--- a/NEWS Wed Jan 28 10:43:31 2009 +0100
+++ b/NEWS Wed Jan 28 11:04:10 2009 +0100
@@ -193,6 +193,8 @@
*** HOL ***
+* Theory "Reflection" now resides in HOL/Library.
+
* Entry point to Word library now simply named "Word". INCOMPATIBILITY.
* Made source layout more coherent with logical distribution
--- a/src/HOL/IsaMakefile Wed Jan 28 10:43:31 2009 +0100
+++ b/src/HOL/IsaMakefile Wed Jan 28 11:04:10 2009 +0100
@@ -331,10 +331,11 @@
Library/Binomial.thy Library/Eval_Witness.thy \
Library/Code_Index.thy Library/Code_Char.thy \
Library/Code_Char_chr.thy Library/Code_Integer.thy \
- Library/Numeral_Type.thy \
+ Library/Numeral_Type.thy Library/Reflection.thy \
Library/Boolean_Algebra.thy Library/Countable.thy \
Library/RBT.thy Library/Univ_Poly.thy \
- Library/Enum.thy Library/Float.thy $(SRC)/Tools/float.ML $(SRC)/HOL/Tools/float_arith.ML
+ Library/Enum.thy Library/Float.thy $(SRC)/Tools/float.ML $(SRC)/HOL/Tools/float_arith.ML \
+ Library/reify_data.ML Library/reflection.ML
@cd Library; $(ISABELLE_TOOL) usedir $(OUT)/HOL Library
@@ -809,14 +810,14 @@
ex/Lagrange.thy ex/LocaleTest2.thy ex/MT.thy \
ex/MergeSort.thy ex/MonoidGroup.thy ex/Multiquote.thy ex/NatSum.thy \
ex/Numeral.thy ex/PER.thy ex/PresburgerEx.thy ex/Primrec.thy \
- ex/Quickcheck_Examples.thy ex/Reflection.thy ex/reflection_data.ML \
+ ex/Quickcheck_Examples.thy \
ex/ReflectionEx.thy ex/ROOT.ML ex/Recdefs.thy ex/Records.thy \
ex/Reflected_Presburger.thy ex/coopertac.ML \
ex/Refute_Examples.thy ex/SAT_Examples.thy ex/SVC_Oracle.thy \
ex/Subarray.thy ex/Sublist.thy \
ex/Sudoku.thy ex/Tarski.thy ex/Termination.thy ex/Term_Of_Syntax.thy \
ex/Unification.thy ex/document/root.bib \
- ex/document/root.tex ex/Meson_Test.thy ex/reflection.ML ex/set.thy \
+ ex/document/root.tex ex/Meson_Test.thy ex/set.thy \
ex/svc_funcs.ML ex/svc_test.thy \
ex/ImperativeQuicksort.thy \
ex/BigO_Complex.thy \
@@ -968,7 +969,7 @@
HOL-Word: HOL $(OUT)/HOL-Word
-$(OUT)/HOL-Word: $(OUT)/HOL Word/ROOT.ML Library/Infinite_Set.thy \
+$(OUT)/HOL-Word: $(OUT)/HOL Word/ROOT.ML \
Library/Boolean_Algebra.thy \
Library/Numeral_Type.thy Word/Num_Lemmas.thy Word/TdThs.thy \
Word/Size.thy Word/BinGeneral.thy Word/BinOperations.thy \
--- a/src/HOL/Library/Library.thy Wed Jan 28 10:43:31 2009 +0100
+++ b/src/HOL/Library/Library.thy Wed Jan 28 11:04:10 2009 +0100
@@ -35,6 +35,7 @@
Quicksort
Quotient
Ramsey
+ Reflection
RBT
State_Monad
Univ_Poly
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Library/Reflection.thy Wed Jan 28 11:04:10 2009 +0100
@@ -0,0 +1,45 @@
+(* Title: HOL/Library/Reflection.thy
+ Author: Amine Chaieb, TU Muenchen
+*)
+
+header {* Generic reflection and reification *}
+
+theory Reflection
+imports Main
+uses "reify_data.ML" ("reflection.ML")
+begin
+
+setup {* Reify_Data.setup *}
+
+lemma ext2: "(\<forall>x. f x = g x) \<Longrightarrow> f = g"
+ by (blast intro: ext)
+
+use "reflection.ML"
+
+method_setup reify = {* fn src =>
+ Method.syntax (Attrib.thms --
+ Scan.option (Scan.lift (Args.$$$ "(") |-- Args.term --| Scan.lift (Args.$$$ ")") )) src #>
+ (fn ((eqs, to), ctxt) => Method.SIMPLE_METHOD' (Reflection.genreify_tac ctxt (eqs @ (fst (Reify_Data.get ctxt))) to))
+*} "partial automatic reification"
+
+method_setup reflection = {*
+let
+ fun keyword k = Scan.lift (Args.$$$ k -- Args.colon) >> K ();
+ val onlyN = "only";
+ val rulesN = "rules";
+ val any_keyword = keyword onlyN || keyword rulesN;
+ val thms = Scan.repeat (Scan.unless any_keyword Attrib.multi_thm) >> flat;
+ val terms = thms >> map (term_of o Drule.dest_term);
+ fun optional scan = Scan.optional scan [];
+in fn src =>
+ Method.syntax (thms -- optional (keyword rulesN |-- thms) -- Scan.option (keyword onlyN |-- Args.term)) src #>
+ (fn (((eqs,ths),to), ctxt) =>
+ let
+ val (ceqs,cths) = Reify_Data.get ctxt
+ val corr_thms = ths@cths
+ val raw_eqs = eqs@ceqs
+ in Method.SIMPLE_METHOD' (Reflection.reflection_tac ctxt corr_thms raw_eqs to)
+ end) end
+*} "reflection method"
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Library/reflection.ML Wed Jan 28 11:04:10 2009 +0100
@@ -0,0 +1,327 @@
+(* Title: HOL/Library/reflection.ML
+ Author: Amine Chaieb, TU Muenchen
+
+A trial for automatical reification.
+*)
+
+signature REFLECTION =
+sig
+ val genreify_tac: Proof.context -> thm list -> term option -> int -> tactic
+ val reflection_tac: Proof.context -> thm list -> thm list -> term option -> int -> tactic
+ val gen_reflection_tac: Proof.context -> (cterm -> thm)
+ -> thm list -> thm list -> term option -> int -> tactic
+end;
+
+structure Reflection : REFLECTION =
+struct
+
+val ext2 = @{thm ext2};
+val nth_Cons_0 = @{thm nth_Cons_0};
+val nth_Cons_Suc = @{thm nth_Cons_Suc};
+
+ (* Make a congruence rule out of a defining equation for the interpretation *)
+ (* th is one defining equation of f, i.e.
+ th is "f (Cp ?t1 ... ?tn) = P(f ?t1, .., f ?tn)" *)
+ (* Cp is a constructor pattern and P is a pattern *)
+
+ (* The result is:
+ [|?A1 = f ?t1 ; .. ; ?An= f ?tn |] ==> P (?A1, .., ?An) = f (Cp ?t1 .. ?tn) *)
+ (* + the a list of names of the A1 .. An, Those are fresh in the ctxt*)
+
+
+fun mk_congeq ctxt fs th =
+ let
+ val (f as Const(fN,fT)) = th |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq
+ |> fst |> strip_comb |> fst
+ val thy = ProofContext.theory_of ctxt
+ val cert = Thm.cterm_of thy
+ val (((_,_),[th']), ctxt') = Variable.import_thms true [th] ctxt
+ val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop (Thm.prop_of th'))
+ fun add_fterms (t as t1 $ t2) =
+ if exists (fn f => Term.could_unify (t |> strip_comb |> fst, f)) fs then insert (op aconv) t
+ else add_fterms t1 #> add_fterms t2
+ | add_fterms (t as Abs(xn,xT,t')) =
+ if exists_Const (fn (c, _) => c = fN) t then (fn _ => [t]) else (fn _ => [])
+ | add_fterms _ = I
+ val fterms = add_fterms rhs []
+ val (xs, ctxt'') = Variable.variant_fixes (replicate (length fterms) "x") ctxt'
+ val tys = map fastype_of fterms
+ val vs = map Free (xs ~~ tys)
+ val env = fterms ~~ vs
+ (* FIXME!!!!*)
+ fun replace_fterms (t as t1 $ t2) =
+ (case AList.lookup (op aconv) env t of
+ SOME v => v
+ | NONE => replace_fterms t1 $ replace_fterms t2)
+ | replace_fterms t = (case AList.lookup (op aconv) env t of
+ SOME v => v
+ | NONE => t)
+
+ fun mk_def (Abs(x,xT,t),v) = HOLogic.mk_Trueprop ((HOLogic.all_const xT)$ Abs(x,xT,HOLogic.mk_eq(v$(Bound 0), t)))
+ | mk_def (t, v) = HOLogic.mk_Trueprop (HOLogic.mk_eq (v, t))
+ fun tryext x = (x RS ext2 handle THM _ => x)
+ val cong = (Goal.prove ctxt'' [] (map mk_def env)
+ (HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, replace_fterms rhs)))
+ (fn x => LocalDefs.unfold_tac (#context x) (map tryext (#prems x))
+ THEN rtac th' 1)) RS sym
+
+ val (cong' :: vars') =
+ Variable.export ctxt'' ctxt (cong :: map (Drule.mk_term o cert) vs)
+ val vs' = map (fst o fst o Term.dest_Var o Thm.term_of o Drule.dest_term) vars'
+
+ in (vs', cong') end;
+ (* congs is a list of pairs (P,th) where th is a theorem for *)
+ (* [| f p1 = A1; ...; f pn = An|] ==> f (C p1 .. pn) = P *)
+val FWD = curry (op OF);
+
+ (* da is the decomposition for atoms, ie. it returns ([],g) where g
+ returns the right instance f (AtC n) = t , where AtC is the Atoms
+ constructor and n is the number of the atom corresponding to t *)
+
+(* Generic decomp for reification : matches the actual term with the
+rhs of one cong rule. The result of the matching guides the
+proof synthesis: The matches of the introduced Variables A1 .. An are
+processed recursively
+ The rest is instantiated in the cong rule,i.e. no reification is needed *)
+
+exception REIF of string;
+
+val bds = ref ([]: (typ * ((term list) * (term list))) list);
+
+fun index_of t =
+ let
+ val tt = HOLogic.listT (fastype_of t)
+ in
+ (case AList.lookup Type.could_unify (!bds) tt of
+ NONE => error "index_of : type not found in environements!"
+ | SOME (tbs,tats) =>
+ let
+ val i = find_index_eq t tats
+ val j = find_index_eq t tbs
+ in (if j= ~1 then
+ if i= ~1
+ then (bds := AList.update Type.could_unify (tt,(tbs,tats@[t])) (!bds) ;
+ length tbs + length tats)
+ else i else j)
+ end)
+ end;
+
+fun dest_listT (Type ("List.list", [T])) = T;
+
+fun decomp_genreif da cgns (t,ctxt) =
+ let
+ val thy = ProofContext.theory_of ctxt
+ val cert = cterm_of thy
+ fun tryabsdecomp (s,ctxt) =
+ (case s of
+ Abs(xn,xT,ta) =>
+ (let
+ val ([xn],ctxt') = Variable.variant_fixes ["x"] ctxt
+ val (xn,ta) = variant_abs (xn,xT,ta)
+ val x = Free(xn,xT)
+ val _ = (case AList.lookup Type.could_unify (!bds) (HOLogic.listT xT)
+ of NONE => error "tryabsdecomp: Type not found in the Environement"
+ | SOME (bsT,atsT) =>
+ (bds := AList.update Type.could_unify (HOLogic.listT xT, ((x::bsT), atsT)) (!bds)))
+ in ([(ta, ctxt')] ,
+ fn [th] => ((let val (bsT,asT) = the(AList.lookup Type.could_unify (!bds) (HOLogic.listT xT))
+ in (bds := AList.update Type.could_unify (HOLogic.listT xT,(tl bsT,asT)) (!bds))
+ end) ;
+ hd (Variable.export ctxt' ctxt [(forall_intr (cert x) th) COMP allI])))
+ end)
+ | _ => da (s,ctxt))
+ in
+ (case cgns of
+ [] => tryabsdecomp (t,ctxt)
+ | ((vns,cong)::congs) => ((let
+ val cert = cterm_of thy
+ val certy = ctyp_of thy
+ val (tyenv, tmenv) =
+ Pattern.match thy
+ ((fst o HOLogic.dest_eq o HOLogic.dest_Trueprop) (concl_of cong), t)
+ (Envir.type_env (Envir.empty 0), Vartab.empty)
+ val (fnvs,invs) = List.partition (fn ((vn,_),_) => vn mem vns) (Vartab.dest tmenv)
+ val (fts,its) =
+ (map (snd o snd) fnvs,
+ map (fn ((vn,vi),(tT,t)) => (cert(Var ((vn,vi),tT)), cert t)) invs)
+ val ctyenv = map (fn ((vn,vi),(s,ty)) => (certy (TVar((vn,vi),s)), certy ty)) (Vartab.dest tyenv)
+ in (fts ~~ (replicate (length fts) ctxt), FWD (instantiate (ctyenv, its) cong))
+ end)
+ handle MATCH => decomp_genreif da congs (t,ctxt)))
+ end;
+
+ (* looks for the atoms equation and instantiates it with the right number *)
+
+
+fun mk_decompatom eqs (t,ctxt) =
+let
+ val tT = fastype_of t
+ fun isat eq =
+ let
+ val rhs = eq |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> snd
+ in exists_Const
+ (fn (n,ty) => n="List.nth"
+ andalso
+ AList.defined Type.could_unify (!bds) (domain_type ty)) rhs
+ andalso Type.could_unify (fastype_of rhs, tT)
+ end
+ fun get_nths t acc =
+ case t of
+ Const("List.nth",_)$vs$n => insert (fn ((a,_),(b,_)) => a aconv b) (t,(vs,n)) acc
+ | t1$t2 => get_nths t1 (get_nths t2 acc)
+ | Abs(_,_,t') => get_nths t' acc
+ | _ => acc
+
+ fun
+ tryeqs [] = error "Can not find the atoms equation"
+ | tryeqs (eq::eqs) = ((
+ let
+ val rhs = eq |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> snd
+ val nths = get_nths rhs []
+ val (vss,ns) = fold_rev (fn (_,(vs,n)) => fn (vss,ns) =>
+ (insert (op aconv) vs vss, insert (op aconv) n ns)) nths ([],[])
+ val (vsns, ctxt') = Variable.variant_fixes (replicate (length vss) "vs") ctxt
+ val (xns, ctxt'') = Variable.variant_fixes (replicate (length nths) "x") ctxt'
+ val thy = ProofContext.theory_of ctxt''
+ val cert = cterm_of thy
+ val certT = ctyp_of thy
+ val vsns_map = vss ~~ vsns
+ val xns_map = (fst (split_list nths)) ~~ xns
+ val subst = map (fn (nt, xn) => (nt, Var ((xn,0), fastype_of nt))) xns_map
+ val rhs_P = subst_free subst rhs
+ val (tyenv, tmenv) = Pattern.match
+ thy (rhs_P, t)
+ (Envir.type_env (Envir.empty 0), Vartab.empty)
+ val sbst = Envir.subst_vars (tyenv, tmenv)
+ val sbsT = Envir.typ_subst_TVars tyenv
+ val subst_ty = map (fn (n,(s,t)) => (certT (TVar (n, s)), certT t))
+ (Vartab.dest tyenv)
+ val tml = Vartab.dest tmenv
+ val t's = map (fn xn => snd (valOf (AList.lookup (op =) tml (xn,0)))) xns (* FIXME : Express with sbst*)
+ val subst_ns = map (fn (Const _ $ vs $ n, Var (xn0,T)) =>
+ (cert n, snd (valOf (AList.lookup (op =) tml xn0))
+ |> (index_of #> HOLogic.mk_nat #> cert)))
+ subst
+ val subst_vs =
+ let
+ fun ty (Const _ $ (vs as Var (vsn,lT)) $ n, Var (xn0,T)) = (certT T, certT (sbsT T))
+ fun h (Const _ $ (vs as Var (vsn,lT)) $ n, Var (xn0,T)) =
+ let
+ val cns = sbst (Const("List.list.Cons", T --> lT --> lT))
+ val lT' = sbsT lT
+ val (bsT,asT) = the (AList.lookup Type.could_unify (!bds) lT)
+ val vsn = valOf (AList.lookup (op =) vsns_map vs)
+ val cvs = cert (fold_rev (fn x => fn xs => cns$x$xs) bsT (Free (vsn, lT')))
+ in (cert vs, cvs) end
+ in map h subst end
+ val cts = map (fn ((vn,vi),(tT,t)) => (cert(Var ((vn,vi),tT)), cert t))
+ (fold (AList.delete (fn (((a: string),_),(b,_)) => a = b))
+ (map (fn n => (n,0)) xns) tml)
+ val substt =
+ let val ih = Drule.cterm_rule (Thm.instantiate (subst_ty,[]))
+ in map (fn (v,t) => (ih v, ih t)) (subst_ns@subst_vs@cts) end
+ val th = (instantiate (subst_ty, substt) eq) RS sym
+ in hd (Variable.export ctxt'' ctxt [th]) end)
+ handle MATCH => tryeqs eqs)
+in ([], fn _ => tryeqs (filter isat eqs))
+end;
+
+ (* Generic reification procedure: *)
+ (* creates all needed cong rules and then just uses the theorem synthesis *)
+
+ fun mk_congs ctxt raw_eqs =
+ let
+ val fs = fold_rev (fn eq =>
+ insert (op =) (eq |> prop_of |> HOLogic.dest_Trueprop
+ |> HOLogic.dest_eq |> fst |> strip_comb
+ |> fst)) raw_eqs []
+ val tys = fold_rev (fn f => fn ts => (f |> fastype_of |> binder_types |> tl)
+ union ts) fs []
+ val _ = bds := AList.make (fn _ => ([],[])) tys
+ val (vs, ctxt') = Variable.variant_fixes (replicate (length tys) "vs") ctxt
+ val thy = ProofContext.theory_of ctxt'
+ val cert = cterm_of thy
+ val vstys = map (fn (t,v) => (t,SOME (cert (Free(v,t)))))
+ (tys ~~ vs)
+ val is_Var = can dest_Var
+ fun insteq eq vs =
+ let
+ val subst = map (fn (v as Var(n,t)) => (cert v, (valOf o valOf) (AList.lookup (op =) vstys t)))
+ (filter is_Var vs)
+ in Thm.instantiate ([],subst) eq
+ end
+ val eqs = map (fn eq => eq |> prop_of |> HOLogic.dest_Trueprop
+ |> HOLogic.dest_eq |> fst |> strip_comb |> snd |> tl
+ |> (insteq eq)) raw_eqs
+ val (ps,congs) = split_list (map (mk_congeq ctxt' fs) eqs)
+in ps ~~ (Variable.export ctxt' ctxt congs)
+end
+
+fun partition P [] = ([],[])
+ | partition P (x::xs) =
+ let val (yes,no) = partition P xs
+ in if P x then (x::yes,no) else (yes, x::no) end
+
+fun rearrange congs =
+let
+ fun P (_, th) =
+ let val @{term "Trueprop"}$(Const ("op =",_) $l$_) = concl_of th
+ in can dest_Var l end
+ val (yes,no) = partition P congs
+ in no @ yes end
+
+
+
+fun genreif ctxt raw_eqs t =
+ let
+ val congs = rearrange (mk_congs ctxt raw_eqs)
+ val th = divide_and_conquer (decomp_genreif (mk_decompatom raw_eqs) congs) (t,ctxt)
+ fun is_listVar (Var (_,t)) = can dest_listT t
+ | is_listVar _ = false
+ val vars = th |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> snd
+ |> strip_comb |> snd |> filter is_listVar
+ val cert = cterm_of (ProofContext.theory_of ctxt)
+ val cvs = map (fn (v as Var(n,t)) => (cert v, the (AList.lookup Type.could_unify (!bds) t) |> snd |> HOLogic.mk_list (dest_listT t) |> cert)) vars
+ val th' = instantiate ([], cvs) th
+ val t' = (fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o prop_of) th'
+ val th'' = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq (t, t')))
+ (fn _ => simp_tac (local_simpset_of ctxt) 1)
+ val _ = bds := []
+in FWD trans [th'',th']
+end
+
+
+fun genreflect ctxt conv corr_thms raw_eqs t =
+let
+ val reifth = genreif ctxt raw_eqs t
+ fun trytrans [] = error "No suitable correctness theorem found"
+ | trytrans (th::ths) =
+ (FWD trans [reifth, th RS sym] handle THM _ => trytrans ths)
+ val th = trytrans corr_thms
+ val ft = (Thm.dest_arg1 o Thm.dest_arg o Thm.dest_arg o cprop_of) th
+ val rth = conv ft
+in simplify (HOL_basic_ss addsimps raw_eqs addsimps [nth_Cons_0, nth_Cons_Suc])
+ (simplify (HOL_basic_ss addsimps [rth]) th)
+end
+
+fun genreify_tac ctxt eqs to i = (fn st =>
+ let
+ val P = HOLogic.dest_Trueprop (List.nth (prems_of st, i - 1))
+ val t = (case to of NONE => P | SOME x => x)
+ val th = (genreif ctxt eqs t) RS ssubst
+ in rtac th i st
+ end);
+
+ (* Reflection calls reification and uses the correctness *)
+ (* theorem assumed to be the dead of the list *)
+fun gen_reflection_tac ctxt conv corr_thms raw_eqs to i = (fn st =>
+ let
+ val P = HOLogic.dest_Trueprop (nth (prems_of st) (i - 1));
+ val t = the_default P to;
+ val th = genreflect ctxt conv corr_thms raw_eqs t
+ RS ssubst;
+ in (rtac th i THEN TRY(rtac TrueI i)) st end);
+
+fun reflection_tac ctxt = gen_reflection_tac ctxt Codegen.evaluation_conv;
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Library/reify_data.ML Wed Jan 28 11:04:10 2009 +0100
@@ -0,0 +1,39 @@
+(* Title: HOL/Library/reflection_data.ML
+ Author: Amine Chaieb, TU Muenchen
+
+Data for the reification and reflection methods.
+*)
+
+signature REIFY_DATA =
+sig
+ val get: Proof.context -> thm list * thm list
+ val add: attribute
+ val del: attribute
+ val radd: attribute
+ val rdel: attribute
+ val setup: theory -> theory
+end;
+
+structure Reify_Data : REIFY_DATA =
+struct
+
+structure Data = GenericDataFun
+(
+ type T = thm list * thm list;
+ val empty = ([], []);
+ val extend = I;
+ fun merge _ = pairself Thm.merge_thms;
+);
+
+val get = Data.get o Context.Proof;
+
+val add = Thm.declaration_attribute (Data.map o apfst o Thm.add_thm);
+val del = Thm.declaration_attribute (Data.map o apfst o Thm.del_thm);
+val radd = Thm.declaration_attribute (Data.map o apsnd o Thm.add_thm);
+val rdel = Thm.declaration_attribute (Data.map o apsnd o Thm.del_thm);
+
+val setup = Attrib.add_attributes
+ [("reify", Attrib.add_del_args add del, "Reify data"),
+ ("reflection", Attrib.add_del_args radd rdel, "Reflection data")];
+
+end;
--- a/src/HOL/ex/ROOT.ML Wed Jan 28 10:43:31 2009 +0100
+++ b/src/HOL/ex/ROOT.ML Wed Jan 28 11:04:10 2009 +0100
@@ -63,7 +63,6 @@
"Dense_Linear_Order_Ex",
"PresburgerEx",
"Reflected_Presburger",
- "Reflection",
"ReflectionEx",
"BinEx",
"Sqrt",
--- a/src/HOL/ex/Reflection.thy Wed Jan 28 10:43:31 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,48 +0,0 @@
-(*
- ID: $Id$
- Author: Amine Chaieb, TU Muenchen
-*)
-
-header {* Generic reflection and reification *}
-
-theory Reflection
-imports Main
- uses "reflection_data.ML" ("reflection.ML")
-begin
-
-setup {* Reify_Data.setup*}
-
-
-lemma ext2: "(\<forall>x. f x = g x) \<Longrightarrow> f = g"
- by (blast intro: ext)
-
-use "reflection.ML"
-
-method_setup reify = {*
- fn src =>
- Method.syntax (Attrib.thms --
- Scan.option (Scan.lift (Args.$$$ "(") |-- Args.term --| Scan.lift (Args.$$$ ")") )) src #>
- (fn ((eqs, to), ctxt) => Method.SIMPLE_METHOD' (Reflection.genreify_tac ctxt (eqs @ (fst (Reify_Data.get ctxt))) to))
-*} "partial automatic reification"
-
-method_setup reflection = {*
-let
-fun keyword k = Scan.lift (Args.$$$ k -- Args.colon) >> K ();
-val onlyN = "only";
-val rulesN = "rules";
-val any_keyword = keyword onlyN || keyword rulesN;
-val thms = Scan.repeat (Scan.unless any_keyword Attrib.multi_thm) >> flat;
-val terms = thms >> map (term_of o Drule.dest_term);
-fun optional scan = Scan.optional scan [];
-in
-fn src =>
- Method.syntax (thms -- optional (keyword rulesN |-- thms) -- Scan.option (keyword onlyN |-- Args.term)) src #>
- (fn (((eqs,ths),to), ctxt) =>
- let
- val (ceqs,cths) = Reify_Data.get ctxt
- val corr_thms = ths@cths
- val raw_eqs = eqs@ceqs
- in Method.SIMPLE_METHOD' (Reflection.reflection_tac ctxt corr_thms raw_eqs to)
- end) end
-*} "reflection method"
-end
--- a/src/HOL/ex/ReflectionEx.thy Wed Jan 28 10:43:31 2009 +0100
+++ b/src/HOL/ex/ReflectionEx.thy Wed Jan 28 11:04:10 2009 +0100
@@ -1,9 +1,9 @@
-(*
- ID: $Id$
+(* Title: HOL/ex/ReflectionEx.thy
Author: Amine Chaieb, TU Muenchen
*)
header {* Examples for generic reflection and reification *}
+
theory ReflectionEx
imports Reflection
begin
--- a/src/HOL/ex/reflection.ML Wed Jan 28 10:43:31 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,325 +0,0 @@
-(* Author: Amine Chaieb, TU Muenchen
-
-A trial for automatical reification.
-*)
-
-signature REFLECTION =
-sig
- val genreify_tac: Proof.context -> thm list -> term option -> int -> tactic
- val reflection_tac: Proof.context -> thm list -> thm list -> term option -> int -> tactic
- val gen_reflection_tac: Proof.context -> (cterm -> thm)
- -> thm list -> thm list -> term option -> int -> tactic
-end;
-
-structure Reflection : REFLECTION =
-struct
-
-val ext2 = thm "ext2";
-val nth_Cons_0 = thm "nth_Cons_0";
-val nth_Cons_Suc = thm "nth_Cons_Suc";
-
- (* Make a congruence rule out of a defining equation for the interpretation *)
- (* th is one defining equation of f, i.e.
- th is "f (Cp ?t1 ... ?tn) = P(f ?t1, .., f ?tn)" *)
- (* Cp is a constructor pattern and P is a pattern *)
-
- (* The result is:
- [|?A1 = f ?t1 ; .. ; ?An= f ?tn |] ==> P (?A1, .., ?An) = f (Cp ?t1 .. ?tn) *)
- (* + the a list of names of the A1 .. An, Those are fresh in the ctxt*)
-
-
-fun mk_congeq ctxt fs th =
- let
- val (f as Const(fN,fT)) = th |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq
- |> fst |> strip_comb |> fst
- val thy = ProofContext.theory_of ctxt
- val cert = Thm.cterm_of thy
- val (((_,_),[th']), ctxt') = Variable.import_thms true [th] ctxt
- val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop (Thm.prop_of th'))
- fun add_fterms (t as t1 $ t2) =
- if exists (fn f => Term.could_unify (t |> strip_comb |> fst, f)) fs then insert (op aconv) t
- else add_fterms t1 #> add_fterms t2
- | add_fterms (t as Abs(xn,xT,t')) =
- if exists_Const (fn (c, _) => c = fN) t then (fn _ => [t]) else (fn _ => [])
- | add_fterms _ = I
- val fterms = add_fterms rhs []
- val (xs, ctxt'') = Variable.variant_fixes (replicate (length fterms) "x") ctxt'
- val tys = map fastype_of fterms
- val vs = map Free (xs ~~ tys)
- val env = fterms ~~ vs
- (* FIXME!!!!*)
- fun replace_fterms (t as t1 $ t2) =
- (case AList.lookup (op aconv) env t of
- SOME v => v
- | NONE => replace_fterms t1 $ replace_fterms t2)
- | replace_fterms t = (case AList.lookup (op aconv) env t of
- SOME v => v
- | NONE => t)
-
- fun mk_def (Abs(x,xT,t),v) = HOLogic.mk_Trueprop ((HOLogic.all_const xT)$ Abs(x,xT,HOLogic.mk_eq(v$(Bound 0), t)))
- | mk_def (t, v) = HOLogic.mk_Trueprop (HOLogic.mk_eq (v, t))
- fun tryext x = (x RS ext2 handle THM _ => x)
- val cong = (Goal.prove ctxt'' [] (map mk_def env)
- (HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, replace_fterms rhs)))
- (fn x => LocalDefs.unfold_tac (#context x) (map tryext (#prems x))
- THEN rtac th' 1)) RS sym
-
- val (cong' :: vars') =
- Variable.export ctxt'' ctxt (cong :: map (Drule.mk_term o cert) vs)
- val vs' = map (fst o fst o Term.dest_Var o Thm.term_of o Drule.dest_term) vars'
-
- in (vs', cong') end;
- (* congs is a list of pairs (P,th) where th is a theorem for *)
- (* [| f p1 = A1; ...; f pn = An|] ==> f (C p1 .. pn) = P *)
-val FWD = curry (op OF);
-
- (* da is the decomposition for atoms, ie. it returns ([],g) where g
- returns the right instance f (AtC n) = t , where AtC is the Atoms
- constructor and n is the number of the atom corresponding to t *)
-
-(* Generic decomp for reification : matches the actual term with the
-rhs of one cong rule. The result of the matching guides the
-proof synthesis: The matches of the introduced Variables A1 .. An are
-processed recursively
- The rest is instantiated in the cong rule,i.e. no reification is needed *)
-
-exception REIF of string;
-
-val bds = ref ([]: (typ * ((term list) * (term list))) list);
-
-fun index_of t =
- let
- val tt = HOLogic.listT (fastype_of t)
- in
- (case AList.lookup Type.could_unify (!bds) tt of
- NONE => error "index_of : type not found in environements!"
- | SOME (tbs,tats) =>
- let
- val i = find_index_eq t tats
- val j = find_index_eq t tbs
- in (if j= ~1 then
- if i= ~1
- then (bds := AList.update Type.could_unify (tt,(tbs,tats@[t])) (!bds) ;
- length tbs + length tats)
- else i else j)
- end)
- end;
-
-fun dest_listT (Type ("List.list", [T])) = T;
-
-fun decomp_genreif da cgns (t,ctxt) =
- let
- val thy = ProofContext.theory_of ctxt
- val cert = cterm_of thy
- fun tryabsdecomp (s,ctxt) =
- (case s of
- Abs(xn,xT,ta) =>
- (let
- val ([xn],ctxt') = Variable.variant_fixes ["x"] ctxt
- val (xn,ta) = variant_abs (xn,xT,ta)
- val x = Free(xn,xT)
- val _ = (case AList.lookup Type.could_unify (!bds) (HOLogic.listT xT)
- of NONE => error "tryabsdecomp: Type not found in the Environement"
- | SOME (bsT,atsT) =>
- (bds := AList.update Type.could_unify (HOLogic.listT xT, ((x::bsT), atsT)) (!bds)))
- in ([(ta, ctxt')] ,
- fn [th] => ((let val (bsT,asT) = the(AList.lookup Type.could_unify (!bds) (HOLogic.listT xT))
- in (bds := AList.update Type.could_unify (HOLogic.listT xT,(tl bsT,asT)) (!bds))
- end) ;
- hd (Variable.export ctxt' ctxt [(forall_intr (cert x) th) COMP allI])))
- end)
- | _ => da (s,ctxt))
- in
- (case cgns of
- [] => tryabsdecomp (t,ctxt)
- | ((vns,cong)::congs) => ((let
- val cert = cterm_of thy
- val certy = ctyp_of thy
- val (tyenv, tmenv) =
- Pattern.match thy
- ((fst o HOLogic.dest_eq o HOLogic.dest_Trueprop) (concl_of cong), t)
- (Envir.type_env (Envir.empty 0), Vartab.empty)
- val (fnvs,invs) = List.partition (fn ((vn,_),_) => vn mem vns) (Vartab.dest tmenv)
- val (fts,its) =
- (map (snd o snd) fnvs,
- map (fn ((vn,vi),(tT,t)) => (cert(Var ((vn,vi),tT)), cert t)) invs)
- val ctyenv = map (fn ((vn,vi),(s,ty)) => (certy (TVar((vn,vi),s)), certy ty)) (Vartab.dest tyenv)
- in (fts ~~ (replicate (length fts) ctxt), FWD (instantiate (ctyenv, its) cong))
- end)
- handle MATCH => decomp_genreif da congs (t,ctxt)))
- end;
-
- (* looks for the atoms equation and instantiates it with the right number *)
-
-
-fun mk_decompatom eqs (t,ctxt) =
-let
- val tT = fastype_of t
- fun isat eq =
- let
- val rhs = eq |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> snd
- in exists_Const
- (fn (n,ty) => n="List.nth"
- andalso
- AList.defined Type.could_unify (!bds) (domain_type ty)) rhs
- andalso Type.could_unify (fastype_of rhs, tT)
- end
- fun get_nths t acc =
- case t of
- Const("List.nth",_)$vs$n => insert (fn ((a,_),(b,_)) => a aconv b) (t,(vs,n)) acc
- | t1$t2 => get_nths t1 (get_nths t2 acc)
- | Abs(_,_,t') => get_nths t' acc
- | _ => acc
-
- fun
- tryeqs [] = error "Can not find the atoms equation"
- | tryeqs (eq::eqs) = ((
- let
- val rhs = eq |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> snd
- val nths = get_nths rhs []
- val (vss,ns) = fold_rev (fn (_,(vs,n)) => fn (vss,ns) =>
- (insert (op aconv) vs vss, insert (op aconv) n ns)) nths ([],[])
- val (vsns, ctxt') = Variable.variant_fixes (replicate (length vss) "vs") ctxt
- val (xns, ctxt'') = Variable.variant_fixes (replicate (length nths) "x") ctxt'
- val thy = ProofContext.theory_of ctxt''
- val cert = cterm_of thy
- val certT = ctyp_of thy
- val vsns_map = vss ~~ vsns
- val xns_map = (fst (split_list nths)) ~~ xns
- val subst = map (fn (nt, xn) => (nt, Var ((xn,0), fastype_of nt))) xns_map
- val rhs_P = subst_free subst rhs
- val (tyenv, tmenv) = Pattern.match
- thy (rhs_P, t)
- (Envir.type_env (Envir.empty 0), Vartab.empty)
- val sbst = Envir.subst_vars (tyenv, tmenv)
- val sbsT = Envir.typ_subst_TVars tyenv
- val subst_ty = map (fn (n,(s,t)) => (certT (TVar (n, s)), certT t))
- (Vartab.dest tyenv)
- val tml = Vartab.dest tmenv
- val t's = map (fn xn => snd (valOf (AList.lookup (op =) tml (xn,0)))) xns (* FIXME : Express with sbst*)
- val subst_ns = map (fn (Const _ $ vs $ n, Var (xn0,T)) =>
- (cert n, snd (valOf (AList.lookup (op =) tml xn0))
- |> (index_of #> HOLogic.mk_nat #> cert)))
- subst
- val subst_vs =
- let
- fun ty (Const _ $ (vs as Var (vsn,lT)) $ n, Var (xn0,T)) = (certT T, certT (sbsT T))
- fun h (Const _ $ (vs as Var (vsn,lT)) $ n, Var (xn0,T)) =
- let
- val cns = sbst (Const("List.list.Cons", T --> lT --> lT))
- val lT' = sbsT lT
- val (bsT,asT) = the (AList.lookup Type.could_unify (!bds) lT)
- val vsn = valOf (AList.lookup (op =) vsns_map vs)
- val cvs = cert (fold_rev (fn x => fn xs => cns$x$xs) bsT (Free (vsn, lT')))
- in (cert vs, cvs) end
- in map h subst end
- val cts = map (fn ((vn,vi),(tT,t)) => (cert(Var ((vn,vi),tT)), cert t))
- (fold (AList.delete (fn (((a: string),_),(b,_)) => a = b))
- (map (fn n => (n,0)) xns) tml)
- val substt =
- let val ih = Drule.cterm_rule (Thm.instantiate (subst_ty,[]))
- in map (fn (v,t) => (ih v, ih t)) (subst_ns@subst_vs@cts) end
- val th = (instantiate (subst_ty, substt) eq) RS sym
- in hd (Variable.export ctxt'' ctxt [th]) end)
- handle MATCH => tryeqs eqs)
-in ([], fn _ => tryeqs (filter isat eqs))
-end;
-
- (* Generic reification procedure: *)
- (* creates all needed cong rules and then just uses the theorem synthesis *)
-
- fun mk_congs ctxt raw_eqs =
- let
- val fs = fold_rev (fn eq =>
- insert (op =) (eq |> prop_of |> HOLogic.dest_Trueprop
- |> HOLogic.dest_eq |> fst |> strip_comb
- |> fst)) raw_eqs []
- val tys = fold_rev (fn f => fn ts => (f |> fastype_of |> binder_types |> tl)
- union ts) fs []
- val _ = bds := AList.make (fn _ => ([],[])) tys
- val (vs, ctxt') = Variable.variant_fixes (replicate (length tys) "vs") ctxt
- val thy = ProofContext.theory_of ctxt'
- val cert = cterm_of thy
- val vstys = map (fn (t,v) => (t,SOME (cert (Free(v,t)))))
- (tys ~~ vs)
- val is_Var = can dest_Var
- fun insteq eq vs =
- let
- val subst = map (fn (v as Var(n,t)) => (cert v, (valOf o valOf) (AList.lookup (op =) vstys t)))
- (filter is_Var vs)
- in Thm.instantiate ([],subst) eq
- end
- val eqs = map (fn eq => eq |> prop_of |> HOLogic.dest_Trueprop
- |> HOLogic.dest_eq |> fst |> strip_comb |> snd |> tl
- |> (insteq eq)) raw_eqs
- val (ps,congs) = split_list (map (mk_congeq ctxt' fs) eqs)
-in ps ~~ (Variable.export ctxt' ctxt congs)
-end
-
-fun partition P [] = ([],[])
- | partition P (x::xs) =
- let val (yes,no) = partition P xs
- in if P x then (x::yes,no) else (yes, x::no) end
-
-fun rearrange congs =
-let
- fun P (_, th) =
- let val @{term "Trueprop"}$(Const ("op =",_) $l$_) = concl_of th
- in can dest_Var l end
- val (yes,no) = partition P congs
- in no @ yes end
-
-
-
-fun genreif ctxt raw_eqs t =
- let
- val congs = rearrange (mk_congs ctxt raw_eqs)
- val th = divide_and_conquer (decomp_genreif (mk_decompatom raw_eqs) congs) (t,ctxt)
- fun is_listVar (Var (_,t)) = can dest_listT t
- | is_listVar _ = false
- val vars = th |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> snd
- |> strip_comb |> snd |> filter is_listVar
- val cert = cterm_of (ProofContext.theory_of ctxt)
- val cvs = map (fn (v as Var(n,t)) => (cert v, the (AList.lookup Type.could_unify (!bds) t) |> snd |> HOLogic.mk_list (dest_listT t) |> cert)) vars
- val th' = instantiate ([], cvs) th
- val t' = (fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o prop_of) th'
- val th'' = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq (t, t')))
- (fn _ => simp_tac (local_simpset_of ctxt) 1)
- val _ = bds := []
-in FWD trans [th'',th']
-end
-
-
-fun genreflect ctxt conv corr_thms raw_eqs t =
-let
- val reifth = genreif ctxt raw_eqs t
- fun trytrans [] = error "No suitable correctness theorem found"
- | trytrans (th::ths) =
- (FWD trans [reifth, th RS sym] handle THM _ => trytrans ths)
- val th = trytrans corr_thms
- val ft = (Thm.dest_arg1 o Thm.dest_arg o Thm.dest_arg o cprop_of) th
- val rth = conv ft
-in simplify (HOL_basic_ss addsimps raw_eqs addsimps [nth_Cons_0, nth_Cons_Suc])
- (simplify (HOL_basic_ss addsimps [rth]) th)
-end
-
-fun genreify_tac ctxt eqs to i = (fn st =>
- let
- val P = HOLogic.dest_Trueprop (List.nth (prems_of st, i - 1))
- val t = (case to of NONE => P | SOME x => x)
- val th = (genreif ctxt eqs t) RS ssubst
- in rtac th i st
- end);
-
- (* Reflection calls reification and uses the correctness *)
- (* theorem assumed to be the dead of the list *)
-fun gen_reflection_tac ctxt conv corr_thms raw_eqs to i = (fn st =>
- let
- val P = HOLogic.dest_Trueprop (nth (prems_of st) (i - 1));
- val t = the_default P to;
- val th = genreflect ctxt conv corr_thms raw_eqs t
- RS ssubst;
- in (rtac th i THEN TRY(rtac TrueI i)) st end);
-
-fun reflection_tac ctxt = gen_reflection_tac ctxt Codegen.evaluation_conv;
-end
--- a/src/HOL/ex/reflection_data.ML Wed Jan 28 10:43:31 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,69 +0,0 @@
-(* Title: HOL/ex/reflection_data.ML
- ID: $Id$
- Author: Amine Chaieb, TU Muenchen
-
-Data for the reification and reflection methods.
-*)
-
-signature REIFY_DATA =
-sig
- type entry = thm list * thm list
- val get: Proof.context -> entry
- val del: attribute
- val add: attribute
- val setup: theory -> theory
-end;
-
-structure Reify_Data : REIFY_DATA =
-struct
-
-type entry = thm list * thm list;
-
-structure Data = GenericDataFun
-(
- type T = entry
- val empty = ([], [])
- val extend = I
- fun merge _ = pairself Thm.merge_thms
-);
-
-val get = Data.get o Context.Proof;
-
-val add = Thm.declaration_attribute (fn th => fn context =>
- context |> Data.map (apfst (Thm.add_thm th)))
-
-val del = Thm.declaration_attribute (fn th => fn context =>
- context |> Data.map (apfst (Thm.del_thm th)))
-
-val radd = Thm.declaration_attribute (fn th => fn context =>
- context |> Data.map (apsnd (Thm.add_thm th)))
-
-val rdel = Thm.declaration_attribute (fn th => fn context =>
- context |> Data.map (apsnd (Thm.del_thm th)))
-
-(* concrete syntax *)
-(*
-local
-fun keyword k = Scan.lift (Args.$$$ k -- Args.colon) >> K ();
-
-val constsN = "consts";
-val addN = "add";
-val delN = "del";
-val any_keyword = keyword constsN || keyword addN || keyword delN;
-val thms = Scan.repeat (Scan.unless any_keyword Attrib.multi_thm) >> flat;
-val terms = thms >> map (term_of o Drule.dest_term);
-
-fun optional scan = Scan.optional scan [];
-
-in
-val att_syntax = Attrib.syntax
- ((Scan.lift (Args.$$$ "del") |-- thms) >> del ||
- optional (keyword addN |-- thms) >> add)
-end;
-*)
-
-(* theory setup *)
- val setup =
- Attrib.add_attributes [("reify", Attrib.add_del_args add del, "Reify data"),
- ("reflection", Attrib.add_del_args radd rdel, "Reflection data")];
-end;