(* Title: Pure/Isar/obtain.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
License: GPL (GNU GENERAL PUBLIC LICENSE)
The 'obtain' language element -- generalized existence at the level of
proof texts.
<chain_facts>
obtain x where "P x" <proof> ==
{
fix thesis
assume that [intro]: "!!x. P x ==> thesis"
<chain_facts> have thesis <proof (insert that)>
}
fix x assm (obtained) "P x"
*)
signature OBTAIN =
sig
val obtain: ((string list * string option) * Comment.text) list
* (((string * Args.src list) * (string * (string list * string list)) list)
* Comment.text) list -> ProofHistory.T -> ProofHistory.T
val obtain_i: ((string list * typ option) * Comment.text) list
* (((string * Proof.context attribute list) * (term * (term list * term list)) list)
* Comment.text) list -> ProofHistory.T -> ProofHistory.T
end;
structure Obtain: OBTAIN =
struct
(** disch_obtained **)
fun disch_obtained state parms rule cprops thm =
let
val {sign, prop, maxidx, ...} = Thm.rep_thm thm;
val cparms = map (Thm.cterm_of sign) parms;
val thm' = thm
|> Drule.implies_intr_list cprops
|> Drule.forall_intr_list cparms
|> Drule.forall_elim_vars (maxidx + 1);
val elim_tacs = replicate (length cprops) Proof.hard_asm_tac;
val concl = Logic.strip_assums_concl prop;
val bads = parms inter (Term.term_frees concl);
in
if not (null bads) then
raise Proof.STATE ("Conclusion contains obtained parameters: " ^
space_implode " " (map (Sign.string_of_term sign) bads), state)
else if not (ObjectLogic.is_judgment sign (Logic.strip_assums_concl prop)) then
raise Proof.STATE ("Conclusions of 'obtain' context must be object-logic judgments", state)
else (Tactic.rtac thm' THEN' RANGE elim_tacs) 1 rule
end;
(** obtain(_i) **)
val thatN = "that";
fun gen_obtain prep_vars prep_propp prep_att (raw_vars, raw_asms) state =
let
val _ = Proof.assert_forward_or_chain state;
val chain_facts = if Proof.is_chain state then Proof.the_facts state else [];
val thy = Proof.theory_of state;
val sign = Theory.sign_of thy;
(*obtain vars*)
val (vars_ctxt, vars) =
foldl_map prep_vars (Proof.context_of state, map Comment.ignore raw_vars);
val xs = flat (map fst vars);
val fix_ctxt = vars_ctxt |> ProofContext.fix_i vars;
(*obtain asms*)
val (asms_ctxt, proppss) = prep_propp (fix_ctxt, map (snd o Comment.ignore) raw_asms);
val asm_props = flat (map (map fst) proppss);
fun prep_asm ((name, src), propps) = ((name, map (prep_att thy) src), propps);
val asms = map2 prep_asm (map (fst o Comment.ignore) raw_asms, proppss);
val _ = ProofContext.warn_extra_tfrees fix_ctxt asms_ctxt;
(*that_prop*)
val thesisN = Term.variant xs AutoBind.thesisN;
val bound_thesis =
ProofContext.bind_skolem fix_ctxt [thesisN] (ObjectLogic.fixed_judgment sign thesisN);
fun occs_var x = Library.get_first (fn t =>
ProofContext.find_free t (ProofContext.get_skolem fix_ctxt x)) asm_props;
val raw_parms = map occs_var xs;
val parms = mapfilter I raw_parms;
val parm_names =
mapfilter (fn (Some (Free a), x) => Some (a, x) | _ => None) (raw_parms ~~ xs);
val that_prop =
Term.list_all_free (map #1 parm_names, Logic.list_implies (asm_props, bound_thesis))
|> Library.curry Logic.list_rename_params (map #2 parm_names);
fun export_obtained rule =
(disch_obtained state parms rule, fn _ => fn _ => []);
fun after_qed st = st
|> Proof.end_block
|> Seq.map (fn st' => st'
|> Proof.fix_i vars
|> Proof.assm_i (export_obtained (Proof.the_fact st')) asms);
in
state
|> Proof.enter_forward
|> Proof.begin_block
|> Proof.fix_i [([thesisN], None)]
|> Proof.assume_i [((thatN, [Method.intro_local]), [(that_prop, ([], []))])]
|> (fn state' =>
state'
|> Proof.from_facts chain_facts
|> Proof.have_i after_qed "" [] (bound_thesis, ([], []))
|> Method.refine (Method.Basic (K (Method.insert (Proof.the_facts state')))))
end;
val obtain = ProofHistory.applys o
(gen_obtain ProofContext.read_vars ProofContext.read_propp Attrib.local_attribute);
val obtain_i = ProofHistory.applys o
(gen_obtain ProofContext.cert_vars ProofContext.cert_propp (K I));
(** outer syntax **)
local structure P = OuterParse and K = OuterSyntax.Keyword in
val obtainP =
OuterSyntax.command "obtain" "generalized existence"
K.prf_asm_goal
(Scan.optional
(P.and_list1 (Scan.repeat1 P.name -- Scan.option (P.$$$ "::" |-- P.typ) -- P.marg_comment)
--| P.$$$ "where") [] --
P.and_list1 (P.opt_thm_name ":" -- Scan.repeat1 P.propp -- P.marg_comment)
>> (Toplevel.print oo (Toplevel.proof o obtain)));
val _ = OuterSyntax.add_keywords ["where"];
val _ = OuterSyntax.add_parsers [obtainP];
end;
end;