author | wenzelm |
Tue, 21 Mar 2000 00:18:54 +0100 | |
changeset 8543 | f54926bded7b |
parent 8109 | aca11f954993 |
child 8614 | 30cc975727f1 |
permissions | -rw-r--r-- |
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The 'obtain' language element -- achieves (eliminated) existential
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(* Title: Pure/Isar/obtain.ML |
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The 'obtain' language element -- achieves (eliminated) existential
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ID: $Id$ |
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The 'obtain' language element -- achieves (eliminated) existential
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Author: Markus Wenzel, TU Muenchen |
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The 'obtain' language element -- generalized existence at the level of |
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proof texts. |
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The common case: |
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<goal_facts> |
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have/show C |
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obtain a in P[a] <proof> == |
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<goal_facts> |
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have/show C |
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proof succeed |
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def thesis == C |
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presume that: !!a. P a ==> thesis |
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from goal_facts show thesis <proof> |
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next |
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fix a |
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assume P a |
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The 'obtain' language element -- achieves (eliminated) existential
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The general case: |
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<goal_facts> |
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have/show !!x. G x ==> C x |
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obtain a in P[a] <proof> == |
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<goal_facts> |
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have/show !!x. G x ==> C x |
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proof succeed |
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fix x |
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assume hyps: G x |
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def thesis == C x |
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presume that: !!a. P a ==> thesis |
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from goal_facts show thesis <proof> |
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next |
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fix a |
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assume P a |
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*) |
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signature OBTAIN_DATA = |
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sig |
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val that_atts: Proof.context attribute list |
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end; |
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signature OBTAIN = |
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sig |
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val obtain: ((string list * string option) * Comment.text) list |
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* ((string * Args.src list * (string * (string list * string list)) list) |
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* Comment.text) list -> ProofHistory.T -> ProofHistory.T |
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val obtain_i: ((string list * typ option) * Comment.text) list |
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* ((string * Proof.context attribute list * (term * (term list * term list)) list) |
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* Comment.text) list -> ProofHistory.T -> ProofHistory.T |
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end; |
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functor ObtainFun(Data: OBTAIN_DATA): OBTAIN = |
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struct |
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(** obtain(_i) **) |
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val thatN = "that"; |
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val hypsN = "hyps"; |
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fun gen_obtain prep_vars prep_propp prep_att (raw_vars, raw_asms) state = |
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let |
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val _ = Proof.assert_backward state; |
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(*obtain vars*) |
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val (vars_ctxt, vars) = |
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foldl_map prep_vars (Proof.context_of state, map Comment.ignore raw_vars); |
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val xs = flat (map fst vars); |
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(*obtain asms*) |
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fun prep_asm (ctxt, (name, src, raw_propps)) = |
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let |
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val atts = map (prep_att (ProofContext.theory_of ctxt)) src; |
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val (ctxt', propps) = foldl_map prep_propp (ctxt, raw_propps); |
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in (ctxt', (name, atts, propps)) end; |
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val (asms_ctxt, asms) = foldl_map prep_asm (vars_ctxt, map Comment.ignore raw_asms); |
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val asm_props = flat (map (map fst o #3) asms); |
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val _ = ProofContext.warn_extra_tfrees vars_ctxt asms_ctxt; |
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(*thesis*) |
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val (prop, (goal_facts, goal)) = Proof.get_goal state; |
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val parms = Logic.strip_params prop; |
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val parm_names = Term.variantlist (map #1 parms, Term.add_term_names (prop, xs)); |
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val parm_types = map #2 parms; |
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val parm_vars = map Library.single parm_names ~~ map Some parm_types; |
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val frees = map2 Free (parm_names, parm_types); |
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val rev_frees = rev frees; |
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val hyps = map (fn t => Term.subst_bounds (rev_frees, t)) (Logic.strip_assums_hyp prop); |
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val concl = Term.subst_bounds (rev_frees, Logic.strip_assums_concl prop); |
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val ((thesis_name, thesis_term), atomic_thesis) = AutoBind.atomic_thesis concl; |
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(*that_prop*) |
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fun find_free x t = |
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(case Proof.find_free t x of Some (Free a) => Some a | _ => None); |
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fun occs_var x = Library.get_first (find_free x) asm_props; |
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val that_prop = |
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Term.list_all_free (mapfilter occs_var xs, Logic.list_implies (asm_props, atomic_thesis)); |
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fun after_qed st = |
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st |
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|> Proof.next_block |
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|> Proof.fix_i vars |
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|> Proof.assume_i asms |
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|> Seq.single; |
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in |
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state |
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|> Method.proof (Some (Method.Basic (K Method.succeed))) |
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|> Seq.map (fn st => st |
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|> Proof.fix_i parm_vars |
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|> Proof.assume_i [(hypsN, [], map (rpair ([], [])) hyps)] |
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|> LocalDefs.def_i "" [] ((thesis_name, None), (thesis_term, [])) |
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|> Proof.presume_i [(thatN, Data.that_atts, [(that_prop, ([], []))])] |
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|> Proof.from_facts goal_facts |
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|> Proof.show_i after_qed "" [] (atomic_thesis, ([], []))) |
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end; |
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val obtain = ProofHistory.applys o |
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(gen_obtain ProofContext.read_vars ProofContext.read_propp Attrib.local_attribute); |
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val obtain_i = ProofHistory.applys o |
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(gen_obtain ProofContext.cert_vars ProofContext.cert_propp (K I)); |
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(** outer syntax **) |
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local structure P = OuterParse and K = OuterSyntax.Keyword in |
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val obtainP = |
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OuterSyntax.command "obtain" "generalized existence" |
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K.prf_asm_goal |
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(Scan.optional |
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(P.and_list1 (Scan.repeat1 P.name -- Scan.option (P.$$$ "::" |-- P.typ) -- P.marg_comment) |
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--| P.$$$ "where") [] -- |
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P.and_list1 ((P.opt_thm_name ":" -- Scan.repeat1 P.propp >> P.triple1) -- P.marg_comment) |
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>> (Toplevel.print oo (Toplevel.proof o obtain))); |
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val _ = OuterSyntax.add_keywords ["where"]; |
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val _ = OuterSyntax.add_parsers [obtainP]; |
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end; |
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end; |