wenzelm@30160
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(* Title: Tools/eqsubst.ML
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wenzelm@29269
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Author: Lucas Dixon, University of Edinburgh
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wenzelm@18598
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wenzelm@18598
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A proof method to perform a substiution using an equation.
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paulson@15481
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*)
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paulson@15481
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wenzelm@18591
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signature EQSUBST =
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paulson@15481
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sig
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wenzelm@29269
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(* a type abbreviation for match information *)
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dixon@19871
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type match =
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dixon@19871
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((indexname * (sort * typ)) list (* type instantiations *)
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* (indexname * (typ * term)) list) (* term instantiations *)
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* (string * typ) list (* fake named type abs env *)
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* (string * typ) list (* type abs env *)
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* term (* outer term *)
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type searchinfo =
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theory
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* int (* maxidx *)
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* Zipper.T (* focusterm to search under *)
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exception eqsubst_occL_exp of
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string * int list * thm list * int * thm
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(* low level substitution functions *)
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val apply_subst_in_asm :
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int ->
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thm ->
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thm ->
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(cterm list * int * 'a * thm) * match -> thm Seq.seq
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dixon@19871
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val apply_subst_in_concl :
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dixon@19871
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int ->
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wenzelm@31301
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thm ->
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cterm list * thm ->
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thm -> match -> thm Seq.seq
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(* matching/unification within zippers *)
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val clean_match_z :
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theory -> term -> Zipper.T -> match option
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val clean_unify_z :
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theory -> int -> term -> Zipper.T -> match Seq.seq
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(* skipping things in seq seq's *)
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(* skipping non-empty sub-sequences but when we reach the end
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of the seq, remembering how much we have left to skip. *)
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datatype 'a skipseq = SkipMore of int
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| SkipSeq of 'a Seq.seq Seq.seq;
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val skip_first_asm_occs_search :
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('a -> 'b -> 'c Seq.seq Seq.seq) ->
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'a -> int -> 'b -> 'c skipseq
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val skip_first_occs_search :
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int -> ('a -> 'b -> 'c Seq.seq Seq.seq) -> 'a -> 'b -> 'c Seq.seq
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val skipto_skipseq : int -> 'a Seq.seq Seq.seq -> 'a skipseq
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(* tactics *)
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val eqsubst_asm_tac :
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Proof.context ->
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int list -> thm list -> int -> tactic
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val eqsubst_asm_tac' :
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Proof.context ->
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(searchinfo -> int -> term -> match skipseq) ->
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int -> thm -> int -> tactic
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val eqsubst_tac :
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Proof.context ->
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int list -> (* list of occurences to rewrite, use [0] for any *)
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thm list -> int -> tactic
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val eqsubst_tac' :
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Proof.context -> (* proof context *)
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(searchinfo -> term -> match Seq.seq) (* search function *)
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-> thm (* equation theorem to rewrite with *)
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dixon@22727
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-> int (* subgoal number in goal theorem *)
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-> thm (* goal theorem *)
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-> thm Seq.seq (* rewritten goal theorem *)
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val fakefree_badbounds :
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wenzelm@31301
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(string * typ) list ->
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term ->
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(string * typ) list * (string * typ) list * term
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val mk_foo_match :
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(term -> term) ->
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('a * typ) list -> term -> term
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(* preparing substitution *)
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val prep_meta_eq : Proof.context -> thm -> thm list
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val prep_concl_subst :
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int -> thm -> (cterm list * thm) * searchinfo
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val prep_subst_in_asm :
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int -> thm -> int ->
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(cterm list * int * int * thm) * searchinfo
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val prep_subst_in_asms :
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int -> thm ->
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((cterm list * int * int * thm) * searchinfo) list
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val prep_zipper_match :
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Zipper.T -> term * ((string * typ) list * (string * typ) list * term)
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(* search for substitutions *)
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val valid_match_start : Zipper.T -> bool
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val search_lr_all : Zipper.T -> Zipper.T Seq.seq
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val search_lr_valid : (Zipper.T -> bool) -> Zipper.T -> Zipper.T Seq.seq
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val searchf_lr_unify_all :
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searchinfo -> term -> match Seq.seq Seq.seq
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val searchf_lr_unify_valid :
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searchinfo -> term -> match Seq.seq Seq.seq
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val searchf_bt_unify_valid :
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wenzelm@31301
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searchinfo -> term -> match Seq.seq Seq.seq
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(* syntax tools *)
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wenzelm@30518
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val ith_syntax : int list parser
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wenzelm@30518
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val options_syntax : bool parser
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dixon@19871
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(* Isar level hooks *)
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wenzelm@31301
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val eqsubst_asm_meth : Proof.context -> int list -> thm list -> Proof.method
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val eqsubst_meth : Proof.context -> int list -> thm list -> Proof.method
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val setup : theory -> theory
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paulson@15481
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end;
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dixon@19835
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structure EqSubst
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: EQSUBST
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= struct
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dixon@16004
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structure Z = Zipper;
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(* changes object "=" to meta "==" which prepares a given rewrite rule *)
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fun prep_meta_eq ctxt =
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wenzelm@32149
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Simplifier.mksimps (simpset_of ctxt) #> map Drule.zero_var_indexes;
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wenzelm@18598
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paulson@15481
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dixon@15915
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(* a type abriviation for match information *)
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wenzelm@16978
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type match =
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wenzelm@16978
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((indexname * (sort * typ)) list (* type instantiations *)
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wenzelm@16978
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* (indexname * (typ * term)) list) (* term instantiations *)
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wenzelm@16978
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* (string * typ) list (* fake named type abs env *)
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wenzelm@16978
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* (string * typ) list (* type abs env *)
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wenzelm@16978
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* term (* outer term *)
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dixon@15550
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wenzelm@16978
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type searchinfo =
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wenzelm@18598
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theory
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dixon@16004
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* int (* maxidx *)
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dixon@19835
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* Zipper.T (* focusterm to search under *)
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dixon@19835
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dixon@19835
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dixon@19835
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(* skipping non-empty sub-sequences but when we reach the end
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dixon@19835
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of the seq, remembering how much we have left to skip. *)
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dixon@19835
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datatype 'a skipseq = SkipMore of int
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dixon@19835
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| SkipSeq of 'a Seq.seq Seq.seq;
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(* given a seqseq, skip the first m non-empty seq's, note deficit *)
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dixon@19835
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fun skipto_skipseq m s =
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let
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fun skip_occs n sq =
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case Seq.pull sq of
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NONE => SkipMore n
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| SOME (h,t) =>
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(case Seq.pull h of NONE => skip_occs n t
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| SOME _ => if n <= 1 then SkipSeq (Seq.cons h t)
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else skip_occs (n - 1) t)
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in (skip_occs m s) end;
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dixon@19835
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dixon@19835
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(* note: outerterm is the taget with the match replaced by a bound
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variable : ie: "P lhs" beocmes "%x. P x"
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insts is the types of instantiations of vars in lhs
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and typinsts is the type instantiations of types in the lhs
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Note: Final rule is the rule lifted into the ontext of the
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taget thm. *)
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dixon@19835
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fun mk_foo_match mkuptermfunc Ts t =
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let
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val ty = Term.type_of t
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val bigtype = (rev (map snd Ts)) ---> ty
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fun mk_foo 0 t = t
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| mk_foo i t = mk_foo (i - 1) (t $ (Bound (i - 1)))
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val num_of_bnds = (length Ts)
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(* foo_term = "fooabs y0 ... yn" where y's are local bounds *)
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val foo_term = mk_foo num_of_bnds (Bound num_of_bnds)
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in Abs("fooabs", bigtype, mkuptermfunc foo_term) end;
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(* T is outer bound vars, n is number of locally bound vars *)
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(* THINK: is order of Ts correct...? or reversed? *)
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fun fakefree_badbounds Ts t =
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let val (FakeTs,Ts,newnames) =
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dixon@19835
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List.foldr (fn ((n,ty),(FakeTs,Ts,usednames)) =>
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wenzelm@20071
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let val newname = Name.variant usednames n
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dixon@19835
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in ((RWTools.mk_fake_bound_name newname,ty)::FakeTs,
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(newname,ty)::Ts,
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newname::usednames) end)
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([],[],[])
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Ts
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in (FakeTs, Ts, Term.subst_bounds (map Free FakeTs, t)) end;
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(* before matching we need to fake the bound vars that are missing an
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dixon@19835
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abstraction. In this function we additionally construct the
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dixon@19835
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abstraction environment, and an outer context term (with the focus
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dixon@19835
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abstracted out) for use in rewriting with RWInst.rw *)
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dixon@19835
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fun prep_zipper_match z =
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dixon@19835
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let
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val t = Z.trm z
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val c = Z.ctxt z
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val Ts = Z.C.nty_ctxt c
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val (FakeTs', Ts', t') = fakefree_badbounds Ts t
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val absterm = mk_foo_match (Z.C.apply c) Ts' t'
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in
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(t', (FakeTs', Ts', absterm))
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end;
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dixon@19835
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dixon@19835
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(* Matching and Unification with exception handled *)
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dixon@19835
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fun clean_match thy (a as (pat, t)) =
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dixon@19835
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let val (tyenv, tenv) = Pattern.match thy a (Vartab.empty, Vartab.empty)
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in SOME (Vartab.dest tyenv, Vartab.dest tenv)
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end handle Pattern.MATCH => NONE;
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dixon@27033
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dixon@19835
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(* given theory, max var index, pat, tgt; returns Seq of instantiations *)
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dixon@27033
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fun clean_unify thry ix (a as (pat, tgt)) =
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dixon@19835
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let
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dixon@19835
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(* type info will be re-derived, maybe this can be cached
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for efficiency? *)
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val pat_ty = Term.type_of pat;
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val tgt_ty = Term.type_of tgt;
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dixon@19835
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(* is it OK to ignore the type instantiation info?
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dixon@19835
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or should I be using it? *)
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dixon@19835
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val typs_unify =
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wenzelm@29269
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SOME (Sign.typ_unify thry (pat_ty, tgt_ty) (Vartab.empty, ix))
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dixon@19835
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handle Type.TUNIFY => NONE;
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dixon@19835
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in
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case typs_unify of
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dixon@19835
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SOME (typinsttab, ix2) =>
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dixon@19835
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let
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dixon@19835
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(* is it right to throw away the flexes?
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dixon@19835
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or should I be using them somehow? *)
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dixon@19835
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fun mk_insts env =
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dixon@19835
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(Vartab.dest (Envir.type_env env),
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wenzelm@32043
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Vartab.dest (Envir.term_env env));
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wenzelm@32043
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val initenv =
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wenzelm@32043
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Envir.Envir {maxidx = ix2, tenv = Vartab.empty, tyenv = typinsttab};
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dixon@27033
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val useq = Unify.smash_unifiers thry [a] initenv
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dixon@19835
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handle UnequalLengths => Seq.empty
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dixon@19835
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| Term.TERM _ => Seq.empty;
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dixon@19835
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fun clean_unify' useq () =
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dixon@19835
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(case (Seq.pull useq) of
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dixon@19835
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NONE => NONE
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dixon@19835
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| SOME (h,t) => SOME (mk_insts h, Seq.make (clean_unify' t)))
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dixon@27033
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handle UnequalLengths => NONE
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dixon@27033
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| Term.TERM _ => NONE
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dixon@19835
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in
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dixon@19835
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(Seq.make (clean_unify' useq))
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dixon@19835
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end
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dixon@19835
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| NONE => Seq.empty
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dixon@19835
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end;
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dixon@19835
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dixon@19835
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(* Matching and Unification for zippers *)
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dixon@19835
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(* Note: Ts is a modified version of the original names of the outer
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dixon@19835
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bound variables. New names have been introduced to make sure they are
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dixon@19835
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unique w.r.t all names in the term and each other. usednames' is
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dixon@19835
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oldnames + new names. *)
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dixon@19835
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fun clean_match_z thy pat z =
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dixon@19835
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let val (t, (FakeTs,Ts,absterm)) = prep_zipper_match z in
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dixon@19835
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case clean_match thy (pat, t) of
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dixon@19835
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NONE => NONE
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dixon@19835
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| SOME insts => SOME (insts, FakeTs, Ts, absterm) end;
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dixon@19835
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(* ix = max var index *)
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dixon@19835
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fun clean_unify_z sgn ix pat z =
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dixon@19835
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let val (t, (FakeTs, Ts,absterm)) = prep_zipper_match z in
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dixon@19835
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Seq.map (fn insts => (insts, FakeTs, Ts, absterm))
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dixon@19835
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(clean_unify sgn ix (t, pat)) end;
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dixon@19835
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dixon@15550
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dixon@15538
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(* FOR DEBUGGING...
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dixon@15538
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type trace_subst_errT = int (* subgoal *)
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wenzelm@16978
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* thm (* thm with all goals *)
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dixon@15538
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* (Thm.cterm list (* certified free var placeholders for vars *)
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wenzelm@16978
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* thm) (* trivial thm of goal concl *)
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dixon@15538
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(* possible matches/unifiers *)
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wenzelm@16978
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* thm (* rule *)
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wenzelm@16978
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* (((indexname * typ) list (* type instantiations *)
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wenzelm@16978
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* (indexname * term) list ) (* term instantiations *)
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wenzelm@16978
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* (string * typ) list (* Type abs env *)
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wenzelm@16978
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* term) (* outer term *);
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dixon@15538
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wenzelm@32740
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val trace_subst_err = (Unsynchronized.ref NONE : trace_subst_errT option Unsynchronized.ref);
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wenzelm@32740
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val trace_subst_search = Unsynchronized.ref false;
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dixon@15538
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exception trace_subst_exp of trace_subst_errT;
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dixon@19835
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*)
|
dixon@19835
|
285 |
|
dixon@19835
|
286 |
|
dixon@19835
|
287 |
fun bot_left_leaf_of (l $ r) = bot_left_leaf_of l
|
dixon@19835
|
288 |
| bot_left_leaf_of (Abs(s,ty,t)) = bot_left_leaf_of t
|
dixon@19835
|
289 |
| bot_left_leaf_of x = x;
|
dixon@19835
|
290 |
|
dixon@19975
|
291 |
(* Avoid considering replacing terms which have a var at the head as
|
dixon@19975
|
292 |
they always succeed trivially, and uninterestingly. *)
|
dixon@19835
|
293 |
fun valid_match_start z =
|
dixon@19835
|
294 |
(case bot_left_leaf_of (Z.trm z) of
|
dixon@19975
|
295 |
Var _ => false
|
dixon@19975
|
296 |
| _ => true);
|
dixon@19975
|
297 |
|
dixon@19835
|
298 |
(* search from top, left to right, then down *)
|
dixon@19871
|
299 |
val search_lr_all = ZipperSearch.all_bl_ur;
|
dixon@15538
|
300 |
|
dixon@15814
|
301 |
(* search from top, left to right, then down *)
|
dixon@19871
|
302 |
fun search_lr_valid validf =
|
dixon@19835
|
303 |
let
|
dixon@19835
|
304 |
fun sf_valid_td_lr z =
|
dixon@19835
|
305 |
let val here = if validf z then [Z.Here z] else [] in
|
dixon@19835
|
306 |
case Z.trm z
|
dixon@19871
|
307 |
of _ $ _ => [Z.LookIn (Z.move_down_left z)]
|
dixon@19871
|
308 |
@ here
|
dixon@19871
|
309 |
@ [Z.LookIn (Z.move_down_right z)]
|
dixon@19835
|
310 |
| Abs _ => here @ [Z.LookIn (Z.move_down_abs z)]
|
dixon@19835
|
311 |
| _ => here
|
dixon@19835
|
312 |
end;
|
dixon@19835
|
313 |
in Z.lzy_search sf_valid_td_lr end;
|
dixon@15814
|
314 |
|
narboux@23064
|
315 |
(* search from bottom to top, left to right *)
|
narboux@23064
|
316 |
|
narboux@23064
|
317 |
fun search_bt_valid validf =
|
narboux@23064
|
318 |
let
|
narboux@23064
|
319 |
fun sf_valid_td_lr z =
|
narboux@23064
|
320 |
let val here = if validf z then [Z.Here z] else [] in
|
narboux@23064
|
321 |
case Z.trm z
|
narboux@23064
|
322 |
of _ $ _ => [Z.LookIn (Z.move_down_left z),
|
narboux@23064
|
323 |
Z.LookIn (Z.move_down_right z)] @ here
|
narboux@23064
|
324 |
| Abs _ => [Z.LookIn (Z.move_down_abs z)] @ here
|
narboux@23064
|
325 |
| _ => here
|
narboux@23064
|
326 |
end;
|
narboux@23064
|
327 |
in Z.lzy_search sf_valid_td_lr end;
|
narboux@23064
|
328 |
|
narboux@23064
|
329 |
fun searchf_unify_gen f (sgn, maxidx, z) lhs =
|
narboux@23064
|
330 |
Seq.map (clean_unify_z sgn maxidx lhs)
|
narboux@23064
|
331 |
(Z.limit_apply f z);
|
narboux@23064
|
332 |
|
dixon@15814
|
333 |
(* search all unifications *)
|
narboux@23064
|
334 |
val searchf_lr_unify_all =
|
narboux@23064
|
335 |
searchf_unify_gen search_lr_all;
|
paulson@15481
|
336 |
|
dixon@15814
|
337 |
(* search only for 'valid' unifiers (non abs subterms and non vars) *)
|
narboux@23064
|
338 |
val searchf_lr_unify_valid =
|
narboux@23064
|
339 |
searchf_unify_gen (search_lr_valid valid_match_start);
|
dixon@15929
|
340 |
|
narboux@23064
|
341 |
val searchf_bt_unify_valid =
|
narboux@23064
|
342 |
searchf_unify_gen (search_bt_valid valid_match_start);
|
dixon@15814
|
343 |
|
dixon@15538
|
344 |
(* apply a substitution in the conclusion of the theorem th *)
|
dixon@15538
|
345 |
(* cfvs are certified free var placeholders for goal params *)
|
dixon@15538
|
346 |
(* conclthm is a theorem of for just the conclusion *)
|
dixon@15538
|
347 |
(* m is instantiation/match information *)
|
dixon@15538
|
348 |
(* rule is the equation for substitution *)
|
wenzelm@16978
|
349 |
fun apply_subst_in_concl i th (cfvs, conclthm) rule m =
|
dixon@15538
|
350 |
(RWInst.rw m rule conclthm)
|
dixon@15855
|
351 |
|> IsaND.unfix_frees cfvs
|
dixon@15915
|
352 |
|> RWInst.beta_eta_contract
|
dixon@15538
|
353 |
|> (fn r => Tactic.rtac r i th);
|
paulson@15481
|
354 |
|
paulson@15481
|
355 |
(* substitute within the conclusion of goal i of gth, using a meta
|
dixon@15538
|
356 |
equation rule. Note that we assume rule has var indicies zero'd *)
|
wenzelm@16978
|
357 |
fun prep_concl_subst i gth =
|
wenzelm@16978
|
358 |
let
|
paulson@15481
|
359 |
val th = Thm.incr_indexes 1 gth;
|
paulson@15481
|
360 |
val tgt_term = Thm.prop_of th;
|
paulson@15481
|
361 |
|
wenzelm@22578
|
362 |
val sgn = Thm.theory_of_thm th;
|
paulson@15481
|
363 |
val ctermify = Thm.cterm_of sgn;
|
paulson@15481
|
364 |
val trivify = Thm.trivial o ctermify;
|
paulson@15481
|
365 |
|
paulson@15481
|
366 |
val (fixedbody, fvs) = IsaND.fix_alls_term i tgt_term;
|
paulson@15481
|
367 |
val cfvs = rev (map ctermify fvs);
|
paulson@15481
|
368 |
|
dixon@15538
|
369 |
val conclterm = Logic.strip_imp_concl fixedbody;
|
dixon@15538
|
370 |
val conclthm = trivify conclterm;
|
dixon@27033
|
371 |
val maxidx = Thm.maxidx_of th;
|
dixon@19835
|
372 |
val ft = ((Z.move_down_right (* ==> *)
|
dixon@19835
|
373 |
o Z.move_down_left (* Trueprop *)
|
dixon@19835
|
374 |
o Z.mktop
|
dixon@16004
|
375 |
o Thm.prop_of) conclthm)
|
paulson@15481
|
376 |
in
|
dixon@16004
|
377 |
((cfvs, conclthm), (sgn, maxidx, ft))
|
paulson@15481
|
378 |
end;
|
paulson@15481
|
379 |
|
paulson@15481
|
380 |
(* substitute using an object or meta level equality *)
|
wenzelm@18598
|
381 |
fun eqsubst_tac' ctxt searchf instepthm i th =
|
wenzelm@16978
|
382 |
let
|
dixon@16004
|
383 |
val (cvfsconclthm, searchinfo) = prep_concl_subst i th;
|
wenzelm@18598
|
384 |
val stepthms = Seq.of_list (prep_meta_eq ctxt instepthm);
|
dixon@15538
|
385 |
fun rewrite_with_thm r =
|
dixon@15538
|
386 |
let val (lhs,_) = Logic.dest_equals (Thm.concl_of r);
|
wenzelm@18598
|
387 |
in searchf searchinfo lhs
|
wenzelm@18598
|
388 |
|> Seq.maps (apply_subst_in_concl i th cvfsconclthm r) end;
|
wenzelm@18598
|
389 |
in stepthms |> Seq.maps rewrite_with_thm end;
|
dixon@15538
|
390 |
|
dixon@15538
|
391 |
|
wenzelm@19047
|
392 |
(* distinct subgoals *)
|
wenzelm@19047
|
393 |
fun distinct_subgoals th =
|
wenzelm@19047
|
394 |
the_default th (SINGLE distinct_subgoals_tac th);
|
dixon@15959
|
395 |
|
wenzelm@19047
|
396 |
(* General substitution of multiple occurances using one of
|
dixon@15936
|
397 |
the given theorems*)
|
dixon@19835
|
398 |
|
dixon@19835
|
399 |
|
wenzelm@16978
|
400 |
exception eqsubst_occL_exp of
|
wenzelm@16978
|
401 |
string * (int list) * (thm list) * int * thm;
|
wenzelm@16978
|
402 |
fun skip_first_occs_search occ srchf sinfo lhs =
|
dixon@19835
|
403 |
case (skipto_skipseq occ (srchf sinfo lhs)) of
|
dixon@19835
|
404 |
SkipMore _ => Seq.empty
|
dixon@19835
|
405 |
| SkipSeq ss => Seq.flat ss;
|
dixon@16004
|
406 |
|
dixon@22727
|
407 |
(* The occL is a list of integers indicating which occurence
|
dixon@22727
|
408 |
w.r.t. the search order, to rewrite. Backtracking will also find later
|
dixon@22727
|
409 |
occurences, but all earlier ones are skipped. Thus you can use [0] to
|
dixon@22727
|
410 |
just find all rewrites. *)
|
dixon@22727
|
411 |
|
wenzelm@18598
|
412 |
fun eqsubst_tac ctxt occL thms i th =
|
dixon@15936
|
413 |
let val nprems = Thm.nprems_of th in
|
dixon@15936
|
414 |
if nprems < i then Seq.empty else
|
wenzelm@16978
|
415 |
let val thmseq = (Seq.of_list thms)
|
wenzelm@16978
|
416 |
fun apply_occ occ th =
|
wenzelm@18598
|
417 |
thmseq |> Seq.maps
|
dixon@19835
|
418 |
(fn r => eqsubst_tac'
|
dixon@19835
|
419 |
ctxt
|
dixon@19835
|
420 |
(skip_first_occs_search
|
dixon@19871
|
421 |
occ searchf_lr_unify_valid) r
|
dixon@15936
|
422 |
(i + ((Thm.nprems_of th) - nprems))
|
dixon@15936
|
423 |
th);
|
wenzelm@16978
|
424 |
val sortedoccL =
|
dixon@16004
|
425 |
Library.sort (Library.rev_order o Library.int_ord) occL;
|
dixon@15936
|
426 |
in
|
dixon@16004
|
427 |
Seq.map distinct_subgoals (Seq.EVERY (map apply_occ sortedoccL) th)
|
dixon@15936
|
428 |
end
|
dixon@15959
|
429 |
end
|
dixon@15959
|
430 |
handle THM _ => raise eqsubst_occL_exp ("THM",occL,thms,i,th);
|
dixon@15959
|
431 |
|
paulson@15481
|
432 |
|
paulson@15481
|
433 |
(* inthms are the given arguments in Isar, and treated as eqstep with
|
paulson@15481
|
434 |
the first one, then the second etc *)
|
wenzelm@18598
|
435 |
fun eqsubst_meth ctxt occL inthms =
|
wenzelm@30515
|
436 |
SIMPLE_METHOD' (eqsubst_tac ctxt occL inthms);
|
paulson@15481
|
437 |
|
dixon@16004
|
438 |
(* apply a substitution inside assumption j, keeps asm in the same place *)
|
wenzelm@16978
|
439 |
fun apply_subst_in_asm i th rule ((cfvs, j, ngoalprems, pth),m) =
|
wenzelm@16978
|
440 |
let
|
dixon@16004
|
441 |
val th2 = Thm.rotate_rule (j - 1) i th; (* put premice first *)
|
wenzelm@16978
|
442 |
val preelimrule =
|
dixon@16004
|
443 |
(RWInst.rw m rule pth)
|
wenzelm@21708
|
444 |
|> (Seq.hd o prune_params_tac)
|
dixon@16004
|
445 |
|> Thm.permute_prems 0 ~1 (* put old asm first *)
|
dixon@16004
|
446 |
|> IsaND.unfix_frees cfvs (* unfix any global params *)
|
dixon@16004
|
447 |
|> RWInst.beta_eta_contract; (* normal form *)
|
wenzelm@16978
|
448 |
(* val elimrule =
|
dixon@16004
|
449 |
preelimrule
|
dixon@16004
|
450 |
|> Tactic.make_elim (* make into elim rule *)
|
dixon@16004
|
451 |
|> Thm.lift_rule (th2, i); (* lift into context *)
|
dixon@16007
|
452 |
*)
|
dixon@16004
|
453 |
in
|
dixon@16004
|
454 |
(* ~j because new asm starts at back, thus we subtract 1 *)
|
dixon@16007
|
455 |
Seq.map (Thm.rotate_rule (~j) ((Thm.nprems_of rule) + i))
|
dixon@16007
|
456 |
(Tactic.dtac preelimrule i th2)
|
dixon@16007
|
457 |
|
wenzelm@16978
|
458 |
(* (Thm.bicompose
|
dixon@16004
|
459 |
false (* use unification *)
|
dixon@16004
|
460 |
(true, (* elim resolution *)
|
dixon@16007
|
461 |
elimrule, (2 + (Thm.nprems_of rule)) - ngoalprems)
|
dixon@16007
|
462 |
i th2) *)
|
dixon@16004
|
463 |
end;
|
dixon@15538
|
464 |
|
dixon@15538
|
465 |
|
dixon@15538
|
466 |
(* prepare to substitute within the j'th premise of subgoal i of gth,
|
dixon@15538
|
467 |
using a meta-level equation. Note that we assume rule has var indicies
|
dixon@15538
|
468 |
zero'd. Note that we also assume that premt is the j'th premice of
|
dixon@15538
|
469 |
subgoal i of gth. Note the repetition of work done for each
|
dixon@15538
|
470 |
assumption, i.e. this can be made more efficient for search over
|
dixon@15538
|
471 |
multiple assumptions. *)
|
wenzelm@16978
|
472 |
fun prep_subst_in_asm i gth j =
|
wenzelm@16978
|
473 |
let
|
paulson@15481
|
474 |
val th = Thm.incr_indexes 1 gth;
|
paulson@15481
|
475 |
val tgt_term = Thm.prop_of th;
|
paulson@15481
|
476 |
|
wenzelm@22578
|
477 |
val sgn = Thm.theory_of_thm th;
|
paulson@15481
|
478 |
val ctermify = Thm.cterm_of sgn;
|
paulson@15481
|
479 |
val trivify = Thm.trivial o ctermify;
|
paulson@15481
|
480 |
|
paulson@15481
|
481 |
val (fixedbody, fvs) = IsaND.fix_alls_term i tgt_term;
|
paulson@15481
|
482 |
val cfvs = rev (map ctermify fvs);
|
paulson@15481
|
483 |
|
haftmann@18011
|
484 |
val asmt = nth (Logic.strip_imp_prems fixedbody) (j - 1);
|
dixon@15538
|
485 |
val asm_nprems = length (Logic.strip_imp_prems asmt);
|
dixon@15538
|
486 |
|
dixon@15538
|
487 |
val pth = trivify asmt;
|
dixon@27033
|
488 |
val maxidx = Thm.maxidx_of th;
|
dixon@15538
|
489 |
|
dixon@19835
|
490 |
val ft = ((Z.move_down_right (* trueprop *)
|
dixon@19835
|
491 |
o Z.mktop
|
dixon@16004
|
492 |
o Thm.prop_of) pth)
|
dixon@16004
|
493 |
in ((cfvs, j, asm_nprems, pth), (sgn, maxidx, ft)) end;
|
paulson@15481
|
494 |
|
dixon@15538
|
495 |
(* prepare subst in every possible assumption *)
|
wenzelm@16978
|
496 |
fun prep_subst_in_asms i gth =
|
dixon@16004
|
497 |
map (prep_subst_in_asm i gth)
|
dixon@19835
|
498 |
((fn l => Library.upto (1, length l))
|
dixon@16004
|
499 |
(Logic.prems_of_goal (Thm.prop_of gth) i));
|
dixon@15538
|
500 |
|
dixon@15538
|
501 |
|
dixon@15538
|
502 |
(* substitute in an assumption using an object or meta level equality *)
|
wenzelm@18598
|
503 |
fun eqsubst_asm_tac' ctxt searchf skipocc instepthm i th =
|
wenzelm@16978
|
504 |
let
|
dixon@16004
|
505 |
val asmpreps = prep_subst_in_asms i th;
|
wenzelm@18598
|
506 |
val stepthms = Seq.of_list (prep_meta_eq ctxt instepthm);
|
dixon@16004
|
507 |
fun rewrite_with_thm r =
|
dixon@16004
|
508 |
let val (lhs,_) = Logic.dest_equals (Thm.concl_of r)
|
dixon@16004
|
509 |
fun occ_search occ [] = Seq.empty
|
dixon@16004
|
510 |
| occ_search occ ((asminfo, searchinfo)::moreasms) =
|
wenzelm@16978
|
511 |
(case searchf searchinfo occ lhs of
|
dixon@19835
|
512 |
SkipMore i => occ_search i moreasms
|
dixon@19835
|
513 |
| SkipSeq ss =>
|
wenzelm@19861
|
514 |
Seq.append (Seq.map (Library.pair asminfo) (Seq.flat ss))
|
wenzelm@19861
|
515 |
(occ_search 1 moreasms))
|
dixon@16004
|
516 |
(* find later substs also *)
|
wenzelm@16978
|
517 |
in
|
wenzelm@18598
|
518 |
occ_search skipocc asmpreps |> Seq.maps (apply_subst_in_asm i th r)
|
dixon@16004
|
519 |
end;
|
wenzelm@18598
|
520 |
in stepthms |> Seq.maps rewrite_with_thm end;
|
dixon@15538
|
521 |
|
dixon@16004
|
522 |
|
wenzelm@16978
|
523 |
fun skip_first_asm_occs_search searchf sinfo occ lhs =
|
dixon@19835
|
524 |
skipto_skipseq occ (searchf sinfo lhs);
|
dixon@16004
|
525 |
|
wenzelm@18598
|
526 |
fun eqsubst_asm_tac ctxt occL thms i th =
|
wenzelm@16978
|
527 |
let val nprems = Thm.nprems_of th
|
dixon@15538
|
528 |
in
|
dixon@16004
|
529 |
if nprems < i then Seq.empty else
|
wenzelm@16978
|
530 |
let val thmseq = (Seq.of_list thms)
|
wenzelm@16978
|
531 |
fun apply_occ occK th =
|
wenzelm@18598
|
532 |
thmseq |> Seq.maps
|
wenzelm@16978
|
533 |
(fn r =>
|
wenzelm@18598
|
534 |
eqsubst_asm_tac' ctxt (skip_first_asm_occs_search
|
dixon@19871
|
535 |
searchf_lr_unify_valid) occK r
|
dixon@16004
|
536 |
(i + ((Thm.nprems_of th) - nprems))
|
dixon@16004
|
537 |
th);
|
wenzelm@16978
|
538 |
val sortedoccs =
|
dixon@16004
|
539 |
Library.sort (Library.rev_order o Library.int_ord) occL
|
dixon@16004
|
540 |
in
|
dixon@16004
|
541 |
Seq.map distinct_subgoals
|
dixon@16004
|
542 |
(Seq.EVERY (map apply_occ sortedoccs) th)
|
dixon@16004
|
543 |
end
|
dixon@16004
|
544 |
end
|
dixon@16004
|
545 |
handle THM _ => raise eqsubst_occL_exp ("THM",occL,thms,i,th);
|
paulson@15481
|
546 |
|
paulson@15481
|
547 |
(* inthms are the given arguments in Isar, and treated as eqstep with
|
paulson@15481
|
548 |
the first one, then the second etc *)
|
wenzelm@18598
|
549 |
fun eqsubst_asm_meth ctxt occL inthms =
|
wenzelm@30515
|
550 |
SIMPLE_METHOD' (eqsubst_asm_tac ctxt occL inthms);
|
paulson@15481
|
551 |
|
paulson@15481
|
552 |
(* syntax for options, given "(asm)" will give back true, without
|
paulson@15481
|
553 |
gives back false *)
|
paulson@15481
|
554 |
val options_syntax =
|
paulson@15481
|
555 |
(Args.parens (Args.$$$ "asm") >> (K true)) ||
|
paulson@15481
|
556 |
(Scan.succeed false);
|
dixon@15936
|
557 |
|
dixon@15929
|
558 |
val ith_syntax =
|
wenzelm@27809
|
559 |
Scan.optional (Args.parens (Scan.repeat OuterParse.nat)) [0];
|
paulson@15481
|
560 |
|
wenzelm@18598
|
561 |
(* combination method that takes a flag (true indicates that subst
|
wenzelm@31301
|
562 |
should be done to an assumption, false = apply to the conclusion of
|
wenzelm@31301
|
563 |
the goal) as well as the theorems to use *)
|
wenzelm@16978
|
564 |
val setup =
|
wenzelm@31301
|
565 |
Method.setup @{binding subst}
|
wenzelm@31301
|
566 |
(Scan.lift (options_syntax -- ith_syntax) -- Attrib.thms >>
|
wenzelm@31301
|
567 |
(fn ((asmflag, occL), inthms) => fn ctxt =>
|
wenzelm@31301
|
568 |
(if asmflag then eqsubst_asm_meth else eqsubst_meth) ctxt occL inthms))
|
wenzelm@31301
|
569 |
"single-step substitution";
|
paulson@15481
|
570 |
|
wenzelm@16978
|
571 |
end;
|