = ring, field = field, idom = idom, ideal = ideal'}, |
|
229 |
(if null f_ops then semiring_funs else field_funs)))) |
|
230 |
end) |
|
231 |
end; |
|
36720 | 232 |
|
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parents:
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changeset
|
233 |
|
36710 | 234 |
(** auxiliary **) |
25253 | 235 |
|
236 |
fun is_comb ct = |
|
237 |
(case Thm.term_of ct of |
|
238 |
_ $ _ => true |
|
239 |
| _ => false); |
|
240 |
||
241 |
val concl = Thm.cprop_of #> Thm.dest_arg; |
|
242 |
||
243 |
fun is_binop ct ct' = |
|
244 |
(case Thm.term_of ct' of |
|
59582 | 245 |
c $ _ $ _ => Thm.term_of ct aconv c |
25253 | 246 |
| _ => false); |
247 |
||
248 |
fun dest_binop ct ct' = |
|
249 |
if is_binop ct ct' then Thm.dest_binop ct' |
|
250 |
else raise CTERM ("dest_binop: bad binop", [ct, ct']) |
|
251 |
||
74282 | 252 |
fun inst_thm inst = |
253 |
Thm.instantiate (TVars.empty, Vars.make (map (apfst (dest_Var o Thm.term_of)) inst)); |
|
25253 | 254 |
|
59582 | 255 |
val dest_number = Thm.term_of #> HOLogic.dest_number #> snd; |
59538 | 256 |
val is_number = can dest_number; |
23252 | 257 |
|
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parents:
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changeset
|
258 |
fun numeral01_conv ctxt = |
61694
6571c78c9667
Removed some legacy theorems; minor adjustments to simplification rules; new material on homotopic paths
paulson <lp15@cam.ac.uk>
parents:
61153
diff
changeset
|
259 |
Simplifier.rewrite (put_simpset HOL_basic_ss ctxt addsimps [@{thm numeral_One}]); |
51717
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wenzelm
parents:
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diff
changeset
|
260 |
|
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simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
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diff
changeset
|
261 |
fun zero1_numeral_conv ctxt = |
61694
6571c78c9667
Removed some legacy theorems; minor adjustments to simplification rules; new material on homotopic paths
paulson <lp15@cam.ac.uk>
parents:
61153
diff
changeset
|
262 |
Simplifier.rewrite (put_simpset HOL_basic_ss ctxt addsimps [@{thm numeral_One} RS sym]); |
51717
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simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
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diff
changeset
|
263 |
|
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
264 |
fun zerone_conv ctxt cv = |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
265 |
zero1_numeral_conv ctxt then_conv cv then_conv numeral01_conv ctxt; |
36700
9b85b9d74b83
dropped auxiliary method sring_norm; integrated normalizer.ML and normalizer_data.ML
haftmann
parents:
35410
diff
changeset
|
266 |
|
61153 | 267 |
val nat_add_ss = simpset_of |
69593 | 268 |
(put_simpset HOL_basic_ss \<^context> |
59547 | 269 |
addsimps @{thms arith_simps} @ @{thms diff_nat_numeral} @ @{thms rel_simps} |
270 |
@ @{thms if_False if_True Nat.add_0 add_Suc add_numeral_left Suc_eq_plus1} |
|
271 |
@ map (fn th => th RS sym) @{thms numerals}); |
|
53078
cc06f17d8057
more static simpsets, which also avoids spurious warnings due to duplicate rules provided here;
wenzelm
parents:
51717
diff
changeset
|
272 |
|
51717
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wenzelm
parents:
47108
diff
changeset
|
273 |
fun nat_add_conv ctxt = |
53078
cc06f17d8057
more static simpsets, which also avoids spurious warnings due to duplicate rules provided here;
wenzelm
parents:
51717
diff
changeset
|
274 |
zerone_conv ctxt (Simplifier.rewrite (put_simpset nat_add_ss ctxt)); |
23252 | 275 |
|
69593 | 276 |
val zeron_tm = \<^cterm>\<open>0::nat\<close>; |
277 |
val onen_tm = \<^cterm>\<open>1::nat\<close>; |
|
278 |
val true_tm = \<^cterm>\<open>True\<close>; |
|
23252 | 279 |
|
280 |
||
36710 | 281 |
(** normalizing conversions **) |
282 |
||
283 |
(* core conversion *) |
|
284 |
||
30866 | 285 |
fun semiring_normalizers_conv vars (sr_ops, sr_rules) (r_ops, r_rules) (f_ops, f_rules) |
23252 | 286 |
(is_semiring_constant, semiring_add_conv, semiring_mul_conv, semiring_pow_conv) = |
287 |
let |
|
288 |
||
289 |
val [pthm_02, pthm_03, pthm_04, pthm_05, pthm_07, pthm_08, |
|
290 |
pthm_09, pthm_10, pthm_11, pthm_12, pthm_13, pthm_14, pthm_15, pthm_16, |
|
291 |
pthm_17, pthm_18, pthm_19, pthm_21, pthm_22, pthm_23, pthm_24, |
|
292 |
pthm_25, pthm_26, pthm_27, pthm_28, pthm_29, pthm_30, pthm_31, pthm_32, |
|
59550 | 293 |
pthm_33, pthm_34, pthm_35, pthm_36, pthm_37, pthm_38, _] = sr_rules; |
23252 | 294 |
|
295 |
val [ca, cb, cc, cd, cm, cn, cp, cq, cx, cy, cz, clx, crx, cly, cry] = vars; |
|
296 |
val [add_pat, mul_pat, pow_pat, zero_tm, one_tm] = sr_ops; |
|
297 |
val [add_tm, mul_tm, pow_tm] = map (Thm.dest_fun o Thm.dest_fun) [add_pat, mul_pat, pow_pat]; |
|
298 |
||
299 |
val dest_add = dest_binop add_tm |
|
300 |
val dest_mul = dest_binop mul_tm |
|
301 |
fun dest_pow tm = |
|
302 |
let val (l,r) = dest_binop pow_tm tm |
|
59538 | 303 |
in if is_number r then (l,r) else raise CTERM ("dest_pow",[tm]) |
23252 | 304 |
end; |
305 |
val is_add = is_binop add_tm |
|
306 |
val is_mul = is_binop mul_tm |
|
307 |
||
59321 | 308 |
val (neg_mul, sub_add, sub_tm, neg_tm, dest_sub, cx', cy') = |
23252 | 309 |
(case (r_ops, r_rules) of |
30866 | 310 |
([sub_pat, neg_pat], [neg_mul, sub_add]) => |
23252 | 311 |
let |
312 |
val sub_tm = Thm.dest_fun (Thm.dest_fun sub_pat) |
|
313 |
val neg_tm = Thm.dest_fun neg_pat |
|
314 |
val dest_sub = dest_binop sub_tm |
|
60642
48dd1cefb4ae
simplified Thm.instantiate and derivatives: the LHS refers to non-certified variables -- this merely serves as index into already certified structures (or is ignored);
wenzelm
parents:
60352
diff
changeset
|
315 |
in (neg_mul, sub_add, sub_tm, neg_tm, dest_sub, neg_mul |> concl |> Thm.dest_arg, |
23252 | 316 |
sub_add |> concl |> Thm.dest_arg |> Thm.dest_arg) |
30866 | 317 |
end |
59321 | 318 |
| _ => (TrueI, TrueI, true_tm, true_tm, (fn t => (t,t)), true_tm, true_tm)); |
30866 | 319 |
|
61153 | 320 |
val (divide_inverse, divide_tm, inverse_tm) = |
321 |
(case (f_ops, f_rules) of |
|
322 |
([divide_pat, inverse_pat], [div_inv, _]) => |
|
30866 | 323 |
let val div_tm = funpow 2 Thm.dest_fun divide_pat |
324 |
val inv_tm = Thm.dest_fun inverse_pat |
|
59321 | 325 |
in (div_inv, div_tm, inv_tm) |
30866 | 326 |
end |
59321 | 327 |
| _ => (TrueI, true_tm, true_tm)); |
30866 | 328 |
|
67562 | 329 |
in fn variable_ord => |
23252 | 330 |
let |
331 |
||
332 |
(* Conversion for "x^n * x^m", with either x^n = x and/or x^m = x possible. *) |
|
333 |
(* Also deals with "const * const", but both terms must involve powers of *) |
|
334 |
(* the same variable, or both be constants, or behaviour may be incorrect. *) |
|
335 |
||
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
336 |
fun powvar_mul_conv ctxt tm = |
23252 | 337 |
let |
338 |
val (l,r) = dest_mul tm |
|
339 |
in if is_semiring_constant l andalso is_semiring_constant r |
|
340 |
then semiring_mul_conv tm |
|
341 |
else |
|
342 |
((let |
|
343 |
val (lx,ln) = dest_pow l |
|
344 |
in |
|
59321 | 345 |
((let val (_, rn) = dest_pow r |
23252 | 346 |
val th1 = inst_thm [(cx,lx),(cp,ln),(cq,rn)] pthm_29 |
347 |
val (tm1,tm2) = Thm.dest_comb(concl th1) in |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
348 |
Thm.transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv ctxt tm2)) end) |
23252 | 349 |
handle CTERM _ => |
350 |
(let val th1 = inst_thm [(cx,lx),(cq,ln)] pthm_31 |
|
351 |
val (tm1,tm2) = Thm.dest_comb(concl th1) in |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
352 |
Thm.transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv ctxt tm2)) end)) end) |
23252 | 353 |
handle CTERM _ => |
354 |
((let val (rx,rn) = dest_pow r |
|
355 |
val th1 = inst_thm [(cx,rx),(cq,rn)] pthm_30 |
|
356 |
val (tm1,tm2) = Thm.dest_comb(concl th1) in |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
357 |
Thm.transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv ctxt tm2)) end) |
23252 | 358 |
handle CTERM _ => inst_thm [(cx,l)] pthm_32 |
359 |
||
360 |
)) |
|
361 |
end; |
|
362 |
||
363 |
(* Remove "1 * m" from a monomial, and just leave m. *) |
|
364 |
||
365 |
fun monomial_deone th = |
|
366 |
(let val (l,r) = dest_mul(concl th) in |
|
367 |
if l aconvc one_tm |
|
36945 | 368 |
then Thm.transitive th (inst_thm [(ca,r)] pthm_13) else th end) |
23252 | 369 |
handle CTERM _ => th; |
370 |
||
371 |
(* Conversion for "(monomial)^n", where n is a numeral. *) |
|
372 |
||
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
373 |
fun monomial_pow_conv ctxt = |
23252 | 374 |
let |
375 |
fun monomial_pow tm bod ntm = |
|
376 |
if not(is_comb bod) |
|
36945 | 377 |
then Thm.reflexive tm |
23252 | 378 |
else |
379 |
if is_semiring_constant bod |
|
380 |
then semiring_pow_conv tm |
|
381 |
else |
|
382 |
let |
|
383 |
val (lopr,r) = Thm.dest_comb bod |
|
384 |
in if not(is_comb lopr) |
|
36945 | 385 |
then Thm.reflexive tm |
23252 | 386 |
else |
387 |
let |
|
388 |
val (opr,l) = Thm.dest_comb lopr |
|
389 |
in |
|
59538 | 390 |
if opr aconvc pow_tm andalso is_number r |
23252 | 391 |
then |
392 |
let val th1 = inst_thm [(cx,l),(cp,r),(cq,ntm)] pthm_34 |
|
393 |
val (l,r) = Thm.dest_comb(concl th1) |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
394 |
in Thm.transitive th1 (Drule.arg_cong_rule l (nat_add_conv ctxt r)) |
23252 | 395 |
end |
396 |
else |
|
397 |
if opr aconvc mul_tm |
|
398 |
then |
|
399 |
let |
|
400 |
val th1 = inst_thm [(cx,l),(cy,r),(cq,ntm)] pthm_33 |
|
401 |
val (xy,z) = Thm.dest_comb(concl th1) |
|
402 |
val (x,y) = Thm.dest_comb xy |
|
403 |
val thl = monomial_pow y l ntm |
|
404 |
val thr = monomial_pow z r ntm |
|
36945 | 405 |
in Thm.transitive th1 (Thm.combination (Drule.arg_cong_rule x thl) thr) |
23252 | 406 |
end |
36945 | 407 |
else Thm.reflexive tm |
23252 | 408 |
end |
409 |
end |
|
410 |
in fn tm => |
|
411 |
let |
|
412 |
val (lopr,r) = Thm.dest_comb tm |
|
413 |
val (opr,l) = Thm.dest_comb lopr |
|
59538 | 414 |
in if not (opr aconvc pow_tm) orelse not(is_number r) |
23252 | 415 |
then raise CTERM ("monomial_pow_conv", [tm]) |
416 |
else if r aconvc zeron_tm |
|
417 |
then inst_thm [(cx,l)] pthm_35 |
|
418 |
else if r aconvc onen_tm |
|
419 |
then inst_thm [(cx,l)] pthm_36 |
|
420 |
else monomial_deone(monomial_pow tm l r) |
|
421 |
end |
|
422 |
end; |
|
423 |
||
424 |
(* Multiplication of canonical monomials. *) |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
425 |
fun monomial_mul_conv ctxt = |
23252 | 426 |
let |
427 |
fun powvar tm = |
|
428 |
if is_semiring_constant tm then one_tm |
|
429 |
else |
|
430 |
((let val (lopr,r) = Thm.dest_comb tm |
|
431 |
val (opr,l) = Thm.dest_comb lopr |
|
61153 | 432 |
in if opr aconvc pow_tm andalso is_number r then l |
23252 | 433 |
else raise CTERM ("monomial_mul_conv",[tm]) end) |
434 |
handle CTERM _ => tm) (* FIXME !? *) |
|
435 |
fun vorder x y = |
|
436 |
if x aconvc y then 0 |
|
437 |
else |
|
438 |
if x aconvc one_tm then ~1 |
|
439 |
else if y aconvc one_tm then 1 |
|
67562 | 440 |
else if is_less (variable_ord (x, y)) then ~1 else 1 |
23252 | 441 |
fun monomial_mul tm l r = |
442 |
((let val (lx,ly) = dest_mul l val vl = powvar lx |
|
443 |
in |
|
444 |
((let |
|
445 |
val (rx,ry) = dest_mul r |
|
446 |
val vr = powvar rx |
|
447 |
val ord = vorder vl vr |
|
448 |
in |
|
449 |
if ord = 0 |
|
450 |
then |
|
451 |
let |
|
452 |
val th1 = inst_thm [(clx,lx),(cly,ly),(crx,rx),(cry,ry)] pthm_15 |
|
453 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
454 |
val (tm3,tm4) = Thm.dest_comb tm1 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
455 |
val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv ctxt tm4)) tm2 |
36945 | 456 |
val th3 = Thm.transitive th1 th2 |
23252 | 457 |
val (tm5,tm6) = Thm.dest_comb(concl th3) |
458 |
val (tm7,tm8) = Thm.dest_comb tm6 |
|
459 |
val th4 = monomial_mul tm6 (Thm.dest_arg tm7) tm8 |
|
36945 | 460 |
in Thm.transitive th3 (Drule.arg_cong_rule tm5 th4) |
23252 | 461 |
end |
462 |
else |
|
463 |
let val th0 = if ord < 0 then pthm_16 else pthm_17 |
|
464 |
val th1 = inst_thm [(clx,lx),(cly,ly),(crx,rx),(cry,ry)] th0 |
|
465 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
466 |
val (tm3,tm4) = Thm.dest_comb tm2 |
|
36945 | 467 |
in Thm.transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4)) |
23252 | 468 |
end |
469 |
end) |
|
470 |
handle CTERM _ => |
|
471 |
(let val vr = powvar r val ord = vorder vl vr |
|
472 |
in |
|
473 |
if ord = 0 then |
|
474 |
let |
|
475 |
val th1 = inst_thm [(clx,lx),(cly,ly),(crx,r)] pthm_18 |
|
476 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
477 |
val (tm3,tm4) = Thm.dest_comb tm1 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
478 |
val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv ctxt tm4)) tm2 |
36945 | 479 |
in Thm.transitive th1 th2 |
23252 | 480 |
end |
481 |
else |
|
482 |
if ord < 0 then |
|
483 |
let val th1 = inst_thm [(clx,lx),(cly,ly),(crx,r)] pthm_19 |
|
484 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
485 |
val (tm3,tm4) = Thm.dest_comb tm2 |
|
36945 | 486 |
in Thm.transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4)) |
23252 | 487 |
end |
488 |
else inst_thm [(ca,l),(cb,r)] pthm_09 |
|
489 |
end)) end) |
|
490 |
handle CTERM _ => |
|
491 |
(let val vl = powvar l in |
|
492 |
((let |
|
493 |
val (rx,ry) = dest_mul r |
|
494 |
val vr = powvar rx |
|
495 |
val ord = vorder vl vr |
|
496 |
in if ord = 0 then |
|
497 |
let val th1 = inst_thm [(clx,l),(crx,rx),(cry,ry)] pthm_21 |
|
498 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
499 |
val (tm3,tm4) = Thm.dest_comb tm1 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
500 |
in Thm.transitive th1 (Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv ctxt tm4)) tm2) |
23252 | 501 |
end |
502 |
else if ord > 0 then |
|
503 |
let val th1 = inst_thm [(clx,l),(crx,rx),(cry,ry)] pthm_22 |
|
504 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
505 |
val (tm3,tm4) = Thm.dest_comb tm2 |
|
36945 | 506 |
in Thm.transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4)) |
23252 | 507 |
end |
36945 | 508 |
else Thm.reflexive tm |
23252 | 509 |
end) |
510 |
handle CTERM _ => |
|
511 |
(let val vr = powvar r |
|
512 |
val ord = vorder vl vr |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
513 |
in if ord = 0 then powvar_mul_conv ctxt tm |
23252 | 514 |
else if ord > 0 then inst_thm [(ca,l),(cb,r)] pthm_09 |
36945 | 515 |
else Thm.reflexive tm |
23252 | 516 |
end)) end)) |
517 |
in fn tm => let val (l,r) = dest_mul tm in monomial_deone(monomial_mul tm l r) |
|
518 |
end |
|
519 |
end; |
|
520 |
(* Multiplication by monomial of a polynomial. *) |
|
521 |
||
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
522 |
fun polynomial_monomial_mul_conv ctxt = |
23252 | 523 |
let |
524 |
fun pmm_conv tm = |
|
525 |
let val (l,r) = dest_mul tm |
|
526 |
in |
|
527 |
((let val (y,z) = dest_add r |
|
528 |
val th1 = inst_thm [(cx,l),(cy,y),(cz,z)] pthm_37 |
|
529 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
530 |
val (tm3,tm4) = Thm.dest_comb tm1 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
531 |
val th2 = |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
532 |
Thm.combination (Drule.arg_cong_rule tm3 (monomial_mul_conv ctxt tm4)) (pmm_conv tm2) |
36945 | 533 |
in Thm.transitive th1 th2 |
23252 | 534 |
end) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
535 |
handle CTERM _ => monomial_mul_conv ctxt tm) |
23252 | 536 |
end |
537 |
in pmm_conv |
|
538 |
end; |
|
539 |
||
540 |
(* Addition of two monomials identical except for constant multiples. *) |
|
541 |
||
542 |
fun monomial_add_conv tm = |
|
543 |
let val (l,r) = dest_add tm |
|
544 |
in if is_semiring_constant l andalso is_semiring_constant r |
|
545 |
then semiring_add_conv tm |
|
546 |
else |
|
547 |
let val th1 = |
|
548 |
if is_mul l andalso is_semiring_constant(Thm.dest_arg1 l) |
|
549 |
then if is_mul r andalso is_semiring_constant(Thm.dest_arg1 r) then |
|
550 |
inst_thm [(ca,Thm.dest_arg1 l),(cm,Thm.dest_arg r), (cb,Thm.dest_arg1 r)] pthm_02 |
|
551 |
else inst_thm [(ca,Thm.dest_arg1 l),(cm,r)] pthm_03 |
|
552 |
else if is_mul r andalso is_semiring_constant(Thm.dest_arg1 r) |
|
553 |
then inst_thm [(cm,l),(ca,Thm.dest_arg1 r)] pthm_04 |
|
554 |
else inst_thm [(cm,r)] pthm_05 |
|
555 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
556 |
val (tm3,tm4) = Thm.dest_comb tm1 |
|
557 |
val th2 = Drule.arg_cong_rule tm3 (semiring_add_conv tm4) |
|
36945 | 558 |
val th3 = Thm.transitive th1 (Drule.fun_cong_rule th2 tm2) |
23252 | 559 |
val tm5 = concl th3 |
560 |
in |
|
561 |
if (Thm.dest_arg1 tm5) aconvc zero_tm |
|
36945 | 562 |
then Thm.transitive th3 (inst_thm [(ca,Thm.dest_arg tm5)] pthm_11) |
23252 | 563 |
else monomial_deone th3 |
564 |
end |
|
565 |
end; |
|
566 |
||
567 |
(* Ordering on monomials. *) |
|
568 |
||
569 |
fun striplist dest = |
|
570 |
let fun strip x acc = |
|
571 |
((let val (l,r) = dest x in |
|
572 |
strip l (strip r acc) end) |
|
573 |
handle CTERM _ => x::acc) (* FIXME !? *) |
|
574 |
in fn x => strip x [] |
|
575 |
end; |
|
576 |
||
577 |
||
578 |
fun powervars tm = |
|
579 |
let val ptms = striplist dest_mul tm |
|
580 |
in if is_semiring_constant (hd ptms) then tl ptms else ptms |
|
581 |
end; |
|
582 |
val num_0 = 0; |
|
583 |
val num_1 = 1; |
|
584 |
fun dest_varpow tm = |
|
59538 | 585 |
((let val (x,n) = dest_pow tm in (x,dest_number n) end) |
23252 | 586 |
handle CTERM _ => |
587 |
(tm,(if is_semiring_constant tm then num_0 else num_1))); |
|
588 |
||
589 |
val morder = |
|
67565 | 590 |
let fun lexorder ls = |
591 |
case ls of |
|
23252 | 592 |
([],[]) => 0 |
59321 | 593 |
| (_ ,[]) => ~1 |
594 |
| ([], _) => 1 |
|
23252 | 595 |
| (((x1,n1)::vs1),((x2,n2)::vs2)) => |
67565 | 596 |
(case variable_ord (x1, x2) of |
597 |
LESS => 1 |
|
598 |
| GREATER => ~1 |
|
599 |
| EQUAL => |
|
600 |
if n1 < n2 then ~1 |
|
601 |
else if n2 < n1 then 1 |
|
602 |
else lexorder (vs1, vs2)) |
|
23252 | 603 |
in fn tm1 => fn tm2 => |
604 |
let val vdegs1 = map dest_varpow (powervars tm1) |
|
605 |
val vdegs2 = map dest_varpow (powervars tm2) |
|
33002 | 606 |
val deg1 = fold (Integer.add o snd) vdegs1 num_0 |
607 |
val deg2 = fold (Integer.add o snd) vdegs2 num_0 |
|
23252 | 608 |
in if deg1 < deg2 then ~1 else if deg1 > deg2 then 1 |
67565 | 609 |
else lexorder (vdegs1, vdegs2) |
23252 | 610 |
end |
611 |
end; |
|
612 |
||
613 |
(* Addition of two polynomials. *) |
|
614 |
||
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
615 |
fun polynomial_add_conv ctxt = |
23252 | 616 |
let |
617 |
fun dezero_rule th = |
|
618 |
let |
|
619 |
val tm = concl th |
|
620 |
in |
|
621 |
if not(is_add tm) then th else |
|
622 |
let val (lopr,r) = Thm.dest_comb tm |
|
623 |
val l = Thm.dest_arg lopr |
|
624 |
in |
|
625 |
if l aconvc zero_tm |
|
36945 | 626 |
then Thm.transitive th (inst_thm [(ca,r)] pthm_07) else |
23252 | 627 |
if r aconvc zero_tm |
36945 | 628 |
then Thm.transitive th (inst_thm [(ca,l)] pthm_08) else th |
23252 | 629 |
end |
630 |
end |
|
631 |
fun padd tm = |
|
632 |
let |
|
633 |
val (l,r) = dest_add tm |
|
634 |
in |
|
635 |
if l aconvc zero_tm then inst_thm [(ca,r)] pthm_07 |
|
636 |
else if r aconvc zero_tm then inst_thm [(ca,l)] pthm_08 |
|
637 |
else |
|
638 |
if is_add l |
|
639 |
then |
|
640 |
let val (a,b) = dest_add l |
|
641 |
in |
|
642 |
if is_add r then |
|
643 |
let val (c,d) = dest_add r |
|
644 |
val ord = morder a c |
|
645 |
in |
|
646 |
if ord = 0 then |
|
647 |
let val th1 = inst_thm [(ca,a),(cb,b),(cc,c),(cd,d)] pthm_23 |
|
648 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
649 |
val (tm3,tm4) = Thm.dest_comb tm1 |
|
650 |
val th2 = Drule.arg_cong_rule tm3 (monomial_add_conv tm4) |
|
36945 | 651 |
in dezero_rule (Thm.transitive th1 (Thm.combination th2 (padd tm2))) |
23252 | 652 |
end |
653 |
else (* ord <> 0*) |
|
654 |
let val th1 = |
|
655 |
if ord > 0 then inst_thm [(ca,a),(cb,b),(cc,r)] pthm_24 |
|
656 |
else inst_thm [(ca,l),(cc,c),(cd,d)] pthm_25 |
|
657 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
36945 | 658 |
in dezero_rule (Thm.transitive th1 (Drule.arg_cong_rule tm1 (padd tm2))) |
23252 | 659 |
end |
660 |
end |
|
661 |
else (* not (is_add r)*) |
|
662 |
let val ord = morder a r |
|
663 |
in |
|
664 |
if ord = 0 then |
|
665 |
let val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_26 |
|
666 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
667 |
val (tm3,tm4) = Thm.dest_comb tm1 |
|
668 |
val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (monomial_add_conv tm4)) tm2 |
|
36945 | 669 |
in dezero_rule (Thm.transitive th1 th2) |
23252 | 670 |
end |
671 |
else (* ord <> 0*) |
|
672 |
if ord > 0 then |
|
673 |
let val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_24 |
|
674 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
36945 | 675 |
in dezero_rule (Thm.transitive th1 (Drule.arg_cong_rule tm1 (padd tm2))) |
23252 | 676 |
end |
677 |
else dezero_rule (inst_thm [(ca,l),(cc,r)] pthm_27) |
|
678 |
end |
|
679 |
end |
|
680 |
else (* not (is_add l)*) |
|
681 |
if is_add r then |
|
682 |
let val (c,d) = dest_add r |
|
683 |
val ord = morder l c |
|
684 |
in |
|
685 |
if ord = 0 then |
|
686 |
let val th1 = inst_thm [(ca,l),(cc,c),(cd,d)] pthm_28 |
|
687 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
688 |
val (tm3,tm4) = Thm.dest_comb tm1 |
|
689 |
val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (monomial_add_conv tm4)) tm2 |
|
36945 | 690 |
in dezero_rule (Thm.transitive th1 th2) |
23252 | 691 |
end |
692 |
else |
|
36945 | 693 |
if ord > 0 then Thm.reflexive tm |
23252 | 694 |
else |
695 |
let val th1 = inst_thm [(ca,l),(cc,c),(cd,d)] pthm_25 |
|
696 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
36945 | 697 |
in dezero_rule (Thm.transitive th1 (Drule.arg_cong_rule tm1 (padd tm2))) |
23252 | 698 |
end |
699 |
end |
|
700 |
else |
|
701 |
let val ord = morder l r |
|
702 |
in |
|
703 |
if ord = 0 then monomial_add_conv tm |
|
36945 | 704 |
else if ord > 0 then dezero_rule(Thm.reflexive tm) |
23252 | 705 |
else dezero_rule (inst_thm [(ca,l),(cc,r)] pthm_27) |
706 |
end |
|
707 |
end |
|
708 |
in padd |
|
709 |
end; |
|
710 |
||
711 |
(* Multiplication of two polynomials. *) |
|
712 |
||
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
713 |
fun polynomial_mul_conv ctxt = |
23252 | 714 |
let |
715 |
fun pmul tm = |
|
716 |
let val (l,r) = dest_mul tm |
|
717 |
in |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
718 |
if not(is_add l) then polynomial_monomial_mul_conv ctxt tm |
23252 | 719 |
else |
720 |
if not(is_add r) then |
|
721 |
let val th1 = inst_thm [(ca,l),(cb,r)] pthm_09 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
722 |
in Thm.transitive th1 (polynomial_monomial_mul_conv ctxt (concl th1)) |
23252 | 723 |
end |
724 |
else |
|
725 |
let val (a,b) = dest_add l |
|
726 |
val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_10 |
|
727 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
|
728 |
val (tm3,tm4) = Thm.dest_comb tm1 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
729 |
val th2 = Drule.arg_cong_rule tm3 (polynomial_monomial_mul_conv ctxt tm4) |
36945 | 730 |
val th3 = Thm.transitive th1 (Thm.combination th2 (pmul tm2)) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
731 |
in Thm.transitive th3 (polynomial_add_conv ctxt (concl th3)) |
23252 | 732 |
end |
733 |
end |
|
734 |
in fn tm => |
|
735 |
let val (l,r) = dest_mul tm |
|
736 |
in |
|
737 |
if l aconvc zero_tm then inst_thm [(ca,r)] pthm_11 |
|
738 |
else if r aconvc zero_tm then inst_thm [(ca,l)] pthm_12 |
|
739 |
else if l aconvc one_tm then inst_thm [(ca,r)] pthm_13 |
|
740 |
else if r aconvc one_tm then inst_thm [(ca,l)] pthm_14 |
|
741 |
else pmul tm |
|
742 |
end |
|
743 |
end; |
|
744 |
||
745 |
(* Power of polynomial (optimized for the monomial and trivial cases). *) |
|
746 |
||
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
747 |
fun num_conv ctxt n = |
69593 | 748 |
nat_add_conv ctxt (Thm.apply \<^cterm>\<open>Suc\<close> (Numeral.mk_cnumber \<^ctyp>\<open>nat\<close> (dest_number n - 1))) |
23580
998a6fda9bb6
moved mk_cnumeral/mk_cnumber to Tools/numeral.ML;
wenzelm
parents:
23559
diff
changeset
|
749 |
|> Thm.symmetric; |
23252 | 750 |
|
751 |
||
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
752 |
fun polynomial_pow_conv ctxt = |
23252 | 753 |
let |
754 |
fun ppow tm = |
|
755 |
let val (l,n) = dest_pow tm |
|
756 |
in |
|
757 |
if n aconvc zeron_tm then inst_thm [(cx,l)] pthm_35 |
|
758 |
else if n aconvc onen_tm then inst_thm [(cx,l)] pthm_36 |
|
759 |
else |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
760 |
let val th1 = num_conv ctxt n |
23252 | 761 |
val th2 = inst_thm [(cx,l),(cq,Thm.dest_arg (concl th1))] pthm_38 |
762 |
val (tm1,tm2) = Thm.dest_comb(concl th2) |
|
36945 | 763 |
val th3 = Thm.transitive th2 (Drule.arg_cong_rule tm1 (ppow tm2)) |
764 |
val th4 = Thm.transitive (Drule.arg_cong_rule (Thm.dest_fun tm) th1) th3 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
765 |
in Thm.transitive th4 (polynomial_mul_conv ctxt (concl th4)) |
23252 | 766 |
end |
767 |
end |
|
768 |
in fn tm => |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
769 |
if is_add(Thm.dest_arg1 tm) then ppow tm else monomial_pow_conv ctxt tm |
23252 | 770 |
end; |
771 |
||
772 |
(* Negation. *) |
|
773 |
||
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
774 |
fun polynomial_neg_conv ctxt tm = |
23252 | 775 |
let val (l,r) = Thm.dest_comb tm in |
776 |
if not (l aconvc neg_tm) then raise CTERM ("polynomial_neg_conv",[tm]) else |
|
60642
48dd1cefb4ae
simplified Thm.instantiate and derivatives: the LHS refers to non-certified variables -- this merely serves as index into already certified structures (or is ignored);
wenzelm
parents:
60352
diff
changeset
|
777 |
let val th1 = inst_thm [(cx', r)] neg_mul |
36945 | 778 |
val th2 = Thm.transitive th1 (Conv.arg1_conv semiring_mul_conv (concl th1)) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
779 |
in Thm.transitive th2 (polynomial_monomial_mul_conv ctxt (concl th2)) |
23252 | 780 |
end |
781 |
end; |
|
782 |
||
783 |
||
784 |
(* Subtraction. *) |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
785 |
fun polynomial_sub_conv ctxt tm = |
23252 | 786 |
let val (l,r) = dest_sub tm |
60642
48dd1cefb4ae
simplified Thm.instantiate and derivatives: the LHS refers to non-certified variables -- this merely serves as index into already certified structures (or is ignored);
wenzelm
parents:
60352
diff
changeset
|
787 |
val th1 = inst_thm [(cx', l), (cy', r)] sub_add |
23252 | 788 |
val (tm1,tm2) = Thm.dest_comb(concl th1) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
789 |
val th2 = Drule.arg_cong_rule tm1 (polynomial_neg_conv ctxt tm2) |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
790 |
in Thm.transitive th1 (Thm.transitive th2 (polynomial_add_conv ctxt (concl th2))) |
23252 | 791 |
end; |
792 |
||
793 |
(* Conversion from HOL term. *) |
|
794 |
||
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
795 |
fun polynomial_conv ctxt tm = |
23407
0e4452fcbeb8
normalizer conversions depend on the proof context; added functions for conversion and wrapper that sill depend on the variable ordering (_ord)
chaieb
parents:
23330
diff
changeset
|
796 |
if is_semiring_constant tm then semiring_add_conv tm |
36945 | 797 |
else if not(is_comb tm) then Thm.reflexive tm |
23252 | 798 |
else |
799 |
let val (lopr,r) = Thm.dest_comb tm |
|
800 |
in if lopr aconvc neg_tm then |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
801 |
let val th1 = Drule.arg_cong_rule lopr (polynomial_conv ctxt r) |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
802 |
in Thm.transitive th1 (polynomial_neg_conv ctxt (concl th1)) |
23252 | 803 |
end |
30866 | 804 |
else if lopr aconvc inverse_tm then |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
805 |
let val th1 = Drule.arg_cong_rule lopr (polynomial_conv ctxt r) |
36945 | 806 |
in Thm.transitive th1 (semiring_mul_conv (concl th1)) |
30866 | 807 |
end |
23252 | 808 |
else |
36945 | 809 |
if not(is_comb lopr) then Thm.reflexive tm |
23252 | 810 |
else |
811 |
let val (opr,l) = Thm.dest_comb lopr |
|
59538 | 812 |
in if opr aconvc pow_tm andalso is_number r |
23252 | 813 |
then |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
814 |
let val th1 = Drule.fun_cong_rule (Drule.arg_cong_rule opr (polynomial_conv ctxt l)) r |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
815 |
in Thm.transitive th1 (polynomial_pow_conv ctxt (concl th1)) |
23252 | 816 |
end |
61153 | 817 |
else if opr aconvc divide_tm |
30866 | 818 |
then |
61153 | 819 |
let val th1 = Thm.combination (Drule.arg_cong_rule opr (polynomial_conv ctxt l)) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
820 |
(polynomial_conv ctxt r) |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
821 |
val th2 = (Conv.rewr_conv divide_inverse then_conv polynomial_mul_conv ctxt) |
30866 | 822 |
(Thm.rhs_of th1) |
36945 | 823 |
in Thm.transitive th1 th2 |
30866 | 824 |
end |
23252 | 825 |
else |
826 |
if opr aconvc add_tm orelse opr aconvc mul_tm orelse opr aconvc sub_tm |
|
827 |
then |
|
36945 | 828 |
let val th1 = |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
829 |
Thm.combination |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
830 |
(Drule.arg_cong_rule opr (polynomial_conv ctxt l)) (polynomial_conv ctxt r) |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
831 |
val f = if opr aconvc add_tm then polynomial_add_conv ctxt |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
832 |
else if opr aconvc mul_tm then polynomial_mul_conv ctxt |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
833 |
else polynomial_sub_conv ctxt |
36945 | 834 |
in Thm.transitive th1 (f (concl th1)) |
23252 | 835 |
end |
36945 | 836 |
else Thm.reflexive tm |
23252 | 837 |
end |
838 |
end; |
|
839 |
in |
|
840 |
{main = polynomial_conv, |
|
841 |
add = polynomial_add_conv, |
|
842 |
mul = polynomial_mul_conv, |
|
843 |
pow = polynomial_pow_conv, |
|
844 |
neg = polynomial_neg_conv, |
|
845 |
sub = polynomial_sub_conv} |
|
846 |
end |
|
847 |
end; |
|
848 |
||
35410 | 849 |
val nat_exp_ss = |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
850 |
simpset_of |
69593 | 851 |
(put_simpset HOL_basic_ss \<^context> |
54249 | 852 |
addsimps (@{thms eval_nat_numeral} @ @{thms diff_nat_numeral} @ @{thms arith_simps} @ @{thms rel_simps}) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
853 |
addsimps [@{thm Let_def}, @{thm if_False}, @{thm if_True}, @{thm Nat.add_0}, @{thm add_Suc}]); |
23252 | 854 |
|
36710 | 855 |
|
856 |
(* various normalizing conversions *) |
|
857 |
||
61153 | 858 |
fun semiring_normalizers_ord_wrapper ctxt ({vars, semiring, ring, field, idom, ideal}, |
67562 | 859 |
{conv, dest_const, mk_const, is_const}) term_ord = |
23252 | 860 |
let |
861 |
val pow_conv = |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
862 |
Conv.arg_conv (Simplifier.rewrite (put_simpset nat_exp_ss ctxt)) |
23252 | 863 |
then_conv Simplifier.rewrite |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
864 |
(put_simpset HOL_basic_ss ctxt addsimps [nth (snd semiring) 31, nth (snd semiring) 34]) |
23330
01c09922ce59
Conversion for computation on constants now depends on the context
chaieb
parents:
23259
diff
changeset
|
865 |
then_conv conv ctxt |
01c09922ce59
Conversion for computation on constants now depends on the context
chaieb
parents:
23259
diff
changeset
|
866 |
val dat = (is_const, conv ctxt, conv ctxt, pow_conv) |
67562 | 867 |
in semiring_normalizers_conv vars semiring ring field dat term_ord end; |
27222 | 868 |
|
67562 | 869 |
fun semiring_normalize_ord_wrapper ctxt |
870 |
({vars, semiring, ring, field, idom, ideal}, {conv, dest_const, mk_const, is_const}) term_ord = |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
871 |
#main (semiring_normalizers_ord_wrapper ctxt |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
47108
diff
changeset
|
872 |
({vars = vars, semiring = semiring, ring = ring, field = field, idom = idom, ideal = ideal}, |
67562 | 873 |
{conv = conv, dest_const = dest_const, mk_const = mk_const, is_const = is_const}) term_ord) ctxt; |
23252 | 874 |
|
61153 | 875 |
fun semiring_normalize_wrapper ctxt data = |
67562 | 876 |
semiring_normalize_ord_wrapper ctxt data Thm.term_ord; |
23407
0e4452fcbeb8
normalizer conversions depend on the proof context; added functions for conversion and wrapper that sill depend on the variable ordering (_ord)
chaieb
parents:
23330
diff
changeset
|
877 |
|
0e4452fcbeb8
normalizer conversions depend on the proof context; added functions for conversion and wrapper that sill depend on the variable ordering (_ord)
chaieb
parents:
23330
diff
changeset
|
878 |
fun semiring_normalize_ord_conv ctxt ord tm = |
36700
9b85b9d74b83
dropped auxiliary method sring_norm; integrated normalizer.ML and normalizer_data.ML
haftmann
parents:
35410
diff
changeset
|
879 |
(case match ctxt tm of |
36945 | 880 |
NONE => Thm.reflexive tm |
23407
0e4452fcbeb8
normalizer conversions depend on the proof context; added functions for conversion and wrapper that sill depend on the variable ordering (_ord)
chaieb
parents:
23330
diff
changeset
|
881 |
| SOME res => semiring_normalize_ord_wrapper ctxt res ord tm); |
61153 | 882 |
|
67562 | 883 |
fun semiring_normalize_conv ctxt = semiring_normalize_ord_conv ctxt Thm.term_ord; |
23252 | 884 |
|
885 |
end; |