From 4f147cba894baa9e372e2b67211140b1a6f7b16c Mon Sep 17 00:00:00 2001 From: Josh Chen Date: Fri, 19 Jun 2020 12:41:54 +0200 Subject: reorganize --- spartan/core/ml/eqsubst.ML | 434 --------------------------------------------- 1 file changed, 434 deletions(-) delete mode 100644 spartan/core/ml/eqsubst.ML (limited to 'spartan/core/ml/eqsubst.ML') diff --git a/spartan/core/ml/eqsubst.ML b/spartan/core/ml/eqsubst.ML deleted file mode 100644 index ea6f098..0000000 --- a/spartan/core/ml/eqsubst.ML +++ /dev/null @@ -1,434 +0,0 @@ -(* Title: eqsubst.ML - Author: Lucas Dixon, University of Edinburgh - Modified: Joshua Chen, University of Innsbruck - -Perform a substitution using an equation. - -This code is slightly modified from the original at Tools/eqsubst..ML, -to incorporate auto-typechecking for type theory. -*) - -signature EQSUBST = -sig - 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 = - Proof.context - * int (* maxidx *) - * Zipper.T (* focusterm to search under *) - - 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 list -> int -> tactic - val eqsubst_asm_tac': Proof.context -> - (searchinfo -> int -> term -> match skipseq) -> int -> thm -> int -> tactic - val eqsubst_tac: Proof.context -> - int list -> (* list of occurrences to rewrite, use [0] for any *) - thm list -> int -> tactic - val eqsubst_tac': Proof.context -> - (searchinfo -> term -> match Seq.seq) (* search function *) - -> thm (* equation theorem to rewrite with *) - -> int (* subgoal number in goal theorem *) - -> thm (* goal theorem *) - -> thm Seq.seq (* rewritten goal theorem *) - - (* 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 -> match Seq.seq Seq.seq - val searchf_lr_unify_valid: searchinfo -> term -> match Seq.seq Seq.seq - val searchf_bt_unify_valid: searchinfo -> term -> match Seq.seq Seq.seq -end; - -structure EqSubst: EQSUBST = -struct - -(* changes object "=" to meta "==" which prepares a given rewrite rule *) -fun prep_meta_eq ctxt = - Simplifier.mksimps ctxt #> map Drule.zero_var_indexes; - -(* make free vars into schematic vars with index zero *) -fun unfix_frees frees = - fold (K (Thm.forall_elim_var 0)) frees o Drule.forall_intr_list frees; - - -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 = - Proof.context - * 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 mk_fake_bound_name n = ":b_" ^ n; -fun fakefree_badbounds Ts t = - let val (FakeTs, Ts, newnames) = - fold_rev (fn (n, ty) => fn (FakeTs, Ts, usednames) => - let - val newname = singleton (Name.variant_list usednames) n - in - ((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 RW_Inst.rw *) -fun prep_zipper_match z = - let - val t = Zipper.trm z - val c = Zipper.ctxt z - val Ts = Zipper.C.nty_ctxt c - val (FakeTs', Ts', t') = fakefree_badbounds Ts t - val absterm = mk_foo_match (Zipper.C.apply c) Ts' t' - in - (t', (FakeTs', Ts', absterm)) - end; - -(* Unification with exception handled *) -(* given context, max var index, pat, tgt; returns Seq of instantiations *) -fun clean_unify ctxt 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; - (* FIXME is it OK to ignore the type instantiation info? - or should I be using it? *) - val typs_unify = - SOME (Sign.typ_unify (Proof_Context.theory_of ctxt) (pat_ty, tgt_ty) (Vartab.empty, ix)) - handle Type.TUNIFY => NONE; - in - (case typs_unify of - SOME (typinsttab, ix2) => - let - (* FIXME 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), - Vartab.dest (Envir.term_env env)); - val initenv = - Envir.Envir {maxidx = ix2, tenv = Vartab.empty, tyenv = typinsttab}; - val useq = Unify.smash_unifiers (Context.Proof ctxt) [a] initenv - handle ListPair.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 ListPair.UnequalLengths => NONE - | Term.TERM _ => NONE; - in - (Seq.make (clean_unify' useq)) - end - | NONE => Seq.empty) - end; - -(* 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_unify_z ctxt maxidx pat z = - let val (t, (FakeTs, Ts, absterm)) = prep_zipper_match z in - Seq.map (fn insts => (insts, FakeTs, Ts, absterm)) - (clean_unify ctxt maxidx (t, pat)) - end; - - -fun bot_left_leaf_of (l $ _) = bot_left_leaf_of l - | bot_left_leaf_of (Abs (_, _, 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 (Zipper.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 [Zipper.Here z] else [] in - (case Zipper.trm z of - _ $ _ => - [Zipper.LookIn (Zipper.move_down_left z)] @ here @ - [Zipper.LookIn (Zipper.move_down_right z)] - | Abs _ => here @ [Zipper.LookIn (Zipper.move_down_abs z)] - | _ => here) - end; - in Zipper.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 [Zipper.Here z] else [] in - (case Zipper.trm z of - _ $ _ => - [Zipper.LookIn (Zipper.move_down_left z), - Zipper.LookIn (Zipper.move_down_right z)] @ here - | Abs _ => [Zipper.LookIn (Zipper.move_down_abs z)] @ here - | _ => here) - end; - in Zipper.lzy_search sf_valid_td_lr end; - -fun searchf_unify_gen f (ctxt, maxidx, z) lhs = - Seq.map (clean_unify_z ctxt maxidx lhs) (Zipper.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 *) -(* 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 ctxt i st (cfvs, conclthm) rule m = - RW_Inst.rw ctxt m rule conclthm - |> unfix_frees cfvs - |> Conv.fconv_rule Drule.beta_eta_conversion - |> (fn r => resolve_tac ctxt [r] i st); - -(* 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 ctxt i gth = - let - val th = Thm.incr_indexes 1 gth; - val tgt_term = Thm.prop_of th; - - val (fixedbody, fvs) = IsaND.fix_alls_term ctxt i tgt_term; - val cfvs = rev (map (Thm.cterm_of ctxt) fvs); - - val conclterm = Logic.strip_imp_concl fixedbody; - val conclthm = Thm.trivial (Thm.cterm_of ctxt conclterm); - val maxidx = Thm.maxidx_of th; - val ft = - (Zipper.move_down_right (* ==> *) - o Zipper.move_down_left (* Trueprop *) - o Zipper.mktop - o Thm.prop_of) conclthm - in - ((cfvs, conclthm), (ctxt, maxidx, ft)) - end; - -(* substitute using an object or meta level equality *) -fun eqsubst_tac' ctxt searchf instepthm i st = - let - val (cvfsconclthm, searchinfo) = prep_concl_subst ctxt i st; - 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 ctxt i st cvfsconclthm r) - end; - in stepthms |> Seq.maps rewrite_with_thm end; - - -(* General substitution of multiple occurrences using one of - the given theorems *) - -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 "occs" argument is a list of integers indicating which occurrence -w.r.t. the search order, to rewrite. Backtracking will also find later -occurrences, but all earlier ones are skipped. Thus you can use [0] to -just find all rewrites. *) - -fun eqsubst_tac ctxt occs thms i st = - let val nprems = Thm.nprems_of st in - if nprems < i then Seq.empty else - let - val thmseq = Seq.of_list thms; - fun apply_occ occ st = - thmseq |> Seq.maps (fn r => - eqsubst_tac' ctxt - (skip_first_occs_search occ searchf_lr_unify_valid) r - (i + (Thm.nprems_of st - nprems)) st); - val sorted_occs = Library.sort (rev_order o int_ord) occs; - in - Seq.maps distinct_subgoals_tac (Seq.EVERY (map apply_occ sorted_occs) st) - end - end; - - -(* apply a substitution inside assumption j, keeps asm in the same place *) -fun apply_subst_in_asm ctxt i st rule ((cfvs, j, _, pth),m) = - let - val st2 = Thm.rotate_rule (j - 1) i st; (* put premice first *) - val preelimrule = - RW_Inst.rw ctxt m rule pth - |> (Seq.hd o prune_params_tac ctxt) - |> Thm.permute_prems 0 ~1 (* put old asm first *) - |> unfix_frees cfvs (* unfix any global params *) - |> Conv.fconv_rule Drule.beta_eta_conversion; (* normal form *) - in - (* ~j because new asm starts at back, thus we subtract 1 *) - Seq.map (Thm.rotate_rule (~ j) (Thm.nprems_of rule + i)) - (dresolve_tac ctxt [preelimrule] i st2) - 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 ctxt i gth j = - let - val th = Thm.incr_indexes 1 gth; - val tgt_term = Thm.prop_of th; - - val (fixedbody, fvs) = IsaND.fix_alls_term ctxt i tgt_term; - val cfvs = rev (map (Thm.cterm_of ctxt) fvs); - - val asmt = nth (Logic.strip_imp_prems fixedbody) (j - 1); - val asm_nprems = length (Logic.strip_imp_prems asmt); - - val pth = Thm.trivial ((Thm.cterm_of ctxt) asmt); - val maxidx = Thm.maxidx_of th; - - val ft = - (Zipper.move_down_right (* trueprop *) - o Zipper.mktop - o Thm.prop_of) pth - in ((cfvs, j, asm_nprems, pth), (ctxt, maxidx, ft)) end; - -(* prepare subst in every possible assumption *) -fun prep_subst_in_asms ctxt i gth = - map (prep_subst_in_asm ctxt 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 st = - let - val asmpreps = prep_subst_in_asms ctxt i st; - 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 ctxt i st 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 occs thms i st = - let val nprems = Thm.nprems_of st in - if nprems < i then Seq.empty - else - let - val thmseq = Seq.of_list thms; - fun apply_occ occ st = - thmseq |> Seq.maps (fn r => - eqsubst_asm_tac' ctxt - (skip_first_asm_occs_search searchf_lr_unify_valid) occ r - (i + (Thm.nprems_of st - nprems)) st); - val sorted_occs = Library.sort (rev_order o int_ord) occs; - in - Seq.maps distinct_subgoals_tac (Seq.EVERY (map apply_occ sorted_occs) st) - end - end; - -(* 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 *) -val _ = - Theory.setup - (Method.setup \<^binding>\sub\ - (Scan.lift (Args.mode "asm" -- Scan.optional (Args.parens (Scan.repeat Parse.nat)) [0]) -- - Attrib.thms >> (fn ((asm, occs), inthms) => fn ctxt => - SIMPLE_METHOD' ((if asm then eqsubst_asm_tac else eqsubst_tac) ctxt occs inthms))) - "single-step substitution" - #> - (Method.setup \<^binding>\subst\ - (Scan.lift (Args.mode "asm" -- Scan.optional (Args.parens (Scan.repeat Parse.nat)) [0]) -- - Attrib.thms >> (fn ((asm, occs), inthms) => fn ctxt => - SIMPLE_METHOD' (SIDE_CONDS - ((if asm then eqsubst_asm_tac else eqsubst_tac) ctxt occs inthms) - ctxt))) - "single-step substitution with auto-typechecking")) - -end; -- cgit v1.2.3