src/Pure/thm.ML
author wenzelm
Wed Jul 06 10:41:45 2005 +0200 (2005-07-06)
changeset 16711 2c1f9640b744
parent 16679 abd1461fa288
child 16725 597830f91930
permissions -rw-r--r--
tuned maxidx;
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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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    sign: theory,       (*obsolete*)
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    T: typ,
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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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  val read_ctyp: theory -> string -> ctyp
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  (*certified terms*)
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  type cterm
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  exception CTERM of string
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  val rep_cterm: cterm ->
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   {thy: theory,
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    sign: theory,       (*obsolete*)
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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 ->
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    {thy: theory, sign: 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 sign_of_cterm: cterm -> theory    (*obsolete*)
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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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  val read_cterm: theory -> string * typ -> cterm
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  val adjust_maxidx: cterm -> cterm
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  val read_def_cterm:
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    theory * (indexname -> typ option) * (indexname -> sort option) ->
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    string list -> bool -> string * typ -> cterm * (indexname * typ) list
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  val read_def_cterms:
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    theory * (indexname -> typ option) * (indexname -> sort option) ->
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    string list -> bool -> (string * typ)list
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    -> cterm list * (indexname * typ)list
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  type tag              (* = string * string list *)
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  (*meta theorems*)
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  type thm
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  val rep_thm: thm ->
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   {thy: theory,
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    sign: theory,       (*obsolete*)
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    der: bool * Proofterm.proof,
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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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    sign: theory,       (*obsolete*)
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    der: bool * Proofterm.proof,
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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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  type 'a attribute     (* = 'a * thm -> 'a * thm *)
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  val eq_thm: thm * thm -> bool
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  val eq_thms: thm list * thm list -> bool
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  val theory_of_thm: thm -> theory
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  val sign_of_thm: thm -> theory    (*obsolete*)
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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 transfer: theory -> 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 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 compress: thm -> 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 -> cterm -> thm
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  val eta_conversion: cterm -> thm
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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 instantiate: (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm
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  val trivial: cterm -> thm
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  val class_triv: theory -> class -> thm
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  val varifyT: thm -> thm
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  val varifyT': (string * sort) list -> thm -> thm * ((string * sort) * indexname) list
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  val freezeT: 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: (thm * int) -> 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 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_abs: string option -> cterm -> 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 no_attributes: 'a -> 'a * 'b attribute list
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  val apply_attributes: ('a * thm) * 'a attribute list -> ('a * thm)
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  val applys_attributes: ('a * thm list) * 'a attribute list -> ('a * thm list)
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  val get_name_tags: thm -> string * tag list
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  val put_name_tags: string * tag list -> thm -> thm
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  val name_of_thm: thm -> string
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  val tags_of_thm: thm -> tag list
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  val name_thm: string * thm -> thm
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  val rename_boundvars: term -> term -> thm -> thm
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  val cterm_match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
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  val cterm_first_order_match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
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  val cterm_incr_indexes: int -> cterm -> cterm
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  val terms_of_tpairs: (term * term) list -> term list
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end;
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structure Thm: THM =
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struct
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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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datatype ctyp = Ctyp of {thy_ref: theory_ref, T: typ, sorts: sort list};
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fun rep_ctyp (Ctyp {thy_ref, T, sorts}) =
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  let val thy = Theory.deref thy_ref
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  in {thy = thy, sign = thy, T = T, 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
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  in Ctyp {thy_ref = Theory.self_ref thy, T = T, sorts = may_insert_typ_sorts thy T []} end;
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fun read_ctyp thy s =
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  let val T = Sign.read_typ (thy, K NONE) s
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  in Ctyp {thy_ref = Theory.self_ref thy, T = T, sorts = may_insert_typ_sorts thy T []} end;
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fun dest_ctyp (Ctyp {thy_ref, T = Type (s, Ts), sorts}) =
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      map (fn T => Ctyp {thy_ref = thy_ref, T = T, 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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datatype 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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exception CTERM of string;
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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, sign = 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, sign = thy, t = t, T = Ctyp {thy_ref = thy_ref, T = T, 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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val sign_of_cterm = theory_of_cterm;
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fun term_of (Cterm {t, ...}) = t;
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fun ctyp_of_term (Cterm {thy_ref, T, sorts, ...}) =
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  Ctyp {thy_ref = thy_ref, T = T, 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 (Sign.pp thy) 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, ...}) (Cterm {thy_ref = r2, ...}) =
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  Theory.merge_refs (r1, r2);
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(*Destruct application in cterms*)
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fun dest_comb (Cterm {t = t $ u, T, thy_ref, maxidx, sorts}) =
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      let val A = Term.argument_type_of t in
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        (Cterm {t = t, T = A --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
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         Cterm {t = u, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
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      end
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  | dest_comb _ = raise CTERM "dest_comb";
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(*Destruct abstraction in cterms*)
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fun dest_abs a (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 (if_none a x, 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 _ _ = raise CTERM "dest_abs";
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(*Makes maxidx precise: it is often too big*)
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fun adjust_maxidx (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
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  if maxidx = ~1 then ct
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  else Cterm {thy_ref = thy_ref, t = t, T = T, maxidx = maxidx_of_term t, sorts = sorts};
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(*Form cterm out of a function and an argument*)
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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"
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  | capply _ _ = raise CTERM "capply: first arg is not a function"
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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 = lambda t1 t2 handle TERM _ => raise CTERM "cabs: first arg is not a variable" 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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(*Matching of cterms*)
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fun gen_cterm_match match
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    (ct1 as Cterm {t = t1, maxidx = maxidx1, sorts = sorts1, ...},
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     ct2 as Cterm {t = t2, maxidx = maxidx2, sorts = sorts2, ...}) =
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  let
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    val thy_ref = merge_thys0 ct1 ct2;
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    val (Tinsts, tinsts) = match (Sign.tsig_of (Theory.deref thy_ref)) (t1, t2);
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    val maxidx = Int.max (maxidx1, maxidx2);
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    val sorts = Sorts.union sorts1 sorts2;
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    fun mk_cTinst (ixn, (S, T)) =
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      (Ctyp {T = TVar (ixn, S), thy_ref = thy_ref, sorts = sorts},
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       Ctyp {T = T, thy_ref = thy_ref, sorts = sorts});
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    fun mk_ctinst (ixn, (T, t)) =
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      let val T = Envir.typ_subst_TVars Tinsts T in
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        (Cterm {t = Var (ixn, T), T = T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
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         Cterm {t = t, T = T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
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      end;
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  in (Vartab.fold (cons o mk_cTinst) Tinsts [], Vartab.fold (cons o mk_ctinst) tinsts []) end;
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val cterm_match = gen_cterm_match Pattern.match;
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val cterm_first_order_match = gen_cterm_match Pattern.first_order_match;
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(*Incrementing indexes*)
wenzelm@16601
   307
fun cterm_incr_indexes i (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   308
  if i < 0 then raise CTERM "negative increment"
wenzelm@16601
   309
  else if i = 0 then ct
wenzelm@16601
   310
  else Cterm {thy_ref = thy_ref, t = Logic.incr_indexes ([], i) t,
wenzelm@16601
   311
    T = Term.incr_tvar i T, maxidx = maxidx + i, sorts = sorts};
berghofe@10416
   312
wenzelm@2509
   313
wenzelm@2509
   314
wenzelm@574
   315
(** read cterms **)   (*exception ERROR*)
wenzelm@250
   316
nipkow@4281
   317
(*read terms, infer types, certify terms*)
wenzelm@16425
   318
fun read_def_cterms (thy, types, sorts) used freeze sTs =
wenzelm@250
   319
  let
wenzelm@16425
   320
    val (ts', tye) = Sign.read_def_terms (thy, types, sorts) used freeze sTs;
wenzelm@16425
   321
    val cts = map (cterm_of thy) ts'
wenzelm@2979
   322
      handle TYPE (msg, _, _) => error msg
wenzelm@2386
   323
           | TERM (msg, _) => error msg;
nipkow@4281
   324
  in (cts, tye) end;
nipkow@4281
   325
nipkow@4281
   326
(*read term, infer types, certify term*)
nipkow@4281
   327
fun read_def_cterm args used freeze aT =
nipkow@4281
   328
  let val ([ct],tye) = read_def_cterms args used freeze [aT]
nipkow@4281
   329
  in (ct,tye) end;
lcp@229
   330
wenzelm@16425
   331
fun read_cterm thy = #1 o read_def_cterm (thy, K NONE, K NONE) [] true;
lcp@229
   332
wenzelm@250
   333
wenzelm@6089
   334
(*tags provide additional comment, apart from the axiom/theorem name*)
wenzelm@6089
   335
type tag = string * string list;
wenzelm@6089
   336
wenzelm@2509
   337
wenzelm@387
   338
(*** Meta theorems ***)
lcp@229
   339
berghofe@11518
   340
structure Pt = Proofterm;
berghofe@11518
   341
clasohm@0
   342
datatype thm = Thm of
wenzelm@16425
   343
 {thy_ref: theory_ref,         (*dynamic reference to theory*)
berghofe@11518
   344
  der: bool * Pt.proof,        (*derivation*)
wenzelm@3967
   345
  maxidx: int,                 (*maximum index of any Var or TVar*)
wenzelm@16601
   346
  shyps: sort list,            (*sort hypotheses as ordered list*)
wenzelm@16601
   347
  hyps: term list,             (*hypotheses as ordered list*)
berghofe@13658
   348
  tpairs: (term * term) list,  (*flex-flex pairs*)
wenzelm@3967
   349
  prop: term};                 (*conclusion*)
clasohm@0
   350
wenzelm@16656
   351
fun terms_of_tpairs tpairs = fold_rev (fn (t, u) => cons t o cons u) tpairs [];
wenzelm@16656
   352
wenzelm@16656
   353
fun eq_tpairs ((t, u), (t', u')) = t aconv t' andalso u aconv u';
wenzelm@16656
   354
val union_tpairs = gen_merge_lists eq_tpairs;
wenzelm@16711
   355
val maxidx_tpairs = fold (fn (t, u) => Term.maxidx_term t o Term.maxidx_term u);
berghofe@13658
   356
berghofe@13658
   357
fun attach_tpairs tpairs prop =
berghofe@13658
   358
  Logic.list_implies (map Logic.mk_equals tpairs, prop);
berghofe@13658
   359
wenzelm@16425
   360
fun rep_thm (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   361
  let val thy = Theory.deref thy_ref in
wenzelm@16425
   362
   {thy = thy, sign = thy, der = der, maxidx = maxidx,
wenzelm@16425
   363
    shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@16425
   364
  end;
clasohm@0
   365
wenzelm@16425
   366
(*version of rep_thm returning cterms instead of terms*)
wenzelm@16425
   367
fun crep_thm (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   368
  let
wenzelm@16425
   369
    val thy = Theory.deref thy_ref;
wenzelm@16601
   370
    fun cterm max t = Cterm {thy_ref = thy_ref, t = t, T = propT, maxidx = max, sorts = shyps};
wenzelm@16425
   371
  in
wenzelm@16425
   372
   {thy = thy, sign = thy, der = der, maxidx = maxidx, shyps = shyps,
wenzelm@16425
   373
    hyps = map (cterm ~1) hyps,
wenzelm@16425
   374
    tpairs = map (pairself (cterm maxidx)) tpairs,
wenzelm@16425
   375
    prop = cterm maxidx prop}
clasohm@1517
   376
  end;
clasohm@1517
   377
wenzelm@387
   378
(*errors involving theorems*)
clasohm@0
   379
exception THM of string * int * thm list;
clasohm@0
   380
wenzelm@16425
   381
(*attributes subsume any kind of rules or context modifiers*)
wenzelm@6089
   382
type 'a attribute = 'a * thm -> 'a * thm;
wenzelm@6089
   383
wenzelm@6089
   384
fun no_attributes x = (x, []);
wenzelm@6089
   385
fun apply_attributes (x_th, atts) = Library.apply atts x_th;
wenzelm@6089
   386
fun applys_attributes (x_ths, atts) = foldl_map (Library.apply atts) x_ths;
wenzelm@6089
   387
wenzelm@16601
   388
wenzelm@16656
   389
(* hyps *)
wenzelm@16601
   390
wenzelm@16679
   391
val remove_hyps = OrdList.remove Term.fast_term_ord;
wenzelm@16679
   392
val union_hyps = OrdList.union Term.fast_term_ord;
wenzelm@16679
   393
val eq_set_hyps = OrdList.eq_set Term.fast_term_ord;
wenzelm@16601
   394
wenzelm@16601
   395
wenzelm@16601
   396
(* eq_thm(s) *)
wenzelm@16601
   397
wenzelm@3994
   398
fun eq_thm (th1, th2) =
wenzelm@3994
   399
  let
wenzelm@16425
   400
    val {thy = thy1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1, prop = prop1, ...} =
wenzelm@9031
   401
      rep_thm th1;
wenzelm@16425
   402
    val {thy = thy2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2, prop = prop2, ...} =
wenzelm@9031
   403
      rep_thm th2;
wenzelm@3994
   404
  in
wenzelm@16601
   405
    Context.joinable (thy1, thy2) andalso
wenzelm@16601
   406
    Sorts.eq_set (shyps1, shyps2) andalso
wenzelm@16601
   407
    eq_set_hyps (hyps1, hyps2) andalso
wenzelm@16656
   408
    equal_lists eq_tpairs (tpairs1, tpairs2) andalso
wenzelm@3994
   409
    prop1 aconv prop2
wenzelm@3994
   410
  end;
wenzelm@387
   411
wenzelm@16135
   412
val eq_thms = Library.equal_lists eq_thm;
wenzelm@16135
   413
wenzelm@16425
   414
fun theory_of_thm (Thm {thy_ref, ...}) = Theory.deref thy_ref;
wenzelm@16425
   415
val sign_of_thm = theory_of_thm;
wenzelm@16425
   416
wenzelm@12803
   417
fun prop_of (Thm {prop, ...}) = prop;
wenzelm@13528
   418
fun proof_of (Thm {der = (_, proof), ...}) = proof;
wenzelm@16601
   419
fun tpairs_of (Thm {tpairs, ...}) = tpairs;
clasohm@0
   420
wenzelm@16601
   421
val concl_of = Logic.strip_imp_concl o prop_of;
wenzelm@16601
   422
val prems_of = Logic.strip_imp_prems o prop_of;
wenzelm@16601
   423
fun nprems_of th = Logic.count_prems (prop_of th, 0);
wenzelm@16601
   424
val no_prems = equal 0 o nprems_of;
wenzelm@16601
   425
wenzelm@16601
   426
fun major_prem_of th =
wenzelm@16601
   427
  (case prems_of th of
wenzelm@16601
   428
    prem :: _ => Logic.strip_assums_concl prem
wenzelm@16601
   429
  | [] => raise THM ("major_prem_of: rule with no premises", 0, [th]));
wenzelm@16601
   430
wenzelm@16601
   431
(*the statement of any thm is a cterm*)
wenzelm@16601
   432
fun cprop_of (Thm {thy_ref, maxidx, shyps, prop, ...}) =
wenzelm@16601
   433
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, t = prop, sorts = shyps};
wenzelm@16601
   434
wenzelm@16656
   435
(*explicit transfer to a super theory*)
wenzelm@16425
   436
fun transfer thy' thm =
wenzelm@3895
   437
  let
wenzelm@16425
   438
    val Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop} = thm;
wenzelm@16425
   439
    val thy = Theory.deref thy_ref;
wenzelm@3895
   440
  in
wenzelm@16425
   441
    if eq_thy (thy, thy') then thm
wenzelm@16425
   442
    else if subthy (thy, thy') then
wenzelm@16425
   443
      Thm {thy_ref = Theory.self_ref thy', der = der, maxidx = maxidx,
berghofe@13658
   444
        shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@3895
   445
    else raise THM ("transfer: not a super theory", 0, [thm])
wenzelm@3895
   446
  end;
wenzelm@387
   447
wenzelm@387
   448
wenzelm@16656
   449
(* merge theories of cterms/thms; raise exception if incompatible *)
wenzelm@16656
   450
wenzelm@16656
   451
fun merge_thys1 (Cterm {thy_ref = r1, ...}) (th as Thm {thy_ref = r2, ...}) =
wenzelm@16656
   452
  Theory.merge_refs (r1, r2) handle TERM (msg, _) => raise THM (msg, 0, [th]);
wenzelm@16656
   453
wenzelm@16656
   454
fun merge_thys2 (th1 as Thm {thy_ref = r1, ...}) (th2 as Thm {thy_ref = r2, ...}) =
wenzelm@16656
   455
  Theory.merge_refs (r1, r2) handle TERM (msg, _) => raise THM (msg, 0, [th1, th2]);
wenzelm@16656
   456
wenzelm@16656
   457
clasohm@0
   458
wenzelm@1238
   459
(** sort contexts of theorems **)
wenzelm@1238
   460
wenzelm@16656
   461
fun present_sorts (Thm {hyps, tpairs, prop, ...}) =
wenzelm@16656
   462
  fold (fn (t, u) => Sorts.insert_term t o Sorts.insert_term u) tpairs
wenzelm@16656
   463
    (Sorts.insert_terms hyps (Sorts.insert_term prop []));
wenzelm@1238
   464
wenzelm@7642
   465
(*remove extra sorts that are non-empty by virtue of type signature information*)
wenzelm@7642
   466
fun strip_shyps (thm as Thm {shyps = [], ...}) = thm
wenzelm@16425
   467
  | strip_shyps (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@7642
   468
      let
wenzelm@16425
   469
        val thy = Theory.deref thy_ref;
wenzelm@16656
   470
        val shyps' =
wenzelm@16656
   471
          if Sign.all_sorts_nonempty thy then []
wenzelm@16656
   472
          else
wenzelm@16656
   473
            let
wenzelm@16656
   474
              val present = present_sorts thm;
wenzelm@16656
   475
              val extra = Sorts.subtract present shyps;
wenzelm@16656
   476
              val witnessed = map #2 (Sign.witness_sorts thy present extra);
wenzelm@16656
   477
            in Sorts.subtract witnessed shyps end;
wenzelm@7642
   478
      in
wenzelm@16425
   479
        Thm {thy_ref = thy_ref, der = der, maxidx = maxidx,
wenzelm@16656
   480
          shyps = shyps', hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@7642
   481
      end;
wenzelm@1238
   482
wenzelm@16656
   483
(*dangling sort constraints of a thm*)
wenzelm@16656
   484
fun extra_shyps (th as Thm {shyps, ...}) = Sorts.subtract (present_sorts th) shyps;
wenzelm@16656
   485
wenzelm@1238
   486
wenzelm@1238
   487
paulson@1529
   488
(** Axioms **)
wenzelm@387
   489
wenzelm@16425
   490
(*look up the named axiom in the theory or its ancestors*)
wenzelm@15672
   491
fun get_axiom_i theory name =
wenzelm@387
   492
  let
wenzelm@16425
   493
    fun get_ax thy =
wenzelm@16425
   494
      Symtab.lookup (#2 (#axioms (Theory.rep_theory thy)), name)
wenzelm@16601
   495
      |> Option.map (fn prop =>
wenzelm@16601
   496
          Thm {thy_ref = Theory.self_ref thy,
wenzelm@16601
   497
            der = Pt.infer_derivs' I (false, Pt.axm_proof name prop),
wenzelm@16601
   498
            maxidx = maxidx_of_term prop,
wenzelm@16656
   499
            shyps = may_insert_term_sorts thy prop [],
wenzelm@16601
   500
            hyps = [],
wenzelm@16601
   501
            tpairs = [],
wenzelm@16601
   502
            prop = prop});
wenzelm@387
   503
  in
wenzelm@16425
   504
    (case get_first get_ax (theory :: Theory.ancestors_of theory) of
skalberg@15531
   505
      SOME thm => thm
skalberg@15531
   506
    | NONE => raise THEORY ("No axiom " ^ quote name, [theory]))
wenzelm@387
   507
  end;
wenzelm@387
   508
wenzelm@16352
   509
fun get_axiom thy =
wenzelm@16425
   510
  get_axiom_i thy o NameSpace.intern (Theory.axiom_space thy);
wenzelm@15672
   511
wenzelm@6368
   512
fun def_name name = name ^ "_def";
wenzelm@6368
   513
fun get_def thy = get_axiom thy o def_name;
wenzelm@4847
   514
paulson@1529
   515
wenzelm@776
   516
(*return additional axioms of this theory node*)
wenzelm@776
   517
fun axioms_of thy =
wenzelm@776
   518
  map (fn (s, _) => (s, get_axiom thy s))
wenzelm@16352
   519
    (Symtab.dest (#2 (#axioms (Theory.rep_theory thy))));
wenzelm@776
   520
wenzelm@6089
   521
wenzelm@6089
   522
(* name and tags -- make proof objects more readable *)
wenzelm@6089
   523
wenzelm@12923
   524
fun get_name_tags (Thm {hyps, prop, der = (_, prf), ...}) =
wenzelm@12923
   525
  Pt.get_name_tags hyps prop prf;
wenzelm@4018
   526
wenzelm@16425
   527
fun put_name_tags x (Thm {thy_ref, der = (ora, prf), maxidx,
wenzelm@16425
   528
      shyps, hyps, tpairs = [], prop}) = Thm {thy_ref = thy_ref,
wenzelm@16425
   529
        der = (ora, Pt.thm_proof (Theory.deref thy_ref) x hyps prop prf),
berghofe@13658
   530
        maxidx = maxidx, shyps = shyps, hyps = hyps, tpairs = [], prop = prop}
berghofe@13658
   531
  | put_name_tags _ thm =
berghofe@13658
   532
      raise THM ("put_name_tags: unsolved flex-flex constraints", 0, [thm]);
wenzelm@6089
   533
wenzelm@6089
   534
val name_of_thm = #1 o get_name_tags;
wenzelm@6089
   535
val tags_of_thm = #2 o get_name_tags;
wenzelm@6089
   536
wenzelm@6089
   537
fun name_thm (name, thm) = put_name_tags (name, tags_of_thm thm) thm;
clasohm@0
   538
clasohm@0
   539
paulson@1529
   540
(*Compression of theorems -- a separate rule, not integrated with the others,
paulson@1529
   541
  as it could be slow.*)
wenzelm@16425
   542
fun compress (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   543
    Thm {thy_ref = thy_ref,
wenzelm@2386
   544
         der = der,     (*No derivation recorded!*)
wenzelm@2386
   545
         maxidx = maxidx,
wenzelm@16425
   546
         shyps = shyps,
wenzelm@16425
   547
         hyps = map Term.compress_term hyps,
berghofe@13658
   548
         tpairs = map (pairself Term.compress_term) tpairs,
wenzelm@2386
   549
         prop = Term.compress_term prop};
wenzelm@564
   550
wenzelm@387
   551
wenzelm@2509
   552
paulson@1529
   553
(*** Meta rules ***)
clasohm@0
   554
wenzelm@16601
   555
(** primitive rules **)
clasohm@0
   556
wenzelm@16656
   557
(*The assumption rule A |- A*)
wenzelm@16601
   558
fun assume raw_ct =
wenzelm@16601
   559
  let val Cterm {thy_ref, t = prop, T, maxidx, sorts} = adjust_maxidx raw_ct in
wenzelm@16601
   560
    if T <> propT then
wenzelm@16601
   561
      raise THM ("assume: assumptions must have type prop", 0, [])
wenzelm@16601
   562
    else if maxidx <> ~1 then
wenzelm@16601
   563
      raise THM ("assume: assumptions may not contain schematic variables", maxidx, [])
wenzelm@16601
   564
    else Thm {thy_ref = thy_ref,
wenzelm@16601
   565
      der = Pt.infer_derivs' I (false, Pt.Hyp prop),
wenzelm@16601
   566
      maxidx = ~1,
wenzelm@16601
   567
      shyps = sorts,
wenzelm@16601
   568
      hyps = [prop],
wenzelm@16601
   569
      tpairs = [],
wenzelm@16601
   570
      prop = prop}
clasohm@0
   571
  end;
clasohm@0
   572
wenzelm@1220
   573
(*Implication introduction
wenzelm@3529
   574
    [A]
wenzelm@3529
   575
     :
wenzelm@3529
   576
     B
wenzelm@1220
   577
  -------
wenzelm@1220
   578
  A ==> B
wenzelm@1220
   579
*)
wenzelm@16601
   580
fun implies_intr
wenzelm@16679
   581
    (ct as Cterm {t = A, T, maxidx = maxidxA, sorts, ...})
wenzelm@16679
   582
    (th as Thm {der, maxidx, hyps, shyps, tpairs, prop, ...}) =
wenzelm@16601
   583
  if T <> propT then
wenzelm@16601
   584
    raise THM ("implies_intr: assumptions must have type prop", 0, [th])
wenzelm@16601
   585
  else
wenzelm@16601
   586
    Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   587
      der = Pt.infer_derivs' (Pt.implies_intr_proof A) der,
wenzelm@16601
   588
      maxidx = Int.max (maxidxA, maxidx),
wenzelm@16601
   589
      shyps = Sorts.union sorts shyps,
wenzelm@16601
   590
      hyps = remove_hyps A hyps,
wenzelm@16601
   591
      tpairs = tpairs,
wenzelm@16601
   592
      prop = implies $ A $ prop};
clasohm@0
   593
paulson@1529
   594
wenzelm@1220
   595
(*Implication elimination
wenzelm@1220
   596
  A ==> B    A
wenzelm@1220
   597
  ------------
wenzelm@1220
   598
        B
wenzelm@1220
   599
*)
wenzelm@16601
   600
fun implies_elim thAB thA =
wenzelm@16601
   601
  let
wenzelm@16601
   602
    val Thm {maxidx = maxA, der = derA, hyps = hypsA, shyps = shypsA, tpairs = tpairsA,
wenzelm@16601
   603
      prop = propA, ...} = thA
wenzelm@16601
   604
    and Thm {der, maxidx, hyps, shyps, tpairs, prop, ...} = thAB;
wenzelm@16601
   605
    fun err () = raise THM ("implies_elim: major premise", 0, [thAB, thA]);
wenzelm@16601
   606
  in
wenzelm@16601
   607
    case prop of
wenzelm@16601
   608
      imp $ A $ B =>
wenzelm@16601
   609
        if imp = Term.implies andalso A aconv propA then
wenzelm@16656
   610
          Thm {thy_ref = merge_thys2 thAB thA,
wenzelm@16601
   611
            der = Pt.infer_derivs (curry Pt.%%) der derA,
wenzelm@16601
   612
            maxidx = Int.max (maxA, maxidx),
wenzelm@16601
   613
            shyps = Sorts.union shypsA shyps,
wenzelm@16601
   614
            hyps = union_hyps hypsA hyps,
wenzelm@16601
   615
            tpairs = union_tpairs tpairsA tpairs,
wenzelm@16601
   616
            prop = B}
wenzelm@16601
   617
        else err ()
wenzelm@16601
   618
    | _ => err ()
wenzelm@16601
   619
  end;
wenzelm@250
   620
wenzelm@1220
   621
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@16656
   622
    [x]
wenzelm@16656
   623
     :
wenzelm@16656
   624
     A
wenzelm@16656
   625
  ------
wenzelm@16656
   626
  !!x. A
wenzelm@1220
   627
*)
wenzelm@16601
   628
fun forall_intr
wenzelm@16601
   629
    (ct as Cterm {t = x, T, sorts, ...})
wenzelm@16679
   630
    (th as Thm {der, maxidx, shyps, hyps, tpairs, prop, ...}) =
wenzelm@16601
   631
  let
wenzelm@16601
   632
    fun result a =
wenzelm@16601
   633
      Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   634
        der = Pt.infer_derivs' (Pt.forall_intr_proof x a) der,
wenzelm@16601
   635
        maxidx = maxidx,
wenzelm@16601
   636
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   637
        hyps = hyps,
wenzelm@16601
   638
        tpairs = tpairs,
wenzelm@16601
   639
        prop = all T $ Abs (a, T, abstract_over (x, prop))};
wenzelm@16601
   640
    fun check_occs x ts =
wenzelm@16601
   641
      if exists (apl (x, Logic.occs)) ts then
wenzelm@16601
   642
        raise THM("forall_intr: variable free in assumptions", 0, [th])
wenzelm@16601
   643
      else ();
wenzelm@16601
   644
  in
wenzelm@16601
   645
    case x of
wenzelm@16601
   646
      Free (a, _) => (check_occs x hyps; check_occs x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   647
    | Var ((a, _), _) => (check_occs x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   648
    | _ => raise THM ("forall_intr: not a variable", 0, [th])
clasohm@0
   649
  end;
clasohm@0
   650
wenzelm@1220
   651
(*Forall elimination
wenzelm@16656
   652
  !!x. A
wenzelm@1220
   653
  ------
wenzelm@1220
   654
  A[t/x]
wenzelm@1220
   655
*)
wenzelm@16601
   656
fun forall_elim
wenzelm@16601
   657
    (ct as Cterm {t, T, maxidx = maxt, sorts, ...})
wenzelm@16601
   658
    (th as Thm {der, maxidx, shyps, hyps, tpairs, prop, ...}) =
wenzelm@16601
   659
  (case prop of
wenzelm@16601
   660
    Const ("all", Type ("fun", [Type ("fun", [qary, _]), _])) $ A =>
wenzelm@16601
   661
      if T <> qary then
wenzelm@16601
   662
        raise THM ("forall_elim: type mismatch", 0, [th])
wenzelm@16601
   663
      else
wenzelm@16601
   664
        Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   665
          der = Pt.infer_derivs' (Pt.% o rpair (SOME t)) der,
wenzelm@16601
   666
          maxidx = Int.max (maxidx, maxt),
wenzelm@16601
   667
          shyps = Sorts.union sorts shyps,
wenzelm@16601
   668
          hyps = hyps,
wenzelm@16601
   669
          tpairs = tpairs,
wenzelm@16601
   670
          prop = Term.betapply (A, t)}
wenzelm@16601
   671
  | _ => raise THM ("forall_elim: not quantified", 0, [th]));
clasohm@0
   672
clasohm@0
   673
wenzelm@1220
   674
(* Equality *)
clasohm@0
   675
wenzelm@16601
   676
(*Reflexivity
wenzelm@16601
   677
  t == t
wenzelm@16601
   678
*)
wenzelm@16601
   679
fun reflexive (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16656
   680
  Thm {thy_ref = thy_ref,
wenzelm@16601
   681
    der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@16601
   682
    maxidx = maxidx,
wenzelm@16601
   683
    shyps = sorts,
wenzelm@16601
   684
    hyps = [],
wenzelm@16601
   685
    tpairs = [],
wenzelm@16601
   686
    prop = Logic.mk_equals (t, t)};
clasohm@0
   687
wenzelm@16601
   688
(*Symmetry
wenzelm@16601
   689
  t == u
wenzelm@16601
   690
  ------
wenzelm@16601
   691
  u == t
wenzelm@1220
   692
*)
wenzelm@16601
   693
fun symmetric (th as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16601
   694
  (case prop of
wenzelm@16601
   695
    (eq as Const ("==", Type (_, [T, _]))) $ t $ u =>
wenzelm@16601
   696
      Thm {thy_ref = thy_ref,
wenzelm@16601
   697
        der = Pt.infer_derivs' Pt.symmetric der,
wenzelm@16601
   698
        maxidx = maxidx,
wenzelm@16601
   699
        shyps = shyps,
wenzelm@16601
   700
        hyps = hyps,
wenzelm@16601
   701
        tpairs = tpairs,
wenzelm@16601
   702
        prop = eq $ u $ t}
wenzelm@16601
   703
    | _ => raise THM ("symmetric", 0, [th]));
clasohm@0
   704
wenzelm@16601
   705
(*Transitivity
wenzelm@16601
   706
  t1 == u    u == t2
wenzelm@16601
   707
  ------------------
wenzelm@16601
   708
       t1 == t2
wenzelm@1220
   709
*)
clasohm@0
   710
fun transitive th1 th2 =
wenzelm@16601
   711
  let
wenzelm@16601
   712
    val Thm {der = der1, maxidx = max1, hyps = hyps1, shyps = shyps1, tpairs = tpairs1,
wenzelm@16601
   713
      prop = prop1, ...} = th1
wenzelm@16601
   714
    and Thm {der = der2, maxidx = max2, hyps = hyps2, shyps = shyps2, tpairs = tpairs2,
wenzelm@16601
   715
      prop = prop2, ...} = th2;
wenzelm@16601
   716
    fun err msg = raise THM ("transitive: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   717
  in
wenzelm@16601
   718
    case (prop1, prop2) of
wenzelm@16601
   719
      ((eq as Const ("==", Type (_, [T, _]))) $ t1 $ u, Const ("==", _) $ u' $ t2) =>
wenzelm@16601
   720
        if not (u aconv u') then err "middle term"
wenzelm@16601
   721
        else
wenzelm@16656
   722
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   723
            der = Pt.infer_derivs (Pt.transitive u T) der1 der2,
wenzelm@16601
   724
            maxidx = Int.max (max1, max2),
wenzelm@16601
   725
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   726
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   727
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   728
            prop = eq $ t1 $ t2}
wenzelm@16601
   729
     | _ =>  err "premises"
clasohm@0
   730
  end;
clasohm@0
   731
wenzelm@16601
   732
(*Beta-conversion
wenzelm@16656
   733
  (%x. t)(u) == t[u/x]
wenzelm@16601
   734
  fully beta-reduces the term if full = true
berghofe@10416
   735
*)
wenzelm@16601
   736
fun beta_conversion full (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   737
  let val t' =
wenzelm@16601
   738
    if full then Envir.beta_norm t
wenzelm@16601
   739
    else
wenzelm@16601
   740
      (case t of Abs (_, _, bodt) $ u => subst_bound (u, bodt)
wenzelm@16601
   741
      | _ => raise THM ("beta_conversion: not a redex", 0, []));
wenzelm@16601
   742
  in
wenzelm@16601
   743
    Thm {thy_ref = thy_ref,
wenzelm@16601
   744
      der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@16601
   745
      maxidx = maxidx,
wenzelm@16601
   746
      shyps = sorts,
wenzelm@16601
   747
      hyps = [],
wenzelm@16601
   748
      tpairs = [],
wenzelm@16601
   749
      prop = Logic.mk_equals (t, t')}
berghofe@10416
   750
  end;
berghofe@10416
   751
wenzelm@16601
   752
fun eta_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   753
  Thm {thy_ref = thy_ref,
wenzelm@16601
   754
    der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@16601
   755
    maxidx = maxidx,
wenzelm@16601
   756
    shyps = sorts,
wenzelm@16601
   757
    hyps = [],
wenzelm@16601
   758
    tpairs = [],
wenzelm@16601
   759
    prop = Logic.mk_equals (t, Pattern.eta_contract t)};
clasohm@0
   760
clasohm@0
   761
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   762
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@16601
   763
      t == u
wenzelm@16601
   764
  --------------
wenzelm@16601
   765
  %x. t == %x. u
wenzelm@1220
   766
*)
wenzelm@16601
   767
fun abstract_rule a
wenzelm@16601
   768
    (Cterm {t = x, T, sorts, ...})
wenzelm@16601
   769
    (th as Thm {thy_ref, der, maxidx, hyps, shyps, tpairs, prop}) =
wenzelm@16601
   770
  let
wenzelm@16601
   771
    val (t, u) = Logic.dest_equals prop
wenzelm@16601
   772
      handle TERM _ => raise THM ("abstract_rule: premise not an equality", 0, [th]);
wenzelm@16601
   773
    val result =
wenzelm@16601
   774
      Thm {thy_ref = thy_ref,
wenzelm@16601
   775
        der = Pt.infer_derivs' (Pt.abstract_rule x a) der,
wenzelm@16601
   776
        maxidx = maxidx,
wenzelm@16601
   777
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   778
        hyps = hyps,
wenzelm@16601
   779
        tpairs = tpairs,
wenzelm@16601
   780
        prop = Logic.mk_equals
wenzelm@16601
   781
          (Abs (a, T, abstract_over (x, t)), Abs (a, T, abstract_over (x, u)))};
wenzelm@16601
   782
    fun check_occs x ts =
wenzelm@16601
   783
      if exists (apl (x, Logic.occs)) ts then
wenzelm@16601
   784
        raise THM ("abstract_rule: variable free in assumptions", 0, [th])
wenzelm@16601
   785
      else ();
wenzelm@16601
   786
  in
wenzelm@16601
   787
    case x of
wenzelm@16601
   788
      Free _ => (check_occs x hyps; check_occs x (terms_of_tpairs tpairs); result)
wenzelm@16601
   789
    | Var _ => (check_occs x (terms_of_tpairs tpairs); result)
wenzelm@16601
   790
    | _ => raise THM ("abstract_rule: not a variable", 0, [th])
clasohm@0
   791
  end;
clasohm@0
   792
clasohm@0
   793
(*The combination rule
wenzelm@3529
   794
  f == g  t == u
wenzelm@3529
   795
  --------------
wenzelm@16601
   796
    f t == g u
wenzelm@1220
   797
*)
clasohm@0
   798
fun combination th1 th2 =
wenzelm@16601
   799
  let
wenzelm@16601
   800
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@16601
   801
      prop = prop1, ...} = th1
wenzelm@16601
   802
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@16601
   803
      prop = prop2, ...} = th2;
wenzelm@16601
   804
    fun chktypes fT tT =
wenzelm@16601
   805
      (case fT of
wenzelm@16601
   806
        Type ("fun", [T1, T2]) =>
wenzelm@16601
   807
          if T1 <> tT then
wenzelm@16601
   808
            raise THM ("combination: types", 0, [th1, th2])
wenzelm@16601
   809
          else ()
wenzelm@16601
   810
      | _ => raise THM ("combination: not function type", 0, [th1, th2]));
wenzelm@16601
   811
  in
wenzelm@16601
   812
    case (prop1, prop2) of
wenzelm@16601
   813
      (Const ("==", Type ("fun", [fT, _])) $ f $ g,
wenzelm@16601
   814
       Const ("==", Type ("fun", [tT, _])) $ t $ u) =>
wenzelm@16601
   815
        (chktypes fT tT;
wenzelm@16601
   816
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   817
            der = Pt.infer_derivs (Pt.combination f g t u fT) der1 der2,
wenzelm@16601
   818
            maxidx = Int.max (max1, max2),
wenzelm@16601
   819
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   820
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   821
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   822
            prop = Logic.mk_equals (f $ t, g $ u)})
wenzelm@16601
   823
     | _ => raise THM ("combination: premises", 0, [th1, th2])
clasohm@0
   824
  end;
clasohm@0
   825
wenzelm@16601
   826
(*Equality introduction
wenzelm@3529
   827
  A ==> B  B ==> A
wenzelm@3529
   828
  ----------------
wenzelm@3529
   829
       A == B
wenzelm@1220
   830
*)
clasohm@0
   831
fun equal_intr th1 th2 =
wenzelm@16601
   832
  let
wenzelm@16601
   833
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@16601
   834
      prop = prop1, ...} = th1
wenzelm@16601
   835
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@16601
   836
      prop = prop2, ...} = th2;
wenzelm@16601
   837
    fun err msg = raise THM ("equal_intr: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   838
  in
wenzelm@16601
   839
    case (prop1, prop2) of
wenzelm@16601
   840
      (Const("==>", _) $ A $ B, Const("==>", _) $ B' $ A') =>
wenzelm@16601
   841
        if A aconv A' andalso B aconv B' then
wenzelm@16601
   842
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   843
            der = Pt.infer_derivs (Pt.equal_intr A B) der1 der2,
wenzelm@16601
   844
            maxidx = Int.max (max1, max2),
wenzelm@16601
   845
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   846
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   847
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   848
            prop = Logic.mk_equals (A, B)}
wenzelm@16601
   849
        else err "not equal"
wenzelm@16601
   850
    | _ =>  err "premises"
paulson@1529
   851
  end;
paulson@1529
   852
paulson@1529
   853
(*The equal propositions rule
wenzelm@3529
   854
  A == B  A
paulson@1529
   855
  ---------
paulson@1529
   856
      B
paulson@1529
   857
*)
paulson@1529
   858
fun equal_elim th1 th2 =
wenzelm@16601
   859
  let
wenzelm@16601
   860
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1,
wenzelm@16601
   861
      tpairs = tpairs1, prop = prop1, ...} = th1
wenzelm@16601
   862
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2,
wenzelm@16601
   863
      tpairs = tpairs2, prop = prop2, ...} = th2;
wenzelm@16601
   864
    fun err msg = raise THM ("equal_elim: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   865
  in
wenzelm@16601
   866
    case prop1 of
wenzelm@16601
   867
      Const ("==", _) $ A $ B =>
wenzelm@16601
   868
        if prop2 aconv A then
wenzelm@16601
   869
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   870
            der = Pt.infer_derivs (Pt.equal_elim A B) der1 der2,
wenzelm@16601
   871
            maxidx = Int.max (max1, max2),
wenzelm@16601
   872
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   873
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   874
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   875
            prop = B}
wenzelm@16601
   876
        else err "not equal"
paulson@1529
   877
     | _ =>  err"major premise"
paulson@1529
   878
  end;
clasohm@0
   879
wenzelm@1220
   880
wenzelm@1220
   881
clasohm@0
   882
(**** Derived rules ****)
clasohm@0
   883
wenzelm@16601
   884
(*Smash unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@250
   885
  Instantiates the theorem and deletes trivial tpairs.
clasohm@0
   886
  Resulting sequence may contain multiple elements if the tpairs are
clasohm@0
   887
    not all flex-flex. *)
wenzelm@16601
   888
fun flexflex_rule (th as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16601
   889
  Unify.smash_unifiers (Theory.deref thy_ref, Envir.empty maxidx, tpairs)
wenzelm@16601
   890
  |> Seq.map (fn env =>
wenzelm@16601
   891
      if Envir.is_empty env then th
wenzelm@16601
   892
      else
wenzelm@16601
   893
        let
wenzelm@16601
   894
          val tpairs' = tpairs |> map (pairself (Envir.norm_term env))
wenzelm@16601
   895
            (*remove trivial tpairs, of the form t==t*)
wenzelm@16601
   896
            |> List.filter (not o op aconv);
wenzelm@16601
   897
          val prop' = Envir.norm_term env prop;
wenzelm@16601
   898
        in
wenzelm@16601
   899
          Thm {thy_ref = thy_ref,
wenzelm@16601
   900
            der = Pt.infer_derivs' (Pt.norm_proof' env) der,
wenzelm@16711
   901
            maxidx = maxidx_tpairs tpairs' (maxidx_of_term prop'),
wenzelm@16656
   902
            shyps = may_insert_env_sorts (Theory.deref thy_ref) env shyps,
wenzelm@16601
   903
            hyps = hyps,
wenzelm@16601
   904
            tpairs = tpairs',
wenzelm@16601
   905
            prop = prop'}
wenzelm@16601
   906
        end);
wenzelm@16601
   907
clasohm@0
   908
clasohm@0
   909
(*Instantiation of Vars
wenzelm@16656
   910
           A
wenzelm@16656
   911
  --------------------
wenzelm@16656
   912
  A[t1/v1, ..., tn/vn]
wenzelm@1220
   913
*)
clasohm@0
   914
wenzelm@6928
   915
local
wenzelm@6928
   916
wenzelm@16425
   917
fun pretty_typing thy t T =
wenzelm@16425
   918
  Pretty.block [Sign.pretty_term thy t, Pretty.str " ::", Pretty.brk 1, Sign.pretty_typ thy T];
berghofe@15797
   919
wenzelm@16656
   920
fun add_ctpair ((thy, sorts), (ct, cu)) =
wenzelm@6928
   921
  let
wenzelm@16656
   922
    val Cterm {t = t, T = T, sorts = sorts1, ...} = ct
wenzelm@16656
   923
    and Cterm {t = u, T = U, sorts = sorts2, ...} = cu;
wenzelm@16656
   924
    val thy' = Theory.merge (thy, Theory.deref (merge_thys0 ct cu));
wenzelm@16656
   925
    val sorts' = Sorts.union sorts2 (Sorts.union sorts1 sorts);
wenzelm@3967
   926
  in
wenzelm@16656
   927
    if T = U then ((thy', sorts'), (t, u))
wenzelm@16601
   928
    else raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16601
   929
     [Pretty.str "instantiate: type conflict",
wenzelm@16656
   930
      Pretty.fbrk, pretty_typing thy' t T,
wenzelm@16656
   931
      Pretty.fbrk, pretty_typing thy' u U]), [T,U], [t,u])
clasohm@0
   932
  end;
clasohm@0
   933
wenzelm@16656
   934
fun add_ctyp ((thy, sorts), (cT, cU)) =
wenzelm@16656
   935
  let
wenzelm@16679
   936
    val Ctyp {T, thy_ref = thy_ref1, sorts = sorts1, ...} = cT
wenzelm@16656
   937
    and Ctyp {T = U, thy_ref = thy_ref2, sorts = sorts2, ...} = cU;
wenzelm@16656
   938
    val thy' = Theory.merge (thy, Theory.deref (Theory.merge_refs (thy_ref1, thy_ref2)));
wenzelm@16656
   939
    val sorts' = Sorts.union sorts2 (Sorts.union sorts1 sorts);
wenzelm@16656
   940
  in
wenzelm@16656
   941
    (case T of TVar (_, S) =>
wenzelm@16656
   942
      if Type.of_sort (Sign.tsig_of thy') (U, S) then ((thy', sorts'), (T, U))
wenzelm@16656
   943
      else raise TYPE ("Type not of sort " ^ Sign.string_of_sort thy' S, [U], [])
wenzelm@16656
   944
    | _ => raise TYPE (Pretty.string_of (Pretty.block
berghofe@15797
   945
        [Pretty.str "instantiate: not a type variable",
wenzelm@16656
   946
         Pretty.fbrk, Sign.pretty_typ thy' T]), [T], []))
wenzelm@16656
   947
  end;
clasohm@0
   948
wenzelm@6928
   949
in
wenzelm@6928
   950
wenzelm@16601
   951
(*Left-to-right replacements: ctpairs = [..., (vi, ti), ...].
clasohm@0
   952
  Instantiates distinct Vars by terms of same type.
wenzelm@16601
   953
  Does NOT normalize the resulting theorem!*)
paulson@1529
   954
fun instantiate ([], []) th = th
wenzelm@16601
   955
  | instantiate (vcTs, ctpairs) th =
wenzelm@16656
   956
      let
wenzelm@16679
   957
        val Thm {thy_ref, der, hyps, shyps, tpairs = dpairs, prop, ...} = th;
wenzelm@16679
   958
        val (context, tpairs) = foldl_map add_ctpair ((Theory.deref thy_ref, shyps), ctpairs);
wenzelm@16679
   959
        val ((thy', shyps'), vTs) = foldl_map add_ctyp (context, vcTs);
wenzelm@16679
   960
        fun subst t = subst_atomic tpairs (subst_atomic_types vTs t);
wenzelm@16656
   961
        val prop' = subst prop;
wenzelm@16656
   962
        val dpairs' = map (pairself subst) dpairs;
wenzelm@16656
   963
      in
wenzelm@16656
   964
        if not (forall (is_Var o #1) tpairs andalso null (gen_duplicates eq_fst tpairs)) then
wenzelm@16656
   965
          raise THM ("instantiate: variables not distinct", 0, [th])
wenzelm@16656
   966
        else if not (null (gen_duplicates eq_fst vTs)) then
wenzelm@16656
   967
          raise THM ("instantiate: type variables not distinct", 0, [th])
wenzelm@16656
   968
        else
wenzelm@16656
   969
          Thm {thy_ref = Theory.self_ref thy',
wenzelm@16656
   970
            der = Pt.infer_derivs' (Pt.instantiate vTs tpairs) der,
wenzelm@16711
   971
            maxidx = maxidx_tpairs dpairs' (maxidx_of_term prop'),
wenzelm@16656
   972
            shyps = shyps',
wenzelm@16656
   973
            hyps = hyps,
wenzelm@16656
   974
            tpairs = dpairs',
wenzelm@16656
   975
            prop = prop'}
wenzelm@16656
   976
      end
wenzelm@16656
   977
      handle TYPE (msg, _, _) => raise THM (msg, 0, [th]);
wenzelm@6928
   978
wenzelm@6928
   979
end;
wenzelm@6928
   980
clasohm@0
   981
wenzelm@16601
   982
(*The trivial implication A ==> A, justified by assume and forall rules.
wenzelm@16601
   983
  A can contain Vars, not so for assume!*)
wenzelm@16601
   984
fun trivial (Cterm {thy_ref, t =A, T, maxidx, sorts}) =
wenzelm@16601
   985
  if T <> propT then
wenzelm@16601
   986
    raise THM ("trivial: the term must have type prop", 0, [])
wenzelm@16601
   987
  else
wenzelm@16601
   988
    Thm {thy_ref = thy_ref,
wenzelm@16601
   989
      der = Pt.infer_derivs' I (false, Pt.AbsP ("H", NONE, Pt.PBound 0)),
wenzelm@16601
   990
      maxidx = maxidx,
wenzelm@16601
   991
      shyps = sorts,
wenzelm@16601
   992
      hyps = [],
wenzelm@16601
   993
      tpairs = [],
wenzelm@16601
   994
      prop = implies $ A $ A};
clasohm@0
   995
paulson@1503
   996
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)" *)
wenzelm@16425
   997
fun class_triv thy c =
wenzelm@16601
   998
  let val Cterm {thy_ref, t, maxidx, sorts, ...} =
wenzelm@16425
   999
    cterm_of thy (Logic.mk_inclass (TVar (("'a", 0), [c]), c))
wenzelm@6368
  1000
      handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@399
  1001
  in
wenzelm@16601
  1002
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1003
      der = Pt.infer_derivs' I (false, Pt.PAxm ("ProtoPure.class_triv:" ^ c, t, SOME [])),
wenzelm@16601
  1004
      maxidx = maxidx,
wenzelm@16601
  1005
      shyps = sorts,
wenzelm@16601
  1006
      hyps = [],
wenzelm@16601
  1007
      tpairs = [],
wenzelm@16601
  1008
      prop = t}
wenzelm@399
  1009
  end;
wenzelm@399
  1010
wenzelm@399
  1011
wenzelm@6786
  1012
(* Replace all TFrees not fixed or in the hyps by new TVars *)
wenzelm@16601
  1013
fun varifyT' fixed (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@12500
  1014
  let
berghofe@15797
  1015
    val tfrees = foldr add_term_tfrees fixed hyps;
berghofe@13658
  1016
    val prop1 = attach_tpairs tpairs prop;
berghofe@13658
  1017
    val (prop2, al) = Type.varify (prop1, tfrees);
wenzelm@16601
  1018
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1019
  in
wenzelm@16601
  1020
    (Thm {thy_ref = thy_ref,
wenzelm@16601
  1021
      der = Pt.infer_derivs' (Pt.varify_proof prop tfrees) der,
wenzelm@16601
  1022
      maxidx = Int.max (0, maxidx),
wenzelm@16601
  1023
      shyps = shyps,
wenzelm@16601
  1024
      hyps = hyps,
wenzelm@16601
  1025
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@16601
  1026
      prop = prop3}, al)
clasohm@0
  1027
  end;
clasohm@0
  1028
wenzelm@12500
  1029
val varifyT = #1 o varifyT' [];
wenzelm@6786
  1030
clasohm@0
  1031
(* Replace all TVars by new TFrees *)
wenzelm@16601
  1032
fun freezeT (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
berghofe@13658
  1033
  let
berghofe@13658
  1034
    val prop1 = attach_tpairs tpairs prop;
wenzelm@16287
  1035
    val prop2 = Type.freeze prop1;
wenzelm@16601
  1036
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1037
  in
wenzelm@16601
  1038
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1039
      der = Pt.infer_derivs' (Pt.freezeT prop1) der,
wenzelm@16601
  1040
      maxidx = maxidx_of_term prop2,
wenzelm@16601
  1041
      shyps = shyps,
wenzelm@16601
  1042
      hyps = hyps,
wenzelm@16601
  1043
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@16601
  1044
      prop = prop3}
wenzelm@1220
  1045
  end;
clasohm@0
  1046
clasohm@0
  1047
clasohm@0
  1048
(*** Inference rules for tactics ***)
clasohm@0
  1049
clasohm@0
  1050
(*Destruct proof state into constraints, other goals, goal(i), rest *)
berghofe@13658
  1051
fun dest_state (state as Thm{prop,tpairs,...}, i) =
berghofe@13658
  1052
  (case  Logic.strip_prems(i, [], prop) of
berghofe@13658
  1053
      (B::rBs, C) => (tpairs, rev rBs, B, C)
berghofe@13658
  1054
    | _ => raise THM("dest_state", i, [state]))
clasohm@0
  1055
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1056
lcp@309
  1057
(*Increment variables and parameters of orule as required for
clasohm@0
  1058
  resolution with goal i of state. *)
clasohm@0
  1059
fun lift_rule (state, i) orule =
wenzelm@16601
  1060
  let
wenzelm@16679
  1061
    val Thm {shyps = sshyps, prop = sprop, maxidx = smax, ...} = state;
wenzelm@16601
  1062
    val (Bi :: _, _) = Logic.strip_prems (i, [], sprop)
wenzelm@16601
  1063
      handle TERM _ => raise THM ("lift_rule", i, [orule, state]);
wenzelm@16601
  1064
    val (lift_abs, lift_all) = Logic.lift_fns (Bi, smax + 1);
wenzelm@16601
  1065
    val (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) = orule;
wenzelm@16601
  1066
    val (As, B) = Logic.strip_horn prop;
wenzelm@16601
  1067
  in
wenzelm@16601
  1068
    Thm {thy_ref = merge_thys2 state orule,
wenzelm@16601
  1069
      der = Pt.infer_derivs' (Pt.lift_proof Bi (smax + 1) prop) der,
wenzelm@16601
  1070
      maxidx = maxidx + smax + 1,
wenzelm@16601
  1071
      shyps = Sorts.union sshyps shyps,
wenzelm@16601
  1072
      hyps = hyps,
wenzelm@16601
  1073
      tpairs = map (pairself lift_abs) tpairs,
wenzelm@16601
  1074
      prop = Logic.list_implies (map lift_all As, lift_all B)}
clasohm@0
  1075
  end;
clasohm@0
  1076
wenzelm@16425
  1077
fun incr_indexes i (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16601
  1078
  if i < 0 then raise THM ("negative increment", 0, [thm])
wenzelm@16601
  1079
  else if i = 0 then thm
wenzelm@16601
  1080
  else
wenzelm@16425
  1081
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1082
      der = Pt.infer_derivs' (Pt.map_proof_terms (Logic.incr_indexes ([], i)) (incr_tvar i)) der,
wenzelm@16601
  1083
      maxidx = maxidx + i,
wenzelm@16601
  1084
      shyps = shyps,
wenzelm@16601
  1085
      hyps = hyps,
wenzelm@16601
  1086
      tpairs = map (pairself (Logic.incr_indexes ([], i))) tpairs,
wenzelm@16601
  1087
      prop = Logic.incr_indexes ([], i) prop};
berghofe@10416
  1088
clasohm@0
  1089
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1090
fun assumption i state =
wenzelm@16601
  1091
  let
wenzelm@16601
  1092
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16656
  1093
    val thy = Theory.deref thy_ref;
wenzelm@16601
  1094
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1095
    fun newth n (env as Envir.Envir {maxidx, ...}, tpairs) =
wenzelm@16601
  1096
      Thm {thy_ref = thy_ref,
wenzelm@16601
  1097
        der = Pt.infer_derivs'
wenzelm@16601
  1098
          ((if Envir.is_empty env then I else (Pt.norm_proof' env)) o
wenzelm@16601
  1099
            Pt.assumption_proof Bs Bi n) der,
wenzelm@16601
  1100
        maxidx = maxidx,
wenzelm@16656
  1101
        shyps = may_insert_env_sorts thy env shyps,
wenzelm@16601
  1102
        hyps = hyps,
wenzelm@16601
  1103
        tpairs =
wenzelm@16601
  1104
          if Envir.is_empty env then tpairs
wenzelm@16601
  1105
          else map (pairself (Envir.norm_term env)) tpairs,
wenzelm@16601
  1106
        prop =
wenzelm@16601
  1107
          if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@16601
  1108
            Logic.list_implies (Bs, C)
wenzelm@16601
  1109
          else (*normalize the new rule fully*)
wenzelm@16601
  1110
            Envir.norm_term env (Logic.list_implies (Bs, C))};
wenzelm@16601
  1111
    fun addprfs [] _ = Seq.empty
wenzelm@16601
  1112
      | addprfs ((t, u) :: apairs) n = Seq.make (fn () => Seq.pull
wenzelm@16601
  1113
          (Seq.mapp (newth n)
wenzelm@16656
  1114
            (Unify.unifiers (thy, Envir.empty maxidx, (t, u) :: tpairs))
wenzelm@16601
  1115
            (addprfs apairs (n + 1))))
wenzelm@16601
  1116
  in addprfs (Logic.assum_pairs (~1, Bi)) 1 end;
clasohm@0
  1117
wenzelm@250
  1118
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1119
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1120
fun eq_assumption i state =
wenzelm@16601
  1121
  let
wenzelm@16601
  1122
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16601
  1123
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1124
  in
wenzelm@16601
  1125
    (case find_index (op aconv) (Logic.assum_pairs (~1, Bi)) of
wenzelm@16601
  1126
      ~1 => raise THM ("eq_assumption", 0, [state])
wenzelm@16601
  1127
    | n =>
wenzelm@16601
  1128
        Thm {thy_ref = thy_ref,
wenzelm@16601
  1129
          der = Pt.infer_derivs' (Pt.assumption_proof Bs Bi (n + 1)) der,
wenzelm@16601
  1130
          maxidx = maxidx,
wenzelm@16601
  1131
          shyps = shyps,
wenzelm@16601
  1132
          hyps = hyps,
wenzelm@16601
  1133
          tpairs = tpairs,
wenzelm@16601
  1134
          prop = Logic.list_implies (Bs, C)})
clasohm@0
  1135
  end;
clasohm@0
  1136
clasohm@0
  1137
paulson@2671
  1138
(*For rotate_tac: fast rotation of assumptions of subgoal i*)
paulson@2671
  1139
fun rotate_rule k i state =
wenzelm@16601
  1140
  let
wenzelm@16601
  1141
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16601
  1142
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1143
    val params = Term.strip_all_vars Bi
wenzelm@16601
  1144
    and rest   = Term.strip_all_body Bi;
wenzelm@16601
  1145
    val asms   = Logic.strip_imp_prems rest
wenzelm@16601
  1146
    and concl  = Logic.strip_imp_concl rest;
wenzelm@16601
  1147
    val n = length asms;
wenzelm@16601
  1148
    val m = if k < 0 then n + k else k;
wenzelm@16601
  1149
    val Bi' =
wenzelm@16601
  1150
      if 0 = m orelse m = n then Bi
wenzelm@16601
  1151
      else if 0 < m andalso m < n then
wenzelm@16601
  1152
        let val (ps, qs) = splitAt (m, asms)
wenzelm@16601
  1153
        in list_all (params, Logic.list_implies (qs @ ps, concl)) end
wenzelm@16601
  1154
      else raise THM ("rotate_rule", k, [state]);
wenzelm@16601
  1155
  in
wenzelm@16601
  1156
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1157
      der = Pt.infer_derivs' (Pt.rotate_proof Bs Bi m) der,
wenzelm@16601
  1158
      maxidx = maxidx,
wenzelm@16601
  1159
      shyps = shyps,
wenzelm@16601
  1160
      hyps = hyps,
wenzelm@16601
  1161
      tpairs = tpairs,
wenzelm@16601
  1162
      prop = Logic.list_implies (Bs @ [Bi'], C)}
paulson@2671
  1163
  end;
paulson@2671
  1164
paulson@2671
  1165
paulson@7248
  1166
(*Rotates a rule's premises to the left by k, leaving the first j premises
paulson@7248
  1167
  unchanged.  Does nothing if k=0 or if k equals n-j, where n is the
wenzelm@16656
  1168
  number of premises.  Useful with etac and underlies defer_tac*)
paulson@7248
  1169
fun permute_prems j k rl =
wenzelm@16601
  1170
  let
wenzelm@16601
  1171
    val Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop} = rl;
wenzelm@16601
  1172
    val prems = Logic.strip_imp_prems prop
wenzelm@16601
  1173
    and concl = Logic.strip_imp_concl prop;
wenzelm@16601
  1174
    val moved_prems = List.drop (prems, j)
wenzelm@16601
  1175
    and fixed_prems = List.take (prems, j)
wenzelm@16601
  1176
      handle Subscript => raise THM ("permute_prems: j", j, [rl]);
wenzelm@16601
  1177
    val n_j = length moved_prems;
wenzelm@16601
  1178
    val m = if k < 0 then n_j + k else k;
wenzelm@16601
  1179
    val prop' =
wenzelm@16601
  1180
      if 0 = m orelse m = n_j then prop
wenzelm@16601
  1181
      else if 0 < m andalso m < n_j then
wenzelm@16601
  1182
        let val (ps, qs) = splitAt (m, moved_prems)
wenzelm@16601
  1183
        in Logic.list_implies (fixed_prems @ qs @ ps, concl) end
wenzelm@16601
  1184
      else raise THM ("permute_prems:k", k, [rl]);
wenzelm@16601
  1185
  in
wenzelm@16601
  1186
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1187
      der = Pt.infer_derivs' (Pt.permute_prems_prf prems j m) der,
wenzelm@16601
  1188
      maxidx = maxidx,
wenzelm@16601
  1189
      shyps = shyps,
wenzelm@16601
  1190
      hyps = hyps,
wenzelm@16601
  1191
      tpairs = tpairs,
wenzelm@16601
  1192
      prop = prop'}
paulson@7248
  1193
  end;
paulson@7248
  1194
paulson@7248
  1195
clasohm@0
  1196
(** User renaming of parameters in a subgoal **)
clasohm@0
  1197
clasohm@0
  1198
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1199
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1200
  The names in cs, if distinct, are used for the innermost parameters;
clasohm@0
  1201
   preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1202
fun rename_params_rule (cs, i) state =
wenzelm@16601
  1203
  let
wenzelm@16601
  1204
    val Thm {thy_ref, der, maxidx, shyps, hyps, ...} = state;
wenzelm@16601
  1205
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1206
    val iparams = map #1 (Logic.strip_params Bi);
wenzelm@16601
  1207
    val short = length iparams - length cs;
wenzelm@16601
  1208
    val newnames =
wenzelm@16601
  1209
      if short < 0 then error "More names than abstractions!"
wenzelm@16601
  1210
      else variantlist (Library.take (short, iparams), cs) @ cs;
wenzelm@16601
  1211
    val freenames = map (#1 o dest_Free) (term_frees Bi);
wenzelm@16601
  1212
    val newBi = Logic.list_rename_params (newnames, Bi);
wenzelm@250
  1213
  in
wenzelm@16601
  1214
    case findrep cs of
wenzelm@16601
  1215
      c :: _ => (warning ("Can't rename.  Bound variables not distinct: " ^ c); state)
wenzelm@16601
  1216
    | [] =>
wenzelm@16601
  1217
      (case cs inter_string freenames of
wenzelm@16601
  1218
        a :: _ => (warning ("Can't rename.  Bound/Free variable clash: " ^ a); state)
wenzelm@16601
  1219
      | [] =>
wenzelm@16601
  1220
        Thm {thy_ref = thy_ref,
wenzelm@16601
  1221
          der = der,
wenzelm@16601
  1222
          maxidx = maxidx,
wenzelm@16601
  1223
          shyps = shyps,
wenzelm@16601
  1224
          hyps = hyps,
wenzelm@16601
  1225
          tpairs = tpairs,
wenzelm@16601
  1226
          prop = Logic.list_implies (Bs @ [newBi], C)})
clasohm@0
  1227
  end;
clasohm@0
  1228
wenzelm@12982
  1229
clasohm@0
  1230
(*** Preservation of bound variable names ***)
clasohm@0
  1231
wenzelm@16601
  1232
fun rename_boundvars pat obj (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@12982
  1233
  (case Term.rename_abs pat obj prop of
skalberg@15531
  1234
    NONE => thm
skalberg@15531
  1235
  | SOME prop' => Thm
wenzelm@16425
  1236
      {thy_ref = thy_ref,
wenzelm@12982
  1237
       der = der,
wenzelm@12982
  1238
       maxidx = maxidx,
wenzelm@12982
  1239
       hyps = hyps,
wenzelm@12982
  1240
       shyps = shyps,
berghofe@13658
  1241
       tpairs = tpairs,
wenzelm@12982
  1242
       prop = prop'});
berghofe@10416
  1243
clasohm@0
  1244
wenzelm@16656
  1245
(* strip_apply f (A, B) strips off all assumptions/parameters from A
clasohm@0
  1246
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
  1247
fun strip_apply f =
clasohm@0
  1248
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@250
  1249
                Const("==>",_)$ _  $ B2) = implies $ A1 $ strip(B1,B2)
wenzelm@250
  1250
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
  1251
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
  1252
        | strip(A,_) = f A
clasohm@0
  1253
  in strip end;
clasohm@0
  1254
clasohm@0
  1255
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1256
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1257
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1258
fun rename_bvs([],_,_,_) = I
clasohm@0
  1259
  | rename_bvs(al,dpairs,tpairs,B) =
skalberg@15574
  1260
    let val vars = foldr add_term_vars []
skalberg@15574
  1261
                        (map fst dpairs @ map fst tpairs @ map snd tpairs)
wenzelm@250
  1262
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1263
        val vids = map (#1 o #1 o dest_Var) vars;
wenzelm@250
  1264
        fun rename(t as Var((x,i),T)) =
wenzelm@250
  1265
                (case assoc(al,x) of
skalberg@15531
  1266
                   SOME(y) => if x mem_string vids orelse y mem_string vids then t
wenzelm@250
  1267
                              else Var((y,i),T)
skalberg@15531
  1268
                 | NONE=> t)
clasohm@0
  1269
          | rename(Abs(x,T,t)) =
wenzelm@16425
  1270
              Abs (if_none (assoc_string (al, x)) x, T, rename t)
clasohm@0
  1271
          | rename(f$t) = rename f $ rename t
clasohm@0
  1272
          | rename(t) = t;
wenzelm@250
  1273
        fun strip_ren Ai = strip_apply rename (Ai,B)
clasohm@0
  1274
    in strip_ren end;
clasohm@0
  1275
clasohm@0
  1276
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
  1277
fun rename_bvars(dpairs, tpairs, B) =
skalberg@15574
  1278
        rename_bvs(foldr Term.match_bvars [] dpairs, dpairs, tpairs, B);
clasohm@0
  1279
clasohm@0
  1280
clasohm@0
  1281
(*** RESOLUTION ***)
clasohm@0
  1282
lcp@721
  1283
(** Lifting optimizations **)
lcp@721
  1284
clasohm@0
  1285
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
  1286
  identical because of lifting*)
wenzelm@250
  1287
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
  1288
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
  1289
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
  1290
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
  1291
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
  1292
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
  1293
  | strip_assums2 BB = BB;
clasohm@0
  1294
clasohm@0
  1295
lcp@721
  1296
(*Faster normalization: skip assumptions that were lifted over*)
lcp@721
  1297
fun norm_term_skip env 0 t = Envir.norm_term env t
lcp@721
  1298
  | norm_term_skip env n (Const("all",_)$Abs(a,T,t)) =
lcp@721
  1299
        let val Envir.Envir{iTs, ...} = env
berghofe@15797
  1300
            val T' = Envir.typ_subst_TVars iTs T
wenzelm@1238
  1301
            (*Must instantiate types of parameters because they are flattened;
lcp@721
  1302
              this could be a NEW parameter*)
lcp@721
  1303
        in  all T' $ Abs(a, T', norm_term_skip env n t)  end
lcp@721
  1304
  | norm_term_skip env n (Const("==>", _) $ A $ B) =
wenzelm@1238
  1305
        implies $ A $ norm_term_skip env (n-1) B
lcp@721
  1306
  | norm_term_skip env n t = error"norm_term_skip: too few assumptions??";
lcp@721
  1307
lcp@721
  1308
clasohm@0
  1309
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
  1310
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
  1311
  If match then forbid instantiations in proof state
clasohm@0
  1312
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
  1313
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
  1314
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
  1315
  Curried so that resolution calls dest_state only once.
clasohm@0
  1316
*)
wenzelm@4270
  1317
local exception COMPOSE
clasohm@0
  1318
in
wenzelm@250
  1319
fun bicompose_aux match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
  1320
                        (eres_flg, orule, nsubgoal) =
paulson@1529
  1321
 let val Thm{der=sder, maxidx=smax, shyps=sshyps, hyps=shyps, ...} = state
wenzelm@16425
  1322
     and Thm{der=rder, maxidx=rmax, shyps=rshyps, hyps=rhyps,
berghofe@13658
  1323
             tpairs=rtpairs, prop=rprop,...} = orule
paulson@1529
  1324
         (*How many hyps to skip over during normalization*)
wenzelm@1238
  1325
     and nlift = Logic.count_prems(strip_all_body Bi,
wenzelm@1238
  1326
                                   if eres_flg then ~1 else 0)
wenzelm@16601
  1327
     val thy_ref = merge_thys2 state orule;
wenzelm@16425
  1328
     val thy = Theory.deref thy_ref;
clasohm@0
  1329
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
berghofe@11518
  1330
     fun addth A (As, oldAs, rder', n) ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
  1331
       let val normt = Envir.norm_term env;
wenzelm@250
  1332
           (*perform minimal copying here by examining env*)
berghofe@13658
  1333
           val (ntpairs, normp) =
berghofe@13658
  1334
             if Envir.is_empty env then (tpairs, (Bs @ As, C))
wenzelm@250
  1335
             else
wenzelm@250
  1336
             let val ntps = map (pairself normt) tpairs
paulson@2147
  1337
             in if Envir.above (smax, env) then
wenzelm@1238
  1338
                  (*no assignments in state; normalize the rule only*)
wenzelm@1238
  1339
                  if lifted
berghofe@13658
  1340
                  then (ntps, (Bs @ map (norm_term_skip env nlift) As, C))
berghofe@13658
  1341
                  else (ntps, (Bs @ map normt As, C))
paulson@1529
  1342
                else if match then raise COMPOSE
wenzelm@250
  1343
                else (*normalize the new rule fully*)
berghofe@13658
  1344
                  (ntps, (map normt (Bs @ As), normt C))
wenzelm@250
  1345
             end
wenzelm@16601
  1346
           val th =
wenzelm@16425
  1347
             Thm{thy_ref = thy_ref,
berghofe@11518
  1348
                 der = Pt.infer_derivs
berghofe@11518
  1349
                   ((if Envir.is_empty env then I
berghofe@11518
  1350
                     else if Envir.above (smax, env) then
berghofe@11518
  1351
                       (fn f => fn der => f (Pt.norm_proof' env der))
berghofe@11518
  1352
                     else
berghofe@11518
  1353
                       curry op oo (Pt.norm_proof' env))
berghofe@11518
  1354
                    (Pt.bicompose_proof Bs oldAs As A n)) rder' sder,
wenzelm@2386
  1355
                 maxidx = maxidx,
wenzelm@16656
  1356
                 shyps = may_insert_env_sorts thy env (Sorts.union rshyps sshyps),
wenzelm@16601
  1357
                 hyps = union_hyps rhyps shyps,
berghofe@13658
  1358
                 tpairs = ntpairs,
berghofe@13658
  1359
                 prop = Logic.list_implies normp}
berghofe@11518
  1360
        in  Seq.cons(th, thq)  end  handle COMPOSE => thq;
berghofe@13658
  1361
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rprop)
clasohm@0
  1362
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
  1363
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
  1364
     fun newAs(As0, n, dpairs, tpairs) =
berghofe@11518
  1365
       let val (As1, rder') =
berghofe@11518
  1366
         if !Logic.auto_rename orelse not lifted then (As0, rder)
berghofe@11518
  1367
         else (map (rename_bvars(dpairs,tpairs,B)) As0,
berghofe@11518
  1368
           Pt.infer_derivs' (Pt.map_proof_terms
berghofe@11518
  1369
             (rename_bvars (dpairs, tpairs, Bound 0)) I) rder);
berghofe@11518
  1370
       in (map (Logic.flatten_params n) As1, As1, rder', n)
wenzelm@250
  1371
          handle TERM _ =>
wenzelm@250
  1372
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
  1373
       end;
paulson@2147
  1374
     val env = Envir.empty(Int.max(rmax,smax));
clasohm@0
  1375
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
  1376
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
  1377
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
berghofe@11518
  1378
     fun tryasms (_, _, _, []) = Seq.empty
berghofe@11518
  1379
       | tryasms (A, As, n, (t,u)::apairs) =
wenzelm@16425
  1380
          (case Seq.pull(Unify.unifiers(thy, env, (t,u)::dpairs))  of
wenzelm@16425
  1381
              NONE                   => tryasms (A, As, n+1, apairs)
wenzelm@16425
  1382
            | cell as SOME((_,tpairs),_) =>
wenzelm@16425
  1383
                Seq.it_right (addth A (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@16425
  1384
                    (Seq.make(fn()=> cell),
wenzelm@16425
  1385
                     Seq.make(fn()=> Seq.pull (tryasms(A, As, n+1, apairs)))))
clasohm@0
  1386
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
skalberg@15531
  1387
       | eres (A1::As) = tryasms(SOME A1, As, 1, Logic.assum_pairs(nlift+1,A1))
clasohm@0
  1388
     (*ordinary resolution*)
skalberg@15531
  1389
     fun res(NONE) = Seq.empty
skalberg@15531
  1390
       | res(cell as SOME((_,tpairs),_)) =
skalberg@15531
  1391
             Seq.it_right (addth NONE (newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@4270
  1392
                       (Seq.make (fn()=> cell), Seq.empty)
clasohm@0
  1393
 in  if eres_flg then eres(rev rAs)
wenzelm@16425
  1394
     else res(Seq.pull(Unify.unifiers(thy, env, dpairs)))
clasohm@0
  1395
 end;
wenzelm@7528
  1396
end;
clasohm@0
  1397
clasohm@0
  1398
clasohm@0
  1399
fun bicompose match arg i state =
clasohm@0
  1400
    bicompose_aux match (state, dest_state(state,i), false) arg;
clasohm@0
  1401
clasohm@0
  1402
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1403
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1404
fun could_bires (Hs, B, eres_flg, rule) =
clasohm@0
  1405
    let fun could_reshyp (A1::_) = exists (apl(A1,could_unify)) Hs
wenzelm@250
  1406
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@250
  1407
    in  could_unify(concl_of rule, B) andalso
wenzelm@250
  1408
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1409
    end;
clasohm@0
  1410
clasohm@0
  1411
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1412
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1413
fun biresolution match brules i state =
clasohm@0
  1414
    let val lift = lift_rule(state, i);
wenzelm@250
  1415
        val (stpairs, Bs, Bi, C) = dest_state(state,i)
wenzelm@250
  1416
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1417
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@250
  1418
        val comp = bicompose_aux match (state, (stpairs, Bs, Bi, C), true);
wenzelm@4270
  1419
        fun res [] = Seq.empty
wenzelm@250
  1420
          | res ((eres_flg, rule)::brules) =
nipkow@13642
  1421
              if !Pattern.trace_unify_fail orelse
nipkow@13642
  1422
                 could_bires (Hs, B, eres_flg, rule)
wenzelm@4270
  1423
              then Seq.make (*delay processing remainder till needed*)
skalberg@15531
  1424
                  (fn()=> SOME(comp (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1425
                               res brules))
wenzelm@250
  1426
              else res brules
wenzelm@4270
  1427
    in  Seq.flat (res brules)  end;
clasohm@0
  1428
clasohm@0
  1429
wenzelm@2509
  1430
(*** Oracles ***)
wenzelm@2509
  1431
wenzelm@16425
  1432
fun invoke_oracle_i thy1 name =
wenzelm@3812
  1433
  let
wenzelm@3812
  1434
    val oracle =
wenzelm@16425
  1435
      (case Symtab.lookup (#2 (#oracles (Theory.rep_theory thy1)), name) of
skalberg@15531
  1436
        NONE => raise THM ("Unknown oracle: " ^ name, 0, [])
skalberg@15531
  1437
      | SOME (f, _) => f);
wenzelm@3812
  1438
  in
wenzelm@16425
  1439
    fn (thy2, data) =>
wenzelm@3812
  1440
      let
wenzelm@16425
  1441
        val thy' = Theory.merge (thy1, thy2);
wenzelm@14828
  1442
        val (prop, T, maxidx) =
wenzelm@16425
  1443
          Sign.certify_term (Sign.pp thy') thy' (oracle (thy', data));
wenzelm@3812
  1444
      in
wenzelm@3812
  1445
        if T <> propT then
wenzelm@3812
  1446
          raise THM ("Oracle's result must have type prop: " ^ name, 0, [])
wenzelm@16601
  1447
        else
wenzelm@16601
  1448
          Thm {thy_ref = Theory.self_ref thy',
berghofe@11518
  1449
            der = (true, Pt.oracle_proof name prop),
wenzelm@3812
  1450
            maxidx = maxidx,
wenzelm@16656
  1451
            shyps = may_insert_term_sorts thy' prop [],
wenzelm@16425
  1452
            hyps = [],
berghofe@13658
  1453
            tpairs = [],
wenzelm@16601
  1454
            prop = prop}
wenzelm@3812
  1455
      end
wenzelm@3812
  1456
  end;
wenzelm@3812
  1457
wenzelm@15672
  1458
fun invoke_oracle thy =
wenzelm@16425
  1459
  invoke_oracle_i thy o NameSpace.intern (Theory.oracle_space thy);
wenzelm@15672
  1460
clasohm@0
  1461
end;
paulson@1503
  1462
wenzelm@6089
  1463
structure BasicThm: BASIC_THM = Thm;
wenzelm@6089
  1464
open BasicThm;