(* Title: Pure/Isar/obtain.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
The 'obtain' language element -- achieves (eliminated) existential
quantification at proof command level.
The common case:
<goal_facts>
have/show C
obtain a in P[a] <proof> ==
<goal_facts>
have/show C
proof succeed
def thesis == C
presume that: !!a. P a ==> thesis
from goal_facts show thesis <proof>
next
fix a
assume P a
The general case:
<goal_facts>
have/show !!x. G x ==> C x
obtain a in P[a] <proof> ==
<goal_facts>
have/show !!x. G x ==> C x
proof succeed
fix x
assume antecedent: G x
def thesis == ?thesis_prop x
presume that: !!a. P a ==> thesis
from goal_facts show thesis <proof>
next
fix a
assume P a
TODO:
- handle general case;
*)
signature OBTAIN =
sig
val obtain: (string list * string option) list
-> (string * Proof.context attribute list * (string * (string list * string list)) list) list
-> Proof.state -> Proof.state Seq.seq
val obtain_i: (string list * typ option) list
-> (string * Proof.context attribute list * (term * (term list * term list)) list) list
-> Proof.state -> Proof.state Seq.seq
end;
structure Obtain: OBTAIN =
struct
val thatN = "that";
fun gen_obtain prep_typ prep_prop fix assume raw_vars raw_asms state =
let
val (prop, (goal_facts, goal)) = Proof.get_goal (Proof.assert_backward state);
val parms = Logic.strip_params prop;
val hyps = Logic.strip_assums_hyp prop;
val concl = Logic.strip_assums_concl prop;
val _ =
if null parms then () else raise Proof.STATE ("Cannot handle params in goal (yet)", state);
val ((thesis_name, thesis_term), atomic_thesis) = AutoBind.atomic_thesis concl;
fun fix_vars (ctxt, (xs, raw_T)) =
let
val T = apsome (prep_typ ctxt) raw_T;
val ctxt' = ProofContext.fix_i [(xs, T)] ctxt;
in (ctxt', map (ProofContext.cert_skolem ctxt') xs) end;
fun prep_asm (ctxt, (_, _, raw_propps)) =
let val ts = map (prep_prop ctxt) (map fst raw_propps);
in (ctxt |> ProofContext.declare_terms ts, ts) end;
val (fix_ctxt, skolems) = apsnd flat (foldl_map fix_vars (Proof.context_of state, raw_vars));
val (asms_ctxt, asms) = apsnd flat (foldl_map prep_asm (fix_ctxt, raw_asms));
fun find_free x t =
(case Proof.find_free t x of Some (Free a) => Some a | _ => None);
fun find_skolem x = Library.get_first (find_free x) asms;
val skolemTs = mapfilter find_skolem skolems;
val that_prop =
Logic.list_rename_params (map (Syntax.dest_skolem o #1) skolemTs,
Term.list_all_free (skolemTs, Logic.list_implies (asms, atomic_thesis)));
val presume_stateq =
state
|> Method.proof (Some (Method.Basic (K Method.succeed)))
|> Seq.map (fn st => st
|> LocalDefs.def_i "" [] ((thesis_name, None), (thesis_term, []))
|> Proof.presume_i [(thatN, [], [(that_prop, ([], []))])]);
fun after_qed st =
st
|> Proof.next_block
|> fix raw_vars (*prepared twice!*)
|> assume raw_asms (*prepared twice!*)
|> Seq.single;
in
presume_stateq
|> Seq.map (fn st => st
|> Proof.from_facts goal_facts
|> Proof.show_i after_qed "" [] (atomic_thesis, ([], []))
|> Method.refine (Method.Basic (K (Method.insert (Proof.the_facts st)))))
|> Seq.flat
end;
val obtain = gen_obtain ProofContext.read_typ ProofContext.read_prop Proof.fix Proof.assume;
val obtain_i = gen_obtain ProofContext.cert_typ ProofContext.cert_prop Proof.fix_i Proof.assume_i;
end;