src/Pure/thm.ML
author wenzelm
Mon Jul 04 17:07:13 2005 +0200 (2005-07-04)
changeset 16679 abd1461fa288
parent 16656 18b0cb22057d
child 16711 2c1f9640b744
permissions -rw-r--r--
dest_ctyp: raise exception for non-constructor;
dest_comb: replaced expensive fastype_of by Term.argument_type;
dest_abs: replaced expensive variant_abs by Term.dest_abs;
hyps: fast_term_ord;
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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;
berghofe@10416
   304
val cterm_first_order_match = gen_cterm_match Pattern.first_order_match;
berghofe@10416
   305
berghofe@10416
   306
(*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;
berghofe@13658
   355
berghofe@13658
   356
fun attach_tpairs tpairs prop =
berghofe@13658
   357
  Logic.list_implies (map Logic.mk_equals tpairs, prop);
berghofe@13658
   358
wenzelm@16425
   359
fun rep_thm (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   360
  let val thy = Theory.deref thy_ref in
wenzelm@16425
   361
   {thy = thy, sign = thy, der = der, maxidx = maxidx,
wenzelm@16425
   362
    shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@16425
   363
  end;
clasohm@0
   364
wenzelm@16425
   365
(*version of rep_thm returning cterms instead of terms*)
wenzelm@16425
   366
fun crep_thm (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   367
  let
wenzelm@16425
   368
    val thy = Theory.deref thy_ref;
wenzelm@16601
   369
    fun cterm max t = Cterm {thy_ref = thy_ref, t = t, T = propT, maxidx = max, sorts = shyps};
wenzelm@16425
   370
  in
wenzelm@16425
   371
   {thy = thy, sign = thy, der = der, maxidx = maxidx, shyps = shyps,
wenzelm@16425
   372
    hyps = map (cterm ~1) hyps,
wenzelm@16425
   373
    tpairs = map (pairself (cterm maxidx)) tpairs,
wenzelm@16425
   374
    prop = cterm maxidx prop}
clasohm@1517
   375
  end;
clasohm@1517
   376
wenzelm@387
   377
(*errors involving theorems*)
clasohm@0
   378
exception THM of string * int * thm list;
clasohm@0
   379
wenzelm@16425
   380
(*attributes subsume any kind of rules or context modifiers*)
wenzelm@6089
   381
type 'a attribute = 'a * thm -> 'a * thm;
wenzelm@6089
   382
wenzelm@6089
   383
fun no_attributes x = (x, []);
wenzelm@6089
   384
fun apply_attributes (x_th, atts) = Library.apply atts x_th;
wenzelm@6089
   385
fun applys_attributes (x_ths, atts) = foldl_map (Library.apply atts) x_ths;
wenzelm@6089
   386
wenzelm@16601
   387
wenzelm@16656
   388
(* hyps *)
wenzelm@16601
   389
wenzelm@16679
   390
val remove_hyps = OrdList.remove Term.fast_term_ord;
wenzelm@16679
   391
val union_hyps = OrdList.union Term.fast_term_ord;
wenzelm@16679
   392
val eq_set_hyps = OrdList.eq_set Term.fast_term_ord;
wenzelm@16601
   393
wenzelm@16601
   394
wenzelm@16601
   395
(* eq_thm(s) *)
wenzelm@16601
   396
wenzelm@3994
   397
fun eq_thm (th1, th2) =
wenzelm@3994
   398
  let
wenzelm@16425
   399
    val {thy = thy1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1, prop = prop1, ...} =
wenzelm@9031
   400
      rep_thm th1;
wenzelm@16425
   401
    val {thy = thy2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2, prop = prop2, ...} =
wenzelm@9031
   402
      rep_thm th2;
wenzelm@3994
   403
  in
wenzelm@16601
   404
    Context.joinable (thy1, thy2) andalso
wenzelm@16601
   405
    Sorts.eq_set (shyps1, shyps2) andalso
wenzelm@16601
   406
    eq_set_hyps (hyps1, hyps2) andalso
wenzelm@16656
   407
    equal_lists eq_tpairs (tpairs1, tpairs2) andalso
wenzelm@3994
   408
    prop1 aconv prop2
wenzelm@3994
   409
  end;
wenzelm@387
   410
wenzelm@16135
   411
val eq_thms = Library.equal_lists eq_thm;
wenzelm@16135
   412
wenzelm@16425
   413
fun theory_of_thm (Thm {thy_ref, ...}) = Theory.deref thy_ref;
wenzelm@16425
   414
val sign_of_thm = theory_of_thm;
wenzelm@16425
   415
wenzelm@12803
   416
fun prop_of (Thm {prop, ...}) = prop;
wenzelm@13528
   417
fun proof_of (Thm {der = (_, proof), ...}) = proof;
wenzelm@16601
   418
fun tpairs_of (Thm {tpairs, ...}) = tpairs;
clasohm@0
   419
wenzelm@16601
   420
val concl_of = Logic.strip_imp_concl o prop_of;
wenzelm@16601
   421
val prems_of = Logic.strip_imp_prems o prop_of;
wenzelm@16601
   422
fun nprems_of th = Logic.count_prems (prop_of th, 0);
wenzelm@16601
   423
val no_prems = equal 0 o nprems_of;
wenzelm@16601
   424
wenzelm@16601
   425
fun major_prem_of th =
wenzelm@16601
   426
  (case prems_of th of
wenzelm@16601
   427
    prem :: _ => Logic.strip_assums_concl prem
wenzelm@16601
   428
  | [] => raise THM ("major_prem_of: rule with no premises", 0, [th]));
wenzelm@16601
   429
wenzelm@16601
   430
(*the statement of any thm is a cterm*)
wenzelm@16601
   431
fun cprop_of (Thm {thy_ref, maxidx, shyps, prop, ...}) =
wenzelm@16601
   432
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, t = prop, sorts = shyps};
wenzelm@16601
   433
wenzelm@16656
   434
(*explicit transfer to a super theory*)
wenzelm@16425
   435
fun transfer thy' thm =
wenzelm@3895
   436
  let
wenzelm@16425
   437
    val Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop} = thm;
wenzelm@16425
   438
    val thy = Theory.deref thy_ref;
wenzelm@3895
   439
  in
wenzelm@16425
   440
    if eq_thy (thy, thy') then thm
wenzelm@16425
   441
    else if subthy (thy, thy') then
wenzelm@16425
   442
      Thm {thy_ref = Theory.self_ref thy', der = der, maxidx = maxidx,
berghofe@13658
   443
        shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@3895
   444
    else raise THM ("transfer: not a super theory", 0, [thm])
wenzelm@3895
   445
  end;
wenzelm@387
   446
wenzelm@387
   447
wenzelm@16656
   448
(* merge theories of cterms/thms; raise exception if incompatible *)
wenzelm@16656
   449
wenzelm@16656
   450
fun merge_thys1 (Cterm {thy_ref = r1, ...}) (th as Thm {thy_ref = r2, ...}) =
wenzelm@16656
   451
  Theory.merge_refs (r1, r2) handle TERM (msg, _) => raise THM (msg, 0, [th]);
wenzelm@16656
   452
wenzelm@16656
   453
fun merge_thys2 (th1 as Thm {thy_ref = r1, ...}) (th2 as Thm {thy_ref = r2, ...}) =
wenzelm@16656
   454
  Theory.merge_refs (r1, r2) handle TERM (msg, _) => raise THM (msg, 0, [th1, th2]);
wenzelm@16656
   455
wenzelm@16656
   456
clasohm@0
   457
wenzelm@1238
   458
(** sort contexts of theorems **)
wenzelm@1238
   459
wenzelm@16656
   460
fun present_sorts (Thm {hyps, tpairs, prop, ...}) =
wenzelm@16656
   461
  fold (fn (t, u) => Sorts.insert_term t o Sorts.insert_term u) tpairs
wenzelm@16656
   462
    (Sorts.insert_terms hyps (Sorts.insert_term prop []));
wenzelm@1238
   463
wenzelm@7642
   464
(*remove extra sorts that are non-empty by virtue of type signature information*)
wenzelm@7642
   465
fun strip_shyps (thm as Thm {shyps = [], ...}) = thm
wenzelm@16425
   466
  | strip_shyps (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@7642
   467
      let
wenzelm@16425
   468
        val thy = Theory.deref thy_ref;
wenzelm@16656
   469
        val shyps' =
wenzelm@16656
   470
          if Sign.all_sorts_nonempty thy then []
wenzelm@16656
   471
          else
wenzelm@16656
   472
            let
wenzelm@16656
   473
              val present = present_sorts thm;
wenzelm@16656
   474
              val extra = Sorts.subtract present shyps;
wenzelm@16656
   475
              val witnessed = map #2 (Sign.witness_sorts thy present extra);
wenzelm@16656
   476
            in Sorts.subtract witnessed shyps end;
wenzelm@7642
   477
      in
wenzelm@16425
   478
        Thm {thy_ref = thy_ref, der = der, maxidx = maxidx,
wenzelm@16656
   479
          shyps = shyps', hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@7642
   480
      end;
wenzelm@1238
   481
wenzelm@16656
   482
(*dangling sort constraints of a thm*)
wenzelm@16656
   483
fun extra_shyps (th as Thm {shyps, ...}) = Sorts.subtract (present_sorts th) shyps;
wenzelm@16656
   484
wenzelm@1238
   485
wenzelm@1238
   486
paulson@1529
   487
(** Axioms **)
wenzelm@387
   488
wenzelm@16425
   489
(*look up the named axiom in the theory or its ancestors*)
wenzelm@15672
   490
fun get_axiom_i theory name =
wenzelm@387
   491
  let
wenzelm@16425
   492
    fun get_ax thy =
wenzelm@16425
   493
      Symtab.lookup (#2 (#axioms (Theory.rep_theory thy)), name)
wenzelm@16601
   494
      |> Option.map (fn prop =>
wenzelm@16601
   495
          Thm {thy_ref = Theory.self_ref thy,
wenzelm@16601
   496
            der = Pt.infer_derivs' I (false, Pt.axm_proof name prop),
wenzelm@16601
   497
            maxidx = maxidx_of_term prop,
wenzelm@16656
   498
            shyps = may_insert_term_sorts thy prop [],
wenzelm@16601
   499
            hyps = [],
wenzelm@16601
   500
            tpairs = [],
wenzelm@16601
   501
            prop = prop});
wenzelm@387
   502
  in
wenzelm@16425
   503
    (case get_first get_ax (theory :: Theory.ancestors_of theory) of
skalberg@15531
   504
      SOME thm => thm
skalberg@15531
   505
    | NONE => raise THEORY ("No axiom " ^ quote name, [theory]))
wenzelm@387
   506
  end;
wenzelm@387
   507
wenzelm@16352
   508
fun get_axiom thy =
wenzelm@16425
   509
  get_axiom_i thy o NameSpace.intern (Theory.axiom_space thy);
wenzelm@15672
   510
wenzelm@6368
   511
fun def_name name = name ^ "_def";
wenzelm@6368
   512
fun get_def thy = get_axiom thy o def_name;
wenzelm@4847
   513
paulson@1529
   514
wenzelm@776
   515
(*return additional axioms of this theory node*)
wenzelm@776
   516
fun axioms_of thy =
wenzelm@776
   517
  map (fn (s, _) => (s, get_axiom thy s))
wenzelm@16352
   518
    (Symtab.dest (#2 (#axioms (Theory.rep_theory thy))));
wenzelm@776
   519
wenzelm@6089
   520
wenzelm@6089
   521
(* name and tags -- make proof objects more readable *)
wenzelm@6089
   522
wenzelm@12923
   523
fun get_name_tags (Thm {hyps, prop, der = (_, prf), ...}) =
wenzelm@12923
   524
  Pt.get_name_tags hyps prop prf;
wenzelm@4018
   525
wenzelm@16425
   526
fun put_name_tags x (Thm {thy_ref, der = (ora, prf), maxidx,
wenzelm@16425
   527
      shyps, hyps, tpairs = [], prop}) = Thm {thy_ref = thy_ref,
wenzelm@16425
   528
        der = (ora, Pt.thm_proof (Theory.deref thy_ref) x hyps prop prf),
berghofe@13658
   529
        maxidx = maxidx, shyps = shyps, hyps = hyps, tpairs = [], prop = prop}
berghofe@13658
   530
  | put_name_tags _ thm =
berghofe@13658
   531
      raise THM ("put_name_tags: unsolved flex-flex constraints", 0, [thm]);
wenzelm@6089
   532
wenzelm@6089
   533
val name_of_thm = #1 o get_name_tags;
wenzelm@6089
   534
val tags_of_thm = #2 o get_name_tags;
wenzelm@6089
   535
wenzelm@6089
   536
fun name_thm (name, thm) = put_name_tags (name, tags_of_thm thm) thm;
clasohm@0
   537
clasohm@0
   538
paulson@1529
   539
(*Compression of theorems -- a separate rule, not integrated with the others,
paulson@1529
   540
  as it could be slow.*)
wenzelm@16425
   541
fun compress (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   542
    Thm {thy_ref = thy_ref,
wenzelm@2386
   543
         der = der,     (*No derivation recorded!*)
wenzelm@2386
   544
         maxidx = maxidx,
wenzelm@16425
   545
         shyps = shyps,
wenzelm@16425
   546
         hyps = map Term.compress_term hyps,
berghofe@13658
   547
         tpairs = map (pairself Term.compress_term) tpairs,
wenzelm@2386
   548
         prop = Term.compress_term prop};
wenzelm@564
   549
wenzelm@387
   550
wenzelm@2509
   551
paulson@1529
   552
(*** Meta rules ***)
clasohm@0
   553
wenzelm@16601
   554
(** primitive rules **)
clasohm@0
   555
wenzelm@16656
   556
(*The assumption rule A |- A*)
wenzelm@16601
   557
fun assume raw_ct =
wenzelm@16601
   558
  let val Cterm {thy_ref, t = prop, T, maxidx, sorts} = adjust_maxidx raw_ct in
wenzelm@16601
   559
    if T <> propT then
wenzelm@16601
   560
      raise THM ("assume: assumptions must have type prop", 0, [])
wenzelm@16601
   561
    else if maxidx <> ~1 then
wenzelm@16601
   562
      raise THM ("assume: assumptions may not contain schematic variables", maxidx, [])
wenzelm@16601
   563
    else Thm {thy_ref = thy_ref,
wenzelm@16601
   564
      der = Pt.infer_derivs' I (false, Pt.Hyp prop),
wenzelm@16601
   565
      maxidx = ~1,
wenzelm@16601
   566
      shyps = sorts,
wenzelm@16601
   567
      hyps = [prop],
wenzelm@16601
   568
      tpairs = [],
wenzelm@16601
   569
      prop = prop}
clasohm@0
   570
  end;
clasohm@0
   571
wenzelm@1220
   572
(*Implication introduction
wenzelm@3529
   573
    [A]
wenzelm@3529
   574
     :
wenzelm@3529
   575
     B
wenzelm@1220
   576
  -------
wenzelm@1220
   577
  A ==> B
wenzelm@1220
   578
*)
wenzelm@16601
   579
fun implies_intr
wenzelm@16679
   580
    (ct as Cterm {t = A, T, maxidx = maxidxA, sorts, ...})
wenzelm@16679
   581
    (th as Thm {der, maxidx, hyps, shyps, tpairs, prop, ...}) =
wenzelm@16601
   582
  if T <> propT then
wenzelm@16601
   583
    raise THM ("implies_intr: assumptions must have type prop", 0, [th])
wenzelm@16601
   584
  else
wenzelm@16601
   585
    Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   586
      der = Pt.infer_derivs' (Pt.implies_intr_proof A) der,
wenzelm@16601
   587
      maxidx = Int.max (maxidxA, maxidx),
wenzelm@16601
   588
      shyps = Sorts.union sorts shyps,
wenzelm@16601
   589
      hyps = remove_hyps A hyps,
wenzelm@16601
   590
      tpairs = tpairs,
wenzelm@16601
   591
      prop = implies $ A $ prop};
clasohm@0
   592
paulson@1529
   593
wenzelm@1220
   594
(*Implication elimination
wenzelm@1220
   595
  A ==> B    A
wenzelm@1220
   596
  ------------
wenzelm@1220
   597
        B
wenzelm@1220
   598
*)
wenzelm@16601
   599
fun implies_elim thAB thA =
wenzelm@16601
   600
  let
wenzelm@16601
   601
    val Thm {maxidx = maxA, der = derA, hyps = hypsA, shyps = shypsA, tpairs = tpairsA,
wenzelm@16601
   602
      prop = propA, ...} = thA
wenzelm@16601
   603
    and Thm {der, maxidx, hyps, shyps, tpairs, prop, ...} = thAB;
wenzelm@16601
   604
    fun err () = raise THM ("implies_elim: major premise", 0, [thAB, thA]);
wenzelm@16601
   605
  in
wenzelm@16601
   606
    case prop of
wenzelm@16601
   607
      imp $ A $ B =>
wenzelm@16601
   608
        if imp = Term.implies andalso A aconv propA then
wenzelm@16656
   609
          Thm {thy_ref = merge_thys2 thAB thA,
wenzelm@16601
   610
            der = Pt.infer_derivs (curry Pt.%%) der derA,
wenzelm@16601
   611
            maxidx = Int.max (maxA, maxidx),
wenzelm@16601
   612
            shyps = Sorts.union shypsA shyps,
wenzelm@16601
   613
            hyps = union_hyps hypsA hyps,
wenzelm@16601
   614
            tpairs = union_tpairs tpairsA tpairs,
wenzelm@16601
   615
            prop = B}
wenzelm@16601
   616
        else err ()
wenzelm@16601
   617
    | _ => err ()
wenzelm@16601
   618
  end;
wenzelm@250
   619
wenzelm@1220
   620
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@16656
   621
    [x]
wenzelm@16656
   622
     :
wenzelm@16656
   623
     A
wenzelm@16656
   624
  ------
wenzelm@16656
   625
  !!x. A
wenzelm@1220
   626
*)
wenzelm@16601
   627
fun forall_intr
wenzelm@16601
   628
    (ct as Cterm {t = x, T, sorts, ...})
wenzelm@16679
   629
    (th as Thm {der, maxidx, shyps, hyps, tpairs, prop, ...}) =
wenzelm@16601
   630
  let
wenzelm@16601
   631
    fun result a =
wenzelm@16601
   632
      Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   633
        der = Pt.infer_derivs' (Pt.forall_intr_proof x a) der,
wenzelm@16601
   634
        maxidx = maxidx,
wenzelm@16601
   635
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   636
        hyps = hyps,
wenzelm@16601
   637
        tpairs = tpairs,
wenzelm@16601
   638
        prop = all T $ Abs (a, T, abstract_over (x, prop))};
wenzelm@16601
   639
    fun check_occs x ts =
wenzelm@16601
   640
      if exists (apl (x, Logic.occs)) ts then
wenzelm@16601
   641
        raise THM("forall_intr: variable free in assumptions", 0, [th])
wenzelm@16601
   642
      else ();
wenzelm@16601
   643
  in
wenzelm@16601
   644
    case x of
wenzelm@16601
   645
      Free (a, _) => (check_occs x hyps; check_occs x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   646
    | Var ((a, _), _) => (check_occs x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   647
    | _ => raise THM ("forall_intr: not a variable", 0, [th])
clasohm@0
   648
  end;
clasohm@0
   649
wenzelm@1220
   650
(*Forall elimination
wenzelm@16656
   651
  !!x. A
wenzelm@1220
   652
  ------
wenzelm@1220
   653
  A[t/x]
wenzelm@1220
   654
*)
wenzelm@16601
   655
fun forall_elim
wenzelm@16601
   656
    (ct as Cterm {t, T, maxidx = maxt, sorts, ...})
wenzelm@16601
   657
    (th as Thm {der, maxidx, shyps, hyps, tpairs, prop, ...}) =
wenzelm@16601
   658
  (case prop of
wenzelm@16601
   659
    Const ("all", Type ("fun", [Type ("fun", [qary, _]), _])) $ A =>
wenzelm@16601
   660
      if T <> qary then
wenzelm@16601
   661
        raise THM ("forall_elim: type mismatch", 0, [th])
wenzelm@16601
   662
      else
wenzelm@16601
   663
        Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   664
          der = Pt.infer_derivs' (Pt.% o rpair (SOME t)) der,
wenzelm@16601
   665
          maxidx = Int.max (maxidx, maxt),
wenzelm@16601
   666
          shyps = Sorts.union sorts shyps,
wenzelm@16601
   667
          hyps = hyps,
wenzelm@16601
   668
          tpairs = tpairs,
wenzelm@16601
   669
          prop = Term.betapply (A, t)}
wenzelm@16601
   670
  | _ => raise THM ("forall_elim: not quantified", 0, [th]));
clasohm@0
   671
clasohm@0
   672
wenzelm@1220
   673
(* Equality *)
clasohm@0
   674
wenzelm@16601
   675
(*Reflexivity
wenzelm@16601
   676
  t == t
wenzelm@16601
   677
*)
wenzelm@16601
   678
fun reflexive (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16656
   679
  Thm {thy_ref = thy_ref,
wenzelm@16601
   680
    der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@16601
   681
    maxidx = maxidx,
wenzelm@16601
   682
    shyps = sorts,
wenzelm@16601
   683
    hyps = [],
wenzelm@16601
   684
    tpairs = [],
wenzelm@16601
   685
    prop = Logic.mk_equals (t, t)};
clasohm@0
   686
wenzelm@16601
   687
(*Symmetry
wenzelm@16601
   688
  t == u
wenzelm@16601
   689
  ------
wenzelm@16601
   690
  u == t
wenzelm@1220
   691
*)
wenzelm@16601
   692
fun symmetric (th as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16601
   693
  (case prop of
wenzelm@16601
   694
    (eq as Const ("==", Type (_, [T, _]))) $ t $ u =>
wenzelm@16601
   695
      Thm {thy_ref = thy_ref,
wenzelm@16601
   696
        der = Pt.infer_derivs' Pt.symmetric der,
wenzelm@16601
   697
        maxidx = maxidx,
wenzelm@16601
   698
        shyps = shyps,
wenzelm@16601
   699
        hyps = hyps,
wenzelm@16601
   700
        tpairs = tpairs,
wenzelm@16601
   701
        prop = eq $ u $ t}
wenzelm@16601
   702
    | _ => raise THM ("symmetric", 0, [th]));
clasohm@0
   703
wenzelm@16601
   704
(*Transitivity
wenzelm@16601
   705
  t1 == u    u == t2
wenzelm@16601
   706
  ------------------
wenzelm@16601
   707
       t1 == t2
wenzelm@1220
   708
*)
clasohm@0
   709
fun transitive th1 th2 =
wenzelm@16601
   710
  let
wenzelm@16601
   711
    val Thm {der = der1, maxidx = max1, hyps = hyps1, shyps = shyps1, tpairs = tpairs1,
wenzelm@16601
   712
      prop = prop1, ...} = th1
wenzelm@16601
   713
    and Thm {der = der2, maxidx = max2, hyps = hyps2, shyps = shyps2, tpairs = tpairs2,
wenzelm@16601
   714
      prop = prop2, ...} = th2;
wenzelm@16601
   715
    fun err msg = raise THM ("transitive: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   716
  in
wenzelm@16601
   717
    case (prop1, prop2) of
wenzelm@16601
   718
      ((eq as Const ("==", Type (_, [T, _]))) $ t1 $ u, Const ("==", _) $ u' $ t2) =>
wenzelm@16601
   719
        if not (u aconv u') then err "middle term"
wenzelm@16601
   720
        else
wenzelm@16656
   721
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   722
            der = Pt.infer_derivs (Pt.transitive u T) der1 der2,
wenzelm@16601
   723
            maxidx = Int.max (max1, max2),
wenzelm@16601
   724
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   725
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   726
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   727
            prop = eq $ t1 $ t2}
wenzelm@16601
   728
     | _ =>  err "premises"
clasohm@0
   729
  end;
clasohm@0
   730
wenzelm@16601
   731
(*Beta-conversion
wenzelm@16656
   732
  (%x. t)(u) == t[u/x]
wenzelm@16601
   733
  fully beta-reduces the term if full = true
berghofe@10416
   734
*)
wenzelm@16601
   735
fun beta_conversion full (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   736
  let val t' =
wenzelm@16601
   737
    if full then Envir.beta_norm t
wenzelm@16601
   738
    else
wenzelm@16601
   739
      (case t of Abs (_, _, bodt) $ u => subst_bound (u, bodt)
wenzelm@16601
   740
      | _ => raise THM ("beta_conversion: not a redex", 0, []));
wenzelm@16601
   741
  in
wenzelm@16601
   742
    Thm {thy_ref = thy_ref,
wenzelm@16601
   743
      der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@16601
   744
      maxidx = maxidx,
wenzelm@16601
   745
      shyps = sorts,
wenzelm@16601
   746
      hyps = [],
wenzelm@16601
   747
      tpairs = [],
wenzelm@16601
   748
      prop = Logic.mk_equals (t, t')}
berghofe@10416
   749
  end;
berghofe@10416
   750
wenzelm@16601
   751
fun eta_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   752
  Thm {thy_ref = thy_ref,
wenzelm@16601
   753
    der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@16601
   754
    maxidx = maxidx,
wenzelm@16601
   755
    shyps = sorts,
wenzelm@16601
   756
    hyps = [],
wenzelm@16601
   757
    tpairs = [],
wenzelm@16601
   758
    prop = Logic.mk_equals (t, Pattern.eta_contract t)};
clasohm@0
   759
clasohm@0
   760
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   761
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@16601
   762
      t == u
wenzelm@16601
   763
  --------------
wenzelm@16601
   764
  %x. t == %x. u
wenzelm@1220
   765
*)
wenzelm@16601
   766
fun abstract_rule a
wenzelm@16601
   767
    (Cterm {t = x, T, sorts, ...})
wenzelm@16601
   768
    (th as Thm {thy_ref, der, maxidx, hyps, shyps, tpairs, prop}) =
wenzelm@16601
   769
  let
wenzelm@16601
   770
    val (t, u) = Logic.dest_equals prop
wenzelm@16601
   771
      handle TERM _ => raise THM ("abstract_rule: premise not an equality", 0, [th]);
wenzelm@16601
   772
    val result =
wenzelm@16601
   773
      Thm {thy_ref = thy_ref,
wenzelm@16601
   774
        der = Pt.infer_derivs' (Pt.abstract_rule x a) der,
wenzelm@16601
   775
        maxidx = maxidx,
wenzelm@16601
   776
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   777
        hyps = hyps,
wenzelm@16601
   778
        tpairs = tpairs,
wenzelm@16601
   779
        prop = Logic.mk_equals
wenzelm@16601
   780
          (Abs (a, T, abstract_over (x, t)), Abs (a, T, abstract_over (x, u)))};
wenzelm@16601
   781
    fun check_occs x ts =
wenzelm@16601
   782
      if exists (apl (x, Logic.occs)) ts then
wenzelm@16601
   783
        raise THM ("abstract_rule: variable free in assumptions", 0, [th])
wenzelm@16601
   784
      else ();
wenzelm@16601
   785
  in
wenzelm@16601
   786
    case x of
wenzelm@16601
   787
      Free _ => (check_occs x hyps; check_occs x (terms_of_tpairs tpairs); result)
wenzelm@16601
   788
    | Var _ => (check_occs x (terms_of_tpairs tpairs); result)
wenzelm@16601
   789
    | _ => raise THM ("abstract_rule: not a variable", 0, [th])
clasohm@0
   790
  end;
clasohm@0
   791
clasohm@0
   792
(*The combination rule
wenzelm@3529
   793
  f == g  t == u
wenzelm@3529
   794
  --------------
wenzelm@16601
   795
    f t == g u
wenzelm@1220
   796
*)
clasohm@0
   797
fun combination th1 th2 =
wenzelm@16601
   798
  let
wenzelm@16601
   799
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@16601
   800
      prop = prop1, ...} = th1
wenzelm@16601
   801
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@16601
   802
      prop = prop2, ...} = th2;
wenzelm@16601
   803
    fun chktypes fT tT =
wenzelm@16601
   804
      (case fT of
wenzelm@16601
   805
        Type ("fun", [T1, T2]) =>
wenzelm@16601
   806
          if T1 <> tT then
wenzelm@16601
   807
            raise THM ("combination: types", 0, [th1, th2])
wenzelm@16601
   808
          else ()
wenzelm@16601
   809
      | _ => raise THM ("combination: not function type", 0, [th1, th2]));
wenzelm@16601
   810
  in
wenzelm@16601
   811
    case (prop1, prop2) of
wenzelm@16601
   812
      (Const ("==", Type ("fun", [fT, _])) $ f $ g,
wenzelm@16601
   813
       Const ("==", Type ("fun", [tT, _])) $ t $ u) =>
wenzelm@16601
   814
        (chktypes fT tT;
wenzelm@16601
   815
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   816
            der = Pt.infer_derivs (Pt.combination f g t u fT) der1 der2,
wenzelm@16601
   817
            maxidx = Int.max (max1, max2),
wenzelm@16601
   818
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   819
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   820
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   821
            prop = Logic.mk_equals (f $ t, g $ u)})
wenzelm@16601
   822
     | _ => raise THM ("combination: premises", 0, [th1, th2])
clasohm@0
   823
  end;
clasohm@0
   824
wenzelm@16601
   825
(*Equality introduction
wenzelm@3529
   826
  A ==> B  B ==> A
wenzelm@3529
   827
  ----------------
wenzelm@3529
   828
       A == B
wenzelm@1220
   829
*)
clasohm@0
   830
fun equal_intr th1 th2 =
wenzelm@16601
   831
  let
wenzelm@16601
   832
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@16601
   833
      prop = prop1, ...} = th1
wenzelm@16601
   834
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@16601
   835
      prop = prop2, ...} = th2;
wenzelm@16601
   836
    fun err msg = raise THM ("equal_intr: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   837
  in
wenzelm@16601
   838
    case (prop1, prop2) of
wenzelm@16601
   839
      (Const("==>", _) $ A $ B, Const("==>", _) $ B' $ A') =>
wenzelm@16601
   840
        if A aconv A' andalso B aconv B' then
wenzelm@16601
   841
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   842
            der = Pt.infer_derivs (Pt.equal_intr A B) der1 der2,
wenzelm@16601
   843
            maxidx = Int.max (max1, max2),
wenzelm@16601
   844
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   845
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   846
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   847
            prop = Logic.mk_equals (A, B)}
wenzelm@16601
   848
        else err "not equal"
wenzelm@16601
   849
    | _ =>  err "premises"
paulson@1529
   850
  end;
paulson@1529
   851
paulson@1529
   852
(*The equal propositions rule
wenzelm@3529
   853
  A == B  A
paulson@1529
   854
  ---------
paulson@1529
   855
      B
paulson@1529
   856
*)
paulson@1529
   857
fun equal_elim th1 th2 =
wenzelm@16601
   858
  let
wenzelm@16601
   859
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1,
wenzelm@16601
   860
      tpairs = tpairs1, prop = prop1, ...} = th1
wenzelm@16601
   861
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2,
wenzelm@16601
   862
      tpairs = tpairs2, prop = prop2, ...} = th2;
wenzelm@16601
   863
    fun err msg = raise THM ("equal_elim: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   864
  in
wenzelm@16601
   865
    case prop1 of
wenzelm@16601
   866
      Const ("==", _) $ A $ B =>
wenzelm@16601
   867
        if prop2 aconv A then
wenzelm@16601
   868
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   869
            der = Pt.infer_derivs (Pt.equal_elim A B) der1 der2,
wenzelm@16601
   870
            maxidx = Int.max (max1, max2),
wenzelm@16601
   871
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   872
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   873
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   874
            prop = B}
wenzelm@16601
   875
        else err "not equal"
paulson@1529
   876
     | _ =>  err"major premise"
paulson@1529
   877
  end;
clasohm@0
   878
wenzelm@1220
   879
wenzelm@1220
   880
clasohm@0
   881
(**** Derived rules ****)
clasohm@0
   882
wenzelm@16601
   883
(*Smash unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@250
   884
  Instantiates the theorem and deletes trivial tpairs.
clasohm@0
   885
  Resulting sequence may contain multiple elements if the tpairs are
clasohm@0
   886
    not all flex-flex. *)
wenzelm@16601
   887
fun flexflex_rule (th as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16601
   888
  Unify.smash_unifiers (Theory.deref thy_ref, Envir.empty maxidx, tpairs)
wenzelm@16601
   889
  |> Seq.map (fn env =>
wenzelm@16601
   890
      if Envir.is_empty env then th
wenzelm@16601
   891
      else
wenzelm@16601
   892
        let
wenzelm@16601
   893
          val tpairs' = tpairs |> map (pairself (Envir.norm_term env))
wenzelm@16601
   894
            (*remove trivial tpairs, of the form t==t*)
wenzelm@16601
   895
            |> List.filter (not o op aconv);
wenzelm@16601
   896
          val prop' = Envir.norm_term env prop;
wenzelm@16601
   897
        in
wenzelm@16601
   898
          Thm {thy_ref = thy_ref,
wenzelm@16601
   899
            der = Pt.infer_derivs' (Pt.norm_proof' env) der,
wenzelm@16601
   900
            maxidx = maxidx_of_terms (prop' :: terms_of_tpairs tpairs'),
wenzelm@16656
   901
            shyps = may_insert_env_sorts (Theory.deref thy_ref) env shyps,
wenzelm@16601
   902
            hyps = hyps,
wenzelm@16601
   903
            tpairs = tpairs',
wenzelm@16601
   904
            prop = prop'}
wenzelm@16601
   905
        end);
wenzelm@16601
   906
clasohm@0
   907
clasohm@0
   908
(*Instantiation of Vars
wenzelm@16656
   909
           A
wenzelm@16656
   910
  --------------------
wenzelm@16656
   911
  A[t1/v1, ..., tn/vn]
wenzelm@1220
   912
*)
clasohm@0
   913
wenzelm@6928
   914
local
wenzelm@6928
   915
wenzelm@16425
   916
fun pretty_typing thy t T =
wenzelm@16425
   917
  Pretty.block [Sign.pretty_term thy t, Pretty.str " ::", Pretty.brk 1, Sign.pretty_typ thy T];
berghofe@15797
   918
wenzelm@16656
   919
fun add_ctpair ((thy, sorts), (ct, cu)) =
wenzelm@6928
   920
  let
wenzelm@16656
   921
    val Cterm {t = t, T = T, sorts = sorts1, ...} = ct
wenzelm@16656
   922
    and Cterm {t = u, T = U, sorts = sorts2, ...} = cu;
wenzelm@16656
   923
    val thy' = Theory.merge (thy, Theory.deref (merge_thys0 ct cu));
wenzelm@16656
   924
    val sorts' = Sorts.union sorts2 (Sorts.union sorts1 sorts);
wenzelm@3967
   925
  in
wenzelm@16656
   926
    if T = U then ((thy', sorts'), (t, u))
wenzelm@16601
   927
    else raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16601
   928
     [Pretty.str "instantiate: type conflict",
wenzelm@16656
   929
      Pretty.fbrk, pretty_typing thy' t T,
wenzelm@16656
   930
      Pretty.fbrk, pretty_typing thy' u U]), [T,U], [t,u])
clasohm@0
   931
  end;
clasohm@0
   932
wenzelm@16656
   933
fun add_ctyp ((thy, sorts), (cT, cU)) =
wenzelm@16656
   934
  let
wenzelm@16679
   935
    val Ctyp {T, thy_ref = thy_ref1, sorts = sorts1, ...} = cT
wenzelm@16656
   936
    and Ctyp {T = U, thy_ref = thy_ref2, sorts = sorts2, ...} = cU;
wenzelm@16656
   937
    val thy' = Theory.merge (thy, Theory.deref (Theory.merge_refs (thy_ref1, thy_ref2)));
wenzelm@16656
   938
    val sorts' = Sorts.union sorts2 (Sorts.union sorts1 sorts);
wenzelm@16656
   939
  in
wenzelm@16656
   940
    (case T of TVar (_, S) =>
wenzelm@16656
   941
      if Type.of_sort (Sign.tsig_of thy') (U, S) then ((thy', sorts'), (T, U))
wenzelm@16656
   942
      else raise TYPE ("Type not of sort " ^ Sign.string_of_sort thy' S, [U], [])
wenzelm@16656
   943
    | _ => raise TYPE (Pretty.string_of (Pretty.block
berghofe@15797
   944
        [Pretty.str "instantiate: not a type variable",
wenzelm@16656
   945
         Pretty.fbrk, Sign.pretty_typ thy' T]), [T], []))
wenzelm@16656
   946
  end;
clasohm@0
   947
wenzelm@6928
   948
in
wenzelm@6928
   949
wenzelm@16601
   950
(*Left-to-right replacements: ctpairs = [..., (vi, ti), ...].
clasohm@0
   951
  Instantiates distinct Vars by terms of same type.
wenzelm@16601
   952
  Does NOT normalize the resulting theorem!*)
paulson@1529
   953
fun instantiate ([], []) th = th
wenzelm@16601
   954
  | instantiate (vcTs, ctpairs) th =
wenzelm@16656
   955
      let
wenzelm@16679
   956
        val Thm {thy_ref, der, hyps, shyps, tpairs = dpairs, prop, ...} = th;
wenzelm@16679
   957
        val (context, tpairs) = foldl_map add_ctpair ((Theory.deref thy_ref, shyps), ctpairs);
wenzelm@16679
   958
        val ((thy', shyps'), vTs) = foldl_map add_ctyp (context, vcTs);
wenzelm@16679
   959
        fun subst t = subst_atomic tpairs (subst_atomic_types vTs t);
wenzelm@16656
   960
        val prop' = subst prop;
wenzelm@16656
   961
        val dpairs' = map (pairself subst) dpairs;
wenzelm@16656
   962
      in
wenzelm@16656
   963
        if not (forall (is_Var o #1) tpairs andalso null (gen_duplicates eq_fst tpairs)) then
wenzelm@16656
   964
          raise THM ("instantiate: variables not distinct", 0, [th])
wenzelm@16656
   965
        else if not (null (gen_duplicates eq_fst vTs)) then
wenzelm@16656
   966
          raise THM ("instantiate: type variables not distinct", 0, [th])
wenzelm@16656
   967
        else
wenzelm@16656
   968
          Thm {thy_ref = Theory.self_ref thy',
wenzelm@16656
   969
            der = Pt.infer_derivs' (Pt.instantiate vTs tpairs) der,
wenzelm@16656
   970
            maxidx = maxidx_of_terms (prop' :: terms_of_tpairs dpairs'),
wenzelm@16656
   971
            shyps = shyps',
wenzelm@16656
   972
            hyps = hyps,
wenzelm@16656
   973
            tpairs = dpairs',
wenzelm@16656
   974
            prop = prop'}
wenzelm@16656
   975
      end
wenzelm@16656
   976
      handle TYPE (msg, _, _) => raise THM (msg, 0, [th]);
wenzelm@6928
   977
wenzelm@6928
   978
end;
wenzelm@6928
   979
clasohm@0
   980
wenzelm@16601
   981
(*The trivial implication A ==> A, justified by assume and forall rules.
wenzelm@16601
   982
  A can contain Vars, not so for assume!*)
wenzelm@16601
   983
fun trivial (Cterm {thy_ref, t =A, T, maxidx, sorts}) =
wenzelm@16601
   984
  if T <> propT then
wenzelm@16601
   985
    raise THM ("trivial: the term must have type prop", 0, [])
wenzelm@16601
   986
  else
wenzelm@16601
   987
    Thm {thy_ref = thy_ref,
wenzelm@16601
   988
      der = Pt.infer_derivs' I (false, Pt.AbsP ("H", NONE, Pt.PBound 0)),
wenzelm@16601
   989
      maxidx = maxidx,
wenzelm@16601
   990
      shyps = sorts,
wenzelm@16601
   991
      hyps = [],
wenzelm@16601
   992
      tpairs = [],
wenzelm@16601
   993
      prop = implies $ A $ A};
clasohm@0
   994
paulson@1503
   995
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)" *)
wenzelm@16425
   996
fun class_triv thy c =
wenzelm@16601
   997
  let val Cterm {thy_ref, t, maxidx, sorts, ...} =
wenzelm@16425
   998
    cterm_of thy (Logic.mk_inclass (TVar (("'a", 0), [c]), c))
wenzelm@6368
   999
      handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@399
  1000
  in
wenzelm@16601
  1001
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1002
      der = Pt.infer_derivs' I (false, Pt.PAxm ("ProtoPure.class_triv:" ^ c, t, SOME [])),
wenzelm@16601
  1003
      maxidx = maxidx,
wenzelm@16601
  1004
      shyps = sorts,
wenzelm@16601
  1005
      hyps = [],
wenzelm@16601
  1006
      tpairs = [],
wenzelm@16601
  1007
      prop = t}
wenzelm@399
  1008
  end;
wenzelm@399
  1009
wenzelm@399
  1010
wenzelm@6786
  1011
(* Replace all TFrees not fixed or in the hyps by new TVars *)
wenzelm@16601
  1012
fun varifyT' fixed (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@12500
  1013
  let
berghofe@15797
  1014
    val tfrees = foldr add_term_tfrees fixed hyps;
berghofe@13658
  1015
    val prop1 = attach_tpairs tpairs prop;
berghofe@13658
  1016
    val (prop2, al) = Type.varify (prop1, tfrees);
wenzelm@16601
  1017
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1018
  in
wenzelm@16601
  1019
    (Thm {thy_ref = thy_ref,
wenzelm@16601
  1020
      der = Pt.infer_derivs' (Pt.varify_proof prop tfrees) der,
wenzelm@16601
  1021
      maxidx = Int.max (0, maxidx),
wenzelm@16601
  1022
      shyps = shyps,
wenzelm@16601
  1023
      hyps = hyps,
wenzelm@16601
  1024
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@16601
  1025
      prop = prop3}, al)
clasohm@0
  1026
  end;
clasohm@0
  1027
wenzelm@12500
  1028
val varifyT = #1 o varifyT' [];
wenzelm@6786
  1029
clasohm@0
  1030
(* Replace all TVars by new TFrees *)
wenzelm@16601
  1031
fun freezeT (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
berghofe@13658
  1032
  let
berghofe@13658
  1033
    val prop1 = attach_tpairs tpairs prop;
wenzelm@16287
  1034
    val prop2 = Type.freeze prop1;
wenzelm@16601
  1035
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1036
  in
wenzelm@16601
  1037
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1038
      der = Pt.infer_derivs' (Pt.freezeT prop1) der,
wenzelm@16601
  1039
      maxidx = maxidx_of_term prop2,
wenzelm@16601
  1040
      shyps = shyps,
wenzelm@16601
  1041
      hyps = hyps,
wenzelm@16601
  1042
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@16601
  1043
      prop = prop3}
wenzelm@1220
  1044
  end;
clasohm@0
  1045
clasohm@0
  1046
clasohm@0
  1047
(*** Inference rules for tactics ***)
clasohm@0
  1048
clasohm@0
  1049
(*Destruct proof state into constraints, other goals, goal(i), rest *)
berghofe@13658
  1050
fun dest_state (state as Thm{prop,tpairs,...}, i) =
berghofe@13658
  1051
  (case  Logic.strip_prems(i, [], prop) of
berghofe@13658
  1052
      (B::rBs, C) => (tpairs, rev rBs, B, C)
berghofe@13658
  1053
    | _ => raise THM("dest_state", i, [state]))
clasohm@0
  1054
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1055
lcp@309
  1056
(*Increment variables and parameters of orule as required for
clasohm@0
  1057
  resolution with goal i of state. *)
clasohm@0
  1058
fun lift_rule (state, i) orule =
wenzelm@16601
  1059
  let
wenzelm@16679
  1060
    val Thm {shyps = sshyps, prop = sprop, maxidx = smax, ...} = state;
wenzelm@16601
  1061
    val (Bi :: _, _) = Logic.strip_prems (i, [], sprop)
wenzelm@16601
  1062
      handle TERM _ => raise THM ("lift_rule", i, [orule, state]);
wenzelm@16601
  1063
    val (lift_abs, lift_all) = Logic.lift_fns (Bi, smax + 1);
wenzelm@16601
  1064
    val (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) = orule;
wenzelm@16601
  1065
    val (As, B) = Logic.strip_horn prop;
wenzelm@16601
  1066
  in
wenzelm@16601
  1067
    Thm {thy_ref = merge_thys2 state orule,
wenzelm@16601
  1068
      der = Pt.infer_derivs' (Pt.lift_proof Bi (smax + 1) prop) der,
wenzelm@16601
  1069
      maxidx = maxidx + smax + 1,
wenzelm@16601
  1070
      shyps = Sorts.union sshyps shyps,
wenzelm@16601
  1071
      hyps = hyps,
wenzelm@16601
  1072
      tpairs = map (pairself lift_abs) tpairs,
wenzelm@16601
  1073
      prop = Logic.list_implies (map lift_all As, lift_all B)}
clasohm@0
  1074
  end;
clasohm@0
  1075
wenzelm@16425
  1076
fun incr_indexes i (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16601
  1077
  if i < 0 then raise THM ("negative increment", 0, [thm])
wenzelm@16601
  1078
  else if i = 0 then thm
wenzelm@16601
  1079
  else
wenzelm@16425
  1080
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1081
      der = Pt.infer_derivs' (Pt.map_proof_terms (Logic.incr_indexes ([], i)) (incr_tvar i)) der,
wenzelm@16601
  1082
      maxidx = maxidx + i,
wenzelm@16601
  1083
      shyps = shyps,
wenzelm@16601
  1084
      hyps = hyps,
wenzelm@16601
  1085
      tpairs = map (pairself (Logic.incr_indexes ([], i))) tpairs,
wenzelm@16601
  1086
      prop = Logic.incr_indexes ([], i) prop};
berghofe@10416
  1087
clasohm@0
  1088
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1089
fun assumption i state =
wenzelm@16601
  1090
  let
wenzelm@16601
  1091
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16656
  1092
    val thy = Theory.deref thy_ref;
wenzelm@16601
  1093
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1094
    fun newth n (env as Envir.Envir {maxidx, ...}, tpairs) =
wenzelm@16601
  1095
      Thm {thy_ref = thy_ref,
wenzelm@16601
  1096
        der = Pt.infer_derivs'
wenzelm@16601
  1097
          ((if Envir.is_empty env then I else (Pt.norm_proof' env)) o
wenzelm@16601
  1098
            Pt.assumption_proof Bs Bi n) der,
wenzelm@16601
  1099
        maxidx = maxidx,
wenzelm@16656
  1100
        shyps = may_insert_env_sorts thy env shyps,
wenzelm@16601
  1101
        hyps = hyps,
wenzelm@16601
  1102
        tpairs =
wenzelm@16601
  1103
          if Envir.is_empty env then tpairs
wenzelm@16601
  1104
          else map (pairself (Envir.norm_term env)) tpairs,
wenzelm@16601
  1105
        prop =
wenzelm@16601
  1106
          if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@16601
  1107
            Logic.list_implies (Bs, C)
wenzelm@16601
  1108
          else (*normalize the new rule fully*)
wenzelm@16601
  1109
            Envir.norm_term env (Logic.list_implies (Bs, C))};
wenzelm@16601
  1110
    fun addprfs [] _ = Seq.empty
wenzelm@16601
  1111
      | addprfs ((t, u) :: apairs) n = Seq.make (fn () => Seq.pull
wenzelm@16601
  1112
          (Seq.mapp (newth n)
wenzelm@16656
  1113
            (Unify.unifiers (thy, Envir.empty maxidx, (t, u) :: tpairs))
wenzelm@16601
  1114
            (addprfs apairs (n + 1))))
wenzelm@16601
  1115
  in addprfs (Logic.assum_pairs (~1, Bi)) 1 end;
clasohm@0
  1116
wenzelm@250
  1117
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1118
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1119
fun eq_assumption i state =
wenzelm@16601
  1120
  let
wenzelm@16601
  1121
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16601
  1122
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1123
  in
wenzelm@16601
  1124
    (case find_index (op aconv) (Logic.assum_pairs (~1, Bi)) of
wenzelm@16601
  1125
      ~1 => raise THM ("eq_assumption", 0, [state])
wenzelm@16601
  1126
    | n =>
wenzelm@16601
  1127
        Thm {thy_ref = thy_ref,
wenzelm@16601
  1128
          der = Pt.infer_derivs' (Pt.assumption_proof Bs Bi (n + 1)) der,
wenzelm@16601
  1129
          maxidx = maxidx,
wenzelm@16601
  1130
          shyps = shyps,
wenzelm@16601
  1131
          hyps = hyps,
wenzelm@16601
  1132
          tpairs = tpairs,
wenzelm@16601
  1133
          prop = Logic.list_implies (Bs, C)})
clasohm@0
  1134
  end;
clasohm@0
  1135
clasohm@0
  1136
paulson@2671
  1137
(*For rotate_tac: fast rotation of assumptions of subgoal i*)
paulson@2671
  1138
fun rotate_rule k i state =
wenzelm@16601
  1139
  let
wenzelm@16601
  1140
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16601
  1141
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1142
    val params = Term.strip_all_vars Bi
wenzelm@16601
  1143
    and rest   = Term.strip_all_body Bi;
wenzelm@16601
  1144
    val asms   = Logic.strip_imp_prems rest
wenzelm@16601
  1145
    and concl  = Logic.strip_imp_concl rest;
wenzelm@16601
  1146
    val n = length asms;
wenzelm@16601
  1147
    val m = if k < 0 then n + k else k;
wenzelm@16601
  1148
    val Bi' =
wenzelm@16601
  1149
      if 0 = m orelse m = n then Bi
wenzelm@16601
  1150
      else if 0 < m andalso m < n then
wenzelm@16601
  1151
        let val (ps, qs) = splitAt (m, asms)
wenzelm@16601
  1152
        in list_all (params, Logic.list_implies (qs @ ps, concl)) end
wenzelm@16601
  1153
      else raise THM ("rotate_rule", k, [state]);
wenzelm@16601
  1154
  in
wenzelm@16601
  1155
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1156
      der = Pt.infer_derivs' (Pt.rotate_proof Bs Bi m) der,
wenzelm@16601
  1157
      maxidx = maxidx,
wenzelm@16601
  1158
      shyps = shyps,
wenzelm@16601
  1159
      hyps = hyps,
wenzelm@16601
  1160
      tpairs = tpairs,
wenzelm@16601
  1161
      prop = Logic.list_implies (Bs @ [Bi'], C)}
paulson@2671
  1162
  end;
paulson@2671
  1163
paulson@2671
  1164
paulson@7248
  1165
(*Rotates a rule's premises to the left by k, leaving the first j premises
paulson@7248
  1166
  unchanged.  Does nothing if k=0 or if k equals n-j, where n is the
wenzelm@16656
  1167
  number of premises.  Useful with etac and underlies defer_tac*)
paulson@7248
  1168
fun permute_prems j k rl =
wenzelm@16601
  1169
  let
wenzelm@16601
  1170
    val Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop} = rl;
wenzelm@16601
  1171
    val prems = Logic.strip_imp_prems prop
wenzelm@16601
  1172
    and concl = Logic.strip_imp_concl prop;
wenzelm@16601
  1173
    val moved_prems = List.drop (prems, j)
wenzelm@16601
  1174
    and fixed_prems = List.take (prems, j)
wenzelm@16601
  1175
      handle Subscript => raise THM ("permute_prems: j", j, [rl]);
wenzelm@16601
  1176
    val n_j = length moved_prems;
wenzelm@16601
  1177
    val m = if k < 0 then n_j + k else k;
wenzelm@16601
  1178
    val prop' =
wenzelm@16601
  1179
      if 0 = m orelse m = n_j then prop
wenzelm@16601
  1180
      else if 0 < m andalso m < n_j then
wenzelm@16601
  1181
        let val (ps, qs) = splitAt (m, moved_prems)
wenzelm@16601
  1182
        in Logic.list_implies (fixed_prems @ qs @ ps, concl) end
wenzelm@16601
  1183
      else raise THM ("permute_prems:k", k, [rl]);
wenzelm@16601
  1184
  in
wenzelm@16601
  1185
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1186
      der = Pt.infer_derivs' (Pt.permute_prems_prf prems j m) der,
wenzelm@16601
  1187
      maxidx = maxidx,
wenzelm@16601
  1188
      shyps = shyps,
wenzelm@16601
  1189
      hyps = hyps,
wenzelm@16601
  1190
      tpairs = tpairs,
wenzelm@16601
  1191
      prop = prop'}
paulson@7248
  1192
  end;
paulson@7248
  1193
paulson@7248
  1194
clasohm@0
  1195
(** User renaming of parameters in a subgoal **)
clasohm@0
  1196
clasohm@0
  1197
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1198
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1199
  The names in cs, if distinct, are used for the innermost parameters;
clasohm@0
  1200
   preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1201
fun rename_params_rule (cs, i) state =
wenzelm@16601
  1202
  let
wenzelm@16601
  1203
    val Thm {thy_ref, der, maxidx, shyps, hyps, ...} = state;
wenzelm@16601
  1204
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1205
    val iparams = map #1 (Logic.strip_params Bi);
wenzelm@16601
  1206
    val short = length iparams - length cs;
wenzelm@16601
  1207
    val newnames =
wenzelm@16601
  1208
      if short < 0 then error "More names than abstractions!"
wenzelm@16601
  1209
      else variantlist (Library.take (short, iparams), cs) @ cs;
wenzelm@16601
  1210
    val freenames = map (#1 o dest_Free) (term_frees Bi);
wenzelm@16601
  1211
    val newBi = Logic.list_rename_params (newnames, Bi);
wenzelm@250
  1212
  in
wenzelm@16601
  1213
    case findrep cs of
wenzelm@16601
  1214
      c :: _ => (warning ("Can't rename.  Bound variables not distinct: " ^ c); state)
wenzelm@16601
  1215
    | [] =>
wenzelm@16601
  1216
      (case cs inter_string freenames of
wenzelm@16601
  1217
        a :: _ => (warning ("Can't rename.  Bound/Free variable clash: " ^ a); state)
wenzelm@16601
  1218
      | [] =>
wenzelm@16601
  1219
        Thm {thy_ref = thy_ref,
wenzelm@16601
  1220
          der = der,
wenzelm@16601
  1221
          maxidx = maxidx,
wenzelm@16601
  1222
          shyps = shyps,
wenzelm@16601
  1223
          hyps = hyps,
wenzelm@16601
  1224
          tpairs = tpairs,
wenzelm@16601
  1225
          prop = Logic.list_implies (Bs @ [newBi], C)})
clasohm@0
  1226
  end;
clasohm@0
  1227
wenzelm@12982
  1228
clasohm@0
  1229
(*** Preservation of bound variable names ***)
clasohm@0
  1230
wenzelm@16601
  1231
fun rename_boundvars pat obj (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@12982
  1232
  (case Term.rename_abs pat obj prop of
skalberg@15531
  1233
    NONE => thm
skalberg@15531
  1234
  | SOME prop' => Thm
wenzelm@16425
  1235
      {thy_ref = thy_ref,
wenzelm@12982
  1236
       der = der,
wenzelm@12982
  1237
       maxidx = maxidx,
wenzelm@12982
  1238
       hyps = hyps,
wenzelm@12982
  1239
       shyps = shyps,
berghofe@13658
  1240
       tpairs = tpairs,
wenzelm@12982
  1241
       prop = prop'});
berghofe@10416
  1242
clasohm@0
  1243
wenzelm@16656
  1244
(* strip_apply f (A, B) strips off all assumptions/parameters from A
clasohm@0
  1245
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
  1246
fun strip_apply f =
clasohm@0
  1247
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@250
  1248
                Const("==>",_)$ _  $ B2) = implies $ A1 $ strip(B1,B2)
wenzelm@250
  1249
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
  1250
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
  1251
        | strip(A,_) = f A
clasohm@0
  1252
  in strip end;
clasohm@0
  1253
clasohm@0
  1254
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1255
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1256
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1257
fun rename_bvs([],_,_,_) = I
clasohm@0
  1258
  | rename_bvs(al,dpairs,tpairs,B) =
skalberg@15574
  1259
    let val vars = foldr add_term_vars []
skalberg@15574
  1260
                        (map fst dpairs @ map fst tpairs @ map snd tpairs)
wenzelm@250
  1261
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1262
        val vids = map (#1 o #1 o dest_Var) vars;
wenzelm@250
  1263
        fun rename(t as Var((x,i),T)) =
wenzelm@250
  1264
                (case assoc(al,x) of
skalberg@15531
  1265
                   SOME(y) => if x mem_string vids orelse y mem_string vids then t
wenzelm@250
  1266
                              else Var((y,i),T)
skalberg@15531
  1267
                 | NONE=> t)
clasohm@0
  1268
          | rename(Abs(x,T,t)) =
wenzelm@16425
  1269
              Abs (if_none (assoc_string (al, x)) x, T, rename t)
clasohm@0
  1270
          | rename(f$t) = rename f $ rename t
clasohm@0
  1271
          | rename(t) = t;
wenzelm@250
  1272
        fun strip_ren Ai = strip_apply rename (Ai,B)
clasohm@0
  1273
    in strip_ren end;
clasohm@0
  1274
clasohm@0
  1275
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
  1276
fun rename_bvars(dpairs, tpairs, B) =
skalberg@15574
  1277
        rename_bvs(foldr Term.match_bvars [] dpairs, dpairs, tpairs, B);
clasohm@0
  1278
clasohm@0
  1279
clasohm@0
  1280
(*** RESOLUTION ***)
clasohm@0
  1281
lcp@721
  1282
(** Lifting optimizations **)
lcp@721
  1283
clasohm@0
  1284
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
  1285
  identical because of lifting*)
wenzelm@250
  1286
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
  1287
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
  1288
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
  1289
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
  1290
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
  1291
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
  1292
  | strip_assums2 BB = BB;
clasohm@0
  1293
clasohm@0
  1294
lcp@721
  1295
(*Faster normalization: skip assumptions that were lifted over*)
lcp@721
  1296
fun norm_term_skip env 0 t = Envir.norm_term env t
lcp@721
  1297
  | norm_term_skip env n (Const("all",_)$Abs(a,T,t)) =
lcp@721
  1298
        let val Envir.Envir{iTs, ...} = env
berghofe@15797
  1299
            val T' = Envir.typ_subst_TVars iTs T
wenzelm@1238
  1300
            (*Must instantiate types of parameters because they are flattened;
lcp@721
  1301
              this could be a NEW parameter*)
lcp@721
  1302
        in  all T' $ Abs(a, T', norm_term_skip env n t)  end
lcp@721
  1303
  | norm_term_skip env n (Const("==>", _) $ A $ B) =
wenzelm@1238
  1304
        implies $ A $ norm_term_skip env (n-1) B
lcp@721
  1305
  | norm_term_skip env n t = error"norm_term_skip: too few assumptions??";
lcp@721
  1306
lcp@721
  1307
clasohm@0
  1308
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
  1309
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
  1310
  If match then forbid instantiations in proof state
clasohm@0
  1311
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
  1312
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
  1313
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
  1314
  Curried so that resolution calls dest_state only once.
clasohm@0
  1315
*)
wenzelm@4270
  1316
local exception COMPOSE
clasohm@0
  1317
in
wenzelm@250
  1318
fun bicompose_aux match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
  1319
                        (eres_flg, orule, nsubgoal) =
paulson@1529
  1320
 let val Thm{der=sder, maxidx=smax, shyps=sshyps, hyps=shyps, ...} = state
wenzelm@16425
  1321
     and Thm{der=rder, maxidx=rmax, shyps=rshyps, hyps=rhyps,
berghofe@13658
  1322
             tpairs=rtpairs, prop=rprop,...} = orule
paulson@1529
  1323
         (*How many hyps to skip over during normalization*)
wenzelm@1238
  1324
     and nlift = Logic.count_prems(strip_all_body Bi,
wenzelm@1238
  1325
                                   if eres_flg then ~1 else 0)
wenzelm@16601
  1326
     val thy_ref = merge_thys2 state orule;
wenzelm@16425
  1327
     val thy = Theory.deref thy_ref;
clasohm@0
  1328
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
berghofe@11518
  1329
     fun addth A (As, oldAs, rder', n) ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
  1330
       let val normt = Envir.norm_term env;
wenzelm@250
  1331
           (*perform minimal copying here by examining env*)
berghofe@13658
  1332
           val (ntpairs, normp) =
berghofe@13658
  1333
             if Envir.is_empty env then (tpairs, (Bs @ As, C))
wenzelm@250
  1334
             else
wenzelm@250
  1335
             let val ntps = map (pairself normt) tpairs
paulson@2147
  1336
             in if Envir.above (smax, env) then
wenzelm@1238
  1337
                  (*no assignments in state; normalize the rule only*)
wenzelm@1238
  1338
                  if lifted
berghofe@13658
  1339
                  then (ntps, (Bs @ map (norm_term_skip env nlift) As, C))
berghofe@13658
  1340
                  else (ntps, (Bs @ map normt As, C))
paulson@1529
  1341
                else if match then raise COMPOSE
wenzelm@250
  1342
                else (*normalize the new rule fully*)
berghofe@13658
  1343
                  (ntps, (map normt (Bs @ As), normt C))
wenzelm@250
  1344
             end
wenzelm@16601
  1345
           val th =
wenzelm@16425
  1346
             Thm{thy_ref = thy_ref,
berghofe@11518
  1347
                 der = Pt.infer_derivs
berghofe@11518
  1348
                   ((if Envir.is_empty env then I
berghofe@11518
  1349
                     else if Envir.above (smax, env) then
berghofe@11518
  1350
                       (fn f => fn der => f (Pt.norm_proof' env der))
berghofe@11518
  1351
                     else
berghofe@11518
  1352
                       curry op oo (Pt.norm_proof' env))
berghofe@11518
  1353
                    (Pt.bicompose_proof Bs oldAs As A n)) rder' sder,
wenzelm@2386
  1354
                 maxidx = maxidx,
wenzelm@16656
  1355
                 shyps = may_insert_env_sorts thy env (Sorts.union rshyps sshyps),
wenzelm@16601
  1356
                 hyps = union_hyps rhyps shyps,
berghofe@13658
  1357
                 tpairs = ntpairs,
berghofe@13658
  1358
                 prop = Logic.list_implies normp}
berghofe@11518
  1359
        in  Seq.cons(th, thq)  end  handle COMPOSE => thq;
berghofe@13658
  1360
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rprop)
clasohm@0
  1361
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
  1362
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
  1363
     fun newAs(As0, n, dpairs, tpairs) =
berghofe@11518
  1364
       let val (As1, rder') =
berghofe@11518
  1365
         if !Logic.auto_rename orelse not lifted then (As0, rder)
berghofe@11518
  1366
         else (map (rename_bvars(dpairs,tpairs,B)) As0,
berghofe@11518
  1367
           Pt.infer_derivs' (Pt.map_proof_terms
berghofe@11518
  1368
             (rename_bvars (dpairs, tpairs, Bound 0)) I) rder);
berghofe@11518
  1369
       in (map (Logic.flatten_params n) As1, As1, rder', n)
wenzelm@250
  1370
          handle TERM _ =>
wenzelm@250
  1371
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
  1372
       end;
paulson@2147
  1373
     val env = Envir.empty(Int.max(rmax,smax));
clasohm@0
  1374
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
  1375
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
  1376
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
berghofe@11518
  1377
     fun tryasms (_, _, _, []) = Seq.empty
berghofe@11518
  1378
       | tryasms (A, As, n, (t,u)::apairs) =
wenzelm@16425
  1379
          (case Seq.pull(Unify.unifiers(thy, env, (t,u)::dpairs))  of
wenzelm@16425
  1380
              NONE                   => tryasms (A, As, n+1, apairs)
wenzelm@16425
  1381
            | cell as SOME((_,tpairs),_) =>
wenzelm@16425
  1382
                Seq.it_right (addth A (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@16425
  1383
                    (Seq.make(fn()=> cell),
wenzelm@16425
  1384
                     Seq.make(fn()=> Seq.pull (tryasms(A, As, n+1, apairs)))))
clasohm@0
  1385
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
skalberg@15531
  1386
       | eres (A1::As) = tryasms(SOME A1, As, 1, Logic.assum_pairs(nlift+1,A1))
clasohm@0
  1387
     (*ordinary resolution*)
skalberg@15531
  1388
     fun res(NONE) = Seq.empty
skalberg@15531
  1389
       | res(cell as SOME((_,tpairs),_)) =
skalberg@15531
  1390
             Seq.it_right (addth NONE (newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@4270
  1391
                       (Seq.make (fn()=> cell), Seq.empty)
clasohm@0
  1392
 in  if eres_flg then eres(rev rAs)
wenzelm@16425
  1393
     else res(Seq.pull(Unify.unifiers(thy, env, dpairs)))
clasohm@0
  1394
 end;
wenzelm@7528
  1395
end;
clasohm@0
  1396
clasohm@0
  1397
clasohm@0
  1398
fun bicompose match arg i state =
clasohm@0
  1399
    bicompose_aux match (state, dest_state(state,i), false) arg;
clasohm@0
  1400
clasohm@0
  1401
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1402
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1403
fun could_bires (Hs, B, eres_flg, rule) =
clasohm@0
  1404
    let fun could_reshyp (A1::_) = exists (apl(A1,could_unify)) Hs
wenzelm@250
  1405
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@250
  1406
    in  could_unify(concl_of rule, B) andalso
wenzelm@250
  1407
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1408
    end;
clasohm@0
  1409
clasohm@0
  1410
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1411
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1412
fun biresolution match brules i state =
clasohm@0
  1413
    let val lift = lift_rule(state, i);
wenzelm@250
  1414
        val (stpairs, Bs, Bi, C) = dest_state(state,i)
wenzelm@250
  1415
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1416
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@250
  1417
        val comp = bicompose_aux match (state, (stpairs, Bs, Bi, C), true);
wenzelm@4270
  1418
        fun res [] = Seq.empty
wenzelm@250
  1419
          | res ((eres_flg, rule)::brules) =
nipkow@13642
  1420
              if !Pattern.trace_unify_fail orelse
nipkow@13642
  1421
                 could_bires (Hs, B, eres_flg, rule)
wenzelm@4270
  1422
              then Seq.make (*delay processing remainder till needed*)
skalberg@15531
  1423
                  (fn()=> SOME(comp (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1424
                               res brules))
wenzelm@250
  1425
              else res brules
wenzelm@4270
  1426
    in  Seq.flat (res brules)  end;
clasohm@0
  1427
clasohm@0
  1428
wenzelm@2509
  1429
(*** Oracles ***)
wenzelm@2509
  1430
wenzelm@16425
  1431
fun invoke_oracle_i thy1 name =
wenzelm@3812
  1432
  let
wenzelm@3812
  1433
    val oracle =
wenzelm@16425
  1434
      (case Symtab.lookup (#2 (#oracles (Theory.rep_theory thy1)), name) of
skalberg@15531
  1435
        NONE => raise THM ("Unknown oracle: " ^ name, 0, [])
skalberg@15531
  1436
      | SOME (f, _) => f);
wenzelm@3812
  1437
  in
wenzelm@16425
  1438
    fn (thy2, data) =>
wenzelm@3812
  1439
      let
wenzelm@16425
  1440
        val thy' = Theory.merge (thy1, thy2);
wenzelm@14828
  1441
        val (prop, T, maxidx) =
wenzelm@16425
  1442
          Sign.certify_term (Sign.pp thy') thy' (oracle (thy', data));
wenzelm@3812
  1443
      in
wenzelm@3812
  1444
        if T <> propT then
wenzelm@3812
  1445
          raise THM ("Oracle's result must have type prop: " ^ name, 0, [])
wenzelm@16601
  1446
        else
wenzelm@16601
  1447
          Thm {thy_ref = Theory.self_ref thy',
berghofe@11518
  1448
            der = (true, Pt.oracle_proof name prop),
wenzelm@3812
  1449
            maxidx = maxidx,
wenzelm@16656
  1450
            shyps = may_insert_term_sorts thy' prop [],
wenzelm@16425
  1451
            hyps = [],
berghofe@13658
  1452
            tpairs = [],
wenzelm@16601
  1453
            prop = prop}
wenzelm@3812
  1454
      end
wenzelm@3812
  1455
  end;
wenzelm@3812
  1456
wenzelm@15672
  1457
fun invoke_oracle thy =
wenzelm@16425
  1458
  invoke_oracle_i thy o NameSpace.intern (Theory.oracle_space thy);
wenzelm@15672
  1459
clasohm@0
  1460
end;
paulson@1503
  1461
wenzelm@6089
  1462
structure BasicThm: BASIC_THM = Thm;
wenzelm@6089
  1463
open BasicThm;