diff -r 41137dc935ff -r 8193bbaa07fe Nominal-General/nominal_thmdecls.ML --- a/Nominal-General/nominal_thmdecls.ML Sun Nov 14 12:09:14 2010 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,237 +0,0 @@ -(* Title: nominal_thmdecls.ML - Author: Christian Urban - - Infrastructure for the lemma collection "eqvts". - - Provides the attributes [eqvt] and [eqvt_raw], and the theorem - lists eqvts and eqvts_raw. The first attribute will store the - theorem in the eqvts list and also in the eqvts_raw list. For - the latter the theorem is expected to be of the form - - p o (c x1 x2 ...) = c (p o x1) (p o x2) ... (1) - - or - - c x1 x2 ... ==> c (p o x1) (p o x2) ... (2) - - and it is stored in the form - - p o c == c - - The [eqvt_raw] attribute just adds the theorem to eqvts_raw. - - TODO: In case of the form in (2) one should also - add the equational form to eqvts -*) - -signature NOMINAL_THMDECLS = -sig - val eqvt_add: attribute - val eqvt_del: attribute - val eqvt_raw_add: attribute - val eqvt_raw_del: attribute - val setup: theory -> theory - val get_eqvts_thms: Proof.context -> thm list - val get_eqvts_raw_thms: Proof.context -> thm list - val eqvt_transform: Proof.context -> thm -> thm - val is_eqvt: Proof.context -> term -> bool -end; - -structure Nominal_ThmDecls: NOMINAL_THMDECLS = -struct - -structure EqvtData = Generic_Data -( type T = thm Item_Net.T; - val empty = Thm.full_rules; - val extend = I; - val merge = Item_Net.merge); - -structure EqvtRawData = Generic_Data -( type T = thm Termtab.table; - val empty = Termtab.empty; - val extend = I; - val merge = Termtab.merge (K true)); - -val eqvts = Item_Net.content o EqvtData.get; -val eqvts_raw = map snd o Termtab.dest o EqvtRawData.get; - -val get_eqvts_thms = eqvts o Context.Proof; -val get_eqvts_raw_thms = eqvts_raw o Context.Proof; - -val add_thm = EqvtData.map o Item_Net.update; -val del_thm = EqvtData.map o Item_Net.remove; - -fun add_raw_thm thm = - case prop_of thm of - Const ("==", _) $ _ $ (c as Const _) => EqvtRawData.map (Termtab.update (c, thm)) - | _ => raise THM ("Theorem must be a meta-equality where the right-hand side is a constant.", 0, [thm]) - -fun del_raw_thm thm = - case prop_of thm of - Const ("==", _) $ _ $ (c as Const _) => EqvtRawData.map (Termtab.delete c) - | _ => raise THM ("Theorem must be a meta-equality where the right-hand side is a constant.", 0, [thm]) - -fun is_eqvt ctxt trm = - case trm of - (c as Const _) => Termtab.defined (EqvtRawData.get (Context.Proof ctxt)) c - | _ => raise TERM ("Term must be a constsnt.", [trm]) - - - -(** transformation of eqvt lemmas **) - -fun get_perms trm = - case trm of - Const (@{const_name permute}, _) $ _ $ (Bound _) => - raise TERM ("get_perms called on bound", [trm]) - | Const (@{const_name permute}, _) $ p $ _ => [p] - | t $ u => get_perms t @ get_perms u - | Abs (_, _, t) => get_perms t - | _ => [] - -fun put_perm p trm = - case trm of - Bound _ => trm - | Const _ => trm - | t $ u => put_perm p t $ put_perm p u - | Abs (x, ty, t) => Abs (x, ty, put_perm p t) - | _ => mk_perm p trm - -(* tests whether there is a disagreement between the permutations, - and that there is at least one permutation *) -fun is_bad_list [] = true - | is_bad_list [_] = false - | is_bad_list (p::q::ps) = if p = q then is_bad_list (q::ps) else true - - -(* transforms equations into the "p o c == c"-form - from p o (c x1 ...xn) = c (p o x1) ... (p o xn) *) - -fun eqvt_transform_eq_tac thm = -let - val ss_thms = @{thms permute_minus_cancel permute_prod.simps split_paired_all} -in - REPEAT o FIRST' - [CHANGED o simp_tac (HOL_basic_ss addsimps ss_thms), - rtac (thm RS @{thm trans}), - rtac @{thm trans[OF permute_fun_def]} THEN' rtac @{thm ext}] -end - -fun eqvt_transform_eq ctxt thm = - let - val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm)) - handle TERM _ => error "Equivariance lemma must be an equality." - val (p, t) = dest_perm lhs - handle TERM _ => error "Equivariance lemma is not of the form p \ c... = c..." - - val ps = get_perms rhs handle TERM _ => [] - val (c, c') = (head_of t, head_of rhs) - val msg = "Equivariance lemma is not of the right form " - in - if c <> c' - then error (msg ^ "(constants do not agree).") - else if is_bad_list (p :: ps) - then error (msg ^ "(permutations do not agree).") - else if not (rhs aconv (put_perm p t)) - then error (msg ^ "(arguments do not agree).") - else if is_Const t - then safe_mk_equiv thm - else - let - val goal = HOLogic.mk_Trueprop (HOLogic.mk_eq (mk_perm p c, c)) - val ([goal', p'], ctxt') = Variable.import_terms false [goal, p] ctxt - in - Goal.prove ctxt [] [] goal' (fn _ => eqvt_transform_eq_tac thm 1) - |> singleton (ProofContext.export ctxt' ctxt) - |> safe_mk_equiv - |> zero_var_indexes - end - end - -(* transforms equations into the "p o c == c"-form - from R x1 ...xn ==> R (p o x1) ... (p o xn) *) - -fun eqvt_transform_imp_tac ctxt p p' thm = - let - val thy = ProofContext.theory_of ctxt - val cp = Thm.cterm_of thy p - val cp' = Thm.cterm_of thy (mk_minus p') - val thm' = Drule.cterm_instantiate [(cp, cp')] thm - val simp = HOL_basic_ss addsimps @{thms permute_minus_cancel(2)} - in - EVERY' [rtac @{thm iffI}, dtac @{thm permute_boolE}, rtac thm, atac, - rtac @{thm permute_boolI}, dtac thm', full_simp_tac simp] - end - -fun eqvt_transform_imp ctxt thm = - let - val (prem, concl) = pairself HOLogic.dest_Trueprop (Logic.dest_implies (prop_of thm)) - val (c, c') = (head_of prem, head_of concl) - val ps = get_perms concl handle TERM _ => [] - val p = try hd ps - val msg = "Equivariance lemma is not of the right form " - in - if c <> c' - then error (msg ^ "(constants do not agree).") - else if is_bad_list ps - then error (msg ^ "(permutations do not agree).") - else if not (concl aconv (put_perm (the p) prem)) - then error (msg ^ "(arguments do not agree).") - else - let - val prem' = mk_perm (the p) prem - val goal = HOLogic.mk_Trueprop (HOLogic.mk_eq (prem', concl)) - val ([goal', p'], ctxt') = Variable.import_terms false [goal, the p] ctxt - in - Goal.prove ctxt' [] [] goal' - (fn _ => eqvt_transform_imp_tac ctxt' (the p) p' thm 1) - |> singleton (ProofContext.export ctxt' ctxt) - end - end - -fun eqvt_transform ctxt thm = - case (prop_of thm) of - @{const "Trueprop"} $ (Const (@{const_name "HOL.eq"}, _) $ - (Const (@{const_name "permute"}, _) $ _ $ _) $ _) => - eqvt_transform_eq ctxt thm - | @{const "==>"} $ (@{const "Trueprop"} $ _) $ (@{const "Trueprop"} $ _) => - eqvt_transform_imp ctxt thm |> eqvt_transform_eq ctxt - | _ => raise error "Only _ = _ and _ ==> _ cases are implemented." - - -(** attributes **) - -val eqvt_add = Thm.declaration_attribute - (fn thm => fn context => - let - val thm' = eqvt_transform (Context.proof_of context) thm - in - context |> add_thm thm |> add_raw_thm thm' - end) - -val eqvt_del = Thm.declaration_attribute - (fn thm => fn context => - let - val thm' = eqvt_transform (Context.proof_of context) thm - in - context |> del_thm thm |> del_raw_thm thm' - end) - -val eqvt_raw_add = Thm.declaration_attribute add_raw_thm; -val eqvt_raw_del = Thm.declaration_attribute del_raw_thm; - - -(** setup function **) - -val setup = - Attrib.setup @{binding "eqvt"} (Attrib.add_del eqvt_add eqvt_del) - (cat_lines ["Declaration of equivariance lemmas - they will automtically be", - "brought into the form p o c == c"]) #> - Attrib.setup @{binding "eqvt_raw"} (Attrib.add_del eqvt_raw_add eqvt_raw_del) - (cat_lines ["Declaration of equivariance lemmas - no", - "transformation is performed"]) #> - Global_Theory.add_thms_dynamic (@{binding "eqvts"}, eqvts) #> - Global_Theory.add_thms_dynamic (@{binding "eqvts_raw"}, eqvts_raw); - - -end;