src/Pure/thm.ML
author berghofe
Wed Jul 11 11:59:21 2007 +0200 (2007-07-11)
changeset 23781 ab793a6ddf9f
parent 23657 2332c79f4dc8
child 24143 90a9a6fe0d01
permissions -rw-r--r--
Added function norm_proof for normalizing the proof term
corresponding to a theorem.
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(*  Title:      Pure/thm.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1994  University of Cambridge
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The very core of Isabelle's Meta Logic: certified types and terms,
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meta theorems, meta rules (including lifting and resolution).
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*)
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signature BASIC_THM =
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  sig
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  (*certified types*)
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  type ctyp
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  val rep_ctyp: ctyp ->
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   {thy: theory,
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    T: typ,
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    maxidx: int,
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    sorts: sort list}
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  val theory_of_ctyp: ctyp -> theory
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  val typ_of: ctyp -> typ
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  val ctyp_of: theory -> typ -> ctyp
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  (*certified terms*)
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  type cterm
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  exception CTERM of string * cterm list
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  val rep_cterm: cterm ->
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   {thy: theory,
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    t: term,
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    T: typ,
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    maxidx: int,
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    sorts: sort list}
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  val crep_cterm: cterm -> {thy: theory, t: term, T: ctyp, maxidx: int, sorts: sort list}
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  val theory_of_cterm: cterm -> theory
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  val term_of: cterm -> term
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  val cterm_of: theory -> term -> cterm
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  val ctyp_of_term: cterm -> ctyp
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  (*meta theorems*)
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  type thm
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  type conv = cterm -> thm
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  type attribute = Context.generic * thm -> Context.generic * thm
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  val rep_thm: thm ->
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   {thy: theory,
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    der: bool * Proofterm.proof,
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    tags: Markup.property list,
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    maxidx: int,
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    shyps: sort list,
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    hyps: term list,
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    tpairs: (term * term) list,
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    prop: term}
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  val crep_thm: thm ->
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   {thy: theory,
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    der: bool * Proofterm.proof,
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    tags: Markup.property list,
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    maxidx: int,
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    shyps: sort list,
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    hyps: cterm list,
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    tpairs: (cterm * cterm) list,
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    prop: cterm}
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  exception THM of string * int * thm list
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  val theory_of_thm: thm -> theory
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  val prop_of: thm -> term
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  val proof_of: thm -> Proofterm.proof
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  val tpairs_of: thm -> (term * term) list
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  val concl_of: thm -> term
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  val prems_of: thm -> term list
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  val nprems_of: thm -> int
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  val cprop_of: thm -> cterm
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  val cprem_of: thm -> int -> cterm
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  val transfer: theory -> thm -> thm
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  val weaken: cterm -> thm -> thm
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  val extra_shyps: thm -> sort list
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  val strip_shyps: thm -> thm
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  val get_axiom_i: theory -> string -> thm
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  val get_axiom: theory -> xstring -> thm
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  val def_name: string -> string
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  val def_name_optional: string -> string -> string
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  val get_def: theory -> xstring -> thm
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  val axioms_of: theory -> (string * thm) list
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  (*meta rules*)
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  val assume: cterm -> thm
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  val implies_intr: cterm -> thm -> thm
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  val implies_elim: thm -> thm -> thm
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  val forall_intr: cterm -> thm -> thm
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  val forall_elim: cterm -> thm -> thm
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  val reflexive: cterm -> thm
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  val symmetric: thm -> thm
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  val transitive: thm -> thm -> thm
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  val beta_conversion: bool -> conv
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  val eta_conversion: conv
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  val eta_long_conversion: conv
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  val abstract_rule: string -> cterm -> thm -> thm
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  val combination: thm -> thm -> thm
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  val equal_intr: thm -> thm -> thm
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  val equal_elim: thm -> thm -> thm
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  val flexflex_rule: thm -> thm Seq.seq
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  val generalize: string list * string list -> int -> thm -> thm
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  val instantiate: (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm
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  val instantiate_cterm: (ctyp * ctyp) list * (cterm * cterm) list -> cterm -> cterm
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  val trivial: cterm -> thm
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  val class_triv: theory -> class -> thm
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  val unconstrainT: ctyp -> thm -> thm
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  val dest_state: thm * int -> (term * term) list * term list * term * term
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  val lift_rule: cterm -> thm -> thm
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  val incr_indexes: int -> thm -> thm
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  val assumption: int -> thm -> thm Seq.seq
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  val eq_assumption: int -> thm -> thm
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  val rotate_rule: int -> int -> thm -> thm
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  val permute_prems: int -> int -> thm -> thm
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  val rename_params_rule: string list * int -> thm -> thm
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  val compose_no_flatten: bool -> thm * int -> int -> thm -> thm Seq.seq
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  val bicompose: bool -> bool * thm * int -> int -> thm -> thm Seq.seq
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  val biresolution: bool -> (bool * thm) list -> int -> thm -> thm Seq.seq
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  val invoke_oracle: theory -> xstring -> theory * Object.T -> thm
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  val invoke_oracle_i: theory -> string -> theory * Object.T -> thm
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end;
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signature THM =
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sig
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  include BASIC_THM
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  val dest_ctyp: ctyp -> ctyp list
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  val dest_comb: cterm -> cterm * cterm
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  val dest_fun: cterm -> cterm
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  val dest_arg: cterm -> cterm
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  val dest_fun2: cterm -> cterm
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  val dest_arg1: cterm -> cterm
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  val dest_abs: string option -> cterm -> cterm * cterm
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  val adjust_maxidx_cterm: int -> cterm -> cterm
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  val capply: cterm -> cterm -> cterm
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  val cabs: cterm -> cterm -> cterm
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  val major_prem_of: thm -> term
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  val no_prems: thm -> bool
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  val terms_of_tpairs: (term * term) list -> term list
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  val maxidx_of: thm -> int
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  val maxidx_thm: thm -> int -> int
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  val hyps_of: thm -> term list
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  val full_prop_of: thm -> term
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  val get_name: thm -> string
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  val put_name: string -> thm -> thm
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  val get_tags: thm -> Markup.property list
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  val map_tags: (Markup.property list -> Markup.property list) -> thm -> thm
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  val compress: thm -> thm
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  val norm_proof: thm -> thm
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  val adjust_maxidx_thm: int -> thm -> thm
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  val rename_boundvars: term -> term -> thm -> thm
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  val match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
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  val first_order_match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
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  val incr_indexes_cterm: int -> cterm -> cterm
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  val varifyT: thm -> thm
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  val varifyT': (string * sort) list -> thm -> ((string * sort) * indexname) list * thm
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  val freezeT: thm -> thm
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end;
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structure Thm: THM =
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struct
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structure Pt = Proofterm;
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(*** Certified terms and types ***)
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(** collect occurrences of sorts -- unless all sorts non-empty **)
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fun may_insert_typ_sorts thy T = if Sign.all_sorts_nonempty thy then I else Sorts.insert_typ T;
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fun may_insert_term_sorts thy t = if Sign.all_sorts_nonempty thy then I else Sorts.insert_term t;
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(*NB: type unification may invent new sorts*)
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fun may_insert_env_sorts thy (env as Envir.Envir {iTs, ...}) =
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  if Sign.all_sorts_nonempty thy then I
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  else Vartab.fold (fn (_, (_, T)) => Sorts.insert_typ T) iTs;
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(** certified types **)
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abstype ctyp = Ctyp of
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 {thy_ref: theory_ref,
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  T: typ,
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  maxidx: int,
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  sorts: sort list}
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with
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fun rep_ctyp (Ctyp {thy_ref, T, maxidx, sorts}) =
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  let val thy = Theory.deref thy_ref
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  in {thy = thy, T = T, maxidx = maxidx, sorts = sorts} end;
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fun theory_of_ctyp (Ctyp {thy_ref, ...}) = Theory.deref thy_ref;
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fun typ_of (Ctyp {T, ...}) = T;
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fun ctyp_of thy raw_T =
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  let val T = Sign.certify_typ thy raw_T in
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    Ctyp {thy_ref = Theory.self_ref thy, T = T,
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      maxidx = Term.maxidx_of_typ T, sorts = may_insert_typ_sorts thy T []}
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  end;
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fun dest_ctyp (Ctyp {thy_ref, T = Type (s, Ts), maxidx, sorts}) =
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      map (fn T => Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts}) Ts
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  | dest_ctyp cT = raise TYPE ("dest_ctyp", [typ_of cT], []);
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(** certified terms **)
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(*certified terms with checked typ, maxidx, and sorts*)
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abstype cterm = Cterm of
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 {thy_ref: theory_ref,
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  t: term,
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  T: typ,
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  maxidx: int,
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  sorts: sort list}
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with
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exception CTERM of string * cterm list;
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fun rep_cterm (Cterm {thy_ref, t, T, maxidx, sorts}) =
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  let val thy =  Theory.deref thy_ref
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  in {thy = thy, t = t, T = T, maxidx = maxidx, sorts = sorts} end;
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fun crep_cterm (Cterm {thy_ref, t, T, maxidx, sorts}) =
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  let val thy = Theory.deref thy_ref in
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   {thy = thy, t = t,
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      T = Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts},
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    maxidx = maxidx, sorts = sorts}
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  end;
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fun theory_of_cterm (Cterm {thy_ref, ...}) = Theory.deref thy_ref;
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fun term_of (Cterm {t, ...}) = t;
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fun ctyp_of_term (Cterm {thy_ref, T, maxidx, sorts, ...}) =
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  Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts};
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fun cterm_of thy tm =
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  let
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    val (t, T, maxidx) = Sign.certify_term thy tm;
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    val sorts = may_insert_term_sorts thy t [];
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  in Cterm {thy_ref = Theory.self_ref thy, t = t, T = T, maxidx = maxidx, sorts = sorts} end;
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fun merge_thys0 (Cterm {thy_ref = r1, t = t1, ...}) (Cterm {thy_ref = r2, t = t2, ...}) =
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  Theory.merge_refs (r1, r2);
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(* destructors *)
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fun dest_comb (ct as Cterm {t = c $ a, T, thy_ref, maxidx, sorts}) =
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      let val A = Term.argument_type_of c 0 in
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        (Cterm {t = c, T = A --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
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         Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
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      end
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  | dest_comb ct = raise CTERM ("dest_comb", [ct]);
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fun dest_fun (ct as Cterm {t = c $ _, T, thy_ref, maxidx, sorts}) =
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      let val A = Term.argument_type_of c 0
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      in Cterm {t = c, T = A --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
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  | dest_fun ct = raise CTERM ("dest_fun", [ct]);
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fun dest_arg (ct as Cterm {t = c $ a, T = _, thy_ref, maxidx, sorts}) =
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      let val A = Term.argument_type_of c 0
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      in Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
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  | dest_arg ct = raise CTERM ("dest_arg", [ct]);
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fun dest_fun2 (Cterm {t = c $ a $ b, T, thy_ref, maxidx, sorts}) =
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      let
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        val A = Term.argument_type_of c 0;
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        val B = Term.argument_type_of c 1;
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      in Cterm {t = c, T = A --> B --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
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  | dest_fun2 ct = raise CTERM ("dest_fun2", [ct]);
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fun dest_arg1 (Cterm {t = c $ a $ _, T = _, thy_ref, maxidx, sorts}) =
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      let val A = Term.argument_type_of c 0
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      in Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
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  | dest_arg1 ct = raise CTERM ("dest_arg1", [ct]);
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fun dest_abs a (ct as
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        Cterm {t = Abs (x, T, t), T = Type ("fun", [_, U]), thy_ref, maxidx, sorts}) =
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      let val (y', t') = Term.dest_abs (the_default x a, T, t) in
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        (Cterm {t = Free (y', T), T = T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
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          Cterm {t = t', T = U, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
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      end
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  | dest_abs _ ct = raise CTERM ("dest_abs", [ct]);
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(* constructors *)
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fun capply
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  (cf as Cterm {t = f, T = Type ("fun", [dty, rty]), maxidx = maxidx1, sorts = sorts1, ...})
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  (cx as Cterm {t = x, T, maxidx = maxidx2, sorts = sorts2, ...}) =
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    if T = dty then
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      Cterm {thy_ref = merge_thys0 cf cx,
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        t = f $ x,
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        T = rty,
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        maxidx = Int.max (maxidx1, maxidx2),
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        sorts = Sorts.union sorts1 sorts2}
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      else raise CTERM ("capply: types don't agree", [cf, cx])
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  | capply cf cx = raise CTERM ("capply: first arg is not a function", [cf, cx]);
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fun cabs
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  (ct1 as Cterm {t = t1, T = T1, maxidx = maxidx1, sorts = sorts1, ...})
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  (ct2 as Cterm {t = t2, T = T2, maxidx = maxidx2, sorts = sorts2, ...}) =
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    let val t = Term.lambda t1 t2 in
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      Cterm {thy_ref = merge_thys0 ct1 ct2,
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        t = t, T = T1 --> T2,
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        maxidx = Int.max (maxidx1, maxidx2),
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        sorts = Sorts.union sorts1 sorts2}
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    end;
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(* indexes *)
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fun adjust_maxidx_cterm i (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
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  if maxidx = i then ct
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  else if maxidx < i then
wenzelm@20580
   315
    Cterm {maxidx = i, thy_ref = thy_ref, t = t, T = T, sorts = sorts}
wenzelm@20580
   316
  else
wenzelm@20580
   317
    Cterm {maxidx = Int.max (maxidx_of_term t, i), thy_ref = thy_ref, t = t, T = T, sorts = sorts};
wenzelm@20580
   318
wenzelm@22909
   319
fun incr_indexes_cterm i (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@22909
   320
  if i < 0 then raise CTERM ("negative increment", [ct])
wenzelm@22909
   321
  else if i = 0 then ct
wenzelm@22909
   322
  else Cterm {thy_ref = thy_ref, t = Logic.incr_indexes ([], i) t,
wenzelm@22909
   323
    T = Logic.incr_tvar i T, maxidx = maxidx + i, sorts = sorts};
wenzelm@22909
   324
wenzelm@22909
   325
wenzelm@22909
   326
(* matching *)
wenzelm@22909
   327
wenzelm@22909
   328
local
wenzelm@22909
   329
wenzelm@22909
   330
fun gen_match match
wenzelm@20512
   331
    (ct1 as Cterm {t = t1, sorts = sorts1, ...},
wenzelm@20815
   332
     ct2 as Cterm {t = t2, sorts = sorts2, maxidx = maxidx2, ...}) =
berghofe@10416
   333
  let
wenzelm@16656
   334
    val thy_ref = merge_thys0 ct1 ct2;
wenzelm@18184
   335
    val (Tinsts, tinsts) = match (Theory.deref thy_ref) (t1, t2) (Vartab.empty, Vartab.empty);
wenzelm@16601
   336
    val sorts = Sorts.union sorts1 sorts2;
wenzelm@20512
   337
    fun mk_cTinst ((a, i), (S, T)) =
wenzelm@20512
   338
      (Ctyp {T = TVar ((a, i), S), thy_ref = thy_ref, maxidx = i, sorts = sorts},
wenzelm@20815
   339
       Ctyp {T = T, thy_ref = thy_ref, maxidx = maxidx2, sorts = sorts});
wenzelm@20512
   340
    fun mk_ctinst ((x, i), (T, t)) =
wenzelm@16601
   341
      let val T = Envir.typ_subst_TVars Tinsts T in
wenzelm@20512
   342
        (Cterm {t = Var ((x, i), T), T = T, thy_ref = thy_ref, maxidx = i, sorts = sorts},
wenzelm@20815
   343
         Cterm {t = t, T = T, thy_ref = thy_ref, maxidx = maxidx2, sorts = sorts})
berghofe@10416
   344
      end;
wenzelm@16656
   345
  in (Vartab.fold (cons o mk_cTinst) Tinsts [], Vartab.fold (cons o mk_ctinst) tinsts []) end;
berghofe@10416
   346
wenzelm@22909
   347
in
berghofe@10416
   348
wenzelm@22909
   349
val match = gen_match Pattern.match;
wenzelm@22909
   350
val first_order_match = gen_match Pattern.first_order_match;
wenzelm@22909
   351
wenzelm@22909
   352
end;
berghofe@10416
   353
wenzelm@2509
   354
wenzelm@2509
   355
wenzelm@387
   356
(*** Meta theorems ***)
lcp@229
   357
wenzelm@22237
   358
abstype thm = Thm of
wenzelm@16425
   359
 {thy_ref: theory_ref,         (*dynamic reference to theory*)
berghofe@11518
   360
  der: bool * Pt.proof,        (*derivation*)
wenzelm@23657
   361
  tags: Markup.property list,  (*additional annotations/comments*)
wenzelm@3967
   362
  maxidx: int,                 (*maximum index of any Var or TVar*)
wenzelm@16601
   363
  shyps: sort list,            (*sort hypotheses as ordered list*)
wenzelm@16601
   364
  hyps: term list,             (*hypotheses as ordered list*)
berghofe@13658
   365
  tpairs: (term * term) list,  (*flex-flex pairs*)
wenzelm@22237
   366
  prop: term}                  (*conclusion*)
wenzelm@22237
   367
with
clasohm@0
   368
wenzelm@23601
   369
type conv = cterm -> thm;
wenzelm@23601
   370
wenzelm@22365
   371
(*attributes subsume any kind of rules or context modifiers*)
wenzelm@22365
   372
type attribute = Context.generic * thm -> Context.generic * thm;
wenzelm@22365
   373
wenzelm@16725
   374
(*errors involving theorems*)
wenzelm@16725
   375
exception THM of string * int * thm list;
berghofe@13658
   376
wenzelm@21646
   377
fun rep_thm (Thm {thy_ref, der, tags, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   378
  let val thy = Theory.deref thy_ref in
wenzelm@22596
   379
   {thy = thy, der = der, tags = tags, maxidx = maxidx,
wenzelm@16425
   380
    shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@16425
   381
  end;
clasohm@0
   382
wenzelm@16425
   383
(*version of rep_thm returning cterms instead of terms*)
wenzelm@21646
   384
fun crep_thm (Thm {thy_ref, der, tags, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   385
  let
wenzelm@16425
   386
    val thy = Theory.deref thy_ref;
wenzelm@16601
   387
    fun cterm max t = Cterm {thy_ref = thy_ref, t = t, T = propT, maxidx = max, sorts = shyps};
wenzelm@16425
   388
  in
wenzelm@22596
   389
   {thy = thy, der = der, tags = tags, maxidx = maxidx, shyps = shyps,
wenzelm@16425
   390
    hyps = map (cterm ~1) hyps,
wenzelm@16425
   391
    tpairs = map (pairself (cterm maxidx)) tpairs,
wenzelm@16425
   392
    prop = cterm maxidx prop}
clasohm@1517
   393
  end;
clasohm@1517
   394
wenzelm@16725
   395
fun terms_of_tpairs tpairs = fold_rev (fn (t, u) => cons t o cons u) tpairs [];
wenzelm@16725
   396
wenzelm@16725
   397
fun eq_tpairs ((t, u), (t', u')) = t aconv t' andalso u aconv u';
wenzelm@18944
   398
fun union_tpairs ts us = Library.merge eq_tpairs (ts, us);
wenzelm@16884
   399
val maxidx_tpairs = fold (fn (t, u) => Term.maxidx_term t #> Term.maxidx_term u);
wenzelm@16725
   400
wenzelm@16725
   401
fun attach_tpairs tpairs prop =
wenzelm@16725
   402
  Logic.list_implies (map Logic.mk_equals tpairs, prop);
wenzelm@16725
   403
wenzelm@16725
   404
fun full_prop_of (Thm {tpairs, prop, ...}) = attach_tpairs tpairs prop;
wenzelm@16945
   405
wenzelm@22365
   406
val union_hyps = OrdList.union Term.fast_term_ord;
wenzelm@22365
   407
wenzelm@16945
   408
wenzelm@16945
   409
(* merge theories of cterms/thms; raise exception if incompatible *)
wenzelm@16945
   410
wenzelm@16945
   411
fun merge_thys1 (Cterm {thy_ref = r1, ...}) (th as Thm {thy_ref = r2, ...}) =
wenzelm@23601
   412
  Theory.merge_refs (r1, r2);
wenzelm@16945
   413
wenzelm@16945
   414
fun merge_thys2 (th1 as Thm {thy_ref = r1, ...}) (th2 as Thm {thy_ref = r2, ...}) =
wenzelm@23601
   415
  Theory.merge_refs (r1, r2);
wenzelm@16945
   416
clasohm@0
   417
wenzelm@22365
   418
(* basic components *)
wenzelm@16135
   419
wenzelm@16425
   420
fun theory_of_thm (Thm {thy_ref, ...}) = Theory.deref thy_ref;
wenzelm@19429
   421
fun maxidx_of (Thm {maxidx, ...}) = maxidx;
wenzelm@19910
   422
fun maxidx_thm th i = Int.max (maxidx_of th, i);
wenzelm@19881
   423
fun hyps_of (Thm {hyps, ...}) = hyps;
wenzelm@12803
   424
fun prop_of (Thm {prop, ...}) = prop;
wenzelm@13528
   425
fun proof_of (Thm {der = (_, proof), ...}) = proof;
wenzelm@16601
   426
fun tpairs_of (Thm {tpairs, ...}) = tpairs;
clasohm@0
   427
wenzelm@16601
   428
val concl_of = Logic.strip_imp_concl o prop_of;
wenzelm@16601
   429
val prems_of = Logic.strip_imp_prems o prop_of;
wenzelm@21576
   430
val nprems_of = Logic.count_prems o prop_of;
wenzelm@19305
   431
fun no_prems th = nprems_of th = 0;
wenzelm@16601
   432
wenzelm@16601
   433
fun major_prem_of th =
wenzelm@16601
   434
  (case prems_of th of
wenzelm@16601
   435
    prem :: _ => Logic.strip_assums_concl prem
wenzelm@16601
   436
  | [] => raise THM ("major_prem_of: rule with no premises", 0, [th]));
wenzelm@16601
   437
wenzelm@16601
   438
(*the statement of any thm is a cterm*)
wenzelm@16601
   439
fun cprop_of (Thm {thy_ref, maxidx, shyps, prop, ...}) =
wenzelm@16601
   440
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, t = prop, sorts = shyps};
wenzelm@16601
   441
wenzelm@18145
   442
fun cprem_of (th as Thm {thy_ref, maxidx, shyps, prop, ...}) i =
wenzelm@18035
   443
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, sorts = shyps,
wenzelm@18145
   444
    t = Logic.nth_prem (i, prop) handle TERM _ => raise THM ("cprem_of", i, [th])};
wenzelm@18035
   445
wenzelm@16656
   446
(*explicit transfer to a super theory*)
wenzelm@16425
   447
fun transfer thy' thm =
wenzelm@3895
   448
  let
wenzelm@21646
   449
    val Thm {thy_ref, der, tags, maxidx, shyps, hyps, tpairs, prop} = thm;
wenzelm@16425
   450
    val thy = Theory.deref thy_ref;
wenzelm@3895
   451
  in
wenzelm@16945
   452
    if not (subthy (thy, thy')) then
wenzelm@16945
   453
      raise THM ("transfer: not a super theory", 0, [thm])
wenzelm@16945
   454
    else if eq_thy (thy, thy') then thm
wenzelm@16945
   455
    else
wenzelm@16945
   456
      Thm {thy_ref = Theory.self_ref thy',
wenzelm@16945
   457
        der = der,
wenzelm@21646
   458
        tags = tags,
wenzelm@16945
   459
        maxidx = maxidx,
wenzelm@16945
   460
        shyps = shyps,
wenzelm@16945
   461
        hyps = hyps,
wenzelm@16945
   462
        tpairs = tpairs,
wenzelm@16945
   463
        prop = prop}
wenzelm@3895
   464
  end;
wenzelm@387
   465
wenzelm@16945
   466
(*explicit weakening: maps |- B to A |- B*)
wenzelm@16945
   467
fun weaken raw_ct th =
wenzelm@16945
   468
  let
wenzelm@20261
   469
    val ct as Cterm {t = A, T, sorts, maxidx = maxidxA, ...} = adjust_maxidx_cterm ~1 raw_ct;
wenzelm@21646
   470
    val Thm {der, tags, maxidx, shyps, hyps, tpairs, prop, ...} = th;
wenzelm@16945
   471
  in
wenzelm@16945
   472
    if T <> propT then
wenzelm@16945
   473
      raise THM ("weaken: assumptions must have type prop", 0, [])
wenzelm@16945
   474
    else if maxidxA <> ~1 then
wenzelm@16945
   475
      raise THM ("weaken: assumptions may not contain schematic variables", maxidxA, [])
wenzelm@16945
   476
    else
wenzelm@16945
   477
      Thm {thy_ref = merge_thys1 ct th,
wenzelm@16945
   478
        der = der,
wenzelm@21646
   479
        tags = tags,
wenzelm@16945
   480
        maxidx = maxidx,
wenzelm@16945
   481
        shyps = Sorts.union sorts shyps,
wenzelm@22365
   482
        hyps = OrdList.insert Term.fast_term_ord A hyps,
wenzelm@16945
   483
        tpairs = tpairs,
wenzelm@16945
   484
        prop = prop}
wenzelm@16945
   485
  end;
wenzelm@16656
   486
wenzelm@16656
   487
clasohm@0
   488
wenzelm@1238
   489
(** sort contexts of theorems **)
wenzelm@1238
   490
wenzelm@16656
   491
fun present_sorts (Thm {hyps, tpairs, prop, ...}) =
wenzelm@16656
   492
  fold (fn (t, u) => Sorts.insert_term t o Sorts.insert_term u) tpairs
wenzelm@16656
   493
    (Sorts.insert_terms hyps (Sorts.insert_term prop []));
wenzelm@1238
   494
wenzelm@7642
   495
(*remove extra sorts that are non-empty by virtue of type signature information*)
wenzelm@7642
   496
fun strip_shyps (thm as Thm {shyps = [], ...}) = thm
wenzelm@21646
   497
  | strip_shyps (thm as Thm {thy_ref, der, tags, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@7642
   498
      let
wenzelm@16425
   499
        val thy = Theory.deref thy_ref;
wenzelm@16656
   500
        val shyps' =
wenzelm@16656
   501
          if Sign.all_sorts_nonempty thy then []
wenzelm@16656
   502
          else
wenzelm@16656
   503
            let
wenzelm@16656
   504
              val present = present_sorts thm;
wenzelm@16656
   505
              val extra = Sorts.subtract present shyps;
wenzelm@16656
   506
              val witnessed = map #2 (Sign.witness_sorts thy present extra);
wenzelm@16656
   507
            in Sorts.subtract witnessed shyps end;
wenzelm@7642
   508
      in
wenzelm@21646
   509
        Thm {thy_ref = thy_ref, der = der, tags = tags, maxidx = maxidx,
wenzelm@16656
   510
          shyps = shyps', hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@7642
   511
      end;
wenzelm@1238
   512
wenzelm@16656
   513
(*dangling sort constraints of a thm*)
wenzelm@16656
   514
fun extra_shyps (th as Thm {shyps, ...}) = Sorts.subtract (present_sorts th) shyps;
wenzelm@16656
   515
wenzelm@1238
   516
wenzelm@1238
   517
paulson@1529
   518
(** Axioms **)
wenzelm@387
   519
wenzelm@16425
   520
(*look up the named axiom in the theory or its ancestors*)
wenzelm@15672
   521
fun get_axiom_i theory name =
wenzelm@387
   522
  let
wenzelm@16425
   523
    fun get_ax thy =
wenzelm@22685
   524
      Symtab.lookup (Theory.axiom_table thy) name
wenzelm@16601
   525
      |> Option.map (fn prop =>
wenzelm@16601
   526
          Thm {thy_ref = Theory.self_ref thy,
wenzelm@16601
   527
            der = Pt.infer_derivs' I (false, Pt.axm_proof name prop),
wenzelm@21646
   528
            tags = [],
wenzelm@16601
   529
            maxidx = maxidx_of_term prop,
wenzelm@16656
   530
            shyps = may_insert_term_sorts thy prop [],
wenzelm@16601
   531
            hyps = [],
wenzelm@16601
   532
            tpairs = [],
wenzelm@16601
   533
            prop = prop});
wenzelm@387
   534
  in
wenzelm@16425
   535
    (case get_first get_ax (theory :: Theory.ancestors_of theory) of
skalberg@15531
   536
      SOME thm => thm
skalberg@15531
   537
    | NONE => raise THEORY ("No axiom " ^ quote name, [theory]))
wenzelm@387
   538
  end;
wenzelm@387
   539
wenzelm@16352
   540
fun get_axiom thy =
wenzelm@16425
   541
  get_axiom_i thy o NameSpace.intern (Theory.axiom_space thy);
wenzelm@15672
   542
wenzelm@20884
   543
fun def_name c = c ^ "_def";
wenzelm@20884
   544
wenzelm@20884
   545
fun def_name_optional c "" = def_name c
wenzelm@20884
   546
  | def_name_optional _ name = name;
wenzelm@20884
   547
wenzelm@6368
   548
fun get_def thy = get_axiom thy o def_name;
wenzelm@4847
   549
paulson@1529
   550
wenzelm@776
   551
(*return additional axioms of this theory node*)
wenzelm@776
   552
fun axioms_of thy =
wenzelm@22685
   553
  map (fn s => (s, get_axiom_i thy s)) (Symtab.keys (Theory.axiom_table thy));
wenzelm@776
   554
wenzelm@6089
   555
wenzelm@21646
   556
(* official name and additional tags *)
wenzelm@6089
   557
wenzelm@21646
   558
fun get_name (Thm {hyps, prop, der = (_, prf), ...}) =
wenzelm@21646
   559
  Pt.get_name hyps prop prf;
wenzelm@4018
   560
wenzelm@21646
   561
fun put_name name (Thm {thy_ref, der = (ora, prf), tags, maxidx, shyps, hyps, tpairs = [], prop}) =
wenzelm@21646
   562
      Thm {thy_ref = thy_ref,
wenzelm@21646
   563
        der = (ora, Pt.thm_proof (Theory.deref thy_ref) name hyps prop prf),
wenzelm@21646
   564
        tags = tags, maxidx = maxidx, shyps = shyps, hyps = hyps, tpairs = [], prop = prop}
wenzelm@21646
   565
  | put_name _ thm = raise THM ("name_thm: unsolved flex-flex constraints", 0, [thm]);
wenzelm@6089
   566
wenzelm@21646
   567
val get_tags = #tags o rep_thm;
wenzelm@6089
   568
wenzelm@21646
   569
fun map_tags f (Thm {thy_ref, der, tags, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@21646
   570
  Thm {thy_ref = thy_ref, der = der, tags = f tags, maxidx = maxidx,
wenzelm@21646
   571
    shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop};
clasohm@0
   572
clasohm@0
   573
paulson@1529
   574
(*Compression of theorems -- a separate rule, not integrated with the others,
paulson@1529
   575
  as it could be slow.*)
wenzelm@21646
   576
fun compress (Thm {thy_ref, der, tags, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16991
   577
  let val thy = Theory.deref thy_ref in
wenzelm@16991
   578
    Thm {thy_ref = thy_ref,
wenzelm@16991
   579
      der = der,
wenzelm@21646
   580
      tags = tags,
wenzelm@16991
   581
      maxidx = maxidx,
wenzelm@16991
   582
      shyps = shyps,
wenzelm@16991
   583
      hyps = map (Compress.term thy) hyps,
wenzelm@16991
   584
      tpairs = map (pairself (Compress.term thy)) tpairs,
wenzelm@16991
   585
      prop = Compress.term thy prop}
wenzelm@16991
   586
  end;
wenzelm@16945
   587
berghofe@23781
   588
fun norm_proof (Thm {thy_ref, der, tags, maxidx, shyps, hyps, tpairs, prop}) =
berghofe@23781
   589
  let val thy = Theory.deref thy_ref in
berghofe@23781
   590
    Thm {thy_ref = thy_ref,
berghofe@23781
   591
      der = Pt.infer_derivs' (Pt.rew_proof thy) der,
berghofe@23781
   592
      tags = tags,
berghofe@23781
   593
      maxidx = maxidx,
berghofe@23781
   594
      shyps = shyps,
berghofe@23781
   595
      hyps = hyps,
berghofe@23781
   596
      tpairs = tpairs,
berghofe@23781
   597
      prop = prop}
berghofe@23781
   598
  end;
berghofe@23781
   599
wenzelm@21646
   600
fun adjust_maxidx_thm i (th as Thm {thy_ref, der, tags, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@20261
   601
  if maxidx = i then th
wenzelm@20261
   602
  else if maxidx < i then
wenzelm@21646
   603
    Thm {maxidx = i, thy_ref = thy_ref, der = der, tags = tags, shyps = shyps,
wenzelm@20261
   604
      hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@20261
   605
  else
wenzelm@21646
   606
    Thm {maxidx = Int.max (maxidx_tpairs tpairs (maxidx_of_term prop), i), thy_ref = thy_ref,
wenzelm@21646
   607
      der = der, tags = tags, shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop};
wenzelm@564
   608
wenzelm@387
   609
wenzelm@2509
   610
paulson@1529
   611
(*** Meta rules ***)
clasohm@0
   612
wenzelm@16601
   613
(** primitive rules **)
clasohm@0
   614
wenzelm@16656
   615
(*The assumption rule A |- A*)
wenzelm@16601
   616
fun assume raw_ct =
wenzelm@20261
   617
  let val Cterm {thy_ref, t = prop, T, maxidx, sorts} = adjust_maxidx_cterm ~1 raw_ct in
wenzelm@16601
   618
    if T <> propT then
mengj@19230
   619
      raise THM ("assume: prop", 0, [])
wenzelm@16601
   620
    else if maxidx <> ~1 then
mengj@19230
   621
      raise THM ("assume: variables", maxidx, [])
wenzelm@16601
   622
    else Thm {thy_ref = thy_ref,
wenzelm@16601
   623
      der = Pt.infer_derivs' I (false, Pt.Hyp prop),
wenzelm@21646
   624
      tags = [],
wenzelm@16601
   625
      maxidx = ~1,
wenzelm@16601
   626
      shyps = sorts,
wenzelm@16601
   627
      hyps = [prop],
wenzelm@16601
   628
      tpairs = [],
wenzelm@16601
   629
      prop = prop}
clasohm@0
   630
  end;
clasohm@0
   631
wenzelm@1220
   632
(*Implication introduction
wenzelm@3529
   633
    [A]
wenzelm@3529
   634
     :
wenzelm@3529
   635
     B
wenzelm@1220
   636
  -------
wenzelm@1220
   637
  A ==> B
wenzelm@1220
   638
*)
wenzelm@16601
   639
fun implies_intr
wenzelm@16679
   640
    (ct as Cterm {t = A, T, maxidx = maxidxA, sorts, ...})
wenzelm@16679
   641
    (th as Thm {der, maxidx, hyps, shyps, tpairs, prop, ...}) =
wenzelm@16601
   642
  if T <> propT then
wenzelm@16601
   643
    raise THM ("implies_intr: assumptions must have type prop", 0, [th])
wenzelm@16601
   644
  else
wenzelm@16601
   645
    Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   646
      der = Pt.infer_derivs' (Pt.implies_intr_proof A) der,
wenzelm@21646
   647
      tags = [],
wenzelm@16601
   648
      maxidx = Int.max (maxidxA, maxidx),
wenzelm@16601
   649
      shyps = Sorts.union sorts shyps,
wenzelm@22365
   650
      hyps = OrdList.remove Term.fast_term_ord A hyps,
wenzelm@16601
   651
      tpairs = tpairs,
wenzelm@16601
   652
      prop = implies $ A $ prop};
clasohm@0
   653
paulson@1529
   654
wenzelm@1220
   655
(*Implication elimination
wenzelm@1220
   656
  A ==> B    A
wenzelm@1220
   657
  ------------
wenzelm@1220
   658
        B
wenzelm@1220
   659
*)
wenzelm@16601
   660
fun implies_elim thAB thA =
wenzelm@16601
   661
  let
wenzelm@16601
   662
    val Thm {maxidx = maxA, der = derA, hyps = hypsA, shyps = shypsA, tpairs = tpairsA,
wenzelm@16601
   663
      prop = propA, ...} = thA
wenzelm@16601
   664
    and Thm {der, maxidx, hyps, shyps, tpairs, prop, ...} = thAB;
wenzelm@16601
   665
    fun err () = raise THM ("implies_elim: major premise", 0, [thAB, thA]);
wenzelm@16601
   666
  in
wenzelm@16601
   667
    case prop of
wenzelm@20512
   668
      Const ("==>", _) $ A $ B =>
wenzelm@20512
   669
        if A aconv propA then
wenzelm@16656
   670
          Thm {thy_ref = merge_thys2 thAB thA,
wenzelm@16601
   671
            der = Pt.infer_derivs (curry Pt.%%) der derA,
wenzelm@21646
   672
            tags = [],
wenzelm@16601
   673
            maxidx = Int.max (maxA, maxidx),
wenzelm@16601
   674
            shyps = Sorts.union shypsA shyps,
wenzelm@16601
   675
            hyps = union_hyps hypsA hyps,
wenzelm@16601
   676
            tpairs = union_tpairs tpairsA tpairs,
wenzelm@16601
   677
            prop = B}
wenzelm@16601
   678
        else err ()
wenzelm@16601
   679
    | _ => err ()
wenzelm@16601
   680
  end;
wenzelm@250
   681
wenzelm@1220
   682
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@16656
   683
    [x]
wenzelm@16656
   684
     :
wenzelm@16656
   685
     A
wenzelm@16656
   686
  ------
wenzelm@16656
   687
  !!x. A
wenzelm@1220
   688
*)
wenzelm@16601
   689
fun forall_intr
wenzelm@16601
   690
    (ct as Cterm {t = x, T, sorts, ...})
wenzelm@16679
   691
    (th as Thm {der, maxidx, shyps, hyps, tpairs, prop, ...}) =
wenzelm@16601
   692
  let
wenzelm@16601
   693
    fun result a =
wenzelm@16601
   694
      Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   695
        der = Pt.infer_derivs' (Pt.forall_intr_proof x a) der,
wenzelm@21646
   696
        tags = [],
wenzelm@16601
   697
        maxidx = maxidx,
wenzelm@16601
   698
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   699
        hyps = hyps,
wenzelm@16601
   700
        tpairs = tpairs,
wenzelm@16601
   701
        prop = all T $ Abs (a, T, abstract_over (x, prop))};
wenzelm@21798
   702
    fun check_occs a x ts =
wenzelm@16847
   703
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@21798
   704
        raise THM ("forall_intr: variable " ^ quote a ^ " free in assumptions", 0, [th])
wenzelm@16601
   705
      else ();
wenzelm@16601
   706
  in
wenzelm@16601
   707
    case x of
wenzelm@21798
   708
      Free (a, _) => (check_occs a x hyps; check_occs a x (terms_of_tpairs tpairs); result a)
wenzelm@21798
   709
    | Var ((a, _), _) => (check_occs a x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   710
    | _ => raise THM ("forall_intr: not a variable", 0, [th])
clasohm@0
   711
  end;
clasohm@0
   712
wenzelm@1220
   713
(*Forall elimination
wenzelm@16656
   714
  !!x. A
wenzelm@1220
   715
  ------
wenzelm@1220
   716
  A[t/x]
wenzelm@1220
   717
*)
wenzelm@16601
   718
fun forall_elim
wenzelm@16601
   719
    (ct as Cterm {t, T, maxidx = maxt, sorts, ...})
wenzelm@16601
   720
    (th as Thm {der, maxidx, shyps, hyps, tpairs, prop, ...}) =
wenzelm@16601
   721
  (case prop of
wenzelm@16601
   722
    Const ("all", Type ("fun", [Type ("fun", [qary, _]), _])) $ A =>
wenzelm@16601
   723
      if T <> qary then
wenzelm@16601
   724
        raise THM ("forall_elim: type mismatch", 0, [th])
wenzelm@16601
   725
      else
wenzelm@16601
   726
        Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   727
          der = Pt.infer_derivs' (Pt.% o rpair (SOME t)) der,
wenzelm@21646
   728
          tags = [],
wenzelm@16601
   729
          maxidx = Int.max (maxidx, maxt),
wenzelm@16601
   730
          shyps = Sorts.union sorts shyps,
wenzelm@16601
   731
          hyps = hyps,
wenzelm@16601
   732
          tpairs = tpairs,
wenzelm@16601
   733
          prop = Term.betapply (A, t)}
wenzelm@16601
   734
  | _ => raise THM ("forall_elim: not quantified", 0, [th]));
clasohm@0
   735
clasohm@0
   736
wenzelm@1220
   737
(* Equality *)
clasohm@0
   738
wenzelm@16601
   739
(*Reflexivity
wenzelm@16601
   740
  t == t
wenzelm@16601
   741
*)
wenzelm@16601
   742
fun reflexive (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16656
   743
  Thm {thy_ref = thy_ref,
wenzelm@16601
   744
    der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@21646
   745
    tags = [],
wenzelm@16601
   746
    maxidx = maxidx,
wenzelm@16601
   747
    shyps = sorts,
wenzelm@16601
   748
    hyps = [],
wenzelm@16601
   749
    tpairs = [],
wenzelm@16601
   750
    prop = Logic.mk_equals (t, t)};
clasohm@0
   751
wenzelm@16601
   752
(*Symmetry
wenzelm@16601
   753
  t == u
wenzelm@16601
   754
  ------
wenzelm@16601
   755
  u == t
wenzelm@1220
   756
*)
wenzelm@21646
   757
fun symmetric (th as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop, ...}) =
wenzelm@16601
   758
  (case prop of
wenzelm@16601
   759
    (eq as Const ("==", Type (_, [T, _]))) $ t $ u =>
wenzelm@16601
   760
      Thm {thy_ref = thy_ref,
wenzelm@16601
   761
        der = Pt.infer_derivs' Pt.symmetric der,
wenzelm@21646
   762
        tags = [],
wenzelm@16601
   763
        maxidx = maxidx,
wenzelm@16601
   764
        shyps = shyps,
wenzelm@16601
   765
        hyps = hyps,
wenzelm@16601
   766
        tpairs = tpairs,
wenzelm@16601
   767
        prop = eq $ u $ t}
wenzelm@16601
   768
    | _ => raise THM ("symmetric", 0, [th]));
clasohm@0
   769
wenzelm@16601
   770
(*Transitivity
wenzelm@16601
   771
  t1 == u    u == t2
wenzelm@16601
   772
  ------------------
wenzelm@16601
   773
       t1 == t2
wenzelm@1220
   774
*)
clasohm@0
   775
fun transitive th1 th2 =
wenzelm@16601
   776
  let
wenzelm@16601
   777
    val Thm {der = der1, maxidx = max1, hyps = hyps1, shyps = shyps1, tpairs = tpairs1,
wenzelm@16601
   778
      prop = prop1, ...} = th1
wenzelm@16601
   779
    and Thm {der = der2, maxidx = max2, hyps = hyps2, shyps = shyps2, tpairs = tpairs2,
wenzelm@16601
   780
      prop = prop2, ...} = th2;
wenzelm@16601
   781
    fun err msg = raise THM ("transitive: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   782
  in
wenzelm@16601
   783
    case (prop1, prop2) of
wenzelm@16601
   784
      ((eq as Const ("==", Type (_, [T, _]))) $ t1 $ u, Const ("==", _) $ u' $ t2) =>
wenzelm@16601
   785
        if not (u aconv u') then err "middle term"
wenzelm@16601
   786
        else
wenzelm@16656
   787
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   788
            der = Pt.infer_derivs (Pt.transitive u T) der1 der2,
wenzelm@21646
   789
            tags = [],
wenzelm@16601
   790
            maxidx = Int.max (max1, max2),
wenzelm@16601
   791
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   792
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   793
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   794
            prop = eq $ t1 $ t2}
wenzelm@16601
   795
     | _ =>  err "premises"
clasohm@0
   796
  end;
clasohm@0
   797
wenzelm@16601
   798
(*Beta-conversion
wenzelm@16656
   799
  (%x. t)(u) == t[u/x]
wenzelm@16601
   800
  fully beta-reduces the term if full = true
berghofe@10416
   801
*)
wenzelm@16601
   802
fun beta_conversion full (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   803
  let val t' =
wenzelm@16601
   804
    if full then Envir.beta_norm t
wenzelm@16601
   805
    else
wenzelm@16601
   806
      (case t of Abs (_, _, bodt) $ u => subst_bound (u, bodt)
wenzelm@16601
   807
      | _ => raise THM ("beta_conversion: not a redex", 0, []));
wenzelm@16601
   808
  in
wenzelm@16601
   809
    Thm {thy_ref = thy_ref,
wenzelm@16601
   810
      der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@21646
   811
      tags = [],
wenzelm@16601
   812
      maxidx = maxidx,
wenzelm@16601
   813
      shyps = sorts,
wenzelm@16601
   814
      hyps = [],
wenzelm@16601
   815
      tpairs = [],
wenzelm@16601
   816
      prop = Logic.mk_equals (t, t')}
berghofe@10416
   817
  end;
berghofe@10416
   818
wenzelm@16601
   819
fun eta_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   820
  Thm {thy_ref = thy_ref,
wenzelm@16601
   821
    der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@21646
   822
    tags = [],
wenzelm@16601
   823
    maxidx = maxidx,
wenzelm@16601
   824
    shyps = sorts,
wenzelm@16601
   825
    hyps = [],
wenzelm@16601
   826
    tpairs = [],
wenzelm@18944
   827
    prop = Logic.mk_equals (t, Envir.eta_contract t)};
clasohm@0
   828
wenzelm@23493
   829
fun eta_long_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@23493
   830
  Thm {thy_ref = thy_ref,
wenzelm@23493
   831
    der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@23493
   832
    tags = [],
wenzelm@23493
   833
    maxidx = maxidx,
wenzelm@23493
   834
    shyps = sorts,
wenzelm@23493
   835
    hyps = [],
wenzelm@23493
   836
    tpairs = [],
wenzelm@23493
   837
    prop = Logic.mk_equals (t, Pattern.eta_long [] t)};
wenzelm@23493
   838
clasohm@0
   839
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   840
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@16601
   841
      t == u
wenzelm@16601
   842
  --------------
wenzelm@16601
   843
  %x. t == %x. u
wenzelm@1220
   844
*)
wenzelm@16601
   845
fun abstract_rule a
wenzelm@16601
   846
    (Cterm {t = x, T, sorts, ...})
wenzelm@21646
   847
    (th as Thm {thy_ref, der, maxidx, hyps, shyps, tpairs, prop, ...}) =
wenzelm@16601
   848
  let
wenzelm@16601
   849
    val (t, u) = Logic.dest_equals prop
wenzelm@16601
   850
      handle TERM _ => raise THM ("abstract_rule: premise not an equality", 0, [th]);
wenzelm@16601
   851
    val result =
wenzelm@16601
   852
      Thm {thy_ref = thy_ref,
wenzelm@16601
   853
        der = Pt.infer_derivs' (Pt.abstract_rule x a) der,
wenzelm@21646
   854
        tags = [],
wenzelm@16601
   855
        maxidx = maxidx,
wenzelm@16601
   856
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   857
        hyps = hyps,
wenzelm@16601
   858
        tpairs = tpairs,
wenzelm@16601
   859
        prop = Logic.mk_equals
wenzelm@16601
   860
          (Abs (a, T, abstract_over (x, t)), Abs (a, T, abstract_over (x, u)))};
wenzelm@21798
   861
    fun check_occs a x ts =
wenzelm@16847
   862
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@21798
   863
        raise THM ("abstract_rule: variable " ^ quote a ^ " free in assumptions", 0, [th])
wenzelm@16601
   864
      else ();
wenzelm@16601
   865
  in
wenzelm@16601
   866
    case x of
wenzelm@21798
   867
      Free (a, _) => (check_occs a x hyps; check_occs a x (terms_of_tpairs tpairs); result)
wenzelm@21798
   868
    | Var ((a, _), _) => (check_occs a x (terms_of_tpairs tpairs); result)
wenzelm@21798
   869
    | _ => raise THM ("abstract_rule: not a variable", 0, [th])
clasohm@0
   870
  end;
clasohm@0
   871
clasohm@0
   872
(*The combination rule
wenzelm@3529
   873
  f == g  t == u
wenzelm@3529
   874
  --------------
wenzelm@16601
   875
    f t == g u
wenzelm@1220
   876
*)
clasohm@0
   877
fun combination th1 th2 =
wenzelm@16601
   878
  let
wenzelm@16601
   879
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@16601
   880
      prop = prop1, ...} = th1
wenzelm@16601
   881
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@16601
   882
      prop = prop2, ...} = th2;
wenzelm@16601
   883
    fun chktypes fT tT =
wenzelm@16601
   884
      (case fT of
wenzelm@16601
   885
        Type ("fun", [T1, T2]) =>
wenzelm@16601
   886
          if T1 <> tT then
wenzelm@16601
   887
            raise THM ("combination: types", 0, [th1, th2])
wenzelm@16601
   888
          else ()
wenzelm@16601
   889
      | _ => raise THM ("combination: not function type", 0, [th1, th2]));
wenzelm@16601
   890
  in
wenzelm@16601
   891
    case (prop1, prop2) of
wenzelm@16601
   892
      (Const ("==", Type ("fun", [fT, _])) $ f $ g,
wenzelm@16601
   893
       Const ("==", Type ("fun", [tT, _])) $ t $ u) =>
wenzelm@16601
   894
        (chktypes fT tT;
wenzelm@16601
   895
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   896
            der = Pt.infer_derivs (Pt.combination f g t u fT) der1 der2,
wenzelm@21646
   897
            tags = [],
wenzelm@16601
   898
            maxidx = Int.max (max1, max2),
wenzelm@16601
   899
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   900
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   901
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   902
            prop = Logic.mk_equals (f $ t, g $ u)})
wenzelm@16601
   903
     | _ => raise THM ("combination: premises", 0, [th1, th2])
clasohm@0
   904
  end;
clasohm@0
   905
wenzelm@16601
   906
(*Equality introduction
wenzelm@3529
   907
  A ==> B  B ==> A
wenzelm@3529
   908
  ----------------
wenzelm@3529
   909
       A == B
wenzelm@1220
   910
*)
clasohm@0
   911
fun equal_intr th1 th2 =
wenzelm@16601
   912
  let
wenzelm@16601
   913
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@16601
   914
      prop = prop1, ...} = th1
wenzelm@16601
   915
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@16601
   916
      prop = prop2, ...} = th2;
wenzelm@16601
   917
    fun err msg = raise THM ("equal_intr: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   918
  in
wenzelm@16601
   919
    case (prop1, prop2) of
wenzelm@16601
   920
      (Const("==>", _) $ A $ B, Const("==>", _) $ B' $ A') =>
wenzelm@16601
   921
        if A aconv A' andalso B aconv B' then
wenzelm@16601
   922
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   923
            der = Pt.infer_derivs (Pt.equal_intr A B) der1 der2,
wenzelm@21646
   924
            tags = [],
wenzelm@16601
   925
            maxidx = Int.max (max1, max2),
wenzelm@16601
   926
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   927
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   928
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   929
            prop = Logic.mk_equals (A, B)}
wenzelm@16601
   930
        else err "not equal"
wenzelm@16601
   931
    | _ =>  err "premises"
paulson@1529
   932
  end;
paulson@1529
   933
paulson@1529
   934
(*The equal propositions rule
wenzelm@3529
   935
  A == B  A
paulson@1529
   936
  ---------
paulson@1529
   937
      B
paulson@1529
   938
*)
paulson@1529
   939
fun equal_elim th1 th2 =
wenzelm@16601
   940
  let
wenzelm@16601
   941
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1,
wenzelm@16601
   942
      tpairs = tpairs1, prop = prop1, ...} = th1
wenzelm@16601
   943
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2,
wenzelm@16601
   944
      tpairs = tpairs2, prop = prop2, ...} = th2;
wenzelm@16601
   945
    fun err msg = raise THM ("equal_elim: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   946
  in
wenzelm@16601
   947
    case prop1 of
wenzelm@16601
   948
      Const ("==", _) $ A $ B =>
wenzelm@16601
   949
        if prop2 aconv A then
wenzelm@16601
   950
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   951
            der = Pt.infer_derivs (Pt.equal_elim A B) der1 der2,
wenzelm@21646
   952
            tags = [],
wenzelm@16601
   953
            maxidx = Int.max (max1, max2),
wenzelm@16601
   954
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   955
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   956
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   957
            prop = B}
wenzelm@16601
   958
        else err "not equal"
paulson@1529
   959
     | _ =>  err"major premise"
paulson@1529
   960
  end;
clasohm@0
   961
wenzelm@1220
   962
wenzelm@1220
   963
clasohm@0
   964
(**** Derived rules ****)
clasohm@0
   965
wenzelm@16601
   966
(*Smash unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@250
   967
  Instantiates the theorem and deletes trivial tpairs.
clasohm@0
   968
  Resulting sequence may contain multiple elements if the tpairs are
clasohm@0
   969
    not all flex-flex. *)
wenzelm@21646
   970
fun flexflex_rule (th as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop, ...}) =
wenzelm@19861
   971
  Unify.smash_unifiers (Theory.deref thy_ref) tpairs (Envir.empty maxidx)
wenzelm@16601
   972
  |> Seq.map (fn env =>
wenzelm@16601
   973
      if Envir.is_empty env then th
wenzelm@16601
   974
      else
wenzelm@16601
   975
        let
wenzelm@16601
   976
          val tpairs' = tpairs |> map (pairself (Envir.norm_term env))
wenzelm@16601
   977
            (*remove trivial tpairs, of the form t==t*)
wenzelm@16884
   978
            |> filter_out (op aconv);
wenzelm@16601
   979
          val prop' = Envir.norm_term env prop;
wenzelm@16601
   980
        in
wenzelm@16601
   981
          Thm {thy_ref = thy_ref,
wenzelm@16601
   982
            der = Pt.infer_derivs' (Pt.norm_proof' env) der,
wenzelm@21646
   983
            tags = [],
wenzelm@16711
   984
            maxidx = maxidx_tpairs tpairs' (maxidx_of_term prop'),
wenzelm@16656
   985
            shyps = may_insert_env_sorts (Theory.deref thy_ref) env shyps,
wenzelm@16601
   986
            hyps = hyps,
wenzelm@16601
   987
            tpairs = tpairs',
wenzelm@16601
   988
            prop = prop'}
wenzelm@16601
   989
        end);
wenzelm@16601
   990
clasohm@0
   991
wenzelm@19910
   992
(*Generalization of fixed variables
wenzelm@19910
   993
           A
wenzelm@19910
   994
  --------------------
wenzelm@19910
   995
  A[?'a/'a, ?x/x, ...]
wenzelm@19910
   996
*)
wenzelm@19910
   997
wenzelm@19910
   998
fun generalize ([], []) _ th = th
wenzelm@19910
   999
  | generalize (tfrees, frees) idx th =
wenzelm@19910
  1000
      let
wenzelm@21646
  1001
        val Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop, ...} = th;
wenzelm@19910
  1002
        val _ = idx <= maxidx andalso raise THM ("generalize: bad index", idx, [th]);
wenzelm@19910
  1003
wenzelm@19910
  1004
        val bad_type = if null tfrees then K false else
wenzelm@19910
  1005
          Term.exists_subtype (fn TFree (a, _) => member (op =) tfrees a | _ => false);
wenzelm@19910
  1006
        fun bad_term (Free (x, T)) = bad_type T orelse member (op =) frees x
wenzelm@19910
  1007
          | bad_term (Var (_, T)) = bad_type T
wenzelm@19910
  1008
          | bad_term (Const (_, T)) = bad_type T
wenzelm@19910
  1009
          | bad_term (Abs (_, T, t)) = bad_type T orelse bad_term t
wenzelm@19910
  1010
          | bad_term (t $ u) = bad_term t orelse bad_term u
wenzelm@19910
  1011
          | bad_term (Bound _) = false;
wenzelm@19910
  1012
        val _ = exists bad_term hyps andalso
wenzelm@19910
  1013
          raise THM ("generalize: variable free in assumptions", 0, [th]);
wenzelm@19910
  1014
wenzelm@20512
  1015
        val gen = TermSubst.generalize (tfrees, frees) idx;
wenzelm@19910
  1016
        val prop' = gen prop;
wenzelm@19910
  1017
        val tpairs' = map (pairself gen) tpairs;
wenzelm@19910
  1018
        val maxidx' = maxidx_tpairs tpairs' (maxidx_of_term prop');
wenzelm@19910
  1019
      in
wenzelm@19910
  1020
        Thm {
wenzelm@19910
  1021
          thy_ref = thy_ref,
wenzelm@19910
  1022
          der = Pt.infer_derivs' (Pt.generalize (tfrees, frees) idx) der,
wenzelm@21646
  1023
          tags = [],
wenzelm@19910
  1024
          maxidx = maxidx',
wenzelm@19910
  1025
          shyps = shyps,
wenzelm@19910
  1026
          hyps = hyps,
wenzelm@19910
  1027
          tpairs = tpairs',
wenzelm@19910
  1028
          prop = prop'}
wenzelm@19910
  1029
      end;
wenzelm@19910
  1030
wenzelm@19910
  1031
wenzelm@22584
  1032
(*Instantiation of schematic variables
wenzelm@16656
  1033
           A
wenzelm@16656
  1034
  --------------------
wenzelm@16656
  1035
  A[t1/v1, ..., tn/vn]
wenzelm@1220
  1036
*)
clasohm@0
  1037
wenzelm@6928
  1038
local
wenzelm@6928
  1039
wenzelm@16425
  1040
fun pretty_typing thy t T =
wenzelm@16425
  1041
  Pretty.block [Sign.pretty_term thy t, Pretty.str " ::", Pretty.brk 1, Sign.pretty_typ thy T];
berghofe@15797
  1042
wenzelm@16884
  1043
fun add_inst (ct, cu) (thy_ref, sorts) =
wenzelm@6928
  1044
  let
wenzelm@16884
  1045
    val Cterm {t = t, T = T, ...} = ct
wenzelm@20512
  1046
    and Cterm {t = u, T = U, sorts = sorts_u, maxidx = maxidx_u, ...} = cu;
wenzelm@16884
  1047
    val thy_ref' = Theory.merge_refs (thy_ref, merge_thys0 ct cu);
wenzelm@16884
  1048
    val sorts' = Sorts.union sorts_u sorts;
wenzelm@3967
  1049
  in
wenzelm@16884
  1050
    (case t of Var v =>
wenzelm@20512
  1051
      if T = U then ((v, (u, maxidx_u)), (thy_ref', sorts'))
wenzelm@16884
  1052
      else raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
  1053
       [Pretty.str "instantiate: type conflict",
wenzelm@16884
  1054
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') t T,
wenzelm@16884
  1055
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') u U]), [T, U], [t, u])
wenzelm@16884
  1056
    | _ => raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
  1057
       [Pretty.str "instantiate: not a variable",
wenzelm@16884
  1058
        Pretty.fbrk, Sign.pretty_term (Theory.deref thy_ref') t]), [], [t]))
clasohm@0
  1059
  end;
clasohm@0
  1060
wenzelm@16884
  1061
fun add_instT (cT, cU) (thy_ref, sorts) =
wenzelm@16656
  1062
  let
wenzelm@16884
  1063
    val Ctyp {T, thy_ref = thy_ref1, ...} = cT
wenzelm@20512
  1064
    and Ctyp {T = U, thy_ref = thy_ref2, sorts = sorts_U, maxidx = maxidx_U, ...} = cU;
wenzelm@16884
  1065
    val thy_ref' = Theory.merge_refs (thy_ref, Theory.merge_refs (thy_ref1, thy_ref2));
wenzelm@16884
  1066
    val thy' = Theory.deref thy_ref';
wenzelm@16884
  1067
    val sorts' = Sorts.union sorts_U sorts;
wenzelm@16656
  1068
  in
wenzelm@16884
  1069
    (case T of TVar (v as (_, S)) =>
wenzelm@20512
  1070
      if Sign.of_sort thy' (U, S) then ((v, (U, maxidx_U)), (thy_ref', sorts'))
wenzelm@16656
  1071
      else raise TYPE ("Type not of sort " ^ Sign.string_of_sort thy' S, [U], [])
wenzelm@16656
  1072
    | _ => raise TYPE (Pretty.string_of (Pretty.block
berghofe@15797
  1073
        [Pretty.str "instantiate: not a type variable",
wenzelm@16656
  1074
         Pretty.fbrk, Sign.pretty_typ thy' T]), [T], []))
wenzelm@16656
  1075
  end;
clasohm@0
  1076
wenzelm@6928
  1077
in
wenzelm@6928
  1078
wenzelm@16601
  1079
(*Left-to-right replacements: ctpairs = [..., (vi, ti), ...].
clasohm@0
  1080
  Instantiates distinct Vars by terms of same type.
wenzelm@16601
  1081
  Does NOT normalize the resulting theorem!*)
paulson@1529
  1082
fun instantiate ([], []) th = th
wenzelm@16884
  1083
  | instantiate (instT, inst) th =
wenzelm@16656
  1084
      let
wenzelm@16884
  1085
        val Thm {thy_ref, der, hyps, shyps, tpairs, prop, ...} = th;
wenzelm@16884
  1086
        val (inst', (instT', (thy_ref', shyps'))) =
wenzelm@16884
  1087
          (thy_ref, shyps) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@20512
  1088
        val subst = TermSubst.instantiate_maxidx (instT', inst');
wenzelm@20512
  1089
        val (prop', maxidx1) = subst prop ~1;
wenzelm@20512
  1090
        val (tpairs', maxidx') =
wenzelm@20512
  1091
          fold_map (fn (t, u) => fn i => subst t i ||>> subst u) tpairs maxidx1;
wenzelm@16656
  1092
      in
wenzelm@20545
  1093
        Thm {thy_ref = thy_ref',
wenzelm@20545
  1094
          der = Pt.infer_derivs' (fn d =>
wenzelm@20545
  1095
            Pt.instantiate (map (apsnd #1) instT', map (apsnd #1) inst') d) der,
wenzelm@21646
  1096
          tags = [],
wenzelm@20545
  1097
          maxidx = maxidx',
wenzelm@20545
  1098
          shyps = shyps',
wenzelm@20545
  1099
          hyps = hyps,
wenzelm@20545
  1100
          tpairs = tpairs',
wenzelm@20545
  1101
          prop = prop'}
wenzelm@16656
  1102
      end
wenzelm@16656
  1103
      handle TYPE (msg, _, _) => raise THM (msg, 0, [th]);
wenzelm@6928
  1104
wenzelm@22584
  1105
fun instantiate_cterm ([], []) ct = ct
wenzelm@22584
  1106
  | instantiate_cterm (instT, inst) ct =
wenzelm@22584
  1107
      let
wenzelm@22584
  1108
        val Cterm {thy_ref, t, T, sorts, ...} = ct;
wenzelm@22584
  1109
        val (inst', (instT', (thy_ref', sorts'))) =
wenzelm@22584
  1110
          (thy_ref, sorts) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@22584
  1111
        val subst = TermSubst.instantiate_maxidx (instT', inst');
wenzelm@22584
  1112
        val substT = TermSubst.instantiateT_maxidx instT';
wenzelm@22584
  1113
        val (t', maxidx1) = subst t ~1;
wenzelm@22584
  1114
        val (T', maxidx') = substT T maxidx1;
wenzelm@22584
  1115
      in Cterm {thy_ref = thy_ref', t = t', T = T', sorts = sorts', maxidx = maxidx'} end
wenzelm@22584
  1116
      handle TYPE (msg, _, _) => raise CTERM (msg, [ct]);
wenzelm@22584
  1117
wenzelm@6928
  1118
end;
wenzelm@6928
  1119
clasohm@0
  1120
wenzelm@16601
  1121
(*The trivial implication A ==> A, justified by assume and forall rules.
wenzelm@16601
  1122
  A can contain Vars, not so for assume!*)
wenzelm@16601
  1123
fun trivial (Cterm {thy_ref, t =A, T, maxidx, sorts}) =
wenzelm@16601
  1124
  if T <> propT then
wenzelm@16601
  1125
    raise THM ("trivial: the term must have type prop", 0, [])
wenzelm@16601
  1126
  else
wenzelm@16601
  1127
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1128
      der = Pt.infer_derivs' I (false, Pt.AbsP ("H", NONE, Pt.PBound 0)),
wenzelm@21646
  1129
      tags = [],
wenzelm@16601
  1130
      maxidx = maxidx,
wenzelm@16601
  1131
      shyps = sorts,
wenzelm@16601
  1132
      hyps = [],
wenzelm@16601
  1133
      tpairs = [],
wenzelm@16601
  1134
      prop = implies $ A $ A};
clasohm@0
  1135
paulson@1503
  1136
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)" *)
wenzelm@16425
  1137
fun class_triv thy c =
wenzelm@16601
  1138
  let val Cterm {thy_ref, t, maxidx, sorts, ...} =
wenzelm@19525
  1139
    cterm_of thy (Logic.mk_inclass (TVar (("'a", 0), [c]), Sign.certify_class thy c))
wenzelm@6368
  1140
      handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@399
  1141
  in
wenzelm@16601
  1142
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1143
      der = Pt.infer_derivs' I (false, Pt.PAxm ("ProtoPure.class_triv:" ^ c, t, SOME [])),
wenzelm@21646
  1144
      tags = [],
wenzelm@16601
  1145
      maxidx = maxidx,
wenzelm@16601
  1146
      shyps = sorts,
wenzelm@16601
  1147
      hyps = [],
wenzelm@16601
  1148
      tpairs = [],
wenzelm@16601
  1149
      prop = t}
wenzelm@399
  1150
  end;
wenzelm@399
  1151
wenzelm@19505
  1152
(*Internalize sort constraints of type variable*)
wenzelm@19505
  1153
fun unconstrainT
wenzelm@19505
  1154
    (Ctyp {thy_ref = thy_ref1, T, ...})
wenzelm@21646
  1155
    (th as Thm {thy_ref = thy_ref2, der, maxidx, shyps, hyps, tpairs, prop, ...}) =
wenzelm@19505
  1156
  let
wenzelm@19505
  1157
    val ((x, i), S) = Term.dest_TVar T handle TYPE _ =>
wenzelm@19505
  1158
      raise THM ("unconstrainT: not a type variable", 0, [th]);
wenzelm@19505
  1159
    val T' = TVar ((x, i), []);
wenzelm@20548
  1160
    val unconstrain = Term.map_types (Term.map_atyps (fn U => if U = T then T' else U));
wenzelm@19505
  1161
    val constraints = map (curry Logic.mk_inclass T') S;
wenzelm@19505
  1162
  in
wenzelm@19505
  1163
    Thm {thy_ref = Theory.merge_refs (thy_ref1, thy_ref2),
wenzelm@19505
  1164
      der = Pt.infer_derivs' I (false, Pt.PAxm ("ProtoPure.unconstrainT", prop, SOME [])),
wenzelm@21646
  1165
      tags = [],
wenzelm@19505
  1166
      maxidx = Int.max (maxidx, i),
wenzelm@19505
  1167
      shyps = Sorts.remove_sort S shyps,
wenzelm@19505
  1168
      hyps = hyps,
wenzelm@19505
  1169
      tpairs = map (pairself unconstrain) tpairs,
wenzelm@19505
  1170
      prop = Logic.list_implies (constraints, unconstrain prop)}
wenzelm@19505
  1171
  end;
wenzelm@399
  1172
wenzelm@6786
  1173
(* Replace all TFrees not fixed or in the hyps by new TVars *)
wenzelm@21646
  1174
fun varifyT' fixed (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop, ...}) =
wenzelm@12500
  1175
  let
wenzelm@23178
  1176
    val tfrees = List.foldr add_term_tfrees fixed hyps;
berghofe@13658
  1177
    val prop1 = attach_tpairs tpairs prop;
haftmann@21116
  1178
    val (al, prop2) = Type.varify tfrees prop1;
wenzelm@16601
  1179
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1180
  in
wenzelm@18127
  1181
    (al, Thm {thy_ref = thy_ref,
wenzelm@16601
  1182
      der = Pt.infer_derivs' (Pt.varify_proof prop tfrees) der,
wenzelm@21646
  1183
      tags = [],
wenzelm@16601
  1184
      maxidx = Int.max (0, maxidx),
wenzelm@16601
  1185
      shyps = shyps,
wenzelm@16601
  1186
      hyps = hyps,
wenzelm@16601
  1187
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@18127
  1188
      prop = prop3})
clasohm@0
  1189
  end;
clasohm@0
  1190
wenzelm@18127
  1191
val varifyT = #2 o varifyT' [];
wenzelm@6786
  1192
clasohm@0
  1193
(* Replace all TVars by new TFrees *)
wenzelm@21646
  1194
fun freezeT (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop, ...}) =
berghofe@13658
  1195
  let
berghofe@13658
  1196
    val prop1 = attach_tpairs tpairs prop;
wenzelm@16287
  1197
    val prop2 = Type.freeze prop1;
wenzelm@16601
  1198
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1199
  in
wenzelm@16601
  1200
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1201
      der = Pt.infer_derivs' (Pt.freezeT prop1) der,
wenzelm@21646
  1202
      tags = [],
wenzelm@16601
  1203
      maxidx = maxidx_of_term prop2,
wenzelm@16601
  1204
      shyps = shyps,
wenzelm@16601
  1205
      hyps = hyps,
wenzelm@16601
  1206
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@16601
  1207
      prop = prop3}
wenzelm@1220
  1208
  end;
clasohm@0
  1209
clasohm@0
  1210
clasohm@0
  1211
(*** Inference rules for tactics ***)
clasohm@0
  1212
clasohm@0
  1213
(*Destruct proof state into constraints, other goals, goal(i), rest *)
berghofe@13658
  1214
fun dest_state (state as Thm{prop,tpairs,...}, i) =
berghofe@13658
  1215
  (case  Logic.strip_prems(i, [], prop) of
berghofe@13658
  1216
      (B::rBs, C) => (tpairs, rev rBs, B, C)
berghofe@13658
  1217
    | _ => raise THM("dest_state", i, [state]))
clasohm@0
  1218
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1219
lcp@309
  1220
(*Increment variables and parameters of orule as required for
wenzelm@18035
  1221
  resolution with a goal.*)
wenzelm@18035
  1222
fun lift_rule goal orule =
wenzelm@16601
  1223
  let
wenzelm@18035
  1224
    val Cterm {t = gprop, T, maxidx = gmax, sorts, ...} = goal;
wenzelm@18035
  1225
    val inc = gmax + 1;
wenzelm@18035
  1226
    val lift_abs = Logic.lift_abs inc gprop;
wenzelm@18035
  1227
    val lift_all = Logic.lift_all inc gprop;
wenzelm@18035
  1228
    val Thm {der, maxidx, shyps, hyps, tpairs, prop, ...} = orule;
wenzelm@16601
  1229
    val (As, B) = Logic.strip_horn prop;
wenzelm@16601
  1230
  in
wenzelm@18035
  1231
    if T <> propT then raise THM ("lift_rule: the term must have type prop", 0, [])
wenzelm@18035
  1232
    else
wenzelm@18035
  1233
      Thm {thy_ref = merge_thys1 goal orule,
wenzelm@18035
  1234
        der = Pt.infer_derivs' (Pt.lift_proof gprop inc prop) der,
wenzelm@21646
  1235
        tags = [],
wenzelm@18035
  1236
        maxidx = maxidx + inc,
wenzelm@18035
  1237
        shyps = Sorts.union shyps sorts,  (*sic!*)
wenzelm@18035
  1238
        hyps = hyps,
wenzelm@18035
  1239
        tpairs = map (pairself lift_abs) tpairs,
wenzelm@18035
  1240
        prop = Logic.list_implies (map lift_all As, lift_all B)}
clasohm@0
  1241
  end;
clasohm@0
  1242
wenzelm@21646
  1243
fun incr_indexes i (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop, ...}) =
wenzelm@16601
  1244
  if i < 0 then raise THM ("negative increment", 0, [thm])
wenzelm@16601
  1245
  else if i = 0 then thm
wenzelm@16601
  1246
  else
wenzelm@16425
  1247
    Thm {thy_ref = thy_ref,
wenzelm@16884
  1248
      der = Pt.infer_derivs'
wenzelm@16884
  1249
        (Pt.map_proof_terms (Logic.incr_indexes ([], i)) (Logic.incr_tvar i)) der,
wenzelm@21646
  1250
      tags = [],
wenzelm@16601
  1251
      maxidx = maxidx + i,
wenzelm@16601
  1252
      shyps = shyps,
wenzelm@16601
  1253
      hyps = hyps,
wenzelm@16601
  1254
      tpairs = map (pairself (Logic.incr_indexes ([], i))) tpairs,
wenzelm@16601
  1255
      prop = Logic.incr_indexes ([], i) prop};
berghofe@10416
  1256
clasohm@0
  1257
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1258
fun assumption i state =
wenzelm@16601
  1259
  let
wenzelm@16601
  1260
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16656
  1261
    val thy = Theory.deref thy_ref;
wenzelm@16601
  1262
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1263
    fun newth n (env as Envir.Envir {maxidx, ...}, tpairs) =
wenzelm@16601
  1264
      Thm {thy_ref = thy_ref,
wenzelm@16601
  1265
        der = Pt.infer_derivs'
wenzelm@16601
  1266
          ((if Envir.is_empty env then I else (Pt.norm_proof' env)) o
wenzelm@16601
  1267
            Pt.assumption_proof Bs Bi n) der,
wenzelm@21646
  1268
        tags = [],
wenzelm@16601
  1269
        maxidx = maxidx,
wenzelm@16656
  1270
        shyps = may_insert_env_sorts thy env shyps,
wenzelm@16601
  1271
        hyps = hyps,
wenzelm@16601
  1272
        tpairs =
wenzelm@16601
  1273
          if Envir.is_empty env then tpairs
wenzelm@16601
  1274
          else map (pairself (Envir.norm_term env)) tpairs,
wenzelm@16601
  1275
        prop =
wenzelm@16601
  1276
          if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@16601
  1277
            Logic.list_implies (Bs, C)
wenzelm@16601
  1278
          else (*normalize the new rule fully*)
wenzelm@16601
  1279
            Envir.norm_term env (Logic.list_implies (Bs, C))};
wenzelm@16601
  1280
    fun addprfs [] _ = Seq.empty
wenzelm@16601
  1281
      | addprfs ((t, u) :: apairs) n = Seq.make (fn () => Seq.pull
wenzelm@16601
  1282
          (Seq.mapp (newth n)
wenzelm@16656
  1283
            (Unify.unifiers (thy, Envir.empty maxidx, (t, u) :: tpairs))
wenzelm@16601
  1284
            (addprfs apairs (n + 1))))
wenzelm@16601
  1285
  in addprfs (Logic.assum_pairs (~1, Bi)) 1 end;
clasohm@0
  1286
wenzelm@250
  1287
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1288
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1289
fun eq_assumption i state =
wenzelm@16601
  1290
  let
wenzelm@16601
  1291
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16601
  1292
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1293
  in
wenzelm@16601
  1294
    (case find_index (op aconv) (Logic.assum_pairs (~1, Bi)) of
wenzelm@16601
  1295
      ~1 => raise THM ("eq_assumption", 0, [state])
wenzelm@16601
  1296
    | n =>
wenzelm@16601
  1297
        Thm {thy_ref = thy_ref,
wenzelm@16601
  1298
          der = Pt.infer_derivs' (Pt.assumption_proof Bs Bi (n + 1)) der,
wenzelm@21646
  1299
          tags = [],
wenzelm@16601
  1300
          maxidx = maxidx,
wenzelm@16601
  1301
          shyps = shyps,
wenzelm@16601
  1302
          hyps = hyps,
wenzelm@16601
  1303
          tpairs = tpairs,
wenzelm@16601
  1304
          prop = Logic.list_implies (Bs, C)})
clasohm@0
  1305
  end;
clasohm@0
  1306
clasohm@0
  1307
paulson@2671
  1308
(*For rotate_tac: fast rotation of assumptions of subgoal i*)
paulson@2671
  1309
fun rotate_rule k i state =
wenzelm@16601
  1310
  let
wenzelm@16601
  1311
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16601
  1312
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1313
    val params = Term.strip_all_vars Bi
wenzelm@16601
  1314
    and rest   = Term.strip_all_body Bi;
wenzelm@16601
  1315
    val asms   = Logic.strip_imp_prems rest
wenzelm@16601
  1316
    and concl  = Logic.strip_imp_concl rest;
wenzelm@16601
  1317
    val n = length asms;
wenzelm@16601
  1318
    val m = if k < 0 then n + k else k;
wenzelm@16601
  1319
    val Bi' =
wenzelm@16601
  1320
      if 0 = m orelse m = n then Bi
wenzelm@16601
  1321
      else if 0 < m andalso m < n then
wenzelm@19012
  1322
        let val (ps, qs) = chop m asms
wenzelm@16601
  1323
        in list_all (params, Logic.list_implies (qs @ ps, concl)) end
wenzelm@16601
  1324
      else raise THM ("rotate_rule", k, [state]);
wenzelm@16601
  1325
  in
wenzelm@16601
  1326
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1327
      der = Pt.infer_derivs' (Pt.rotate_proof Bs Bi m) der,
wenzelm@21646
  1328
      tags = [],
wenzelm@16601
  1329
      maxidx = maxidx,
wenzelm@16601
  1330
      shyps = shyps,
wenzelm@16601
  1331
      hyps = hyps,
wenzelm@16601
  1332
      tpairs = tpairs,
wenzelm@16601
  1333
      prop = Logic.list_implies (Bs @ [Bi'], C)}
paulson@2671
  1334
  end;
paulson@2671
  1335
paulson@2671
  1336
paulson@7248
  1337
(*Rotates a rule's premises to the left by k, leaving the first j premises
paulson@7248
  1338
  unchanged.  Does nothing if k=0 or if k equals n-j, where n is the
wenzelm@16656
  1339
  number of premises.  Useful with etac and underlies defer_tac*)
paulson@7248
  1340
fun permute_prems j k rl =
wenzelm@16601
  1341
  let
wenzelm@21646
  1342
    val Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop, ...} = rl;
wenzelm@16601
  1343
    val prems = Logic.strip_imp_prems prop
wenzelm@16601
  1344
    and concl = Logic.strip_imp_concl prop;
wenzelm@16601
  1345
    val moved_prems = List.drop (prems, j)
wenzelm@16601
  1346
    and fixed_prems = List.take (prems, j)
wenzelm@16601
  1347
      handle Subscript => raise THM ("permute_prems: j", j, [rl]);
wenzelm@16601
  1348
    val n_j = length moved_prems;
wenzelm@16601
  1349
    val m = if k < 0 then n_j + k else k;
wenzelm@16601
  1350
    val prop' =
wenzelm@16601
  1351
      if 0 = m orelse m = n_j then prop
wenzelm@16601
  1352
      else if 0 < m andalso m < n_j then
wenzelm@19012
  1353
        let val (ps, qs) = chop m moved_prems
wenzelm@16601
  1354
        in Logic.list_implies (fixed_prems @ qs @ ps, concl) end
wenzelm@16725
  1355
      else raise THM ("permute_prems: k", k, [rl]);
wenzelm@16601
  1356
  in
wenzelm@16601
  1357
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1358
      der = Pt.infer_derivs' (Pt.permute_prems_prf prems j m) der,
wenzelm@21646
  1359
      tags = [],
wenzelm@16601
  1360
      maxidx = maxidx,
wenzelm@16601
  1361
      shyps = shyps,
wenzelm@16601
  1362
      hyps = hyps,
wenzelm@16601
  1363
      tpairs = tpairs,
wenzelm@16601
  1364
      prop = prop'}
paulson@7248
  1365
  end;
paulson@7248
  1366
paulson@7248
  1367
clasohm@0
  1368
(** User renaming of parameters in a subgoal **)
clasohm@0
  1369
clasohm@0
  1370
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1371
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1372
  The names in cs, if distinct, are used for the innermost parameters;
wenzelm@17868
  1373
  preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1374
fun rename_params_rule (cs, i) state =
wenzelm@16601
  1375
  let
wenzelm@21646
  1376
    val Thm {thy_ref, der, tags, maxidx, shyps, hyps, ...} = state;
wenzelm@16601
  1377
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1378
    val iparams = map #1 (Logic.strip_params Bi);
wenzelm@16601
  1379
    val short = length iparams - length cs;
wenzelm@16601
  1380
    val newnames =
wenzelm@16601
  1381
      if short < 0 then error "More names than abstractions!"
wenzelm@20071
  1382
      else Name.variant_list cs (Library.take (short, iparams)) @ cs;
wenzelm@20330
  1383
    val freenames = Term.fold_aterms (fn Free (x, _) => insert (op =) x | _ => I) Bi [];
wenzelm@16601
  1384
    val newBi = Logic.list_rename_params (newnames, Bi);
wenzelm@250
  1385
  in
wenzelm@21182
  1386
    (case duplicates (op =) cs of
wenzelm@21182
  1387
      a :: _ => (warning ("Can't rename.  Bound variables not distinct: " ^ a); state)
wenzelm@21182
  1388
    | [] =>
wenzelm@16601
  1389
      (case cs inter_string freenames of
wenzelm@16601
  1390
        a :: _ => (warning ("Can't rename.  Bound/Free variable clash: " ^ a); state)
wenzelm@16601
  1391
      | [] =>
wenzelm@16601
  1392
        Thm {thy_ref = thy_ref,
wenzelm@16601
  1393
          der = der,
wenzelm@21646
  1394
          tags = tags,
wenzelm@16601
  1395
          maxidx = maxidx,
wenzelm@16601
  1396
          shyps = shyps,
wenzelm@16601
  1397
          hyps = hyps,
wenzelm@16601
  1398
          tpairs = tpairs,
wenzelm@21182
  1399
          prop = Logic.list_implies (Bs @ [newBi], C)}))
clasohm@0
  1400
  end;
clasohm@0
  1401
wenzelm@12982
  1402
clasohm@0
  1403
(*** Preservation of bound variable names ***)
clasohm@0
  1404
wenzelm@21646
  1405
fun rename_boundvars pat obj (thm as Thm {thy_ref, der, tags, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@12982
  1406
  (case Term.rename_abs pat obj prop of
skalberg@15531
  1407
    NONE => thm
skalberg@15531
  1408
  | SOME prop' => Thm
wenzelm@16425
  1409
      {thy_ref = thy_ref,
wenzelm@12982
  1410
       der = der,
wenzelm@21646
  1411
       tags = tags,
wenzelm@12982
  1412
       maxidx = maxidx,
wenzelm@12982
  1413
       hyps = hyps,
wenzelm@12982
  1414
       shyps = shyps,
berghofe@13658
  1415
       tpairs = tpairs,
wenzelm@12982
  1416
       prop = prop'});
berghofe@10416
  1417
clasohm@0
  1418
wenzelm@16656
  1419
(* strip_apply f (A, B) strips off all assumptions/parameters from A
clasohm@0
  1420
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
  1421
fun strip_apply f =
clasohm@0
  1422
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@250
  1423
                Const("==>",_)$ _  $ B2) = implies $ A1 $ strip(B1,B2)
wenzelm@250
  1424
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
  1425
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
  1426
        | strip(A,_) = f A
clasohm@0
  1427
  in strip end;
clasohm@0
  1428
clasohm@0
  1429
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1430
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1431
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1432
fun rename_bvs([],_,_,_) = I
clasohm@0
  1433
  | rename_bvs(al,dpairs,tpairs,B) =
wenzelm@20330
  1434
      let
wenzelm@20330
  1435
        val add_var = fold_aterms (fn Var ((x, _), _) => insert (op =) x | _ => I);
wenzelm@20330
  1436
        val vids = []
wenzelm@20330
  1437
          |> fold (add_var o fst) dpairs
wenzelm@20330
  1438
          |> fold (add_var o fst) tpairs
wenzelm@20330
  1439
          |> fold (add_var o snd) tpairs;
wenzelm@250
  1440
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1441
        fun rename(t as Var((x,i),T)) =
wenzelm@20330
  1442
              (case AList.lookup (op =) al x of
wenzelm@20330
  1443
                SOME y =>
wenzelm@20330
  1444
                  if member (op =) vids x orelse member (op =) vids y then t
wenzelm@20330
  1445
                  else Var((y,i),T)
wenzelm@20330
  1446
              | NONE=> t)
clasohm@0
  1447
          | rename(Abs(x,T,t)) =
wenzelm@18944
  1448
              Abs (the_default x (AList.lookup (op =) al x), T, rename t)
clasohm@0
  1449
          | rename(f$t) = rename f $ rename t
clasohm@0
  1450
          | rename(t) = t;
wenzelm@250
  1451
        fun strip_ren Ai = strip_apply rename (Ai,B)
wenzelm@20330
  1452
      in strip_ren end;
clasohm@0
  1453
clasohm@0
  1454
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
  1455
fun rename_bvars(dpairs, tpairs, B) =
wenzelm@23178
  1456
        rename_bvs(List.foldr Term.match_bvars [] dpairs, dpairs, tpairs, B);
clasohm@0
  1457
clasohm@0
  1458
clasohm@0
  1459
(*** RESOLUTION ***)
clasohm@0
  1460
lcp@721
  1461
(** Lifting optimizations **)
lcp@721
  1462
clasohm@0
  1463
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
  1464
  identical because of lifting*)
wenzelm@250
  1465
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
  1466
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
  1467
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
  1468
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
  1469
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
  1470
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
  1471
  | strip_assums2 BB = BB;
clasohm@0
  1472
clasohm@0
  1473
lcp@721
  1474
(*Faster normalization: skip assumptions that were lifted over*)
lcp@721
  1475
fun norm_term_skip env 0 t = Envir.norm_term env t
lcp@721
  1476
  | norm_term_skip env n (Const("all",_)$Abs(a,T,t)) =
lcp@721
  1477
        let val Envir.Envir{iTs, ...} = env
berghofe@15797
  1478
            val T' = Envir.typ_subst_TVars iTs T
wenzelm@1238
  1479
            (*Must instantiate types of parameters because they are flattened;
lcp@721
  1480
              this could be a NEW parameter*)
lcp@721
  1481
        in  all T' $ Abs(a, T', norm_term_skip env n t)  end
lcp@721
  1482
  | norm_term_skip env n (Const("==>", _) $ A $ B) =
wenzelm@1238
  1483
        implies $ A $ norm_term_skip env (n-1) B
lcp@721
  1484
  | norm_term_skip env n t = error"norm_term_skip: too few assumptions??";
lcp@721
  1485
lcp@721
  1486
clasohm@0
  1487
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
  1488
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
  1489
  If match then forbid instantiations in proof state
clasohm@0
  1490
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
  1491
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
  1492
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
  1493
  Curried so that resolution calls dest_state only once.
clasohm@0
  1494
*)
wenzelm@4270
  1495
local exception COMPOSE
clasohm@0
  1496
in
wenzelm@18486
  1497
fun bicompose_aux flatten match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
  1498
                        (eres_flg, orule, nsubgoal) =
paulson@1529
  1499
 let val Thm{der=sder, maxidx=smax, shyps=sshyps, hyps=shyps, ...} = state
wenzelm@16425
  1500
     and Thm{der=rder, maxidx=rmax, shyps=rshyps, hyps=rhyps,
berghofe@13658
  1501
             tpairs=rtpairs, prop=rprop,...} = orule
paulson@1529
  1502
         (*How many hyps to skip over during normalization*)
wenzelm@21576
  1503
     and nlift = Logic.count_prems (strip_all_body Bi) + (if eres_flg then ~1 else 0)
wenzelm@16601
  1504
     val thy_ref = merge_thys2 state orule;
wenzelm@16425
  1505
     val thy = Theory.deref thy_ref;
clasohm@0
  1506
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
berghofe@11518
  1507
     fun addth A (As, oldAs, rder', n) ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
  1508
       let val normt = Envir.norm_term env;
wenzelm@250
  1509
           (*perform minimal copying here by examining env*)
berghofe@13658
  1510
           val (ntpairs, normp) =
berghofe@13658
  1511
             if Envir.is_empty env then (tpairs, (Bs @ As, C))
wenzelm@250
  1512
             else
wenzelm@250
  1513
             let val ntps = map (pairself normt) tpairs
wenzelm@19861
  1514
             in if Envir.above env smax then
wenzelm@1238
  1515
                  (*no assignments in state; normalize the rule only*)
wenzelm@1238
  1516
                  if lifted
berghofe@13658
  1517
                  then (ntps, (Bs @ map (norm_term_skip env nlift) As, C))
berghofe@13658
  1518
                  else (ntps, (Bs @ map normt As, C))
paulson@1529
  1519
                else if match then raise COMPOSE
wenzelm@250
  1520
                else (*normalize the new rule fully*)
berghofe@13658
  1521
                  (ntps, (map normt (Bs @ As), normt C))
wenzelm@250
  1522
             end
wenzelm@16601
  1523
           val th =
wenzelm@16425
  1524
             Thm{thy_ref = thy_ref,
berghofe@11518
  1525
                 der = Pt.infer_derivs
berghofe@11518
  1526
                   ((if Envir.is_empty env then I
wenzelm@19861
  1527
                     else if Envir.above env smax then
berghofe@11518
  1528
                       (fn f => fn der => f (Pt.norm_proof' env der))
berghofe@11518
  1529
                     else
berghofe@11518
  1530
                       curry op oo (Pt.norm_proof' env))
berghofe@23296
  1531
                    (Pt.bicompose_proof flatten Bs oldAs As A n (nlift+1))) rder' sder,
wenzelm@21646
  1532
                 tags = [],
wenzelm@2386
  1533
                 maxidx = maxidx,
wenzelm@16656
  1534
                 shyps = may_insert_env_sorts thy env (Sorts.union rshyps sshyps),
wenzelm@16601
  1535
                 hyps = union_hyps rhyps shyps,
berghofe@13658
  1536
                 tpairs = ntpairs,
berghofe@13658
  1537
                 prop = Logic.list_implies normp}
wenzelm@19475
  1538
        in  Seq.cons th thq  end  handle COMPOSE => thq;
berghofe@13658
  1539
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rprop)
clasohm@0
  1540
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
  1541
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
  1542
     fun newAs(As0, n, dpairs, tpairs) =
berghofe@11518
  1543
       let val (As1, rder') =
berghofe@11518
  1544
         if !Logic.auto_rename orelse not lifted then (As0, rder)
berghofe@11518
  1545
         else (map (rename_bvars(dpairs,tpairs,B)) As0,
berghofe@11518
  1546
           Pt.infer_derivs' (Pt.map_proof_terms
berghofe@11518
  1547
             (rename_bvars (dpairs, tpairs, Bound 0)) I) rder);
wenzelm@18486
  1548
       in (map (if flatten then (Logic.flatten_params n) else I) As1, As1, rder', n)
wenzelm@250
  1549
          handle TERM _ =>
wenzelm@250
  1550
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
  1551
       end;
paulson@2147
  1552
     val env = Envir.empty(Int.max(rmax,smax));
clasohm@0
  1553
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
  1554
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
  1555
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
berghofe@11518
  1556
     fun tryasms (_, _, _, []) = Seq.empty
berghofe@11518
  1557
       | tryasms (A, As, n, (t,u)::apairs) =
wenzelm@16425
  1558
          (case Seq.pull(Unify.unifiers(thy, env, (t,u)::dpairs))  of
wenzelm@16425
  1559
              NONE                   => tryasms (A, As, n+1, apairs)
wenzelm@16425
  1560
            | cell as SOME((_,tpairs),_) =>
wenzelm@16425
  1561
                Seq.it_right (addth A (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@16425
  1562
                    (Seq.make(fn()=> cell),
wenzelm@16425
  1563
                     Seq.make(fn()=> Seq.pull (tryasms(A, As, n+1, apairs)))))
clasohm@0
  1564
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
skalberg@15531
  1565
       | eres (A1::As) = tryasms(SOME A1, As, 1, Logic.assum_pairs(nlift+1,A1))
clasohm@0
  1566
     (*ordinary resolution*)
skalberg@15531
  1567
     fun res(NONE) = Seq.empty
skalberg@15531
  1568
       | res(cell as SOME((_,tpairs),_)) =
skalberg@15531
  1569
             Seq.it_right (addth NONE (newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@4270
  1570
                       (Seq.make (fn()=> cell), Seq.empty)
clasohm@0
  1571
 in  if eres_flg then eres(rev rAs)
wenzelm@16425
  1572
     else res(Seq.pull(Unify.unifiers(thy, env, dpairs)))
clasohm@0
  1573
 end;
wenzelm@7528
  1574
end;
clasohm@0
  1575
wenzelm@18501
  1576
fun compose_no_flatten match (orule, nsubgoal) i state =
wenzelm@18501
  1577
  bicompose_aux false match (state, dest_state (state, i), false) (false, orule, nsubgoal);
clasohm@0
  1578
wenzelm@18501
  1579
fun bicompose match arg i state =
wenzelm@18501
  1580
  bicompose_aux true match (state, dest_state (state,i), false) arg;
clasohm@0
  1581
clasohm@0
  1582
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1583
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1584
fun could_bires (Hs, B, eres_flg, rule) =
wenzelm@16847
  1585
    let fun could_reshyp (A1::_) = exists (fn H => could_unify (A1, H)) Hs
wenzelm@250
  1586
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@250
  1587
    in  could_unify(concl_of rule, B) andalso
wenzelm@250
  1588
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1589
    end;
clasohm@0
  1590
clasohm@0
  1591
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1592
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1593
fun biresolution match brules i state =
wenzelm@18035
  1594
    let val (stpairs, Bs, Bi, C) = dest_state(state,i);
wenzelm@18145
  1595
        val lift = lift_rule (cprem_of state i);
wenzelm@250
  1596
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1597
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@22573
  1598
        val compose = bicompose_aux true match (state, (stpairs, Bs, Bi, C), true);
wenzelm@4270
  1599
        fun res [] = Seq.empty
wenzelm@250
  1600
          | res ((eres_flg, rule)::brules) =
nipkow@13642
  1601
              if !Pattern.trace_unify_fail orelse
nipkow@13642
  1602
                 could_bires (Hs, B, eres_flg, rule)
wenzelm@4270
  1603
              then Seq.make (*delay processing remainder till needed*)
wenzelm@22573
  1604
                  (fn()=> SOME(compose (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1605
                               res brules))
wenzelm@250
  1606
              else res brules
wenzelm@4270
  1607
    in  Seq.flat (res brules)  end;
clasohm@0
  1608
clasohm@0
  1609
wenzelm@2509
  1610
(*** Oracles ***)
wenzelm@2509
  1611
wenzelm@16425
  1612
fun invoke_oracle_i thy1 name =
wenzelm@3812
  1613
  let
wenzelm@3812
  1614
    val oracle =
wenzelm@22685
  1615
      (case Symtab.lookup (Theory.oracle_table thy1) name of
skalberg@15531
  1616
        NONE => raise THM ("Unknown oracle: " ^ name, 0, [])
skalberg@15531
  1617
      | SOME (f, _) => f);
wenzelm@16847
  1618
    val thy_ref1 = Theory.self_ref thy1;
wenzelm@3812
  1619
  in
wenzelm@16425
  1620
    fn (thy2, data) =>
wenzelm@3812
  1621
      let
wenzelm@16847
  1622
        val thy' = Theory.merge (Theory.deref thy_ref1, thy2);
wenzelm@18969
  1623
        val (prop, T, maxidx) = Sign.certify_term thy' (oracle (thy', data));
wenzelm@3812
  1624
      in
wenzelm@3812
  1625
        if T <> propT then
wenzelm@3812
  1626
          raise THM ("Oracle's result must have type prop: " ^ name, 0, [])
wenzelm@16601
  1627
        else
wenzelm@16601
  1628
          Thm {thy_ref = Theory.self_ref thy',
berghofe@11518
  1629
            der = (true, Pt.oracle_proof name prop),
wenzelm@21646
  1630
            tags = [],
wenzelm@3812
  1631
            maxidx = maxidx,
wenzelm@16656
  1632
            shyps = may_insert_term_sorts thy' prop [],
wenzelm@16425
  1633
            hyps = [],
berghofe@13658
  1634
            tpairs = [],
wenzelm@16601
  1635
            prop = prop}
wenzelm@3812
  1636
      end
wenzelm@3812
  1637
  end;
wenzelm@3812
  1638
wenzelm@15672
  1639
fun invoke_oracle thy =
wenzelm@16425
  1640
  invoke_oracle_i thy o NameSpace.intern (Theory.oracle_space thy);
wenzelm@15672
  1641
wenzelm@22237
  1642
wenzelm@22237
  1643
end;
wenzelm@22237
  1644
end;
wenzelm@22237
  1645
end;
clasohm@0
  1646
end;
paulson@1503
  1647
wenzelm@6089
  1648
structure BasicThm: BASIC_THM = Thm;
wenzelm@6089
  1649
open BasicThm;