(* Author: Amine Chaieb, University of Cambridge, 2009
Author: Jeremy Avigad, Carnegie Mellon University
*)
signature TRANSFER =
sig
type entry
val get: Proof.context -> (thm * entry) list
val del: thm -> Context.generic -> Context.generic
val setup: theory -> theory
end;
structure Transfer : TRANSFER =
struct
(* data administration *)
val direction_of = Thm.dest_binop o Thm.dest_arg o cprop_of;
fun check_morphism_key ctxt key =
let
val _ = (Thm.match o pairself Thm.cprop_of) (@{thm transfer_morphismI}, key)
handle Pattern.MATCH => error
("Transfer: expected theorem of the form " ^ quote (Display.string_of_thm ctxt @{thm transfer_morphismI}));
in direction_of key end;
type entry = { inj : thm list, emb : thm list, ret : thm list, cong : thm list,
guess : bool, hints : string list };
fun merge_entry ({ inj = inj1, emb = emb1, ret = ret1, cong = cong1, guess = guess1, hints = hints1 } : entry,
{ inj = inj2, emb = emb2, ret = ret2, cong = cong2, guess = guess2, hints = hints2 } : entry) =
{ inj = merge Thm.eq_thm (inj1, inj2), emb = merge Thm.eq_thm (emb1, emb2),
ret = merge Thm.eq_thm (ret1, ret2), cong = merge Thm.eq_thm (cong1, cong2),
guess = guess1 andalso guess2, hints = merge (op =) (hints1, hints2) };
structure Data = Generic_Data
(
type T = (thm * entry) list;
val empty = [];
val extend = I;
val merge = AList.join Thm.eq_thm (K merge_entry);
);
(* data lookup *)
fun get_by_direction context (a, D) =
let
val ctxt = Context.proof_of context;
val certify = Thm.cterm_of (Context.theory_of context);
val a0 = certify a;
val D0 = certify D;
fun eq_direction ((a, D), thm') =
let
val (a', D') = direction_of thm';
in a0 aconvc a' andalso D0 aconvc D' end;
in case AList.lookup eq_direction (Data.get context) (a, D) of
SOME e => ((a0, D0), e)
| NONE => error ("Transfer: no such instance: ("
^ Syntax.string_of_term ctxt a ^ ", " ^ Syntax.string_of_term ctxt D ^ ")")
end;
fun get_by_hints context hints =
let
val insts = map_filter (fn (k, e) => if exists (member (op =) (#hints e)) hints
then SOME (direction_of k, e) else NONE) (Data.get context);
val _ = if null insts then error ("Transfer: no such labels: " ^ commas (map quote hints)) else ();
in insts end;
fun splits P [] = []
| splits P (xs as (x :: _)) =
let
val (pss, qss) = List.partition (P x) xs;
in if null pss then [qss] else if null qss then [pss] else pss :: splits P qss end;
fun get_by_prop context t =
let
val tys = map snd (Term.add_vars t []);
val _ = if null tys then error "Transfer: unable to guess instance" else ();
val tyss = splits (curry Type.could_unify) tys;
val get_ty = typ_of o ctyp_of_term o fst o direction_of;
val insts = map_filter (fn tys => get_first (fn (k, ss) =>
if Type.could_unify (hd tys, range_type (get_ty k))
then SOME (direction_of k, ss)
else NONE) (Data.get context)) tyss;
val _ = if null insts then
error "Transfer: no instances, provide direction or hints explicitly" else ();
in insts end;
(* applying transfer data *)
val get = Data.get o Context.Proof;
fun transfer_thm inj_only a0 D0 {inj = inj, emb = emb, ret = ret, cong = cg, guess = g, hints = hints}
leave ctxt0 th =
let
val ([a, D], ctxt) = apfst (map Drule.dest_term o snd)
(Variable.import true (map Drule.mk_term [a0, D0]) ctxt0);
val (aT, bT) =
let val T = typ_of (ctyp_of_term a)
in (Term.range_type T, Term.domain_type T) end;
val ctxt' = (Variable.declare_term (term_of a) o Variable.declare_term (term_of D)
o Variable.declare_thm th) ctxt;
val ns = filter (fn i => Type.could_unify (snd i, aT) andalso
not (member (op =) leave (fst (fst i)))) (Term.add_vars (prop_of th) []);
val (ins, ctxt'') = Variable.variant_fixes (map (fst o fst) ns) ctxt';
val certify = Thm.cterm_of (ProofContext.theory_of ctxt'');
val cns = map (certify o Var) ns;
val cfis = map (certify o (fn n => Free (n, bT))) ins;
val cis = map (Thm.capply a) cfis
val (hs, ctxt''') = Assumption.add_assumes (map (fn ct =>
Thm.capply @{cterm "Trueprop"} (Thm.capply D ct)) cfis) ctxt'';
val th1 = Drule.cterm_instantiate (cns ~~ cis) th;
val th2 = fold Thm.elim_implies hs (fold_rev implies_intr (map cprop_of hs) th1);
val simpset = (Simplifier.context ctxt''' HOL_ss)
addsimps inj addsimps (if inj_only then [] else emb @ ret) addcongs cg;
val th3 = Simplifier.asm_full_simplify simpset
(fold_rev implies_intr (map cprop_of hs) th2);
in hd (Variable.export ctxt''' ctxt0 [th3]) end;
fun transfer_thm_multiple inj_only insts leave ctxt thm =
Conjunction.intr_balanced (map
(fn ((a, D), e) => transfer_thm false a D e leave ctxt thm) insts);
fun transfer_by_direction (a, D) leave (context, thm) =
let
val ((a0, D0), e) = get_by_direction context (a, D);
in (context, transfer_thm false a0 D0 e leave (Context.proof_of context) thm) end;
fun transfer_by_hints hints leave (context, thm) =
(context, transfer_thm_multiple false (get_by_hints context hints)
leave (Context.proof_of context) thm);
fun transfer_by_prop leave (context, thm) =
(context, transfer_thm_multiple false (get_by_prop context (Thm.prop_of thm))
leave (Context.proof_of context) thm);
fun transferred_attribute [] NONE leave = transfer_by_prop leave
| transferred_attribute hints NONE leave = transfer_by_hints hints leave
| transferred_attribute _ (SOME (a, D)) leave = transfer_by_direction (a, D) leave;
(* maintaining transfer data *)
fun merge_update eq m (k, v) [] = [(k, v)]
| merge_update eq m (k, v) ((k', v') :: al) =
if eq (k, k') then (k', m (v, v')) :: al else (k', v') :: merge_update eq m (k, v) al;
(*? fun merge_update eq m (k, v) = AList.map_entry eq k (fn v' => m (v, v'));*)
fun merge_entries {inj = inj0, emb = emb0, ret = ret0, cong = cg0, guess = g0, hints = hints0}
({inj = inj1, emb = emb1, ret = ret1, cong = cg1, guess = g1, hints = hints1},
{inj = inj2, emb = emb2, ret = ret2, cong = cg2, guess = g2, hints = hints2} : entry) =
let
fun h xs0 xs ys = subtract Thm.eq_thm xs0 (merge Thm.eq_thm (xs, ys))
in
{inj = h inj0 inj1 inj2, emb = h emb0 emb1 emb2,
ret = h ret0 ret1 ret2, cong = h cg0 cg1 cg2, guess = g1 andalso g2,
hints = subtract (op =) hints0 (union (op =) hints1 hints2) }
end;
fun add ((inja, injd), (emba, embd), (reta, retd), (cga, cgd), g, (hintsa, hintsd)) key =
Data.map (fn al =>
let
val ctxt0 = ProofContext.init (Thm.theory_of_thm key); (*FIXME*)
val (a0, D0) = check_morphism_key ctxt0 key;
val e0 = {inj = inja, emb = emba, ret = reta, cong = cga, guess = g, hints = hintsa};
val ed = {inj = injd, emb = embd, ret = retd, cong = cgd, guess = g, hints = hintsd};
val entry = if g then
let
val inj' = if null inja then #inj
(case AList.lookup Thm.eq_thm al key of SOME e => e
| NONE => error "Transfer: cannot generate return rules on the fly, either add injectivity axiom or force manual mode with mode: manual")
else inja
val ret' = merge Thm.eq_thm (reta, map
(fn th => transfer_thm true a0 D0 {inj = inj', emb = [], ret = [], cong = cga, guess = g,
hints = hintsa} [] ctxt0 th RS sym) emba);
in {inj = inja, emb = emba, ret = ret', cong = cga, guess = g, hints = hintsa} end
else e0;
in merge_update Thm.eq_thm (merge_entries ed) (key, entry) al end);
fun add_attribute args = Thm.declaration_attribute (add args);
fun del key = Data.map (remove (eq_fst Thm.eq_thm) (key, []));
val del_attribute = Thm.declaration_attribute del;
(* syntax *)
local
fun these scan = Scan.optional scan [];
fun these_pair scan = Scan.optional scan ([], []);
fun keyword k = Scan.lift (Args.$$$ k) >> K ();
fun keyword_colon k = Scan.lift (Args.$$$ k -- Args.colon) >> K ();
val congN = "cong";
val injN = "inj";
val embedN = "embed";
val returnN = "return";
val addN = "add";
val delN = "del";
val modeN = "mode";
val automaticN = "automatic";
val manualN = "manual";
val directionN = "direction";
val labelsN = "labels";
val leavingN = "leaving";
val any_keyword = keyword_colon congN || keyword_colon injN || keyword_colon embedN
|| keyword_colon returnN || keyword_colon directionN || keyword_colon modeN
|| keyword_colon delN || keyword_colon labelsN || keyword_colon leavingN;
val thms = Scan.repeat (Scan.unless any_keyword Attrib.multi_thm) >> flat;
val names = Scan.repeat (Scan.unless any_keyword (Scan.lift Args.name))
val mode = keyword_colon modeN |-- ((Scan.lift (Args.$$$ manualN) >> K false)
|| (Scan.lift (Args.$$$ automaticN) >> K true));
val inj = (keyword_colon injN |-- thms) -- these (keyword_colon delN |-- thms);
val embed = (keyword_colon embedN |-- thms) -- these (keyword_colon delN |-- thms);
val return = (keyword_colon returnN |-- thms) -- these (keyword_colon delN |-- thms);
val cong = (keyword_colon congN |-- thms) -- these (keyword_colon delN |-- thms);
val labels = (keyword_colon labelsN |-- names) -- these (keyword_colon delN |-- names);
val entry = Scan.optional mode true -- these_pair inj -- these_pair embed
-- these_pair return -- these_pair cong -- these_pair labels;
val transfer_directive = these names -- Scan.option (keyword_colon directionN
|-- (Args.term -- Args.term)) -- these (keyword_colon leavingN |-- names);
in
val transfer_syntax = (Scan.lift (Args.$$$ delN >> K del_attribute)
|| Scan.unless any_keyword (keyword addN) |-- entry
>> (fn (((((g, inj), embed), ret), cg), hints) => add_attribute (inj, embed, ret, cg, g, hints)))
val transferred_syntax = transfer_directive
>> (fn ((hints, direction), leave) => transferred_attribute hints direction leave);
end;
(* theory setup *)
val setup =
Attrib.setup @{binding transfer} transfer_syntax
"Installs transfer data" #>
Attrib.setup @{binding transferred} transferred_syntax
"Transfers theorems";
end;