src/Pure/thm.ML
author wenzelm
Fri Jul 01 14:42:00 2005 +0200 (2005-07-01)
changeset 16656 18b0cb22057d
parent 16601 ee8eefade568
child 16679 abd1461fa288
permissions -rw-r--r--
ctyp: added 'sorts' field;
may_insert_typ/term/env_sorts: observe Sign.all_sorts_nonempty;
may_insert_env_sorts: insert sorts of type subst only;
instantiate: insert sorts of insts;
tuned;
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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 =
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  if Sign.all_sorts_nonempty thy then I
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  else Sorts.insert_typ T;
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fun may_insert_term_sorts thy t =
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  if Sign.all_sorts_nonempty thy then I
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  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 = [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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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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exception CTERM of string;
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(*Destruct application in cterms*)
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fun dest_comb (Cterm {thy_ref, T, maxidx, sorts, t = A $ B}) =
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      let
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        val typeA = fastype_of A;
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        val typeB =
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          (case typeA of Type ("fun", [S, T]) => S
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          | _ => sys_error "Function type expected in dest_comb");
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      in
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        (Cterm {t = A, T = typeA, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
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         Cterm {t = B, T = typeB, 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, ty, M), T as Type("fun",[_,S]), thy_ref, maxidx, sorts}) =
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      let val (y, N) = variant_abs (if_none a x, ty, M) in
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        (Cterm {t = Free (y, ty), T = ty, thy_ref = thy_ref, maxidx = 0, sorts = sorts},
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          Cterm {t = N, T = S, 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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   309
         Cterm {t = t, T = T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
berghofe@10416
   310
      end;
wenzelm@16656
   311
  in (Vartab.fold (cons o mk_cTinst) Tinsts [], Vartab.fold (cons o mk_ctinst) tinsts []) end;
berghofe@10416
   312
berghofe@10416
   313
val cterm_match = gen_cterm_match Pattern.match;
berghofe@10416
   314
val cterm_first_order_match = gen_cterm_match Pattern.first_order_match;
berghofe@10416
   315
berghofe@10416
   316
(*Incrementing indexes*)
wenzelm@16601
   317
fun cterm_incr_indexes i (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   318
  if i < 0 then raise CTERM "negative increment"
wenzelm@16601
   319
  else if i = 0 then ct
wenzelm@16601
   320
  else Cterm {thy_ref = thy_ref, t = Logic.incr_indexes ([], i) t,
wenzelm@16601
   321
    T = Term.incr_tvar i T, maxidx = maxidx + i, sorts = sorts};
berghofe@10416
   322
wenzelm@2509
   323
wenzelm@2509
   324
wenzelm@574
   325
(** read cterms **)   (*exception ERROR*)
wenzelm@250
   326
nipkow@4281
   327
(*read terms, infer types, certify terms*)
wenzelm@16425
   328
fun read_def_cterms (thy, types, sorts) used freeze sTs =
wenzelm@250
   329
  let
wenzelm@16425
   330
    val (ts', tye) = Sign.read_def_terms (thy, types, sorts) used freeze sTs;
wenzelm@16425
   331
    val cts = map (cterm_of thy) ts'
wenzelm@2979
   332
      handle TYPE (msg, _, _) => error msg
wenzelm@2386
   333
           | TERM (msg, _) => error msg;
nipkow@4281
   334
  in (cts, tye) end;
nipkow@4281
   335
nipkow@4281
   336
(*read term, infer types, certify term*)
nipkow@4281
   337
fun read_def_cterm args used freeze aT =
nipkow@4281
   338
  let val ([ct],tye) = read_def_cterms args used freeze [aT]
nipkow@4281
   339
  in (ct,tye) end;
lcp@229
   340
wenzelm@16425
   341
fun read_cterm thy = #1 o read_def_cterm (thy, K NONE, K NONE) [] true;
lcp@229
   342
wenzelm@250
   343
wenzelm@6089
   344
(*tags provide additional comment, apart from the axiom/theorem name*)
wenzelm@6089
   345
type tag = string * string list;
wenzelm@6089
   346
wenzelm@2509
   347
wenzelm@387
   348
(*** Meta theorems ***)
lcp@229
   349
berghofe@11518
   350
structure Pt = Proofterm;
berghofe@11518
   351
clasohm@0
   352
datatype thm = Thm of
wenzelm@16425
   353
 {thy_ref: theory_ref,         (*dynamic reference to theory*)
berghofe@11518
   354
  der: bool * Pt.proof,        (*derivation*)
wenzelm@3967
   355
  maxidx: int,                 (*maximum index of any Var or TVar*)
wenzelm@16601
   356
  shyps: sort list,            (*sort hypotheses as ordered list*)
wenzelm@16601
   357
  hyps: term list,             (*hypotheses as ordered list*)
berghofe@13658
   358
  tpairs: (term * term) list,  (*flex-flex pairs*)
wenzelm@3967
   359
  prop: term};                 (*conclusion*)
clasohm@0
   360
wenzelm@16656
   361
fun terms_of_tpairs tpairs = fold_rev (fn (t, u) => cons t o cons u) tpairs [];
wenzelm@16656
   362
wenzelm@16656
   363
fun eq_tpairs ((t, u), (t', u')) = t aconv t' andalso u aconv u';
wenzelm@16656
   364
val union_tpairs = gen_merge_lists eq_tpairs;
berghofe@13658
   365
berghofe@13658
   366
fun attach_tpairs tpairs prop =
berghofe@13658
   367
  Logic.list_implies (map Logic.mk_equals tpairs, prop);
berghofe@13658
   368
wenzelm@16425
   369
fun rep_thm (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   370
  let val thy = Theory.deref thy_ref in
wenzelm@16425
   371
   {thy = thy, sign = thy, der = der, maxidx = maxidx,
wenzelm@16425
   372
    shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@16425
   373
  end;
clasohm@0
   374
wenzelm@16425
   375
(*version of rep_thm returning cterms instead of terms*)
wenzelm@16425
   376
fun crep_thm (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   377
  let
wenzelm@16425
   378
    val thy = Theory.deref thy_ref;
wenzelm@16601
   379
    fun cterm max t = Cterm {thy_ref = thy_ref, t = t, T = propT, maxidx = max, sorts = shyps};
wenzelm@16425
   380
  in
wenzelm@16425
   381
   {thy = thy, sign = thy, der = der, maxidx = maxidx, shyps = shyps,
wenzelm@16425
   382
    hyps = map (cterm ~1) hyps,
wenzelm@16425
   383
    tpairs = map (pairself (cterm maxidx)) tpairs,
wenzelm@16425
   384
    prop = cterm maxidx prop}
clasohm@1517
   385
  end;
clasohm@1517
   386
wenzelm@387
   387
(*errors involving theorems*)
clasohm@0
   388
exception THM of string * int * thm list;
clasohm@0
   389
wenzelm@16425
   390
(*attributes subsume any kind of rules or context modifiers*)
wenzelm@6089
   391
type 'a attribute = 'a * thm -> 'a * thm;
wenzelm@6089
   392
wenzelm@6089
   393
fun no_attributes x = (x, []);
wenzelm@6089
   394
fun apply_attributes (x_th, atts) = Library.apply atts x_th;
wenzelm@6089
   395
fun applys_attributes (x_ths, atts) = foldl_map (Library.apply atts) x_ths;
wenzelm@6089
   396
wenzelm@16601
   397
wenzelm@16656
   398
(* hyps *)
wenzelm@16601
   399
wenzelm@16601
   400
val remove_hyps = OrdList.remove Term.term_ord;
wenzelm@16601
   401
val union_hyps = OrdList.union Term.term_ord;
wenzelm@16601
   402
val eq_set_hyps = OrdList.eq_set Term.term_ord;
wenzelm@16601
   403
wenzelm@16601
   404
wenzelm@16601
   405
(* eq_thm(s) *)
wenzelm@16601
   406
wenzelm@3994
   407
fun eq_thm (th1, th2) =
wenzelm@3994
   408
  let
wenzelm@16425
   409
    val {thy = thy1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1, prop = prop1, ...} =
wenzelm@9031
   410
      rep_thm th1;
wenzelm@16425
   411
    val {thy = thy2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2, prop = prop2, ...} =
wenzelm@9031
   412
      rep_thm th2;
wenzelm@3994
   413
  in
wenzelm@16601
   414
    Context.joinable (thy1, thy2) andalso
wenzelm@16601
   415
    Sorts.eq_set (shyps1, shyps2) andalso
wenzelm@16601
   416
    eq_set_hyps (hyps1, hyps2) andalso
wenzelm@16656
   417
    equal_lists eq_tpairs (tpairs1, tpairs2) andalso
wenzelm@3994
   418
    prop1 aconv prop2
wenzelm@3994
   419
  end;
wenzelm@387
   420
wenzelm@16135
   421
val eq_thms = Library.equal_lists eq_thm;
wenzelm@16135
   422
wenzelm@16425
   423
fun theory_of_thm (Thm {thy_ref, ...}) = Theory.deref thy_ref;
wenzelm@16425
   424
val sign_of_thm = theory_of_thm;
wenzelm@16425
   425
wenzelm@12803
   426
fun prop_of (Thm {prop, ...}) = prop;
wenzelm@13528
   427
fun proof_of (Thm {der = (_, proof), ...}) = proof;
wenzelm@16601
   428
fun tpairs_of (Thm {tpairs, ...}) = tpairs;
clasohm@0
   429
wenzelm@16601
   430
val concl_of = Logic.strip_imp_concl o prop_of;
wenzelm@16601
   431
val prems_of = Logic.strip_imp_prems o prop_of;
wenzelm@16601
   432
fun nprems_of th = Logic.count_prems (prop_of th, 0);
wenzelm@16601
   433
val no_prems = equal 0 o nprems_of;
wenzelm@16601
   434
wenzelm@16601
   435
fun major_prem_of th =
wenzelm@16601
   436
  (case prems_of th of
wenzelm@16601
   437
    prem :: _ => Logic.strip_assums_concl prem
wenzelm@16601
   438
  | [] => raise THM ("major_prem_of: rule with no premises", 0, [th]));
wenzelm@16601
   439
wenzelm@16601
   440
(*the statement of any thm is a cterm*)
wenzelm@16601
   441
fun cprop_of (Thm {thy_ref, maxidx, shyps, prop, ...}) =
wenzelm@16601
   442
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, t = prop, sorts = shyps};
wenzelm@16601
   443
wenzelm@16656
   444
(*explicit transfer to a super theory*)
wenzelm@16425
   445
fun transfer thy' thm =
wenzelm@3895
   446
  let
wenzelm@16425
   447
    val Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop} = thm;
wenzelm@16425
   448
    val thy = Theory.deref thy_ref;
wenzelm@3895
   449
  in
wenzelm@16425
   450
    if eq_thy (thy, thy') then thm
wenzelm@16425
   451
    else if subthy (thy, thy') then
wenzelm@16425
   452
      Thm {thy_ref = Theory.self_ref thy', der = der, maxidx = maxidx,
berghofe@13658
   453
        shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@3895
   454
    else raise THM ("transfer: not a super theory", 0, [thm])
wenzelm@3895
   455
  end;
wenzelm@387
   456
wenzelm@387
   457
wenzelm@16656
   458
(* merge theories of cterms/thms; raise exception if incompatible *)
wenzelm@16656
   459
wenzelm@16656
   460
fun merge_thys1 (Cterm {thy_ref = r1, ...}) (th as Thm {thy_ref = r2, ...}) =
wenzelm@16656
   461
  Theory.merge_refs (r1, r2) handle TERM (msg, _) => raise THM (msg, 0, [th]);
wenzelm@16656
   462
wenzelm@16656
   463
fun merge_thys2 (th1 as Thm {thy_ref = r1, ...}) (th2 as Thm {thy_ref = r2, ...}) =
wenzelm@16656
   464
  Theory.merge_refs (r1, r2) handle TERM (msg, _) => raise THM (msg, 0, [th1, th2]);
wenzelm@16656
   465
wenzelm@16656
   466
clasohm@0
   467
wenzelm@1238
   468
(** sort contexts of theorems **)
wenzelm@1238
   469
wenzelm@16656
   470
fun present_sorts (Thm {hyps, tpairs, prop, ...}) =
wenzelm@16656
   471
  fold (fn (t, u) => Sorts.insert_term t o Sorts.insert_term u) tpairs
wenzelm@16656
   472
    (Sorts.insert_terms hyps (Sorts.insert_term prop []));
wenzelm@1238
   473
wenzelm@7642
   474
(*remove extra sorts that are non-empty by virtue of type signature information*)
wenzelm@7642
   475
fun strip_shyps (thm as Thm {shyps = [], ...}) = thm
wenzelm@16425
   476
  | strip_shyps (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@7642
   477
      let
wenzelm@16425
   478
        val thy = Theory.deref thy_ref;
wenzelm@16656
   479
        val shyps' =
wenzelm@16656
   480
          if Sign.all_sorts_nonempty thy then []
wenzelm@16656
   481
          else
wenzelm@16656
   482
            let
wenzelm@16656
   483
              val present = present_sorts thm;
wenzelm@16656
   484
              val extra = Sorts.subtract present shyps;
wenzelm@16656
   485
              val witnessed = map #2 (Sign.witness_sorts thy present extra);
wenzelm@16656
   486
            in Sorts.subtract witnessed shyps end;
wenzelm@7642
   487
      in
wenzelm@16425
   488
        Thm {thy_ref = thy_ref, der = der, maxidx = maxidx,
wenzelm@16656
   489
          shyps = shyps', hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@7642
   490
      end;
wenzelm@1238
   491
wenzelm@16656
   492
(*dangling sort constraints of a thm*)
wenzelm@16656
   493
fun extra_shyps (th as Thm {shyps, ...}) = Sorts.subtract (present_sorts th) shyps;
wenzelm@16656
   494
wenzelm@1238
   495
wenzelm@1238
   496
paulson@1529
   497
(** Axioms **)
wenzelm@387
   498
wenzelm@16425
   499
(*look up the named axiom in the theory or its ancestors*)
wenzelm@15672
   500
fun get_axiom_i theory name =
wenzelm@387
   501
  let
wenzelm@16425
   502
    fun get_ax thy =
wenzelm@16425
   503
      Symtab.lookup (#2 (#axioms (Theory.rep_theory thy)), name)
wenzelm@16601
   504
      |> Option.map (fn prop =>
wenzelm@16601
   505
          Thm {thy_ref = Theory.self_ref thy,
wenzelm@16601
   506
            der = Pt.infer_derivs' I (false, Pt.axm_proof name prop),
wenzelm@16601
   507
            maxidx = maxidx_of_term prop,
wenzelm@16656
   508
            shyps = may_insert_term_sorts thy prop [],
wenzelm@16601
   509
            hyps = [],
wenzelm@16601
   510
            tpairs = [],
wenzelm@16601
   511
            prop = prop});
wenzelm@387
   512
  in
wenzelm@16425
   513
    (case get_first get_ax (theory :: Theory.ancestors_of theory) of
skalberg@15531
   514
      SOME thm => thm
skalberg@15531
   515
    | NONE => raise THEORY ("No axiom " ^ quote name, [theory]))
wenzelm@387
   516
  end;
wenzelm@387
   517
wenzelm@16352
   518
fun get_axiom thy =
wenzelm@16425
   519
  get_axiom_i thy o NameSpace.intern (Theory.axiom_space thy);
wenzelm@15672
   520
wenzelm@6368
   521
fun def_name name = name ^ "_def";
wenzelm@6368
   522
fun get_def thy = get_axiom thy o def_name;
wenzelm@4847
   523
paulson@1529
   524
wenzelm@776
   525
(*return additional axioms of this theory node*)
wenzelm@776
   526
fun axioms_of thy =
wenzelm@776
   527
  map (fn (s, _) => (s, get_axiom thy s))
wenzelm@16352
   528
    (Symtab.dest (#2 (#axioms (Theory.rep_theory thy))));
wenzelm@776
   529
wenzelm@6089
   530
wenzelm@6089
   531
(* name and tags -- make proof objects more readable *)
wenzelm@6089
   532
wenzelm@12923
   533
fun get_name_tags (Thm {hyps, prop, der = (_, prf), ...}) =
wenzelm@12923
   534
  Pt.get_name_tags hyps prop prf;
wenzelm@4018
   535
wenzelm@16425
   536
fun put_name_tags x (Thm {thy_ref, der = (ora, prf), maxidx,
wenzelm@16425
   537
      shyps, hyps, tpairs = [], prop}) = Thm {thy_ref = thy_ref,
wenzelm@16425
   538
        der = (ora, Pt.thm_proof (Theory.deref thy_ref) x hyps prop prf),
berghofe@13658
   539
        maxidx = maxidx, shyps = shyps, hyps = hyps, tpairs = [], prop = prop}
berghofe@13658
   540
  | put_name_tags _ thm =
berghofe@13658
   541
      raise THM ("put_name_tags: unsolved flex-flex constraints", 0, [thm]);
wenzelm@6089
   542
wenzelm@6089
   543
val name_of_thm = #1 o get_name_tags;
wenzelm@6089
   544
val tags_of_thm = #2 o get_name_tags;
wenzelm@6089
   545
wenzelm@6089
   546
fun name_thm (name, thm) = put_name_tags (name, tags_of_thm thm) thm;
clasohm@0
   547
clasohm@0
   548
paulson@1529
   549
(*Compression of theorems -- a separate rule, not integrated with the others,
paulson@1529
   550
  as it could be slow.*)
wenzelm@16425
   551
fun compress (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   552
    Thm {thy_ref = thy_ref,
wenzelm@2386
   553
         der = der,     (*No derivation recorded!*)
wenzelm@2386
   554
         maxidx = maxidx,
wenzelm@16425
   555
         shyps = shyps,
wenzelm@16425
   556
         hyps = map Term.compress_term hyps,
berghofe@13658
   557
         tpairs = map (pairself Term.compress_term) tpairs,
wenzelm@2386
   558
         prop = Term.compress_term prop};
wenzelm@564
   559
wenzelm@387
   560
wenzelm@2509
   561
paulson@1529
   562
(*** Meta rules ***)
clasohm@0
   563
wenzelm@16601
   564
(** primitive rules **)
clasohm@0
   565
wenzelm@16656
   566
(*The assumption rule A |- A*)
wenzelm@16601
   567
fun assume raw_ct =
wenzelm@16601
   568
  let val Cterm {thy_ref, t = prop, T, maxidx, sorts} = adjust_maxidx raw_ct in
wenzelm@16601
   569
    if T <> propT then
wenzelm@16601
   570
      raise THM ("assume: assumptions must have type prop", 0, [])
wenzelm@16601
   571
    else if maxidx <> ~1 then
wenzelm@16601
   572
      raise THM ("assume: assumptions may not contain schematic variables", maxidx, [])
wenzelm@16601
   573
    else Thm {thy_ref = thy_ref,
wenzelm@16601
   574
      der = Pt.infer_derivs' I (false, Pt.Hyp prop),
wenzelm@16601
   575
      maxidx = ~1,
wenzelm@16601
   576
      shyps = sorts,
wenzelm@16601
   577
      hyps = [prop],
wenzelm@16601
   578
      tpairs = [],
wenzelm@16601
   579
      prop = prop}
clasohm@0
   580
  end;
clasohm@0
   581
wenzelm@1220
   582
(*Implication introduction
wenzelm@3529
   583
    [A]
wenzelm@3529
   584
     :
wenzelm@3529
   585
     B
wenzelm@1220
   586
  -------
wenzelm@1220
   587
  A ==> B
wenzelm@1220
   588
*)
wenzelm@16601
   589
fun implies_intr
wenzelm@16601
   590
    (ct as Cterm {thy_ref = thy_refA, t = A, T, maxidx = maxidxA, sorts})
wenzelm@16601
   591
    (th as Thm {thy_ref, der, maxidx, hyps, shyps, tpairs, prop}) =
wenzelm@16601
   592
  if T <> propT then
wenzelm@16601
   593
    raise THM ("implies_intr: assumptions must have type prop", 0, [th])
wenzelm@16601
   594
  else
wenzelm@16601
   595
    Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   596
      der = Pt.infer_derivs' (Pt.implies_intr_proof A) der,
wenzelm@16601
   597
      maxidx = Int.max (maxidxA, maxidx),
wenzelm@16601
   598
      shyps = Sorts.union sorts shyps,
wenzelm@16601
   599
      hyps = remove_hyps A hyps,
wenzelm@16601
   600
      tpairs = tpairs,
wenzelm@16601
   601
      prop = implies $ A $ prop};
clasohm@0
   602
paulson@1529
   603
wenzelm@1220
   604
(*Implication elimination
wenzelm@1220
   605
  A ==> B    A
wenzelm@1220
   606
  ------------
wenzelm@1220
   607
        B
wenzelm@1220
   608
*)
wenzelm@16601
   609
fun implies_elim thAB thA =
wenzelm@16601
   610
  let
wenzelm@16601
   611
    val Thm {maxidx = maxA, der = derA, hyps = hypsA, shyps = shypsA, tpairs = tpairsA,
wenzelm@16601
   612
      prop = propA, ...} = thA
wenzelm@16601
   613
    and Thm {der, maxidx, hyps, shyps, tpairs, prop, ...} = thAB;
wenzelm@16601
   614
    fun err () = raise THM ("implies_elim: major premise", 0, [thAB, thA]);
wenzelm@16601
   615
  in
wenzelm@16601
   616
    case prop of
wenzelm@16601
   617
      imp $ A $ B =>
wenzelm@16601
   618
        if imp = Term.implies andalso A aconv propA then
wenzelm@16656
   619
          Thm {thy_ref = merge_thys2 thAB thA,
wenzelm@16601
   620
            der = Pt.infer_derivs (curry Pt.%%) der derA,
wenzelm@16601
   621
            maxidx = Int.max (maxA, maxidx),
wenzelm@16601
   622
            shyps = Sorts.union shypsA shyps,
wenzelm@16601
   623
            hyps = union_hyps hypsA hyps,
wenzelm@16601
   624
            tpairs = union_tpairs tpairsA tpairs,
wenzelm@16601
   625
            prop = B}
wenzelm@16601
   626
        else err ()
wenzelm@16601
   627
    | _ => err ()
wenzelm@16601
   628
  end;
wenzelm@250
   629
wenzelm@1220
   630
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@16656
   631
    [x]
wenzelm@16656
   632
     :
wenzelm@16656
   633
     A
wenzelm@16656
   634
  ------
wenzelm@16656
   635
  !!x. A
wenzelm@1220
   636
*)
wenzelm@16601
   637
fun forall_intr
wenzelm@16601
   638
    (ct as Cterm {t = x, T, sorts, ...})
wenzelm@16601
   639
    (th as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16601
   640
  let
wenzelm@16601
   641
    fun result a =
wenzelm@16601
   642
      Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   643
        der = Pt.infer_derivs' (Pt.forall_intr_proof x a) der,
wenzelm@16601
   644
        maxidx = maxidx,
wenzelm@16601
   645
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   646
        hyps = hyps,
wenzelm@16601
   647
        tpairs = tpairs,
wenzelm@16601
   648
        prop = all T $ Abs (a, T, abstract_over (x, prop))};
wenzelm@16601
   649
    fun check_occs x ts =
wenzelm@16601
   650
      if exists (apl (x, Logic.occs)) ts then
wenzelm@16601
   651
        raise THM("forall_intr: variable free in assumptions", 0, [th])
wenzelm@16601
   652
      else ();
wenzelm@16601
   653
  in
wenzelm@16601
   654
    case x of
wenzelm@16601
   655
      Free (a, _) => (check_occs x hyps; check_occs x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   656
    | Var ((a, _), _) => (check_occs x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   657
    | _ => raise THM ("forall_intr: not a variable", 0, [th])
clasohm@0
   658
  end;
clasohm@0
   659
wenzelm@1220
   660
(*Forall elimination
wenzelm@16656
   661
  !!x. A
wenzelm@1220
   662
  ------
wenzelm@1220
   663
  A[t/x]
wenzelm@1220
   664
*)
wenzelm@16601
   665
fun forall_elim
wenzelm@16601
   666
    (ct as Cterm {t, T, maxidx = maxt, sorts, ...})
wenzelm@16601
   667
    (th as Thm {der, maxidx, shyps, hyps, tpairs, prop, ...}) =
wenzelm@16601
   668
  (case prop of
wenzelm@16601
   669
    Const ("all", Type ("fun", [Type ("fun", [qary, _]), _])) $ A =>
wenzelm@16601
   670
      if T <> qary then
wenzelm@16601
   671
        raise THM ("forall_elim: type mismatch", 0, [th])
wenzelm@16601
   672
      else
wenzelm@16601
   673
        Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   674
          der = Pt.infer_derivs' (Pt.% o rpair (SOME t)) der,
wenzelm@16601
   675
          maxidx = Int.max (maxidx, maxt),
wenzelm@16601
   676
          shyps = Sorts.union sorts shyps,
wenzelm@16601
   677
          hyps = hyps,
wenzelm@16601
   678
          tpairs = tpairs,
wenzelm@16601
   679
          prop = Term.betapply (A, t)}
wenzelm@16601
   680
  | _ => raise THM ("forall_elim: not quantified", 0, [th]));
clasohm@0
   681
clasohm@0
   682
wenzelm@1220
   683
(* Equality *)
clasohm@0
   684
wenzelm@16601
   685
(*Reflexivity
wenzelm@16601
   686
  t == t
wenzelm@16601
   687
*)
wenzelm@16601
   688
fun reflexive (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16656
   689
  Thm {thy_ref = thy_ref,
wenzelm@16601
   690
    der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@16601
   691
    maxidx = maxidx,
wenzelm@16601
   692
    shyps = sorts,
wenzelm@16601
   693
    hyps = [],
wenzelm@16601
   694
    tpairs = [],
wenzelm@16601
   695
    prop = Logic.mk_equals (t, t)};
clasohm@0
   696
wenzelm@16601
   697
(*Symmetry
wenzelm@16601
   698
  t == u
wenzelm@16601
   699
  ------
wenzelm@16601
   700
  u == t
wenzelm@1220
   701
*)
wenzelm@16601
   702
fun symmetric (th as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16601
   703
  (case prop of
wenzelm@16601
   704
    (eq as Const ("==", Type (_, [T, _]))) $ t $ u =>
wenzelm@16601
   705
      Thm {thy_ref = thy_ref,
wenzelm@16601
   706
        der = Pt.infer_derivs' Pt.symmetric der,
wenzelm@16601
   707
        maxidx = maxidx,
wenzelm@16601
   708
        shyps = shyps,
wenzelm@16601
   709
        hyps = hyps,
wenzelm@16601
   710
        tpairs = tpairs,
wenzelm@16601
   711
        prop = eq $ u $ t}
wenzelm@16601
   712
    | _ => raise THM ("symmetric", 0, [th]));
clasohm@0
   713
wenzelm@16601
   714
(*Transitivity
wenzelm@16601
   715
  t1 == u    u == t2
wenzelm@16601
   716
  ------------------
wenzelm@16601
   717
       t1 == t2
wenzelm@1220
   718
*)
clasohm@0
   719
fun transitive th1 th2 =
wenzelm@16601
   720
  let
wenzelm@16601
   721
    val Thm {der = der1, maxidx = max1, hyps = hyps1, shyps = shyps1, tpairs = tpairs1,
wenzelm@16601
   722
      prop = prop1, ...} = th1
wenzelm@16601
   723
    and Thm {der = der2, maxidx = max2, hyps = hyps2, shyps = shyps2, tpairs = tpairs2,
wenzelm@16601
   724
      prop = prop2, ...} = th2;
wenzelm@16601
   725
    fun err msg = raise THM ("transitive: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   726
  in
wenzelm@16601
   727
    case (prop1, prop2) of
wenzelm@16601
   728
      ((eq as Const ("==", Type (_, [T, _]))) $ t1 $ u, Const ("==", _) $ u' $ t2) =>
wenzelm@16601
   729
        if not (u aconv u') then err "middle term"
wenzelm@16601
   730
        else
wenzelm@16656
   731
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   732
            der = Pt.infer_derivs (Pt.transitive u T) der1 der2,
wenzelm@16601
   733
            maxidx = Int.max (max1, max2),
wenzelm@16601
   734
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   735
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   736
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   737
            prop = eq $ t1 $ t2}
wenzelm@16601
   738
     | _ =>  err "premises"
clasohm@0
   739
  end;
clasohm@0
   740
wenzelm@16601
   741
(*Beta-conversion
wenzelm@16656
   742
  (%x. t)(u) == t[u/x]
wenzelm@16601
   743
  fully beta-reduces the term if full = true
berghofe@10416
   744
*)
wenzelm@16601
   745
fun beta_conversion full (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   746
  let val t' =
wenzelm@16601
   747
    if full then Envir.beta_norm t
wenzelm@16601
   748
    else
wenzelm@16601
   749
      (case t of Abs (_, _, bodt) $ u => subst_bound (u, bodt)
wenzelm@16601
   750
      | _ => raise THM ("beta_conversion: not a redex", 0, []));
wenzelm@16601
   751
  in
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, t')}
berghofe@10416
   759
  end;
berghofe@10416
   760
wenzelm@16601
   761
fun eta_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   762
  Thm {thy_ref = thy_ref,
wenzelm@16601
   763
    der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@16601
   764
    maxidx = maxidx,
wenzelm@16601
   765
    shyps = sorts,
wenzelm@16601
   766
    hyps = [],
wenzelm@16601
   767
    tpairs = [],
wenzelm@16601
   768
    prop = Logic.mk_equals (t, Pattern.eta_contract t)};
clasohm@0
   769
clasohm@0
   770
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   771
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@16601
   772
      t == u
wenzelm@16601
   773
  --------------
wenzelm@16601
   774
  %x. t == %x. u
wenzelm@1220
   775
*)
wenzelm@16601
   776
fun abstract_rule a
wenzelm@16601
   777
    (Cterm {t = x, T, sorts, ...})
wenzelm@16601
   778
    (th as Thm {thy_ref, der, maxidx, hyps, shyps, tpairs, prop}) =
wenzelm@16601
   779
  let
wenzelm@16601
   780
    val (t, u) = Logic.dest_equals prop
wenzelm@16601
   781
      handle TERM _ => raise THM ("abstract_rule: premise not an equality", 0, [th]);
wenzelm@16601
   782
    val result =
wenzelm@16601
   783
      Thm {thy_ref = thy_ref,
wenzelm@16601
   784
        der = Pt.infer_derivs' (Pt.abstract_rule x a) der,
wenzelm@16601
   785
        maxidx = maxidx,
wenzelm@16601
   786
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   787
        hyps = hyps,
wenzelm@16601
   788
        tpairs = tpairs,
wenzelm@16601
   789
        prop = Logic.mk_equals
wenzelm@16601
   790
          (Abs (a, T, abstract_over (x, t)), Abs (a, T, abstract_over (x, u)))};
wenzelm@16601
   791
    fun check_occs x ts =
wenzelm@16601
   792
      if exists (apl (x, Logic.occs)) ts then
wenzelm@16601
   793
        raise THM ("abstract_rule: variable free in assumptions", 0, [th])
wenzelm@16601
   794
      else ();
wenzelm@16601
   795
  in
wenzelm@16601
   796
    case x of
wenzelm@16601
   797
      Free _ => (check_occs x hyps; check_occs x (terms_of_tpairs tpairs); result)
wenzelm@16601
   798
    | Var _ => (check_occs x (terms_of_tpairs tpairs); result)
wenzelm@16601
   799
    | _ => raise THM ("abstract_rule: not a variable", 0, [th])
clasohm@0
   800
  end;
clasohm@0
   801
clasohm@0
   802
(*The combination rule
wenzelm@3529
   803
  f == g  t == u
wenzelm@3529
   804
  --------------
wenzelm@16601
   805
    f t == g u
wenzelm@1220
   806
*)
clasohm@0
   807
fun combination th1 th2 =
wenzelm@16601
   808
  let
wenzelm@16601
   809
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@16601
   810
      prop = prop1, ...} = th1
wenzelm@16601
   811
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@16601
   812
      prop = prop2, ...} = th2;
wenzelm@16601
   813
    fun chktypes fT tT =
wenzelm@16601
   814
      (case fT of
wenzelm@16601
   815
        Type ("fun", [T1, T2]) =>
wenzelm@16601
   816
          if T1 <> tT then
wenzelm@16601
   817
            raise THM ("combination: types", 0, [th1, th2])
wenzelm@16601
   818
          else ()
wenzelm@16601
   819
      | _ => raise THM ("combination: not function type", 0, [th1, th2]));
wenzelm@16601
   820
  in
wenzelm@16601
   821
    case (prop1, prop2) of
wenzelm@16601
   822
      (Const ("==", Type ("fun", [fT, _])) $ f $ g,
wenzelm@16601
   823
       Const ("==", Type ("fun", [tT, _])) $ t $ u) =>
wenzelm@16601
   824
        (chktypes fT tT;
wenzelm@16601
   825
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   826
            der = Pt.infer_derivs (Pt.combination f g t u fT) der1 der2,
wenzelm@16601
   827
            maxidx = Int.max (max1, max2),
wenzelm@16601
   828
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   829
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   830
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   831
            prop = Logic.mk_equals (f $ t, g $ u)})
wenzelm@16601
   832
     | _ => raise THM ("combination: premises", 0, [th1, th2])
clasohm@0
   833
  end;
clasohm@0
   834
wenzelm@16601
   835
(*Equality introduction
wenzelm@3529
   836
  A ==> B  B ==> A
wenzelm@3529
   837
  ----------------
wenzelm@3529
   838
       A == B
wenzelm@1220
   839
*)
clasohm@0
   840
fun equal_intr th1 th2 =
wenzelm@16601
   841
  let
wenzelm@16601
   842
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@16601
   843
      prop = prop1, ...} = th1
wenzelm@16601
   844
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@16601
   845
      prop = prop2, ...} = th2;
wenzelm@16601
   846
    fun err msg = raise THM ("equal_intr: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   847
  in
wenzelm@16601
   848
    case (prop1, prop2) of
wenzelm@16601
   849
      (Const("==>", _) $ A $ B, Const("==>", _) $ B' $ A') =>
wenzelm@16601
   850
        if A aconv A' andalso B aconv B' then
wenzelm@16601
   851
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   852
            der = Pt.infer_derivs (Pt.equal_intr A B) der1 der2,
wenzelm@16601
   853
            maxidx = Int.max (max1, max2),
wenzelm@16601
   854
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   855
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   856
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   857
            prop = Logic.mk_equals (A, B)}
wenzelm@16601
   858
        else err "not equal"
wenzelm@16601
   859
    | _ =>  err "premises"
paulson@1529
   860
  end;
paulson@1529
   861
paulson@1529
   862
(*The equal propositions rule
wenzelm@3529
   863
  A == B  A
paulson@1529
   864
  ---------
paulson@1529
   865
      B
paulson@1529
   866
*)
paulson@1529
   867
fun equal_elim th1 th2 =
wenzelm@16601
   868
  let
wenzelm@16601
   869
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1,
wenzelm@16601
   870
      tpairs = tpairs1, prop = prop1, ...} = th1
wenzelm@16601
   871
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2,
wenzelm@16601
   872
      tpairs = tpairs2, prop = prop2, ...} = th2;
wenzelm@16601
   873
    fun err msg = raise THM ("equal_elim: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   874
  in
wenzelm@16601
   875
    case prop1 of
wenzelm@16601
   876
      Const ("==", _) $ A $ B =>
wenzelm@16601
   877
        if prop2 aconv A then
wenzelm@16601
   878
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   879
            der = Pt.infer_derivs (Pt.equal_elim A B) der1 der2,
wenzelm@16601
   880
            maxidx = Int.max (max1, max2),
wenzelm@16601
   881
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   882
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   883
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   884
            prop = B}
wenzelm@16601
   885
        else err "not equal"
paulson@1529
   886
     | _ =>  err"major premise"
paulson@1529
   887
  end;
clasohm@0
   888
wenzelm@1220
   889
wenzelm@1220
   890
clasohm@0
   891
(**** Derived rules ****)
clasohm@0
   892
wenzelm@16601
   893
(*Smash unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@250
   894
  Instantiates the theorem and deletes trivial tpairs.
clasohm@0
   895
  Resulting sequence may contain multiple elements if the tpairs are
clasohm@0
   896
    not all flex-flex. *)
wenzelm@16601
   897
fun flexflex_rule (th as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16601
   898
  Unify.smash_unifiers (Theory.deref thy_ref, Envir.empty maxidx, tpairs)
wenzelm@16601
   899
  |> Seq.map (fn env =>
wenzelm@16601
   900
      if Envir.is_empty env then th
wenzelm@16601
   901
      else
wenzelm@16601
   902
        let
wenzelm@16601
   903
          val tpairs' = tpairs |> map (pairself (Envir.norm_term env))
wenzelm@16601
   904
            (*remove trivial tpairs, of the form t==t*)
wenzelm@16601
   905
            |> List.filter (not o op aconv);
wenzelm@16601
   906
          val prop' = Envir.norm_term env prop;
wenzelm@16601
   907
        in
wenzelm@16601
   908
          Thm {thy_ref = thy_ref,
wenzelm@16601
   909
            der = Pt.infer_derivs' (Pt.norm_proof' env) der,
wenzelm@16601
   910
            maxidx = maxidx_of_terms (prop' :: terms_of_tpairs tpairs'),
wenzelm@16656
   911
            shyps = may_insert_env_sorts (Theory.deref thy_ref) env shyps,
wenzelm@16601
   912
            hyps = hyps,
wenzelm@16601
   913
            tpairs = tpairs',
wenzelm@16601
   914
            prop = prop'}
wenzelm@16601
   915
        end);
wenzelm@16601
   916
clasohm@0
   917
clasohm@0
   918
(*Instantiation of Vars
wenzelm@16656
   919
           A
wenzelm@16656
   920
  --------------------
wenzelm@16656
   921
  A[t1/v1, ..., tn/vn]
wenzelm@1220
   922
*)
clasohm@0
   923
wenzelm@6928
   924
local
wenzelm@6928
   925
wenzelm@16425
   926
fun pretty_typing thy t T =
wenzelm@16425
   927
  Pretty.block [Sign.pretty_term thy t, Pretty.str " ::", Pretty.brk 1, Sign.pretty_typ thy T];
berghofe@15797
   928
wenzelm@16656
   929
fun add_ctpair ((thy, sorts), (ct, cu)) =
wenzelm@6928
   930
  let
wenzelm@16656
   931
    val Cterm {t = t, T = T, sorts = sorts1, ...} = ct
wenzelm@16656
   932
    and Cterm {t = u, T = U, sorts = sorts2, ...} = cu;
wenzelm@16656
   933
    val thy' = Theory.merge (thy, Theory.deref (merge_thys0 ct cu));
wenzelm@16656
   934
    val sorts' = Sorts.union sorts2 (Sorts.union sorts1 sorts);
wenzelm@3967
   935
  in
wenzelm@16656
   936
    if T = U then ((thy', sorts'), (t, u))
wenzelm@16601
   937
    else raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16601
   938
     [Pretty.str "instantiate: type conflict",
wenzelm@16656
   939
      Pretty.fbrk, pretty_typing thy' t T,
wenzelm@16656
   940
      Pretty.fbrk, pretty_typing thy' u U]), [T,U], [t,u])
clasohm@0
   941
  end;
clasohm@0
   942
wenzelm@16656
   943
fun add_ctyp ((thy, sorts), (cT, cU)) =
wenzelm@16656
   944
  let
wenzelm@16656
   945
    val Ctyp {T = T, thy_ref = thy_ref1, sorts = sorts1, ...} = cT
wenzelm@16656
   946
    and Ctyp {T = U, thy_ref = thy_ref2, sorts = sorts2, ...} = cU;
wenzelm@16656
   947
    val thy' = Theory.merge (thy, Theory.deref (Theory.merge_refs (thy_ref1, thy_ref2)));
wenzelm@16656
   948
    val sorts' = Sorts.union sorts2 (Sorts.union sorts1 sorts);
wenzelm@16656
   949
  in
wenzelm@16656
   950
    (case T of TVar (_, S) =>
wenzelm@16656
   951
      if Type.of_sort (Sign.tsig_of thy') (U, S) then ((thy', sorts'), (T, U))
wenzelm@16656
   952
      else raise TYPE ("Type not of sort " ^ Sign.string_of_sort thy' S, [U], [])
wenzelm@16656
   953
    | _ => raise TYPE (Pretty.string_of (Pretty.block
berghofe@15797
   954
        [Pretty.str "instantiate: not a type variable",
wenzelm@16656
   955
         Pretty.fbrk, Sign.pretty_typ thy' T]), [T], []))
wenzelm@16656
   956
  end;
clasohm@0
   957
wenzelm@6928
   958
in
wenzelm@6928
   959
wenzelm@16601
   960
(*Left-to-right replacements: ctpairs = [..., (vi, ti), ...].
clasohm@0
   961
  Instantiates distinct Vars by terms of same type.
wenzelm@16601
   962
  Does NOT normalize the resulting theorem!*)
paulson@1529
   963
fun instantiate ([], []) th = th
wenzelm@16601
   964
  | instantiate (vcTs, ctpairs) th =
wenzelm@16656
   965
      let
wenzelm@16656
   966
        val Thm {thy_ref, der, maxidx, hyps, shyps, tpairs = dpairs, prop} = th;
wenzelm@16656
   967
        val (thy_sorts, tpairs) = foldl_map add_ctpair ((Theory.deref thy_ref, shyps), ctpairs);
wenzelm@16656
   968
        val ((thy', shyps'), vTs) = foldl_map add_ctyp (thy_sorts, vcTs);
wenzelm@16656
   969
        fun subst t = subst_atomic tpairs (map_term_types (typ_subst_atomic vTs) t);
wenzelm@16656
   970
        val prop' = subst prop;
wenzelm@16656
   971
        val dpairs' = map (pairself subst) dpairs;
wenzelm@16656
   972
      in
wenzelm@16656
   973
        if not (forall (is_Var o #1) tpairs andalso null (gen_duplicates eq_fst tpairs)) then
wenzelm@16656
   974
          raise THM ("instantiate: variables not distinct", 0, [th])
wenzelm@16656
   975
        else if not (null (gen_duplicates eq_fst vTs)) then
wenzelm@16656
   976
          raise THM ("instantiate: type variables not distinct", 0, [th])
wenzelm@16656
   977
        else
wenzelm@16656
   978
          Thm {thy_ref = Theory.self_ref thy',
wenzelm@16656
   979
            der = Pt.infer_derivs' (Pt.instantiate vTs tpairs) der,
wenzelm@16656
   980
            maxidx = maxidx_of_terms (prop' :: terms_of_tpairs dpairs'),
wenzelm@16656
   981
            shyps = shyps',
wenzelm@16656
   982
            hyps = hyps,
wenzelm@16656
   983
            tpairs = dpairs',
wenzelm@16656
   984
            prop = prop'}
wenzelm@16656
   985
      end
wenzelm@16656
   986
      handle TYPE (msg, _, _) => raise THM (msg, 0, [th]);
wenzelm@6928
   987
wenzelm@6928
   988
end;
wenzelm@6928
   989
clasohm@0
   990
wenzelm@16601
   991
(*The trivial implication A ==> A, justified by assume and forall rules.
wenzelm@16601
   992
  A can contain Vars, not so for assume!*)
wenzelm@16601
   993
fun trivial (Cterm {thy_ref, t =A, T, maxidx, sorts}) =
wenzelm@16601
   994
  if T <> propT then
wenzelm@16601
   995
    raise THM ("trivial: the term must have type prop", 0, [])
wenzelm@16601
   996
  else
wenzelm@16601
   997
    Thm {thy_ref = thy_ref,
wenzelm@16601
   998
      der = Pt.infer_derivs' I (false, Pt.AbsP ("H", NONE, Pt.PBound 0)),
wenzelm@16601
   999
      maxidx = maxidx,
wenzelm@16601
  1000
      shyps = sorts,
wenzelm@16601
  1001
      hyps = [],
wenzelm@16601
  1002
      tpairs = [],
wenzelm@16601
  1003
      prop = implies $ A $ A};
clasohm@0
  1004
paulson@1503
  1005
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)" *)
wenzelm@16425
  1006
fun class_triv thy c =
wenzelm@16601
  1007
  let val Cterm {thy_ref, t, maxidx, sorts, ...} =
wenzelm@16425
  1008
    cterm_of thy (Logic.mk_inclass (TVar (("'a", 0), [c]), c))
wenzelm@6368
  1009
      handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@399
  1010
  in
wenzelm@16601
  1011
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1012
      der = Pt.infer_derivs' I (false, Pt.PAxm ("ProtoPure.class_triv:" ^ c, t, SOME [])),
wenzelm@16601
  1013
      maxidx = maxidx,
wenzelm@16601
  1014
      shyps = sorts,
wenzelm@16601
  1015
      hyps = [],
wenzelm@16601
  1016
      tpairs = [],
wenzelm@16601
  1017
      prop = t}
wenzelm@399
  1018
  end;
wenzelm@399
  1019
wenzelm@399
  1020
wenzelm@6786
  1021
(* Replace all TFrees not fixed or in the hyps by new TVars *)
wenzelm@16601
  1022
fun varifyT' fixed (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@12500
  1023
  let
berghofe@15797
  1024
    val tfrees = foldr add_term_tfrees fixed hyps;
berghofe@13658
  1025
    val prop1 = attach_tpairs tpairs prop;
berghofe@13658
  1026
    val (prop2, al) = Type.varify (prop1, tfrees);
wenzelm@16601
  1027
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1028
  in
wenzelm@16601
  1029
    (Thm {thy_ref = thy_ref,
wenzelm@16601
  1030
      der = Pt.infer_derivs' (Pt.varify_proof prop tfrees) der,
wenzelm@16601
  1031
      maxidx = Int.max (0, maxidx),
wenzelm@16601
  1032
      shyps = shyps,
wenzelm@16601
  1033
      hyps = hyps,
wenzelm@16601
  1034
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@16601
  1035
      prop = prop3}, al)
clasohm@0
  1036
  end;
clasohm@0
  1037
wenzelm@12500
  1038
val varifyT = #1 o varifyT' [];
wenzelm@6786
  1039
clasohm@0
  1040
(* Replace all TVars by new TFrees *)
wenzelm@16601
  1041
fun freezeT (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
berghofe@13658
  1042
  let
berghofe@13658
  1043
    val prop1 = attach_tpairs tpairs prop;
wenzelm@16287
  1044
    val prop2 = Type.freeze prop1;
wenzelm@16601
  1045
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1046
  in
wenzelm@16601
  1047
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1048
      der = Pt.infer_derivs' (Pt.freezeT prop1) der,
wenzelm@16601
  1049
      maxidx = maxidx_of_term prop2,
wenzelm@16601
  1050
      shyps = shyps,
wenzelm@16601
  1051
      hyps = hyps,
wenzelm@16601
  1052
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@16601
  1053
      prop = prop3}
wenzelm@1220
  1054
  end;
clasohm@0
  1055
clasohm@0
  1056
clasohm@0
  1057
(*** Inference rules for tactics ***)
clasohm@0
  1058
clasohm@0
  1059
(*Destruct proof state into constraints, other goals, goal(i), rest *)
berghofe@13658
  1060
fun dest_state (state as Thm{prop,tpairs,...}, i) =
berghofe@13658
  1061
  (case  Logic.strip_prems(i, [], prop) of
berghofe@13658
  1062
      (B::rBs, C) => (tpairs, rev rBs, B, C)
berghofe@13658
  1063
    | _ => raise THM("dest_state", i, [state]))
clasohm@0
  1064
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1065
lcp@309
  1066
(*Increment variables and parameters of orule as required for
clasohm@0
  1067
  resolution with goal i of state. *)
clasohm@0
  1068
fun lift_rule (state, i) orule =
wenzelm@16601
  1069
  let
wenzelm@16601
  1070
    val Thm {shyps = sshyps, prop = sprop, maxidx = smax, thy_ref = sthy_ref,...} = state;
wenzelm@16601
  1071
    val (Bi :: _, _) = Logic.strip_prems (i, [], sprop)
wenzelm@16601
  1072
      handle TERM _ => raise THM ("lift_rule", i, [orule, state]);
wenzelm@16601
  1073
    val (lift_abs, lift_all) = Logic.lift_fns (Bi, smax + 1);
wenzelm@16601
  1074
    val (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) = orule;
wenzelm@16601
  1075
    val (As, B) = Logic.strip_horn prop;
wenzelm@16601
  1076
  in
wenzelm@16601
  1077
    Thm {thy_ref = merge_thys2 state orule,
wenzelm@16601
  1078
      der = Pt.infer_derivs' (Pt.lift_proof Bi (smax + 1) prop) der,
wenzelm@16601
  1079
      maxidx = maxidx + smax + 1,
wenzelm@16601
  1080
      shyps = Sorts.union sshyps shyps,
wenzelm@16601
  1081
      hyps = hyps,
wenzelm@16601
  1082
      tpairs = map (pairself lift_abs) tpairs,
wenzelm@16601
  1083
      prop = Logic.list_implies (map lift_all As, lift_all B)}
clasohm@0
  1084
  end;
clasohm@0
  1085
wenzelm@16425
  1086
fun incr_indexes i (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16601
  1087
  if i < 0 then raise THM ("negative increment", 0, [thm])
wenzelm@16601
  1088
  else if i = 0 then thm
wenzelm@16601
  1089
  else
wenzelm@16425
  1090
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1091
      der = Pt.infer_derivs' (Pt.map_proof_terms (Logic.incr_indexes ([], i)) (incr_tvar i)) der,
wenzelm@16601
  1092
      maxidx = maxidx + i,
wenzelm@16601
  1093
      shyps = shyps,
wenzelm@16601
  1094
      hyps = hyps,
wenzelm@16601
  1095
      tpairs = map (pairself (Logic.incr_indexes ([], i))) tpairs,
wenzelm@16601
  1096
      prop = Logic.incr_indexes ([], i) prop};
berghofe@10416
  1097
clasohm@0
  1098
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1099
fun assumption i state =
wenzelm@16601
  1100
  let
wenzelm@16601
  1101
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16656
  1102
    val thy = Theory.deref thy_ref;
wenzelm@16601
  1103
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1104
    fun newth n (env as Envir.Envir {maxidx, ...}, tpairs) =
wenzelm@16601
  1105
      Thm {thy_ref = thy_ref,
wenzelm@16601
  1106
        der = Pt.infer_derivs'
wenzelm@16601
  1107
          ((if Envir.is_empty env then I else (Pt.norm_proof' env)) o
wenzelm@16601
  1108
            Pt.assumption_proof Bs Bi n) der,
wenzelm@16601
  1109
        maxidx = maxidx,
wenzelm@16656
  1110
        shyps = may_insert_env_sorts thy env shyps,
wenzelm@16601
  1111
        hyps = hyps,
wenzelm@16601
  1112
        tpairs =
wenzelm@16601
  1113
          if Envir.is_empty env then tpairs
wenzelm@16601
  1114
          else map (pairself (Envir.norm_term env)) tpairs,
wenzelm@16601
  1115
        prop =
wenzelm@16601
  1116
          if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@16601
  1117
            Logic.list_implies (Bs, C)
wenzelm@16601
  1118
          else (*normalize the new rule fully*)
wenzelm@16601
  1119
            Envir.norm_term env (Logic.list_implies (Bs, C))};
wenzelm@16601
  1120
    fun addprfs [] _ = Seq.empty
wenzelm@16601
  1121
      | addprfs ((t, u) :: apairs) n = Seq.make (fn () => Seq.pull
wenzelm@16601
  1122
          (Seq.mapp (newth n)
wenzelm@16656
  1123
            (Unify.unifiers (thy, Envir.empty maxidx, (t, u) :: tpairs))
wenzelm@16601
  1124
            (addprfs apairs (n + 1))))
wenzelm@16601
  1125
  in addprfs (Logic.assum_pairs (~1, Bi)) 1 end;
clasohm@0
  1126
wenzelm@250
  1127
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1128
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1129
fun eq_assumption i state =
wenzelm@16601
  1130
  let
wenzelm@16601
  1131
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16601
  1132
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1133
  in
wenzelm@16601
  1134
    (case find_index (op aconv) (Logic.assum_pairs (~1, Bi)) of
wenzelm@16601
  1135
      ~1 => raise THM ("eq_assumption", 0, [state])
wenzelm@16601
  1136
    | n =>
wenzelm@16601
  1137
        Thm {thy_ref = thy_ref,
wenzelm@16601
  1138
          der = Pt.infer_derivs' (Pt.assumption_proof Bs Bi (n + 1)) der,
wenzelm@16601
  1139
          maxidx = maxidx,
wenzelm@16601
  1140
          shyps = shyps,
wenzelm@16601
  1141
          hyps = hyps,
wenzelm@16601
  1142
          tpairs = tpairs,
wenzelm@16601
  1143
          prop = Logic.list_implies (Bs, C)})
clasohm@0
  1144
  end;
clasohm@0
  1145
clasohm@0
  1146
paulson@2671
  1147
(*For rotate_tac: fast rotation of assumptions of subgoal i*)
paulson@2671
  1148
fun rotate_rule k i state =
wenzelm@16601
  1149
  let
wenzelm@16601
  1150
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16601
  1151
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1152
    val params = Term.strip_all_vars Bi
wenzelm@16601
  1153
    and rest   = Term.strip_all_body Bi;
wenzelm@16601
  1154
    val asms   = Logic.strip_imp_prems rest
wenzelm@16601
  1155
    and concl  = Logic.strip_imp_concl rest;
wenzelm@16601
  1156
    val n = length asms;
wenzelm@16601
  1157
    val m = if k < 0 then n + k else k;
wenzelm@16601
  1158
    val Bi' =
wenzelm@16601
  1159
      if 0 = m orelse m = n then Bi
wenzelm@16601
  1160
      else if 0 < m andalso m < n then
wenzelm@16601
  1161
        let val (ps, qs) = splitAt (m, asms)
wenzelm@16601
  1162
        in list_all (params, Logic.list_implies (qs @ ps, concl)) end
wenzelm@16601
  1163
      else raise THM ("rotate_rule", k, [state]);
wenzelm@16601
  1164
  in
wenzelm@16601
  1165
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1166
      der = Pt.infer_derivs' (Pt.rotate_proof Bs Bi m) der,
wenzelm@16601
  1167
      maxidx = maxidx,
wenzelm@16601
  1168
      shyps = shyps,
wenzelm@16601
  1169
      hyps = hyps,
wenzelm@16601
  1170
      tpairs = tpairs,
wenzelm@16601
  1171
      prop = Logic.list_implies (Bs @ [Bi'], C)}
paulson@2671
  1172
  end;
paulson@2671
  1173
paulson@2671
  1174
paulson@7248
  1175
(*Rotates a rule's premises to the left by k, leaving the first j premises
paulson@7248
  1176
  unchanged.  Does nothing if k=0 or if k equals n-j, where n is the
wenzelm@16656
  1177
  number of premises.  Useful with etac and underlies defer_tac*)
paulson@7248
  1178
fun permute_prems j k rl =
wenzelm@16601
  1179
  let
wenzelm@16601
  1180
    val Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop} = rl;
wenzelm@16601
  1181
    val prems = Logic.strip_imp_prems prop
wenzelm@16601
  1182
    and concl = Logic.strip_imp_concl prop;
wenzelm@16601
  1183
    val moved_prems = List.drop (prems, j)
wenzelm@16601
  1184
    and fixed_prems = List.take (prems, j)
wenzelm@16601
  1185
      handle Subscript => raise THM ("permute_prems: j", j, [rl]);
wenzelm@16601
  1186
    val n_j = length moved_prems;
wenzelm@16601
  1187
    val m = if k < 0 then n_j + k else k;
wenzelm@16601
  1188
    val prop' =
wenzelm@16601
  1189
      if 0 = m orelse m = n_j then prop
wenzelm@16601
  1190
      else if 0 < m andalso m < n_j then
wenzelm@16601
  1191
        let val (ps, qs) = splitAt (m, moved_prems)
wenzelm@16601
  1192
        in Logic.list_implies (fixed_prems @ qs @ ps, concl) end
wenzelm@16601
  1193
      else raise THM ("permute_prems:k", k, [rl]);
wenzelm@16601
  1194
  in
wenzelm@16601
  1195
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1196
      der = Pt.infer_derivs' (Pt.permute_prems_prf prems j m) der,
wenzelm@16601
  1197
      maxidx = maxidx,
wenzelm@16601
  1198
      shyps = shyps,
wenzelm@16601
  1199
      hyps = hyps,
wenzelm@16601
  1200
      tpairs = tpairs,
wenzelm@16601
  1201
      prop = prop'}
paulson@7248
  1202
  end;
paulson@7248
  1203
paulson@7248
  1204
clasohm@0
  1205
(** User renaming of parameters in a subgoal **)
clasohm@0
  1206
clasohm@0
  1207
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1208
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1209
  The names in cs, if distinct, are used for the innermost parameters;
clasohm@0
  1210
   preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1211
fun rename_params_rule (cs, i) state =
wenzelm@16601
  1212
  let
wenzelm@16601
  1213
    val Thm {thy_ref, der, maxidx, shyps, hyps, ...} = state;
wenzelm@16601
  1214
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1215
    val iparams = map #1 (Logic.strip_params Bi);
wenzelm@16601
  1216
    val short = length iparams - length cs;
wenzelm@16601
  1217
    val newnames =
wenzelm@16601
  1218
      if short < 0 then error "More names than abstractions!"
wenzelm@16601
  1219
      else variantlist (Library.take (short, iparams), cs) @ cs;
wenzelm@16601
  1220
    val freenames = map (#1 o dest_Free) (term_frees Bi);
wenzelm@16601
  1221
    val newBi = Logic.list_rename_params (newnames, Bi);
wenzelm@250
  1222
  in
wenzelm@16601
  1223
    case findrep cs of
wenzelm@16601
  1224
      c :: _ => (warning ("Can't rename.  Bound variables not distinct: " ^ c); state)
wenzelm@16601
  1225
    | [] =>
wenzelm@16601
  1226
      (case cs inter_string freenames of
wenzelm@16601
  1227
        a :: _ => (warning ("Can't rename.  Bound/Free variable clash: " ^ a); state)
wenzelm@16601
  1228
      | [] =>
wenzelm@16601
  1229
        Thm {thy_ref = thy_ref,
wenzelm@16601
  1230
          der = der,
wenzelm@16601
  1231
          maxidx = maxidx,
wenzelm@16601
  1232
          shyps = shyps,
wenzelm@16601
  1233
          hyps = hyps,
wenzelm@16601
  1234
          tpairs = tpairs,
wenzelm@16601
  1235
          prop = Logic.list_implies (Bs @ [newBi], C)})
clasohm@0
  1236
  end;
clasohm@0
  1237
wenzelm@12982
  1238
clasohm@0
  1239
(*** Preservation of bound variable names ***)
clasohm@0
  1240
wenzelm@16601
  1241
fun rename_boundvars pat obj (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@12982
  1242
  (case Term.rename_abs pat obj prop of
skalberg@15531
  1243
    NONE => thm
skalberg@15531
  1244
  | SOME prop' => Thm
wenzelm@16425
  1245
      {thy_ref = thy_ref,
wenzelm@12982
  1246
       der = der,
wenzelm@12982
  1247
       maxidx = maxidx,
wenzelm@12982
  1248
       hyps = hyps,
wenzelm@12982
  1249
       shyps = shyps,
berghofe@13658
  1250
       tpairs = tpairs,
wenzelm@12982
  1251
       prop = prop'});
berghofe@10416
  1252
clasohm@0
  1253
wenzelm@16656
  1254
(* strip_apply f (A, B) strips off all assumptions/parameters from A
clasohm@0
  1255
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
  1256
fun strip_apply f =
clasohm@0
  1257
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@250
  1258
                Const("==>",_)$ _  $ B2) = implies $ A1 $ strip(B1,B2)
wenzelm@250
  1259
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
  1260
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
  1261
        | strip(A,_) = f A
clasohm@0
  1262
  in strip end;
clasohm@0
  1263
clasohm@0
  1264
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1265
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1266
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1267
fun rename_bvs([],_,_,_) = I
clasohm@0
  1268
  | rename_bvs(al,dpairs,tpairs,B) =
skalberg@15574
  1269
    let val vars = foldr add_term_vars []
skalberg@15574
  1270
                        (map fst dpairs @ map fst tpairs @ map snd tpairs)
wenzelm@250
  1271
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1272
        val vids = map (#1 o #1 o dest_Var) vars;
wenzelm@250
  1273
        fun rename(t as Var((x,i),T)) =
wenzelm@250
  1274
                (case assoc(al,x) of
skalberg@15531
  1275
                   SOME(y) => if x mem_string vids orelse y mem_string vids then t
wenzelm@250
  1276
                              else Var((y,i),T)
skalberg@15531
  1277
                 | NONE=> t)
clasohm@0
  1278
          | rename(Abs(x,T,t)) =
wenzelm@16425
  1279
              Abs (if_none (assoc_string (al, x)) x, T, rename t)
clasohm@0
  1280
          | rename(f$t) = rename f $ rename t
clasohm@0
  1281
          | rename(t) = t;
wenzelm@250
  1282
        fun strip_ren Ai = strip_apply rename (Ai,B)
clasohm@0
  1283
    in strip_ren end;
clasohm@0
  1284
clasohm@0
  1285
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
  1286
fun rename_bvars(dpairs, tpairs, B) =
skalberg@15574
  1287
        rename_bvs(foldr Term.match_bvars [] dpairs, dpairs, tpairs, B);
clasohm@0
  1288
clasohm@0
  1289
clasohm@0
  1290
(*** RESOLUTION ***)
clasohm@0
  1291
lcp@721
  1292
(** Lifting optimizations **)
lcp@721
  1293
clasohm@0
  1294
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
  1295
  identical because of lifting*)
wenzelm@250
  1296
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
  1297
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
  1298
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
  1299
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
  1300
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
  1301
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
  1302
  | strip_assums2 BB = BB;
clasohm@0
  1303
clasohm@0
  1304
lcp@721
  1305
(*Faster normalization: skip assumptions that were lifted over*)
lcp@721
  1306
fun norm_term_skip env 0 t = Envir.norm_term env t
lcp@721
  1307
  | norm_term_skip env n (Const("all",_)$Abs(a,T,t)) =
lcp@721
  1308
        let val Envir.Envir{iTs, ...} = env
berghofe@15797
  1309
            val T' = Envir.typ_subst_TVars iTs T
wenzelm@1238
  1310
            (*Must instantiate types of parameters because they are flattened;
lcp@721
  1311
              this could be a NEW parameter*)
lcp@721
  1312
        in  all T' $ Abs(a, T', norm_term_skip env n t)  end
lcp@721
  1313
  | norm_term_skip env n (Const("==>", _) $ A $ B) =
wenzelm@1238
  1314
        implies $ A $ norm_term_skip env (n-1) B
lcp@721
  1315
  | norm_term_skip env n t = error"norm_term_skip: too few assumptions??";
lcp@721
  1316
lcp@721
  1317
clasohm@0
  1318
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
  1319
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
  1320
  If match then forbid instantiations in proof state
clasohm@0
  1321
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
  1322
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
  1323
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
  1324
  Curried so that resolution calls dest_state only once.
clasohm@0
  1325
*)
wenzelm@4270
  1326
local exception COMPOSE
clasohm@0
  1327
in
wenzelm@250
  1328
fun bicompose_aux match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
  1329
                        (eres_flg, orule, nsubgoal) =
paulson@1529
  1330
 let val Thm{der=sder, maxidx=smax, shyps=sshyps, hyps=shyps, ...} = state
wenzelm@16425
  1331
     and Thm{der=rder, maxidx=rmax, shyps=rshyps, hyps=rhyps,
berghofe@13658
  1332
             tpairs=rtpairs, prop=rprop,...} = orule
paulson@1529
  1333
         (*How many hyps to skip over during normalization*)
wenzelm@1238
  1334
     and nlift = Logic.count_prems(strip_all_body Bi,
wenzelm@1238
  1335
                                   if eres_flg then ~1 else 0)
wenzelm@16601
  1336
     val thy_ref = merge_thys2 state orule;
wenzelm@16425
  1337
     val thy = Theory.deref thy_ref;
clasohm@0
  1338
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
berghofe@11518
  1339
     fun addth A (As, oldAs, rder', n) ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
  1340
       let val normt = Envir.norm_term env;
wenzelm@250
  1341
           (*perform minimal copying here by examining env*)
berghofe@13658
  1342
           val (ntpairs, normp) =
berghofe@13658
  1343
             if Envir.is_empty env then (tpairs, (Bs @ As, C))
wenzelm@250
  1344
             else
wenzelm@250
  1345
             let val ntps = map (pairself normt) tpairs
paulson@2147
  1346
             in if Envir.above (smax, env) then
wenzelm@1238
  1347
                  (*no assignments in state; normalize the rule only*)
wenzelm@1238
  1348
                  if lifted
berghofe@13658
  1349
                  then (ntps, (Bs @ map (norm_term_skip env nlift) As, C))
berghofe@13658
  1350
                  else (ntps, (Bs @ map normt As, C))
paulson@1529
  1351
                else if match then raise COMPOSE
wenzelm@250
  1352
                else (*normalize the new rule fully*)
berghofe@13658
  1353
                  (ntps, (map normt (Bs @ As), normt C))
wenzelm@250
  1354
             end
wenzelm@16601
  1355
           val th =
wenzelm@16425
  1356
             Thm{thy_ref = thy_ref,
berghofe@11518
  1357
                 der = Pt.infer_derivs
berghofe@11518
  1358
                   ((if Envir.is_empty env then I
berghofe@11518
  1359
                     else if Envir.above (smax, env) then
berghofe@11518
  1360
                       (fn f => fn der => f (Pt.norm_proof' env der))
berghofe@11518
  1361
                     else
berghofe@11518
  1362
                       curry op oo (Pt.norm_proof' env))
berghofe@11518
  1363
                    (Pt.bicompose_proof Bs oldAs As A n)) rder' sder,
wenzelm@2386
  1364
                 maxidx = maxidx,
wenzelm@16656
  1365
                 shyps = may_insert_env_sorts thy env (Sorts.union rshyps sshyps),
wenzelm@16601
  1366
                 hyps = union_hyps rhyps shyps,
berghofe@13658
  1367
                 tpairs = ntpairs,
berghofe@13658
  1368
                 prop = Logic.list_implies normp}
berghofe@11518
  1369
        in  Seq.cons(th, thq)  end  handle COMPOSE => thq;
berghofe@13658
  1370
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rprop)
clasohm@0
  1371
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
  1372
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
  1373
     fun newAs(As0, n, dpairs, tpairs) =
berghofe@11518
  1374
       let val (As1, rder') =
berghofe@11518
  1375
         if !Logic.auto_rename orelse not lifted then (As0, rder)
berghofe@11518
  1376
         else (map (rename_bvars(dpairs,tpairs,B)) As0,
berghofe@11518
  1377
           Pt.infer_derivs' (Pt.map_proof_terms
berghofe@11518
  1378
             (rename_bvars (dpairs, tpairs, Bound 0)) I) rder);
berghofe@11518
  1379
       in (map (Logic.flatten_params n) As1, As1, rder', n)
wenzelm@250
  1380
          handle TERM _ =>
wenzelm@250
  1381
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
  1382
       end;
paulson@2147
  1383
     val env = Envir.empty(Int.max(rmax,smax));
clasohm@0
  1384
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
  1385
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
  1386
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
berghofe@11518
  1387
     fun tryasms (_, _, _, []) = Seq.empty
berghofe@11518
  1388
       | tryasms (A, As, n, (t,u)::apairs) =
wenzelm@16425
  1389
          (case Seq.pull(Unify.unifiers(thy, env, (t,u)::dpairs))  of
wenzelm@16425
  1390
              NONE                   => tryasms (A, As, n+1, apairs)
wenzelm@16425
  1391
            | cell as SOME((_,tpairs),_) =>
wenzelm@16425
  1392
                Seq.it_right (addth A (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@16425
  1393
                    (Seq.make(fn()=> cell),
wenzelm@16425
  1394
                     Seq.make(fn()=> Seq.pull (tryasms(A, As, n+1, apairs)))))
clasohm@0
  1395
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
skalberg@15531
  1396
       | eres (A1::As) = tryasms(SOME A1, As, 1, Logic.assum_pairs(nlift+1,A1))
clasohm@0
  1397
     (*ordinary resolution*)
skalberg@15531
  1398
     fun res(NONE) = Seq.empty
skalberg@15531
  1399
       | res(cell as SOME((_,tpairs),_)) =
skalberg@15531
  1400
             Seq.it_right (addth NONE (newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@4270
  1401
                       (Seq.make (fn()=> cell), Seq.empty)
clasohm@0
  1402
 in  if eres_flg then eres(rev rAs)
wenzelm@16425
  1403
     else res(Seq.pull(Unify.unifiers(thy, env, dpairs)))
clasohm@0
  1404
 end;
wenzelm@7528
  1405
end;
clasohm@0
  1406
clasohm@0
  1407
clasohm@0
  1408
fun bicompose match arg i state =
clasohm@0
  1409
    bicompose_aux match (state, dest_state(state,i), false) arg;
clasohm@0
  1410
clasohm@0
  1411
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1412
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1413
fun could_bires (Hs, B, eres_flg, rule) =
clasohm@0
  1414
    let fun could_reshyp (A1::_) = exists (apl(A1,could_unify)) Hs
wenzelm@250
  1415
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@250
  1416
    in  could_unify(concl_of rule, B) andalso
wenzelm@250
  1417
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1418
    end;
clasohm@0
  1419
clasohm@0
  1420
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1421
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1422
fun biresolution match brules i state =
clasohm@0
  1423
    let val lift = lift_rule(state, i);
wenzelm@250
  1424
        val (stpairs, Bs, Bi, C) = dest_state(state,i)
wenzelm@250
  1425
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1426
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@250
  1427
        val comp = bicompose_aux match (state, (stpairs, Bs, Bi, C), true);
wenzelm@4270
  1428
        fun res [] = Seq.empty
wenzelm@250
  1429
          | res ((eres_flg, rule)::brules) =
nipkow@13642
  1430
              if !Pattern.trace_unify_fail orelse
nipkow@13642
  1431
                 could_bires (Hs, B, eres_flg, rule)
wenzelm@4270
  1432
              then Seq.make (*delay processing remainder till needed*)
skalberg@15531
  1433
                  (fn()=> SOME(comp (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1434
                               res brules))
wenzelm@250
  1435
              else res brules
wenzelm@4270
  1436
    in  Seq.flat (res brules)  end;
clasohm@0
  1437
clasohm@0
  1438
wenzelm@2509
  1439
(*** Oracles ***)
wenzelm@2509
  1440
wenzelm@16425
  1441
fun invoke_oracle_i thy1 name =
wenzelm@3812
  1442
  let
wenzelm@3812
  1443
    val oracle =
wenzelm@16425
  1444
      (case Symtab.lookup (#2 (#oracles (Theory.rep_theory thy1)), name) of
skalberg@15531
  1445
        NONE => raise THM ("Unknown oracle: " ^ name, 0, [])
skalberg@15531
  1446
      | SOME (f, _) => f);
wenzelm@3812
  1447
  in
wenzelm@16425
  1448
    fn (thy2, data) =>
wenzelm@3812
  1449
      let
wenzelm@16425
  1450
        val thy' = Theory.merge (thy1, thy2);
wenzelm@14828
  1451
        val (prop, T, maxidx) =
wenzelm@16425
  1452
          Sign.certify_term (Sign.pp thy') thy' (oracle (thy', data));
wenzelm@3812
  1453
      in
wenzelm@3812
  1454
        if T <> propT then
wenzelm@3812
  1455
          raise THM ("Oracle's result must have type prop: " ^ name, 0, [])
wenzelm@16601
  1456
        else
wenzelm@16601
  1457
          Thm {thy_ref = Theory.self_ref thy',
berghofe@11518
  1458
            der = (true, Pt.oracle_proof name prop),
wenzelm@3812
  1459
            maxidx = maxidx,
wenzelm@16656
  1460
            shyps = may_insert_term_sorts thy' prop [],
wenzelm@16425
  1461
            hyps = [],
berghofe@13658
  1462
            tpairs = [],
wenzelm@16601
  1463
            prop = prop}
wenzelm@3812
  1464
      end
wenzelm@3812
  1465
  end;
wenzelm@3812
  1466
wenzelm@15672
  1467
fun invoke_oracle thy =
wenzelm@16425
  1468
  invoke_oracle_i thy o NameSpace.intern (Theory.oracle_space thy);
wenzelm@15672
  1469
clasohm@0
  1470
end;
paulson@1503
  1471
wenzelm@6089
  1472
structure BasicThm: BASIC_THM = Thm;
wenzelm@6089
  1473
open BasicThm;