diff -r 77e1d9f2925e -r c7d4bd9e89e0 Nominal/nominal_function_core.ML --- a/Nominal/nominal_function_core.ML Mon Jun 06 13:11:04 2011 +0100 +++ b/Nominal/nominal_function_core.ML Tue Jun 07 08:52:59 2011 +0100 @@ -7,6 +7,49 @@ Core of the nominal function package. *) + +structure Nominal_Function_Common = +struct + + +(* Configuration management *) +datatype nominal_function_opt + = Sequential + | Default of string + | DomIntros + | No_Partials + | Invariant of string + +datatype nominal_function_config = NominalFunctionConfig of + {sequential: bool, + default: string option, + domintros: bool, + partials: bool, + inv: string option} + +fun apply_opt Sequential (NominalFunctionConfig {sequential, default, domintros, partials, inv}) = + NominalFunctionConfig + {sequential=true, default=default, domintros=domintros, partials=partials, inv=inv} + | apply_opt (Default d) (NominalFunctionConfig {sequential, default, domintros, partials, inv}) = + NominalFunctionConfig + {sequential=sequential, default=SOME d, domintros=domintros, partials=partials, inv=inv} + | apply_opt DomIntros (NominalFunctionConfig {sequential, default, domintros, partials, inv}) = + NominalFunctionConfig + {sequential=sequential, default=default, domintros=true, partials=partials, inv=inv} + | apply_opt No_Partials (NominalFunctionConfig {sequential, default, domintros, partials, inv}) = + NominalFunctionConfig + {sequential=sequential, default=default, domintros=domintros, partials=false, inv=inv} + | apply_opt (Invariant s) (NominalFunctionConfig {sequential, default, domintros, partials, inv}) = + NominalFunctionConfig + {sequential=sequential, default=default, domintros=domintros, partials=partials, inv = SOME s} + +val nominal_default_config = + NominalFunctionConfig { sequential=false, default=NONE, + domintros=false, partials=true, inv=NONE} + +end + + signature NOMINAL_FUNCTION_CORE = sig val trace: bool Unsynchronized.ref @@ -18,7 +61,7 @@ -> local_theory -> (term (* f *) * thm (* goalstate *) - * (thm -> Nominal_Function_Common.function_result) (* continuation *) + * (thm -> Function_Common.function_result) (* continuation *) ) * local_theory end @@ -33,6 +76,7 @@ val mk_eq = HOLogic.mk_eq open Function_Lib +open Function_Common open Nominal_Function_Common datatype globals = Globals of @@ -123,6 +167,20 @@ |> HOLogic.mk_Trueprop end +fun mk_inv inv (f_trm, arg_trm) = + betapplys (inv, [arg_trm, (f_trm $ arg_trm)]) + |> HOLogic.mk_Trueprop + +fun mk_invariant (Globals {x, y, ...}) G invariant = + let + val prem = HOLogic.mk_Trueprop (G $ x $ y) + val concl = HOLogic.mk_Trueprop (betapplys (invariant, [x, y])) + in + Logic.mk_implies (prem, concl) + |> mk_forall_rename ("y", y) + |> mk_forall_rename ("x", x) + end + (** building proof obligations *) fun mk_eqvt_proof_obligation qs fvar (vs, assms, arg) = mk_eqvt_at (fvar, arg) @@ -131,18 +189,27 @@ |> curry Term.list_abs_free qs |> strip_abs_body +fun mk_inv_proof_obligation inv qs fvar (vs, assms, arg) = + mk_inv inv (fvar, arg) + |> curry Logic.list_implies (map prop_of assms) + |> curry Term.list_all_free vs + |> curry Term.list_abs_free qs + |> strip_abs_body + (** building proof obligations *) -fun mk_compat_proof_obligations domT ranT fvar f RCss glrs = +fun mk_compat_proof_obligations domT ranT fvar f RCss inv glrs = let fun mk_impl (((qs, gs, lhs, rhs), RCs), ((qs', gs', lhs', rhs'), _)) = let val shift = incr_boundvars (length qs') val eqvts_proof_obligations = map (shift o mk_eqvt_proof_obligation qs fvar) RCs + val invs_proof_obligations = map (shift o mk_inv_proof_obligation inv qs fvar) RCs in Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.eq_const domT $ shift lhs $ lhs'), HOLogic.mk_Trueprop (HOLogic.eq_const ranT $ shift rhs $ rhs')) |> fold_rev (curry Logic.mk_implies) (map shift gs @ gs') + |> fold_rev (curry Logic.mk_implies) invs_proof_obligations (* nominal *) |> fold_rev (curry Logic.mk_implies) eqvts_proof_obligations (* nominal *) |> fold_rev (fn (n,T) => fn b => Term.all T $ Abs(n,T,b)) (qs @ qs') |> curry abstract_over fvar @@ -152,7 +219,6 @@ map mk_impl (unordered_pairs (glrs ~~ RCss)) end - fun mk_completeness (Globals {x, Pbool, ...}) clauses qglrs = let fun mk_case (ClauseContext {qs, gs, lhs, ...}, (oqs, _, _, _)) = @@ -260,7 +326,7 @@ (* nominal *) (* Returns "Gsi, Gsj, lhs_i = lhs_j |-- rhs_j_f = rhs_i_f" *) (* if j < i, then turn around *) -fun get_compat_thm thy cts eqvtsi eqvtsj i j ctxi ctxj = +fun get_compat_thm thy cts eqvtsi eqvtsj invsi invsj i j ctxi ctxj = let val ClauseContext {cqs=cqsi,ags=agsi,lhs=lhsi,case_hyp=case_hypi,...} = ctxi val ClauseContext {cqs=cqsj,ags=agsj,lhs=lhsj,case_hyp=case_hypj,...} = ctxj @@ -273,6 +339,7 @@ compat (* "!!qj qi. Gsj => Gsi => lhsj = lhsi ==> rhsj = rhsi" *) |> fold Thm.forall_elim (cqsj @ cqsi) (* "Gsj => Gsi => lhsj = lhsi ==> rhsj = rhsi" *) |> fold Thm.elim_implies eqvtsj (* nominal *) + |> fold Thm.elim_implies invsj (* nominal *) |> fold Thm.elim_implies agsj |> fold Thm.elim_implies agsi |> Thm.elim_implies ((Thm.assume lhsi_eq_lhsj) RS sym) (* "Gsj, Gsi, lhsi = lhsj |-- rhsj = rhsi" *) @@ -284,6 +351,7 @@ compat (* "!!qi qj. Gsi => Gsj => lhsi = lhsj ==> rhsi = rhsj" *) |> fold Thm.forall_elim (cqsi @ cqsj) (* "Gsi => Gsj => lhsi = lhsj ==> rhsi = rhsj" *) |> fold Thm.elim_implies eqvtsi (* nominal *) + |> fold Thm.elim_implies invsi (* nominal *) |> fold Thm.elim_implies agsi |> fold Thm.elim_implies agsj |> Thm.elim_implies (Thm.assume lhsi_eq_lhsj) @@ -347,7 +415,31 @@ end (* nominal *) -fun mk_uniqueness_clause thy globals compat_store eqvts clausei clausej RLj = +fun mk_invariant_lemma thy ih_inv clause = + let + val ClauseInfo {cdata=ClauseContext {cqs, ags, case_hyp, ...}, RCs, ...} = clause + + local open Conv in + val ih_conv = arg1_conv o arg_conv o arg_conv + end + + val ih_inv_case = + Conv.fconv_rule (ih_conv (K (case_hyp RS eq_reflection))) ih_inv + + fun prep_inv (RCInfo {llRI, RIvs, CCas, ...}) = + (llRI RS ih_inv_case) + |> fold_rev (Thm.implies_intr o cprop_of) CCas + |> fold_rev (Thm.forall_intr o cterm_of thy o Free) RIvs + in + map prep_inv RCs + |> map (fold_rev (Thm.implies_intr o cprop_of) ags) + |> map (Thm.implies_intr (cprop_of case_hyp)) + |> map (fold_rev Thm.forall_intr cqs) + |> map (Thm.close_derivation) + end + +(* nominal *) +fun mk_uniqueness_clause thy globals compat_store eqvts invs clausei clausej RLj = let val Globals {h, y, x, fvar, ...} = globals val ClauseInfo {no=i, cdata=cctxi as ClauseContext {ctxt=ctxti, lhs=lhsi, case_hyp, cqs = cqsi, @@ -383,7 +475,17 @@ |> map (fold Thm.elim_implies [case_hypj']) |> map (fold Thm.elim_implies agsj') - val compat = get_compat_thm thy compat_store eqvtsi eqvtsj i j cctxi cctxj + val invsi = nth invs (i - 1) + |> map (fold Thm.forall_elim cqsi) + |> map (fold Thm.elim_implies [case_hyp]) + |> map (fold Thm.elim_implies agsi) + + val invsj = nth invs (j - 1) + |> map (fold Thm.forall_elim cqsj') + |> map (fold Thm.elim_implies [case_hypj']) + |> map (fold Thm.elim_implies agsj') + + val compat = get_compat_thm thy compat_store eqvtsi eqvtsj invsi invsj i j cctxi cctxj in (trans OF [case_hyp, lhsi_eq_lhsj']) (* lhs_i = lhs_j' |-- x = lhs_j' *) @@ -402,7 +504,8 @@ end (* nominal *) -fun mk_uniqueness_case thy globals G f ihyp ih_intro G_cases compat_store clauses replems eqvtlems clausei = +fun mk_uniqueness_case thy globals G f ihyp ih_intro G_cases compat_store clauses replems eqvtlems invlems + clausei = let val Globals {x, y, ranT, fvar, ...} = globals val ClauseInfo {cdata = ClauseContext {lhs, rhs, cqs, ags, case_hyp, ...}, lGI, RCs, ...} = clausei @@ -421,7 +524,7 @@ val G_lhs_y = Thm.assume (cterm_of thy (HOLogic.mk_Trueprop (G $ lhs $ y))) val unique_clauses = - map2 (mk_uniqueness_clause thy globals compat_store eqvtlems clausei) clauses replems + map2 (mk_uniqueness_clause thy globals compat_store eqvtlems invlems clausei) clauses replems fun elim_implies_eta A AB = Thm.compose_no_flatten true (A, 0) 1 AB |> Seq.list_of |> the_single @@ -459,7 +562,7 @@ (* nominal *) -fun prove_stuff ctxt globals G f R clauses complete compat compat_store G_elim G_eqvt f_def = +fun prove_stuff ctxt globals G f R clauses complete compat compat_store G_elim G_eqvt invariant f_def = let val Globals {h, domT, ranT, x, ...} = globals val thy = ProofContext.theory_of ctxt @@ -476,17 +579,21 @@ val ih_elim = ihyp_thm RS (f_def RS ex1_implies_un) |> instantiate' [] [NONE, SOME (cterm_of thy h)] val ih_eqvt = ihyp_thm RS (G_eqvt RS (f_def RS @{thm fundef_ex1_eqvt_at})) - + val ih_inv = ihyp_thm RS (invariant COMP (f_def RS @{thm fundef_ex1_prop})) + val _ = trace_msg (K "Proving Replacement lemmas...") val repLemmas = map (mk_replacement_lemma thy h ih_elim) clauses val _ = trace_msg (K "Proving Equivariance lemmas...") val eqvtLemmas = map (mk_eqvt_lemma thy ih_eqvt) clauses + val _ = trace_msg (K "Proving Invariance lemmas...") + val invLemmas = map (mk_invariant_lemma thy ih_inv) clauses + val _ = trace_msg (K "Proving cases for unique existence...") val (ex1s, values) = split_list (map (mk_uniqueness_case thy globals G f - ihyp ih_intro G_elim compat_store clauses repLemmas eqvtLemmas) clauses) + ihyp ih_intro G_elim compat_store clauses repLemmas eqvtLemmas invLemmas) clauses) val _ = trace_msg (K "Proving: Graph is a function") val graph_is_function = complete @@ -499,11 +606,12 @@ |> (fn it => fold (Thm.forall_intr o cterm_of thy o Var) (Term.add_vars (prop_of it) []) it) val goalstate = - Conjunction.intr (Conjunction.intr graph_is_function complete) G_eqvt + Conjunction.intr (Conjunction.intr (Conjunction.intr graph_is_function complete) invariant) G_eqvt |> Thm.close_derivation |> Goal.protect |> fold_rev (Thm.implies_intr o cprop_of) compat |> Thm.implies_intr (cprop_of complete) + |> Thm.implies_intr (cprop_of invariant) |> Thm.implies_intr (cprop_of G_eqvt) in (goalstate, values) @@ -905,9 +1013,10 @@ (* nominal *) fun prepare_nominal_function config defname [((fname, fT), mixfix)] abstract_qglrs lthy = let - val NominalFunctionConfig {domintros, default=default_opt, ...} = config + val NominalFunctionConfig {domintros, default=default_opt, inv=invariant_opt,...} = config val default_str = the_default "%x. undefined" default_opt (*FIXME dynamic scoping*) + val invariant_str = the_default "%x y. True" invariant_opt val fvar = Free (fname, fT) val domT = domain_type fT val ranT = range_type fT @@ -915,6 +1024,9 @@ val default = Syntax.parse_term lthy default_str |> Type.constraint fT |> Syntax.check_term lthy + val invariant_trm = Syntax.parse_term lthy invariant_str + |> Type.constraint ([domT, ranT] ---> @{typ bool}) |> Syntax.check_term lthy + val (globals, ctxt') = fix_globals domT ranT fvar lthy val Globals { x, h, ... } = globals @@ -957,26 +1069,29 @@ mk_completeness globals clauses abstract_qglrs |> cert |> Thm.assume val compat = - mk_compat_proof_obligations domT ranT fvar f RCss abstract_qglrs + mk_compat_proof_obligations domT ranT fvar f RCss invariant_trm abstract_qglrs |> map (cert #> Thm.assume) val G_eqvt = mk_eqvt G |> cert |> Thm.assume + val invariant = mk_invariant globals G invariant_trm |> cert |> Thm.assume + val compat_store = store_compat_thms n compat val (goalstate, values) = PROFILE "prove_stuff" (prove_stuff lthy globals G f R xclauses complete compat - compat_store G_elim G_eqvt) f_defthm + compat_store G_elim G_eqvt invariant) f_defthm fun mk_partial_rules provedgoal = let val newthy = theory_of_thm provedgoal (*FIXME*) - val ((graph_is_function, complete_thm), _) = + val (graph_is_function, complete_thm) = provedgoal + |> fst o Conjunction.elim + |> fst o Conjunction.elim |> Conjunction.elim - |>> Conjunction.elim - |>> apfst (Thm.forall_elim_vars 0) + |> apfst (Thm.forall_elim_vars 0) val f_iff = graph_is_function RS (f_defthm RS ex1_implies_iff)