--- a/src/Provers/eqsubst.ML Wed Mar 04 11:05:02 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,575 +0,0 @@
-(* Title: Provers/eqsubst.ML
- Author: Lucas Dixon, University of Edinburgh
-
-A proof method to perform a substiution using an equation.
-*)
-
-signature EQSUBST =
-sig
- (* a type abbreviation for match information *)
- type match =
- ((indexname * (sort * typ)) list (* type instantiations *)
- * (indexname * (typ * term)) list) (* term instantiations *)
- * (string * typ) list (* fake named type abs env *)
- * (string * typ) list (* type abs env *)
- * term (* outer term *)
-
- type searchinfo =
- theory
- * int (* maxidx *)
- * Zipper.T (* focusterm to search under *)
-
- exception eqsubst_occL_exp of
- string * int list * Thm.thm list * int * Thm.thm
-
- (* low level substitution functions *)
- val apply_subst_in_asm :
- int ->
- Thm.thm ->
- Thm.thm ->
- (Thm.cterm list * int * 'a * Thm.thm) * match -> Thm.thm Seq.seq
- val apply_subst_in_concl :
- int ->
- Thm.thm ->
- Thm.cterm list * Thm.thm ->
- Thm.thm -> match -> Thm.thm Seq.seq
-
- (* matching/unification within zippers *)
- val clean_match_z :
- Context.theory -> Term.term -> Zipper.T -> match option
- val clean_unify_z :
- Context.theory -> int -> Term.term -> Zipper.T -> match Seq.seq
-
- (* skipping things in seq seq's *)
-
- (* skipping non-empty sub-sequences but when we reach the end
- of the seq, remembering how much we have left to skip. *)
- datatype 'a skipseq = SkipMore of int
- | SkipSeq of 'a Seq.seq Seq.seq;
-
- val skip_first_asm_occs_search :
- ('a -> 'b -> 'c Seq.seq Seq.seq) ->
- 'a -> int -> 'b -> 'c skipseq
- val skip_first_occs_search :
- int -> ('a -> 'b -> 'c Seq.seq Seq.seq) -> 'a -> 'b -> 'c Seq.seq
- val skipto_skipseq : int -> 'a Seq.seq Seq.seq -> 'a skipseq
-
- (* tactics *)
- val eqsubst_asm_tac :
- Proof.context ->
- int list -> Thm.thm list -> int -> Thm.thm -> Thm.thm Seq.seq
- val eqsubst_asm_tac' :
- Proof.context ->
- (searchinfo -> int -> Term.term -> match skipseq) ->
- int -> Thm.thm -> int -> Thm.thm -> Thm.thm Seq.seq
- val eqsubst_tac :
- Proof.context ->
- int list -> (* list of occurences to rewrite, use [0] for any *)
- Thm.thm list -> int -> Thm.thm -> Thm.thm Seq.seq
- val eqsubst_tac' :
- Proof.context -> (* proof context *)
- (searchinfo -> Term.term -> match Seq.seq) (* search function *)
- -> Thm.thm (* equation theorem to rewrite with *)
- -> int (* subgoal number in goal theorem *)
- -> Thm.thm (* goal theorem *)
- -> Thm.thm Seq.seq (* rewritten goal theorem *)
-
-
- val fakefree_badbounds :
- (string * Term.typ) list ->
- Term.term ->
- (string * Term.typ) list * (string * Term.typ) list * Term.term
-
- val mk_foo_match :
- (Term.term -> Term.term) ->
- ('a * Term.typ) list -> Term.term -> Term.term
-
- (* preparing substitution *)
- val prep_meta_eq : Proof.context -> Thm.thm -> Thm.thm list
- val prep_concl_subst :
- int -> Thm.thm -> (Thm.cterm list * Thm.thm) * searchinfo
- val prep_subst_in_asm :
- int -> Thm.thm -> int ->
- (Thm.cterm list * int * int * Thm.thm) * searchinfo
- val prep_subst_in_asms :
- int -> Thm.thm ->
- ((Thm.cterm list * int * int * Thm.thm) * searchinfo) list
- val prep_zipper_match :
- Zipper.T -> Term.term * ((string * Term.typ) list * (string * Term.typ) list * Term.term)
-
- (* search for substitutions *)
- val valid_match_start : Zipper.T -> bool
- val search_lr_all : Zipper.T -> Zipper.T Seq.seq
- val search_lr_valid : (Zipper.T -> bool) -> Zipper.T -> Zipper.T Seq.seq
- val searchf_lr_unify_all :
- searchinfo -> Term.term -> match Seq.seq Seq.seq
- val searchf_lr_unify_valid :
- searchinfo -> Term.term -> match Seq.seq Seq.seq
- val searchf_bt_unify_valid :
- searchinfo -> Term.term -> match Seq.seq Seq.seq
-
- (* syntax tools *)
- val ith_syntax : Args.T list -> int list * Args.T list
- val options_syntax : Args.T list -> bool * Args.T list
-
- (* Isar level hooks *)
- val eqsubst_asm_meth : Proof.context -> int list -> Thm.thm list -> Proof.method
- val eqsubst_meth : Proof.context -> int list -> Thm.thm list -> Proof.method
- val subst_meth : Method.src -> Proof.context -> Proof.method
- val setup : theory -> theory
-
-end;
-
-structure EqSubst
-: EQSUBST
-= struct
-
-structure Z = Zipper;
-
-(* changes object "=" to meta "==" which prepares a given rewrite rule *)
-fun prep_meta_eq ctxt =
- let val (_, {mk_rews = {mk, ...}, ...}) = Simplifier.rep_ss (Simplifier.local_simpset_of ctxt)
- in mk #> map Drule.zero_var_indexes end;
-
-
- (* a type abriviation for match information *)
- type match =
- ((indexname * (sort * typ)) list (* type instantiations *)
- * (indexname * (typ * term)) list) (* term instantiations *)
- * (string * typ) list (* fake named type abs env *)
- * (string * typ) list (* type abs env *)
- * term (* outer term *)
-
- type searchinfo =
- theory
- * int (* maxidx *)
- * Zipper.T (* focusterm to search under *)
-
-
-(* skipping non-empty sub-sequences but when we reach the end
- of the seq, remembering how much we have left to skip. *)
-datatype 'a skipseq = SkipMore of int
- | SkipSeq of 'a Seq.seq Seq.seq;
-(* given a seqseq, skip the first m non-empty seq's, note deficit *)
-fun skipto_skipseq m s =
- let
- fun skip_occs n sq =
- case Seq.pull sq of
- NONE => SkipMore n
- | SOME (h,t) =>
- (case Seq.pull h of NONE => skip_occs n t
- | SOME _ => if n <= 1 then SkipSeq (Seq.cons h t)
- else skip_occs (n - 1) t)
- in (skip_occs m s) end;
-
-(* note: outerterm is the taget with the match replaced by a bound
- variable : ie: "P lhs" beocmes "%x. P x"
- insts is the types of instantiations of vars in lhs
- and typinsts is the type instantiations of types in the lhs
- Note: Final rule is the rule lifted into the ontext of the
- taget thm. *)
-fun mk_foo_match mkuptermfunc Ts t =
- let
- val ty = Term.type_of t
- val bigtype = (rev (map snd Ts)) ---> ty
- fun mk_foo 0 t = t
- | mk_foo i t = mk_foo (i - 1) (t $ (Bound (i - 1)))
- val num_of_bnds = (length Ts)
- (* foo_term = "fooabs y0 ... yn" where y's are local bounds *)
- val foo_term = mk_foo num_of_bnds (Bound num_of_bnds)
- in Abs("fooabs", bigtype, mkuptermfunc foo_term) end;
-
-(* T is outer bound vars, n is number of locally bound vars *)
-(* THINK: is order of Ts correct...? or reversed? *)
-fun fakefree_badbounds Ts t =
- let val (FakeTs,Ts,newnames) =
- List.foldr (fn ((n,ty),(FakeTs,Ts,usednames)) =>
- let val newname = Name.variant usednames n
- in ((RWTools.mk_fake_bound_name newname,ty)::FakeTs,
- (newname,ty)::Ts,
- newname::usednames) end)
- ([],[],[])
- Ts
- in (FakeTs, Ts, Term.subst_bounds (map Free FakeTs, t)) end;
-
-(* before matching we need to fake the bound vars that are missing an
-abstraction. In this function we additionally construct the
-abstraction environment, and an outer context term (with the focus
-abstracted out) for use in rewriting with RWInst.rw *)
-fun prep_zipper_match z =
- let
- val t = Z.trm z
- val c = Z.ctxt z
- val Ts = Z.C.nty_ctxt c
- val (FakeTs', Ts', t') = fakefree_badbounds Ts t
- val absterm = mk_foo_match (Z.C.apply c) Ts' t'
- in
- (t', (FakeTs', Ts', absterm))
- end;
-
-(* Matching and Unification with exception handled *)
-fun clean_match thy (a as (pat, t)) =
- let val (tyenv, tenv) = Pattern.match thy a (Vartab.empty, Vartab.empty)
- in SOME (Vartab.dest tyenv, Vartab.dest tenv)
- end handle Pattern.MATCH => NONE;
-
-(* given theory, max var index, pat, tgt; returns Seq of instantiations *)
-fun clean_unify thry ix (a as (pat, tgt)) =
- let
- (* type info will be re-derived, maybe this can be cached
- for efficiency? *)
- val pat_ty = Term.type_of pat;
- val tgt_ty = Term.type_of tgt;
- (* is it OK to ignore the type instantiation info?
- or should I be using it? *)
- val typs_unify =
- SOME (Sign.typ_unify thry (pat_ty, tgt_ty) (Vartab.empty, ix))
- handle Type.TUNIFY => NONE;
- in
- case typs_unify of
- SOME (typinsttab, ix2) =>
- let
- (* is it right to throw away the flexes?
- or should I be using them somehow? *)
- fun mk_insts env =
- (Vartab.dest (Envir.type_env env),
- Envir.alist_of env);
- val initenv = Envir.Envir {asol = Vartab.empty,
- iTs = typinsttab, maxidx = ix2};
- val useq = Unify.smash_unifiers thry [a] initenv
- handle UnequalLengths => Seq.empty
- | Term.TERM _ => Seq.empty;
- fun clean_unify' useq () =
- (case (Seq.pull useq) of
- NONE => NONE
- | SOME (h,t) => SOME (mk_insts h, Seq.make (clean_unify' t)))
- handle UnequalLengths => NONE
- | Term.TERM _ => NONE
- in
- (Seq.make (clean_unify' useq))
- end
- | NONE => Seq.empty
- end;
-
-(* Matching and Unification for zippers *)
-(* Note: Ts is a modified version of the original names of the outer
-bound variables. New names have been introduced to make sure they are
-unique w.r.t all names in the term and each other. usednames' is
-oldnames + new names. *)
-fun clean_match_z thy pat z =
- let val (t, (FakeTs,Ts,absterm)) = prep_zipper_match z in
- case clean_match thy (pat, t) of
- NONE => NONE
- | SOME insts => SOME (insts, FakeTs, Ts, absterm) end;
-(* ix = max var index *)
-fun clean_unify_z sgn ix pat z =
- let val (t, (FakeTs, Ts,absterm)) = prep_zipper_match z in
- Seq.map (fn insts => (insts, FakeTs, Ts, absterm))
- (clean_unify sgn ix (t, pat)) end;
-
-
-(* FOR DEBUGGING...
-type trace_subst_errT = int (* subgoal *)
- * thm (* thm with all goals *)
- * (Thm.cterm list (* certified free var placeholders for vars *)
- * thm) (* trivial thm of goal concl *)
- (* possible matches/unifiers *)
- * thm (* rule *)
- * (((indexname * typ) list (* type instantiations *)
- * (indexname * term) list ) (* term instantiations *)
- * (string * typ) list (* Type abs env *)
- * term) (* outer term *);
-
-val trace_subst_err = (ref NONE : trace_subst_errT option ref);
-val trace_subst_search = ref false;
-exception trace_subst_exp of trace_subst_errT;
-*)
-
-
-fun bot_left_leaf_of (l $ r) = bot_left_leaf_of l
- | bot_left_leaf_of (Abs(s,ty,t)) = bot_left_leaf_of t
- | bot_left_leaf_of x = x;
-
-(* Avoid considering replacing terms which have a var at the head as
- they always succeed trivially, and uninterestingly. *)
-fun valid_match_start z =
- (case bot_left_leaf_of (Z.trm z) of
- Var _ => false
- | _ => true);
-
-(* search from top, left to right, then down *)
-val search_lr_all = ZipperSearch.all_bl_ur;
-
-(* search from top, left to right, then down *)
-fun search_lr_valid validf =
- let
- fun sf_valid_td_lr z =
- let val here = if validf z then [Z.Here z] else [] in
- case Z.trm z
- of _ $ _ => [Z.LookIn (Z.move_down_left z)]
- @ here
- @ [Z.LookIn (Z.move_down_right z)]
- | Abs _ => here @ [Z.LookIn (Z.move_down_abs z)]
- | _ => here
- end;
- in Z.lzy_search sf_valid_td_lr end;
-
-(* search from bottom to top, left to right *)
-
-fun search_bt_valid validf =
- let
- fun sf_valid_td_lr z =
- let val here = if validf z then [Z.Here z] else [] in
- case Z.trm z
- of _ $ _ => [Z.LookIn (Z.move_down_left z),
- Z.LookIn (Z.move_down_right z)] @ here
- | Abs _ => [Z.LookIn (Z.move_down_abs z)] @ here
- | _ => here
- end;
- in Z.lzy_search sf_valid_td_lr end;
-
-fun searchf_unify_gen f (sgn, maxidx, z) lhs =
- Seq.map (clean_unify_z sgn maxidx lhs)
- (Z.limit_apply f z);
-
-(* search all unifications *)
-val searchf_lr_unify_all =
- searchf_unify_gen search_lr_all;
-
-(* search only for 'valid' unifiers (non abs subterms and non vars) *)
-val searchf_lr_unify_valid =
- searchf_unify_gen (search_lr_valid valid_match_start);
-
-val searchf_bt_unify_valid =
- searchf_unify_gen (search_bt_valid valid_match_start);
-
-(* apply a substitution in the conclusion of the theorem th *)
-(* cfvs are certified free var placeholders for goal params *)
-(* conclthm is a theorem of for just the conclusion *)
-(* m is instantiation/match information *)
-(* rule is the equation for substitution *)
-fun apply_subst_in_concl i th (cfvs, conclthm) rule m =
- (RWInst.rw m rule conclthm)
- |> IsaND.unfix_frees cfvs
- |> RWInst.beta_eta_contract
- |> (fn r => Tactic.rtac r i th);
-
-(* substitute within the conclusion of goal i of gth, using a meta
-equation rule. Note that we assume rule has var indicies zero'd *)
-fun prep_concl_subst i gth =
- let
- val th = Thm.incr_indexes 1 gth;
- val tgt_term = Thm.prop_of th;
-
- val sgn = Thm.theory_of_thm th;
- val ctermify = Thm.cterm_of sgn;
- val trivify = Thm.trivial o ctermify;
-
- val (fixedbody, fvs) = IsaND.fix_alls_term i tgt_term;
- val cfvs = rev (map ctermify fvs);
-
- val conclterm = Logic.strip_imp_concl fixedbody;
- val conclthm = trivify conclterm;
- val maxidx = Thm.maxidx_of th;
- val ft = ((Z.move_down_right (* ==> *)
- o Z.move_down_left (* Trueprop *)
- o Z.mktop
- o Thm.prop_of) conclthm)
- in
- ((cfvs, conclthm), (sgn, maxidx, ft))
- end;
-
-(* substitute using an object or meta level equality *)
-fun eqsubst_tac' ctxt searchf instepthm i th =
- let
- val (cvfsconclthm, searchinfo) = prep_concl_subst i th;
- val stepthms = Seq.of_list (prep_meta_eq ctxt instepthm);
- fun rewrite_with_thm r =
- let val (lhs,_) = Logic.dest_equals (Thm.concl_of r);
- in searchf searchinfo lhs
- |> Seq.maps (apply_subst_in_concl i th cvfsconclthm r) end;
- in stepthms |> Seq.maps rewrite_with_thm end;
-
-
-(* distinct subgoals *)
-fun distinct_subgoals th =
- the_default th (SINGLE distinct_subgoals_tac th);
-
-(* General substitution of multiple occurances using one of
- the given theorems*)
-
-
-exception eqsubst_occL_exp of
- string * (int list) * (thm list) * int * thm;
-fun skip_first_occs_search occ srchf sinfo lhs =
- case (skipto_skipseq occ (srchf sinfo lhs)) of
- SkipMore _ => Seq.empty
- | SkipSeq ss => Seq.flat ss;
-
-(* The occL is a list of integers indicating which occurence
-w.r.t. the search order, to rewrite. Backtracking will also find later
-occurences, but all earlier ones are skipped. Thus you can use [0] to
-just find all rewrites. *)
-
-fun eqsubst_tac ctxt occL thms i th =
- let val nprems = Thm.nprems_of th in
- if nprems < i then Seq.empty else
- let val thmseq = (Seq.of_list thms)
- fun apply_occ occ th =
- thmseq |> Seq.maps
- (fn r => eqsubst_tac'
- ctxt
- (skip_first_occs_search
- occ searchf_lr_unify_valid) r
- (i + ((Thm.nprems_of th) - nprems))
- th);
- val sortedoccL =
- Library.sort (Library.rev_order o Library.int_ord) occL;
- in
- Seq.map distinct_subgoals (Seq.EVERY (map apply_occ sortedoccL) th)
- end
- end
- handle THM _ => raise eqsubst_occL_exp ("THM",occL,thms,i,th);
-
-
-(* inthms are the given arguments in Isar, and treated as eqstep with
- the first one, then the second etc *)
-fun eqsubst_meth ctxt occL inthms =
- Method.SIMPLE_METHOD' (eqsubst_tac ctxt occL inthms);
-
-(* apply a substitution inside assumption j, keeps asm in the same place *)
-fun apply_subst_in_asm i th rule ((cfvs, j, ngoalprems, pth),m) =
- let
- val th2 = Thm.rotate_rule (j - 1) i th; (* put premice first *)
- val preelimrule =
- (RWInst.rw m rule pth)
- |> (Seq.hd o prune_params_tac)
- |> Thm.permute_prems 0 ~1 (* put old asm first *)
- |> IsaND.unfix_frees cfvs (* unfix any global params *)
- |> RWInst.beta_eta_contract; (* normal form *)
- (* val elimrule =
- preelimrule
- |> Tactic.make_elim (* make into elim rule *)
- |> Thm.lift_rule (th2, i); (* lift into context *)
- *)
- in
- (* ~j because new asm starts at back, thus we subtract 1 *)
- Seq.map (Thm.rotate_rule (~j) ((Thm.nprems_of rule) + i))
- (Tactic.dtac preelimrule i th2)
-
- (* (Thm.bicompose
- false (* use unification *)
- (true, (* elim resolution *)
- elimrule, (2 + (Thm.nprems_of rule)) - ngoalprems)
- i th2) *)
- end;
-
-
-(* prepare to substitute within the j'th premise of subgoal i of gth,
-using a meta-level equation. Note that we assume rule has var indicies
-zero'd. Note that we also assume that premt is the j'th premice of
-subgoal i of gth. Note the repetition of work done for each
-assumption, i.e. this can be made more efficient for search over
-multiple assumptions. *)
-fun prep_subst_in_asm i gth j =
- let
- val th = Thm.incr_indexes 1 gth;
- val tgt_term = Thm.prop_of th;
-
- val sgn = Thm.theory_of_thm th;
- val ctermify = Thm.cterm_of sgn;
- val trivify = Thm.trivial o ctermify;
-
- val (fixedbody, fvs) = IsaND.fix_alls_term i tgt_term;
- val cfvs = rev (map ctermify fvs);
-
- val asmt = nth (Logic.strip_imp_prems fixedbody) (j - 1);
- val asm_nprems = length (Logic.strip_imp_prems asmt);
-
- val pth = trivify asmt;
- val maxidx = Thm.maxidx_of th;
-
- val ft = ((Z.move_down_right (* trueprop *)
- o Z.mktop
- o Thm.prop_of) pth)
- in ((cfvs, j, asm_nprems, pth), (sgn, maxidx, ft)) end;
-
-(* prepare subst in every possible assumption *)
-fun prep_subst_in_asms i gth =
- map (prep_subst_in_asm i gth)
- ((fn l => Library.upto (1, length l))
- (Logic.prems_of_goal (Thm.prop_of gth) i));
-
-
-(* substitute in an assumption using an object or meta level equality *)
-fun eqsubst_asm_tac' ctxt searchf skipocc instepthm i th =
- let
- val asmpreps = prep_subst_in_asms i th;
- val stepthms = Seq.of_list (prep_meta_eq ctxt instepthm);
- fun rewrite_with_thm r =
- let val (lhs,_) = Logic.dest_equals (Thm.concl_of r)
- fun occ_search occ [] = Seq.empty
- | occ_search occ ((asminfo, searchinfo)::moreasms) =
- (case searchf searchinfo occ lhs of
- SkipMore i => occ_search i moreasms
- | SkipSeq ss =>
- Seq.append (Seq.map (Library.pair asminfo) (Seq.flat ss))
- (occ_search 1 moreasms))
- (* find later substs also *)
- in
- occ_search skipocc asmpreps |> Seq.maps (apply_subst_in_asm i th r)
- end;
- in stepthms |> Seq.maps rewrite_with_thm end;
-
-
-fun skip_first_asm_occs_search searchf sinfo occ lhs =
- skipto_skipseq occ (searchf sinfo lhs);
-
-fun eqsubst_asm_tac ctxt occL thms i th =
- let val nprems = Thm.nprems_of th
- in
- if nprems < i then Seq.empty else
- let val thmseq = (Seq.of_list thms)
- fun apply_occ occK th =
- thmseq |> Seq.maps
- (fn r =>
- eqsubst_asm_tac' ctxt (skip_first_asm_occs_search
- searchf_lr_unify_valid) occK r
- (i + ((Thm.nprems_of th) - nprems))
- th);
- val sortedoccs =
- Library.sort (Library.rev_order o Library.int_ord) occL
- in
- Seq.map distinct_subgoals
- (Seq.EVERY (map apply_occ sortedoccs) th)
- end
- end
- handle THM _ => raise eqsubst_occL_exp ("THM",occL,thms,i,th);
-
-(* inthms are the given arguments in Isar, and treated as eqstep with
- the first one, then the second etc *)
-fun eqsubst_asm_meth ctxt occL inthms =
- Method.SIMPLE_METHOD' (eqsubst_asm_tac ctxt occL inthms);
-
-(* syntax for options, given "(asm)" will give back true, without
- gives back false *)
-val options_syntax =
- (Args.parens (Args.$$$ "asm") >> (K true)) ||
- (Scan.succeed false);
-
-val ith_syntax =
- Scan.optional (Args.parens (Scan.repeat OuterParse.nat)) [0];
-
-(* combination method that takes a flag (true indicates that subst
-should be done to an assumption, false = apply to the conclusion of
-the goal) as well as the theorems to use *)
-fun subst_meth src =
- Method.syntax ((Scan.lift options_syntax) -- (Scan.lift ith_syntax) -- Attrib.thms) src
- #> (fn (((asmflag, occL), inthms), ctxt) =>
- (if asmflag then eqsubst_asm_meth else eqsubst_meth) ctxt occL inthms);
-
-
-val setup =
- Method.add_method ("subst", subst_meth, "single-step substitution");
-
-end;