src/HOL/Tools/transfer.ML

+(*  Author:     Amine Chaieb, University of Cambridge, 2009
+                Jeremy Avigad, Carnegie Mellon University
+*)
+
+signature TRANSFER =
+sig
+  type data
+  type entry
+  val get: Proof.context -> data
+  val del: attribute
+  val setup: theory -> theory
+end;
+
+structure Transfer : TRANSFER =
+struct
+
+val eq_thm = Thm.eq_thm;
+
+type entry = {inj : thm list, emb : thm list, ret : thm list, cong : thm list,
+  guess : bool, hints : string list}; 
+type data = simpset * (thm * entry) list;
+
+structure Data = GenericDataFun
+(
+  type T = data;
+  val empty = (HOL_ss, []);
+  val extend  = I;
+  fun merge _ ((ss1, e1), (ss2, e2)) =
+    (merge_ss (ss1, ss2), AList.merge eq_thm (K true) (e1, e2));
+);
+
+val get = Data.get o Context.Proof;
+
+fun del_data key = apsnd (remove (eq_fst eq_thm) (key, []));
+
+val del = Thm.declaration_attribute (Data.map o del_data);
+val add_ss = Thm.declaration_attribute 
+   (fn th => Data.map (fn (ss,data) => (ss addsimps [th], data)));
+
+val del_ss = Thm.declaration_attribute 
+   (fn th => Data.map (fn (ss,data) => (ss delsimps [th], data)));
+
+val transM_pat = (Thm.dest_arg1 o Thm.dest_arg o cprop_of) @{thm TransferMorphism_def};
+
+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 C f x y = f y x
+
+fun simpset_of_entry injonly {inj = inj, emb = emb, ret = ret, cong = cg, guess = g, hints = hints} = 
+ HOL_ss addsimps inj addsimps (if injonly then [] else emb@ret) addcongs cg;
+
+fun basic_transfer_rule injonly a0 D0 e 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 (fst (fst i) mem_string leave)) (Term.add_vars (prop_of th) [])
+  val (ins, ctxt'') = Variable.variant_fixes (map (fst o fst) ns) ctxt'
+  val cns = map ((cterm_of o ProofContext.theory_of) ctxt'' o Var) ns
+  val cfis = map ((cterm_of o ProofContext.theory_of) ctxt'' 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 (C implies_elim) hs (fold_rev implies_intr (map cprop_of hs) th1)
+  val th3 = Simplifier.asm_full_simplify (Simplifier.context ctxt''' (simpset_of_entry injonly e)) 
+                                         (fold_rev implies_intr (map cprop_of hs) th2)
+in hd (Variable.export ctxt''' ctxt0 [th3]) end;
+
+local
+fun transfer_ruleh a D leave ctxt th = 
+ let val (ss,al) = get ctxt
+     val a0 = cterm_of (ProofContext.theory_of ctxt) a
+     val D0 = cterm_of (ProofContext.theory_of ctxt) D
+     fun h (th', e) = let val (a',D') = (Thm.dest_binop o Thm.dest_arg o cprop_of) th' 
+                 in if a0 aconvc a' andalso D0 aconvc D' then SOME e else NONE
+                 end
+ in case get_first h al of
+      SOME e => basic_transfer_rule false a0 D0 e leave ctxt th
+    | NONE => error "Transfer: corresponding instance not found in context-data"
+ end
+in fun transfer_rule (a,D) leave (gctxt,th) = 
+   (gctxt, transfer_ruleh a D leave (Context.proof_of gctxt) th)
+end;
+
+fun  splits P [] = []
+   | splits P (xxs as (x::xs)) = 
+    let val pss = filter (P x) xxs
+        val qss = filter_out (P x) xxs
+    in if null pss then [qss] else if null qss then [pss] else pss:: splits P qss
+    end
+
+fun all_transfers leave (gctxt,th) = 
+ let 
+  val ctxt = Context.proof_of gctxt
+  val tys = map snd (Term.add_vars (prop_of th) [])
+  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 Thm.dest_binop o Thm.dest_arg o cprop_of
+  val get_aD = Thm.dest_binop o Thm.dest_arg o cprop_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 (get_aD k, ss) 
+                                  else NONE) (snd (get ctxt))) tyss
+  val _ = if null insts then error "Transfer guesser: there were no possible instances, use direction: in order to provide a direction" else ()
+  val ths = map  (fn ((a,D),e) => basic_transfer_rule false a D e leave ctxt th) insts
+  val cth = Conjunction.intr_balanced ths
+ in (gctxt, cth)
+ end;
+
+fun transfer_rule_by_hint ls leave (gctxt,th) = 
+ let 
+  val ctxt = Context.proof_of gctxt
+  val get_aD = Thm.dest_binop o Thm.dest_arg o cprop_of
+  val insts = 
+    map_filter (fn (k,e) => if exists (fn l => l mem_string (#hints e)) ls 
+          then SOME (get_aD k, e) else NONE)
+        (snd (get ctxt))
+  val _ = if null insts then error "Transfer: No labels provided are stored in the context" else ()
+  val ths = map  (fn ((a,D),e) => basic_transfer_rule false a D e leave ctxt th) insts
+  val cth = Conjunction.intr_balanced ths
+ in (gctxt, cth)
+ end;
+
+
+fun transferred_attribute ls NONE leave = 
+         if null ls then all_transfers leave else transfer_rule_by_hint ls leave
+  | transferred_attribute _ (SOME (a,D)) leave = transfer_rule (a,D) leave
+
+                                                    (* Add data to the context *)
+fun gen_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})
+ = 
+ 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 = : string*string -> bool) hints0 
+            (hints1 union_string hints2)}
+ end;
+
+local
+ val h = curry (merge Thm.eq_thm)
+in
+fun merge_entries ({inj = inj1, emb = emb1, ret = ret1, cong = cg1, guess = g1, hints = hints1}, 
+                   {inj = inj2, emb = emb2, ret = ret2, cong = cg2, guess = g2, hints = hints2}) = 
+    {inj = h inj1 inj2, emb = h emb1 emb2, ret = h ret1 ret2, cong = h cg1 cg2, guess = g1 andalso g2, hints = hints1 union_string hints2}
+end; 
+
+fun add ((inja,injd), (emba,embd), (reta,retd), (cga,cgd), g, (hintsa, hintsd)) =
+  Thm.declaration_attribute (fn key => fn context => context |> Data.map
+   (fn (ss, al) => 
+     let
+      val _ = ((let val _ = Thm.match (transM_pat, (Thm.dest_arg o cprop_of) key) 
+                in 0 end) 
+                handle MATCH => error "Attribute expected Theorem of the form : TransferMorphism A a B b")
+      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 (a0,D0) = (Thm.dest_binop o Thm.dest_arg o cprop_of) key
+             val ctxt0 = ProofContext.init (Thm.theory_of_thm key)
+             val inj' = if null inja then #inj (case AList.lookup eq_thm al key of SOME e => e | NONE => error "Transfer: can not 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 => basic_transfer_rule 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 (ss, merge_update eq_thm (gen_merge_entries ed) (key, entry) al)
+    end));
+
+
+
+(* concrete syntax *)
+
+local
+
+fun keyword k = Scan.lift (Args.$$$ k) >> K ()
+fun keywordC k = Scan.lift (Args.$$$ 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 = keywordC congN || keywordC injN || keywordC embedN || keywordC returnN || keywordC directionN || keywordC modeN || keywordC delN || keywordC labelsN || keywordC leavingN
+
+val thms = Scan.repeat (Scan.unless any_keyword Attrib.multi_thm) >> flat
+val terms = thms >> map Drule.dest_term
+val types = thms >> (Logic.dest_type o HOLogic.dest_Trueprop o prop_of o hd) 
+val name = Scan.lift Args.name
+val names = Scan.repeat (Scan.unless any_keyword name)
+fun optional scan = Scan.optional scan []
+fun optional2 scan = Scan.optional scan ([],[])
+
+val mode = keywordC modeN |-- ((Scan.lift (Args.$$$ manualN) >> K false) || (Scan.lift (Args.$$$ automaticN) >> K true))
+val inj = (keywordC injN |-- thms) -- optional (keywordC delN |-- thms)
+val embed = (keywordC embedN |-- thms) -- optional (keywordC delN |-- thms)
+val return = (keywordC returnN |-- thms) -- optional (keywordC delN |-- thms)
+val cong = (keywordC congN |-- thms) -- optional (keywordC delN |-- thms)
+val addscan = Scan.unless any_keyword (keyword addN)
+val labels = (keywordC labelsN |-- names) -- optional (keywordC delN |-- names)
+val entry = Scan.optional mode true -- optional2 inj -- optional2 embed -- optional2 return -- optional2 cong -- optional2 labels
+
+val transf_add = addscan |-- entry
+in
+
+val install_att_syntax =
+  (Scan.lift (Args.$$$ delN >> K del) ||
+    transf_add
+    >> (fn (((((g, inj), embed), ret), cg), hints) => add (inj, embed, ret, cg, g, hints)))
+
+val transferred_att_syntax = (optional names -- Scan.option (keywordC directionN |-- (Args.term -- Args.term))
+  -- optional (keywordC leavingN |-- names) >> (fn ((hints, aD),leave) => transferred_attribute hints aD leave));
+
+end;
+
+
+(* theory setup *)
+
+val setup =
+  Attrib.setup @{binding transfer} install_att_syntax
+    "Installs transfer data" #>
+  Attrib.setup @{binding transfer_simps} (Attrib.add_del add_ss del_ss)
+    "simp rules for transfer" #>
+  Attrib.setup @{binding transferred} transferred_att_syntax
+    "Transfers theorems";
+
+end;