author  wenzelm 
Fri, 01 Oct 1999 20:36:53 +0200  
changeset 7674  99305245f6bd 
child 7677  de2e468a42c8 
permissions  rwrr 
7674
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(* Title: Pure/Isar/obtain.ML 
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ID: $Id$ 
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Author: Markus Wenzel, TU Muenchen 
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4 

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The 'obtain' language element  achieves (eliminated) existential 
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quantification proof command level. 
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7 

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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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23 

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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 antecedent: G x 
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def thesis == ?thesis_prop 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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TODO: 
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 handle general case; 
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*) 
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signature OBTAIN = 
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sig 
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val obtain: (string list * string option) list 
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> (string * Proof.context attribute list * (string * (string list * string list)) list) list 
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> Proof.state > Proof.state Seq.seq 
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val obtain_i: (string list * typ option) list 
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> (string * Proof.context attribute list * (term * (term list * term list)) list) list 
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> Proof.state > Proof.state Seq.seq 
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end; 
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structure Obtain: OBTAIN = 
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struct 
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val thatN = "that"; 
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fun gen_obtain prep_typ prep_prop fix assume raw_vars raw_asms state = 
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let 
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val (prop, (goal_facts, goal)) = Proof.get_goal (Proof.assert_backward state); 
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val parms = Logic.strip_params prop; 
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val hyps = Logic.strip_assums_hyp prop; 
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val concl = Logic.strip_assums_concl prop; 
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val _ = 
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if null parms then () else raise Proof.STATE ("Cannot handle params in goal (yet)", state); 
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val ((thesis_name, thesis_term), atomic_thesis) = AutoBind.atomic_thesis concl; 
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fun fix_vars (ctxt, (xs, raw_T)) = 
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let 
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val T = apsome (prep_typ ctxt) raw_T; 
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val ctxt' = ProofContext.fix_i [(xs, T)] ctxt; 
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in (ctxt', map (ProofContext.cert_skolem ctxt') xs) end; 
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fun prep_asm (ctxt, (_, _, raw_propps)) = 
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let val ts = map (prep_prop ctxt) (map fst raw_propps); 
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in (ctxt > ProofContext.declare_terms ts, ts) end; 
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val (fix_ctxt, skolems) = apsnd flat (foldl_map fix_vars (Proof.context_of state, raw_vars)); 
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val (asms_ctxt, asms) = apsnd flat (foldl_map prep_asm (fix_ctxt, raw_asms)); 
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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 find_skolem x = Library.get_first (find_free x) asms; 
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val skolemTs = mapfilter find_skolem skolems; 
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val that_prop = 
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Logic.list_rename_params (map (Syntax.dest_skolem o #1) skolemTs, 
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Term.list_all_free (skolemTs, Logic.list_implies (asms, atomic_thesis))); 
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val presume_stateq = 
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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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> LocalDefs.def_i "" [] ((thesis_name, None), (thesis_term, [])) 
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> Proof.presume_i [(thatN, [], [(that_prop, ([], []))])]); 
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fun after_qed st = 
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st 
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> Proof.next_block 
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> fix raw_vars (*prepared twice!*) 
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> assume raw_asms (*prepared twice!*) 
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> Seq.single; 
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in 
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presume_stateq 
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> Seq.map (fn st => st 
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> Proof.from_facts goal_facts 
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> Proof.show_i after_qed "" [] (atomic_thesis, ([], [])) 
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> Method.refine (Method.Basic (K (Method.insert (Proof.the_facts st))))) 
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> Seq.flat 
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end; 
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val obtain = gen_obtain ProofContext.read_typ ProofContext.read_prop Proof.fix Proof.assume; 
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val obtain_i = gen_obtain ProofContext.cert_typ ProofContext.cert_prop Proof.fix_i Proof.assume_i; 
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end; 