lucas - added option to select occurance to rewrite e.g. (occ 4)
(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- *)
(* Title: Provers/eqsubst.ML
Author: Lucas Dixon, University of Edinburgh
lucas.dixon@ed.ac.uk
Modified: 18 Feb 2005 - Lucas -
Created: 29 Jan 2005
*)
(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- *)
(* DESCRIPTION:
A Tactic to perform a substiution using an equation.
*)
(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- *)
(* Logic specific data stub *)
signature EQRULE_DATA =
sig
(* to make a meta equality theorem in the current logic *)
val prep_meta_eq : thm -> thm list
end;
(* the signature of an instance of the SQSUBST tactic *)
signature EQSUBST_TAC =
sig
type match =
((Term.indexname * (Term.sort * Term.typ)) list (* type instantiations *)
* (Term.indexname * (Term.typ * Term.term)) list) (* term instantiations *)
* (string * Term.typ) list (* fake named type abs env *)
* (string * Term.typ) list (* type abs env *)
* Term.term (* outer term *)
val prep_subst_in_asm :
(Sign.sg (* sign for matching *)
-> int (* maxidx *)
-> 'a (* input object kind *)
-> BasicIsaFTerm.FcTerm (* focusterm to search under *)
-> 'b) (* result type *)
-> int (* subgoal to subst in *)
-> Thm.thm (* target theorem with subgoals *)
-> int (* premise to subst in *)
-> (Thm.cterm list (* certified free var placeholders for vars *)
* int (* premice no. to subst *)
* int (* number of assumptions of premice *)
* Thm.thm) (* premice as a new theorem for forward reasoning *)
* ('a -> 'b) (* matchf *)
val prep_subst_in_asms :
(Sign.sg -> int -> 'a -> BasicIsaFTerm.FcTerm -> 'b)
-> int (* subgoal to subst in *)
-> Thm.thm (* target theorem with subgoals *)
-> ((Thm.cterm list (* certified free var placeholders for vars *)
* int (* premice no. to subst *)
* int (* number of assumptions of premice *)
* Thm.thm) (* premice as a new theorem for forward reasoning *)
* ('a -> 'b)) (* matchf *)
Seq.seq
val apply_subst_in_asm :
int (* subgoal *)
-> Thm.thm (* overall theorem *)
-> (Thm.cterm list (* certified free var placeholders for vars *)
* int (* assump no being subst *)
* int (* num of premises of asm *)
* Thm.thm) (* premthm *)
-> Thm.thm (* rule *)
-> match
-> Thm.thm Seq.seq
val prep_concl_subst :
(Sign.sg -> int -> 'a -> BasicIsaFTerm.FcTerm -> 'b) (* searchf *)
-> int (* subgoal *)
-> Thm.thm (* overall goal theorem *)
-> (Thm.cterm list * Thm.thm) * ('a -> 'b) (* (cvfs, conclthm), matchf *)
val apply_subst_in_concl :
int (* subgoal *)
-> Thm.thm (* thm with all goals *)
-> Thm.cterm list (* certified free var placeholders for vars *)
* Thm.thm (* trivial thm of goal concl *)
(* possible matches/unifiers *)
-> Thm.thm (* rule *)
-> match
-> Thm.thm Seq.seq (* substituted goal *)
val searchf_tlr_unify_all :
(Sign.sg -> int ->
Term.term ->
BasicIsaFTerm.FcTerm ->
match Seq.seq Seq.seq)
val searchf_tlr_unify_valid :
(Sign.sg -> int ->
Term.term ->
BasicIsaFTerm.FcTerm ->
match Seq.seq Seq.seq)
val eqsubst_asm_meth : int -> Thm.thm list -> Proof.method
val eqsubst_asm_tac : int -> Thm.thm list -> int -> Thm.thm -> Thm.thm Seq.seq
val eqsubst_asm_tac' :
(Sign.sg -> int ->
Term.term ->
BasicIsaFTerm.FcTerm ->
match Seq.seq) -> Thm.thm -> int -> Thm.thm -> Thm.thm Seq.seq
val eqsubst_meth : int -> Thm.thm list -> Proof.method
val eqsubst_tac : int -> Thm.thm list -> int -> Thm.thm -> Thm.thm Seq.seq
val eqsubst_tac' :
(Sign.sg -> int ->
Term.term ->
BasicIsaFTerm.FcTerm ->
match Seq.seq) -> Thm.thm -> int -> Thm.thm -> Thm.thm Seq.seq
val meth : (bool * int) * Thm.thm list -> Proof.context -> Proof.method
val setup : (Theory.theory -> Theory.theory) list
end;
functor EQSubstTacFUN (structure EqRuleData : EQRULE_DATA)
: EQSUBST_TAC
= struct
(* a type abriviation for match information *)
type match =
((Term.indexname * (Term.sort * Term.typ)) list (* type instantiations *)
* (Term.indexname * (Term.typ * Term.term)) list) (* term instantiations *)
* (string * Term.typ) list (* fake named type abs env *)
* (string * Term.typ) list (* type abs env *)
* Term.term (* outer term *)
(* FOR DEBUGGING...
type trace_subst_errT = int (* subgoal *)
* Thm.thm (* thm with all goals *)
* (Thm.cterm list (* certified free var placeholders for vars *)
* Thm.thm) (* trivial thm of goal concl *)
(* possible matches/unifiers *)
* Thm.thm (* rule *)
* (((Term.indexname * Term.typ) list (* type instantiations *)
* (Term.indexname * Term.term) list ) (* term instantiations *)
* (string * Term.typ) list (* Type abs env *)
* Term.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;
*)
(* also defined in /HOL/Tools/inductive_codegen.ML,
maybe move this to seq.ML ? *)
infix 5 :->;
fun s :-> f = Seq.flat (Seq.map f s);
(* search from top, left to right, then down *)
fun search_tlr_all_f f ft =
let
fun maux ft =
let val t' = (IsaFTerm.focus_of_fcterm ft)
(* val _ =
if !trace_subst_search then
(writeln ("Examining: " ^ (TermLib.string_of_term t'));
TermLib.writeterm t'; ())
else (); *)
in
(case t' of
(_ $ _) => Seq.append(maux (IsaFTerm.focus_left ft),
Seq.cons(f ft,
maux (IsaFTerm.focus_right ft)))
| (Abs _) => Seq.cons(f ft, maux (IsaFTerm.focus_abs ft))
| leaf => Seq.single (f ft)) end
in maux ft end;
(* search from top, left to right, then down *)
fun search_tlr_valid_f f ft =
let
fun maux ft =
let
val hereseq = if IsaFTerm.valid_match_start ft then f ft else Seq.empty
in
(case (IsaFTerm.focus_of_fcterm ft) of
(_ $ _) => Seq.append(maux (IsaFTerm.focus_left ft),
Seq.cons(hereseq,
maux (IsaFTerm.focus_right ft)))
| (Abs _) => Seq.cons(hereseq, maux (IsaFTerm.focus_abs ft))
| leaf => Seq.single (hereseq))
end
in maux ft end;
(* search all unifications *)
fun searchf_tlr_unify_all sgn maxidx lhs =
IsaFTerm.find_fcterm_matches
search_tlr_all_f
(IsaFTerm.clean_unify_ft sgn maxidx lhs);
(* search only for 'valid' unifiers (non abs subterms and non vars) *)
fun searchf_tlr_unify_valid sgn maxidx lhs =
IsaFTerm.find_fcterm_matches
search_tlr_valid_f
(IsaFTerm.clean_unify_ft sgn maxidx lhs);
(* special tactic to skip the first "occ" occurances - ie start at the nth match *)
fun skip_first_occs_search occ searchf sgn i t ft =
let
fun skip_occs n sq =
if n <= 1 then sq
else
(case (Seq.pull sq) of NONE => Seq.empty
| SOME (h,t) =>
(case Seq.pull h of NONE => skip_occs n t
| SOME _ => skip_occs (n - 1) t))
in Seq.flat (skip_occs occ (searchf sgn i t ft)) end;
(* 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);
(*
|> (fn r => Thm.bicompose false (false, r, Thm.nprems_of 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 searchf i gth =
let
val th = Thm.incr_indexes 1 gth;
val tgt_term = Thm.prop_of th;
val sgn = Thm.sign_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 = Term.maxidx_of_term conclterm;
in
((cfvs, conclthm),
(fn lhs => searchf sgn maxidx lhs
((IsaFTerm.focus_right
o IsaFTerm.focus_left
o IsaFTerm.fcterm_of_term
o Thm.prop_of) conclthm)))
end;
(* substitute using an object or meta level equality *)
fun eqsubst_tac' searchf instepthm i th =
let
val (cvfsconclthm, findmatchf) =
prep_concl_subst searchf i th;
val stepthms =
Seq.map Drule.zero_var_indexes
(Seq.of_list (EqRuleData.prep_meta_eq instepthm));
fun rewrite_with_thm r =
let val (lhs,_) = Logic.dest_equals (Thm.concl_of r);
in (findmatchf lhs)
:-> (apply_subst_in_concl i th cvfsconclthm r) end;
in (stepthms :-> rewrite_with_thm) end;
(* substitute using one of the given theorems *)
fun eqsubst_tac occ instepthms i th =
if Thm.nprems_of th < i then Seq.empty else
(Seq.of_list instepthms)
:-> (fn r => eqsubst_tac' (skip_first_occs_search
occ searchf_tlr_unify_valid) r i th);
(* inthms are the given arguments in Isar, and treated as eqstep with
the first one, then the second etc *)
fun eqsubst_meth occ inthms =
Method.METHOD
(fn facts =>
HEADGOAL ( Method.insert_tac facts THEN' eqsubst_tac occ inthms ));
fun apply_subst_in_asm i th (cfvs, j, nprems, pth) rule m =
(RWInst.rw m rule pth)
|> Thm.permute_prems 0 ~1
|> IsaND.unfix_frees cfvs
|> RWInst.beta_eta_contract
|> (fn r => Tactic.dtac r i th);
(*
? should I be using bicompose what if we match more than one
assumption, even after instantiation ? (back will work, but it would
be nice to avoid the redudent search)
something like...
|> Thm.lift_rule (th, i)
|> (fn r => Thm.bicompose false (false, r, Thm.nprems_of r - nprems) i th)
*)
(* 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 searchf i gth j =
let
val th = Thm.incr_indexes 1 gth;
val tgt_term = Thm.prop_of th;
val sgn = Thm.sign_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 = Library.nth_elem(j - 1,(Logic.strip_imp_prems fixedbody));
val asm_nprems = length (Logic.strip_imp_prems asmt);
val pth = trivify asmt;
val maxidx = Term.maxidx_of_term asmt;
in
((cfvs, j, asm_nprems, pth),
(fn lhs => (searchf sgn maxidx lhs
((IsaFTerm.focus_right
o IsaFTerm.fcterm_of_term
o Thm.prop_of) pth))))
end;
(* prepare subst in every possible assumption *)
fun prep_subst_in_asms searchf i gth =
Seq.map
(prep_subst_in_asm searchf i gth)
(Seq.of_list (IsaPLib.mk_num_list
(length (Logic.prems_of_goal (Thm.prop_of gth) i))));
(* substitute in an assumption using an object or meta level equality *)
fun eqsubst_asm_tac' searchf instepthm i th =
let
val asmpreps = prep_subst_in_asms searchf i th;
val stepthms =
Seq.map Drule.zero_var_indexes
(Seq.of_list (EqRuleData.prep_meta_eq instepthm))
fun rewrite_with_thm (asminfo, findmatchf) r =
let val (lhs,_) = Logic.dest_equals (Thm.concl_of r);
in (findmatchf lhs)
:-> (apply_subst_in_asm i th asminfo r) end;
in
(asmpreps :-> (fn a => stepthms :-> rewrite_with_thm a))
end;
(* substitute using one of the given theorems *)
fun eqsubst_asm_tac occ instepthms i th =
if Thm.nprems_of th < i then Seq.empty else
(Seq.of_list instepthms)
:-> (fn r => eqsubst_asm_tac' (skip_first_occs_search
occ searchf_tlr_unify_valid) r 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 occ inthms =
Method.METHOD
(fn facts =>
HEADGOAL (Method.insert_tac facts THEN' eqsubst_asm_tac occ inthms ));
(* 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 meth ((asmflag, occ), inthms) ctxt =
if asmflag then eqsubst_asm_meth occ inthms else eqsubst_meth occ inthms;
(* syntax for options, given "(asm)" will give back true, without
gives back false *)
val options_syntax =
(Args.parens (Args.$$$ "asm") >> (K true)) ||
(Scan.succeed false);
val ith_syntax =
(Args.parens ((Args.$$$ "occ") |-- Args.nat))
|| (Scan.succeed 0);
(* method syntax, first take options, then theorems *)
fun meth_syntax meth src ctxt =
meth (snd (Method.syntax ((Scan.lift options_syntax)
-- (Scan.lift ith_syntax)
-- Attrib.local_thms) src ctxt))
ctxt;
(* setup function for adding method to theory. *)
val setup =
[Method.add_method ("subst", meth_syntax meth, "Substiution with an equation. Use \"(asm)\" option to substitute in an assumption.")];
end;