src/Pure/thm.ML
author berghofe
Wed Oct 31 19:37:04 2001 +0100 (2001-10-31)
changeset 11998 b14e7686ce84
parent 11692 6d15ae4b1123
child 12500 0a6667d65e9b
permissions -rw-r--r--
- enter_thmx -> enter_thms
- improved naming of theorems: enter_thms now takes functions pre_name and post_name
as arguments
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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 core of Isabelle's Meta Logic: certified types and terms, meta
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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 -> {sign: Sign.sg, T: typ}
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  val typ_of            : ctyp -> typ
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  val ctyp_of           : Sign.sg -> typ -> ctyp
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  val read_ctyp         : Sign.sg -> 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 -> {sign: Sign.sg, t: term, T: typ, maxidx: int}
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  val crep_cterm        : cterm -> {sign: Sign.sg, t: term, T: ctyp, maxidx: int}
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  val sign_of_cterm	: cterm -> Sign.sg
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  val term_of           : cterm -> term
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  val cterm_of          : Sign.sg -> term -> cterm
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  val ctyp_of_term      : cterm -> ctyp
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  val read_cterm        : Sign.sg -> string * typ -> cterm
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  val cterm_fun         : (term -> term) -> (cterm -> cterm)
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  val adjust_maxidx     : cterm -> cterm
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  val read_def_cterm    :
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    Sign.sg * (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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    Sign.sg * (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 -> {sign: Sign.sg, der: bool * Proofterm.proof, maxidx: int,
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                                  shyps: sort list, hyps: term list, 
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                                  prop: term}
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  val crep_thm          : thm -> {sign: Sign.sg, der: bool * Proofterm.proof, maxidx: int,
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                                  shyps: sort list, hyps: 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 sign_of_thm       : thm -> Sign.sg
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  val transfer_sg	: Sign.sg -> thm -> thm
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  val transfer		: theory -> thm -> thm
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  val tpairs_of         : thm -> (term * term) list
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  val prems_of          : thm -> term list
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  val nprems_of         : thm -> int
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  val concl_of          : thm -> term
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  val cprop_of          : thm -> cterm
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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         : 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 implies_intr_hyps : thm -> thm
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  val flexflex_rule     : thm -> thm Seq.seq
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  val instantiate       :
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    (indexname * ctyp) list * (cterm * cterm) list -> thm -> thm
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  val trivial           : cterm -> thm
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  val class_triv        : Sign.sg -> class -> thm
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  val varifyT           : thm -> thm
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  val varifyT'          : string list -> thm -> thm
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  val freezeT           : thm -> thm
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  val dest_state        : thm * int ->
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    (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 ->
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    int -> thm -> thm Seq.seq
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  val biresolution      : bool -> (bool * thm) list ->
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    int -> thm -> thm Seq.seq
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  val invoke_oracle     : theory -> xstring -> Sign.sg * 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_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 ->
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    (indexname * ctyp) list * (cterm * cterm) list
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  val cterm_first_order_match : cterm * cterm ->
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    (indexname * ctyp) list * (cterm * cterm) list
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  val cterm_incr_indexes : int -> cterm -> cterm
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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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(** certified types **)
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(*certified typs under a signature*)
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datatype ctyp = Ctyp of {sign_ref: Sign.sg_ref, T: typ};
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fun rep_ctyp (Ctyp {sign_ref, T}) = {sign = Sign.deref sign_ref, T = T};
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fun typ_of (Ctyp {T, ...}) = T;
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fun ctyp_of sign T =
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  Ctyp {sign_ref = Sign.self_ref sign, T = Sign.certify_typ sign T};
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fun read_ctyp sign s =
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  Ctyp {sign_ref = Sign.self_ref sign, T = Sign.read_typ (sign, K None) s};
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(** certified terms **)
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(*certified terms under a signature, with checked typ and maxidx of Vars*)
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datatype cterm = Cterm of {sign_ref: Sign.sg_ref, t: term, T: typ, maxidx: int};
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fun rep_cterm (Cterm {sign_ref, t, T, maxidx}) =
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  {sign = Sign.deref sign_ref, t = t, T = T, maxidx = maxidx};
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fun crep_cterm (Cterm {sign_ref, t, T, maxidx}) =
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  {sign = Sign.deref sign_ref, t = t, T = Ctyp {sign_ref = sign_ref, T = T},
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    maxidx = maxidx};
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fun sign_of_cterm (Cterm {sign_ref, ...}) = Sign.deref sign_ref;
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fun term_of (Cterm {t, ...}) = t;
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fun ctyp_of_term (Cterm {sign_ref, T, ...}) = Ctyp {sign_ref = sign_ref, T = T};
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(*create a cterm by checking a "raw" term with respect to a signature*)
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fun cterm_of sign tm =
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  let val (t, T, maxidx) = Sign.certify_term sign tm
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  in  Cterm {sign_ref = Sign.self_ref sign, t = t, T = T, maxidx = maxidx}
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  end;
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fun cterm_fun f (Cterm {sign_ref, t, ...}) = cterm_of (Sign.deref sign_ref) (f t);
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exception CTERM of string;
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(*Destruct application in cterms*)
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fun dest_comb (Cterm {sign_ref, T, maxidx, t = A $ B}) =
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      let 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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                        | _ => error "Function type expected in dest_comb";
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      in
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      (Cterm {sign_ref=sign_ref, maxidx=maxidx, t=A, T=typeA},
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       Cterm {sign_ref=sign_ref, maxidx=maxidx, t=B, T=typeB})
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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 {sign_ref, T as Type("fun",[_,S]), maxidx, t=Abs(x,ty,M)}) = 
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      let val (y,N) = variant_abs (if_none a x,ty,M)
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      in (Cterm {sign_ref = sign_ref, T = ty, maxidx = 0, t = Free(y,ty)},
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          Cterm {sign_ref = sign_ref, T = S, maxidx = maxidx, t = N})
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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 {sign_ref, T, t, maxidx, ...}) =
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  if maxidx = ~1 then ct 
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  else  Cterm {sign_ref = sign_ref, T = T, maxidx = maxidx_of_term t, t = t};
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(*Form cterm out of a function and an argument*)
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fun capply (Cterm {t=f, sign_ref=sign_ref1, T=Type("fun",[dty,rty]), maxidx=maxidx1})
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           (Cterm {t=x, sign_ref=sign_ref2, T, maxidx=maxidx2}) =
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      if T = dty then
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        Cterm{t=Sign.nodup_vars (f$x), sign_ref=Sign.merge_refs(sign_ref1,sign_ref2), T=rty,
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          maxidx=Int.max(maxidx1, maxidx2)}
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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 (Cterm {t=Free(a,ty), sign_ref=sign_ref1, T=T1, maxidx=maxidx1})
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         (Cterm {t=t2, sign_ref=sign_ref2, T=T2, maxidx=maxidx2}) =
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      Cterm {t=Sign.nodup_vars (absfree(a,ty,t2)), sign_ref=Sign.merge_refs(sign_ref1,sign_ref2),
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             T = ty --> T2, maxidx=Int.max(maxidx1, maxidx2)}
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  | cabs _ _ = raise CTERM "cabs: first arg is not a free variable";
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(*Matching of cterms*)
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fun gen_cterm_match mtch
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      (Cterm {sign_ref = sign_ref1, maxidx = maxidx1, t = t1, ...},
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       Cterm {sign_ref = sign_ref2, maxidx = maxidx2, t = t2, ...}) =
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  let
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    val sign_ref = Sign.merge_refs (sign_ref1, sign_ref2);
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    val tsig = Sign.tsig_of (Sign.deref sign_ref);
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    val (Tinsts, tinsts) = mtch tsig (t1, t2);
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    val maxidx = Int.max (maxidx1, maxidx2);
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    val vars = map dest_Var (term_vars t1);
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    fun mk_cTinsts (ixn, T) = (ixn, Ctyp {sign_ref = sign_ref, T = T});
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    fun mk_ctinsts (ixn, t) =
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      let val T = typ_subst_TVars Tinsts (the (assoc (vars, ixn)))
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      in
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        (Cterm {sign_ref = sign_ref, maxidx = maxidx, T = T, t = Var (ixn, T)},
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         Cterm {sign_ref = sign_ref, maxidx = maxidx, T = T, t = t})
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      end;
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  in (map mk_cTinsts Tinsts, map mk_ctinsts tinsts) end;
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val cterm_match = gen_cterm_match Pattern.match;
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val cterm_first_order_match = gen_cterm_match Pattern.first_order_match;
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(*Incrementing indexes*)
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fun cterm_incr_indexes i (ct as Cterm {sign_ref, maxidx, t, T}) =
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  if i < 0 then raise CTERM "negative increment" else 
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  if i = 0 then ct else
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    Cterm {sign_ref = sign_ref, maxidx = maxidx + i,
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      t = Logic.incr_indexes ([], i) t, T = Term.incr_tvar i T};
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(** read cterms **)   (*exception ERROR*)
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(*read terms, infer types, certify terms*)
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fun read_def_cterms (sign, types, sorts) used freeze sTs =
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  let
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    val (ts', tye) = Sign.read_def_terms (sign, types, sorts) used freeze sTs;
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    val cts = map (cterm_of sign) ts'
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      handle TYPE (msg, _, _) => error msg
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           | TERM (msg, _) => error msg;
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  in (cts, tye) end;
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(*read term, infer types, certify term*)
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fun read_def_cterm args used freeze aT =
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  let val ([ct],tye) = read_def_cterms args used freeze [aT]
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  in (ct,tye) end;
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fun read_cterm sign = #1 o read_def_cterm (sign, K None, K None) [] true;
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(*tags provide additional comment, apart from the axiom/theorem name*)
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type tag = string * string list;
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(*** Meta theorems ***)
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structure Pt = Proofterm;
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datatype thm = Thm of
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 {sign_ref: Sign.sg_ref,       (*mutable reference to signature*)
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  der: bool * Pt.proof,        (*derivation*)
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  maxidx: int,                 (*maximum index of any Var or TVar*)
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  shyps: sort list,            (*sort hypotheses*)
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  hyps: term list,             (*hypotheses*)
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  prop: term};                 (*conclusion*)
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fun rep_thm (Thm {sign_ref, der, maxidx, shyps, hyps, prop}) =
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  {sign = Sign.deref sign_ref, der = der, maxidx = maxidx,
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    shyps = shyps, hyps = hyps, prop = prop};
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(*Version of rep_thm returning cterms instead of terms*)
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fun crep_thm (Thm {sign_ref, der, maxidx, shyps, hyps, prop}) =
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  let fun ctermf max t = Cterm{sign_ref=sign_ref, t=t, T=propT, maxidx=max};
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  in {sign = Sign.deref sign_ref, der = der, maxidx = maxidx, shyps = shyps,
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      hyps = map (ctermf ~1) hyps,
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      prop = ctermf maxidx prop}
clasohm@1517
   301
  end;
clasohm@1517
   302
wenzelm@387
   303
(*errors involving theorems*)
clasohm@0
   304
exception THM of string * int * thm list;
clasohm@0
   305
wenzelm@6089
   306
(*attributes subsume any kind of rules or addXXXs modifiers*)
wenzelm@6089
   307
type 'a attribute = 'a * thm -> 'a * thm;
wenzelm@6089
   308
wenzelm@6089
   309
fun no_attributes x = (x, []);
wenzelm@6089
   310
fun apply_attributes (x_th, atts) = Library.apply atts x_th;
wenzelm@6089
   311
fun applys_attributes (x_ths, atts) = foldl_map (Library.apply atts) x_ths;
wenzelm@6089
   312
wenzelm@3994
   313
fun eq_thm (th1, th2) =
wenzelm@3994
   314
  let
berghofe@11518
   315
    val {sign = sg1, shyps = shyps1, hyps = hyps1, prop = prop1, ...} =
wenzelm@9031
   316
      rep_thm th1;
berghofe@11518
   317
    val {sign = sg2, shyps = shyps2, hyps = hyps2, prop = prop2, ...} =
wenzelm@9031
   318
      rep_thm th2;
wenzelm@3994
   319
  in
wenzelm@9031
   320
    Sign.joinable (sg1, sg2) andalso
wenzelm@3994
   321
    eq_set_sort (shyps1, shyps2) andalso
wenzelm@3994
   322
    aconvs (hyps1, hyps2) andalso
wenzelm@3994
   323
    prop1 aconv prop2
wenzelm@3994
   324
  end;
wenzelm@387
   325
wenzelm@3967
   326
fun sign_of_thm (Thm {sign_ref, ...}) = Sign.deref sign_ref;
clasohm@0
   327
wenzelm@387
   328
(*merge signatures of two theorems; raise exception if incompatible*)
wenzelm@3967
   329
fun merge_thm_sgs
wenzelm@3967
   330
    (th1 as Thm {sign_ref = sgr1, ...}, th2 as Thm {sign_ref = sgr2, ...}) =
wenzelm@3967
   331
  Sign.merge_refs (sgr1, sgr2) handle TERM (msg, _) => raise THM (msg, 0, [th1, th2]);
wenzelm@387
   332
wenzelm@3967
   333
(*transfer thm to super theory (non-destructive)*)
wenzelm@4254
   334
fun transfer_sg sign' thm =
wenzelm@3895
   335
  let
wenzelm@3967
   336
    val Thm {sign_ref, der, maxidx, shyps, hyps, prop} = thm;
wenzelm@3967
   337
    val sign = Sign.deref sign_ref;
wenzelm@3895
   338
  in
wenzelm@4254
   339
    if Sign.eq_sg (sign, sign') then thm
wenzelm@4254
   340
    else if Sign.subsig (sign, sign') then
wenzelm@3967
   341
      Thm {sign_ref = Sign.self_ref sign', der = der, maxidx = maxidx,
wenzelm@3895
   342
        shyps = shyps, hyps = hyps, prop = prop}
wenzelm@3895
   343
    else raise THM ("transfer: not a super theory", 0, [thm])
wenzelm@3895
   344
  end;
wenzelm@387
   345
wenzelm@6390
   346
val transfer = transfer_sg o Theory.sign_of;
wenzelm@4254
   347
wenzelm@387
   348
(*maps object-rule to tpairs*)
wenzelm@387
   349
fun tpairs_of (Thm {prop, ...}) = #1 (Logic.strip_flexpairs prop);
wenzelm@387
   350
wenzelm@387
   351
(*maps object-rule to premises*)
wenzelm@387
   352
fun prems_of (Thm {prop, ...}) =
wenzelm@387
   353
  Logic.strip_imp_prems (Logic.skip_flexpairs prop);
clasohm@0
   354
clasohm@0
   355
(*counts premises in a rule*)
wenzelm@387
   356
fun nprems_of (Thm {prop, ...}) =
wenzelm@387
   357
  Logic.count_prems (Logic.skip_flexpairs prop, 0);
clasohm@0
   358
wenzelm@8299
   359
fun major_prem_of thm =
wenzelm@8299
   360
  (case prems_of thm of
wenzelm@11692
   361
    prem :: _ => Logic.strip_assums_concl prem
wenzelm@8299
   362
  | [] => raise THM ("major_prem_of: rule with no premises", 0, [thm]));
wenzelm@8299
   363
wenzelm@7534
   364
fun no_prems thm = nprems_of thm = 0;
wenzelm@7534
   365
wenzelm@387
   366
(*maps object-rule to conclusion*)
wenzelm@387
   367
fun concl_of (Thm {prop, ...}) = Logic.strip_imp_concl prop;
clasohm@0
   368
wenzelm@387
   369
(*the statement of any thm is a cterm*)
wenzelm@3967
   370
fun cprop_of (Thm {sign_ref, maxidx, prop, ...}) =
wenzelm@3967
   371
  Cterm {sign_ref = sign_ref, maxidx = maxidx, T = propT, t = prop};
lcp@229
   372
wenzelm@387
   373
clasohm@0
   374
wenzelm@1238
   375
(** sort contexts of theorems **)
wenzelm@1238
   376
wenzelm@1238
   377
(* basic utils *)
wenzelm@1238
   378
wenzelm@2163
   379
(*accumulate sorts suppressing duplicates; these are coded low levelly
wenzelm@1238
   380
  to improve efficiency a bit*)
wenzelm@1238
   381
wenzelm@1238
   382
fun add_typ_sorts (Type (_, Ts), Ss) = add_typs_sorts (Ts, Ss)
paulson@2177
   383
  | add_typ_sorts (TFree (_, S), Ss) = ins_sort(S,Ss)
paulson@2177
   384
  | add_typ_sorts (TVar (_, S), Ss) = ins_sort(S,Ss)
wenzelm@1238
   385
and add_typs_sorts ([], Ss) = Ss
wenzelm@1238
   386
  | add_typs_sorts (T :: Ts, Ss) = add_typs_sorts (Ts, add_typ_sorts (T, Ss));
wenzelm@1238
   387
wenzelm@1238
   388
fun add_term_sorts (Const (_, T), Ss) = add_typ_sorts (T, Ss)
wenzelm@1238
   389
  | add_term_sorts (Free (_, T), Ss) = add_typ_sorts (T, Ss)
wenzelm@1238
   390
  | add_term_sorts (Var (_, T), Ss) = add_typ_sorts (T, Ss)
wenzelm@1238
   391
  | add_term_sorts (Bound _, Ss) = Ss
paulson@2177
   392
  | add_term_sorts (Abs (_,T,t), Ss) = add_term_sorts (t, add_typ_sorts (T,Ss))
wenzelm@1238
   393
  | add_term_sorts (t $ u, Ss) = add_term_sorts (t, add_term_sorts (u, Ss));
wenzelm@1238
   394
wenzelm@1238
   395
fun add_terms_sorts ([], Ss) = Ss
paulson@2177
   396
  | add_terms_sorts (t::ts, Ss) = add_terms_sorts (ts, add_term_sorts (t,Ss));
wenzelm@1238
   397
berghofe@8407
   398
fun env_codT (Envir.Envir {iTs, ...}) = map snd (Vartab.dest iTs);
wenzelm@1258
   399
berghofe@8407
   400
fun add_env_sorts (Envir.Envir {iTs, asol, ...}, Ss) =
berghofe@8407
   401
  Vartab.foldl (add_term_sorts o swap o apsnd snd)
berghofe@8407
   402
    (Vartab.foldl (add_typ_sorts o swap o apsnd snd) (Ss, iTs), asol);
wenzelm@1258
   403
berghofe@10416
   404
fun add_insts_sorts ((iTs, is), Ss) =
berghofe@10416
   405
  add_typs_sorts (map snd iTs, add_terms_sorts (map snd is, Ss));
berghofe@10416
   406
wenzelm@1238
   407
fun add_thm_sorts (Thm {hyps, prop, ...}, Ss) =
wenzelm@1238
   408
  add_terms_sorts (hyps, add_term_sorts (prop, Ss));
wenzelm@1238
   409
wenzelm@1238
   410
fun add_thms_shyps ([], Ss) = Ss
wenzelm@1238
   411
  | add_thms_shyps (Thm {shyps, ...} :: ths, Ss) =
wenzelm@7642
   412
      add_thms_shyps (ths, union_sort (shyps, Ss));
wenzelm@1238
   413
wenzelm@1238
   414
wenzelm@1238
   415
(*get 'dangling' sort constraints of a thm*)
wenzelm@1238
   416
fun extra_shyps (th as Thm {shyps, ...}) =
wenzelm@7642
   417
  Term.rems_sort (shyps, add_thm_sorts (th, []));
wenzelm@1238
   418
wenzelm@1238
   419
wenzelm@1238
   420
(* fix_shyps *)
wenzelm@1238
   421
wenzelm@7642
   422
fun all_sorts_nonempty sign_ref = is_some (Sign.univ_witness (Sign.deref sign_ref));
wenzelm@7642
   423
wenzelm@1238
   424
(*preserve sort contexts of rule premises and substituted types*)
wenzelm@7642
   425
fun fix_shyps thms Ts (thm as Thm {sign_ref, der, maxidx, hyps, prop, ...}) =
wenzelm@7642
   426
  Thm
wenzelm@7642
   427
   {sign_ref = sign_ref,
wenzelm@7642
   428
    der = der,             (*no new derivation, as other rules call this*)
wenzelm@7642
   429
    maxidx = maxidx,
wenzelm@7642
   430
    shyps =
wenzelm@7642
   431
      if all_sorts_nonempty sign_ref then []
wenzelm@7642
   432
      else add_thm_sorts (thm, add_typs_sorts (Ts, add_thms_shyps (thms, []))),
wenzelm@7642
   433
    hyps = hyps, prop = prop}
wenzelm@1238
   434
wenzelm@1238
   435
wenzelm@7642
   436
(* strip_shyps *)
wenzelm@1238
   437
wenzelm@7642
   438
(*remove extra sorts that are non-empty by virtue of type signature information*)
wenzelm@7642
   439
fun strip_shyps (thm as Thm {shyps = [], ...}) = thm
wenzelm@7642
   440
  | strip_shyps (thm as Thm {sign_ref, der, maxidx, shyps, hyps, prop}) =
wenzelm@7642
   441
      let
wenzelm@7642
   442
        val sign = Sign.deref sign_ref;
wenzelm@1238
   443
wenzelm@7642
   444
        val present_sorts = add_thm_sorts (thm, []);
wenzelm@7642
   445
        val extra_shyps = Term.rems_sort (shyps, present_sorts);
wenzelm@7642
   446
        val witnessed_shyps = Sign.witness_sorts sign present_sorts extra_shyps;
wenzelm@7642
   447
      in
wenzelm@7642
   448
        Thm {sign_ref = sign_ref, der = der, maxidx = maxidx,
wenzelm@7642
   449
             shyps = Term.rems_sort (shyps, map #2 witnessed_shyps),
wenzelm@7642
   450
             hyps = hyps, prop = prop}
wenzelm@7642
   451
      end;
wenzelm@1238
   452
wenzelm@1238
   453
wenzelm@1238
   454
paulson@1529
   455
(** Axioms **)
wenzelm@387
   456
wenzelm@387
   457
(*look up the named axiom in the theory*)
wenzelm@3812
   458
fun get_axiom theory raw_name =
wenzelm@387
   459
  let
wenzelm@4847
   460
    val name = Sign.intern (Theory.sign_of theory) Theory.axiomK raw_name;
wenzelm@4847
   461
wenzelm@4847
   462
    fun get_ax [] = None
paulson@1529
   463
      | get_ax (thy :: thys) =
wenzelm@4847
   464
          let val {sign, axioms, ...} = Theory.rep_theory thy in
wenzelm@4847
   465
            (case Symtab.lookup (axioms, name) of
wenzelm@4847
   466
              Some t =>
wenzelm@4847
   467
                Some (fix_shyps [] []
wenzelm@4847
   468
                  (Thm {sign_ref = Sign.self_ref sign,
berghofe@11518
   469
                    der = Pt.infer_derivs' I
berghofe@11518
   470
                      (false, Pt.axm_proof name t),
wenzelm@4847
   471
                    maxidx = maxidx_of_term t,
wenzelm@4847
   472
                    shyps = [], 
wenzelm@4847
   473
                    hyps = [], 
wenzelm@4847
   474
                    prop = t}))
wenzelm@4847
   475
            | None => get_ax thys)
paulson@1529
   476
          end;
wenzelm@387
   477
  in
wenzelm@4847
   478
    (case get_ax (theory :: Theory.ancestors_of theory) of
wenzelm@4847
   479
      Some thm => thm
wenzelm@4847
   480
    | None => raise THEORY ("No axiom " ^ quote name, [theory]))
wenzelm@387
   481
  end;
wenzelm@387
   482
wenzelm@6368
   483
fun def_name name = name ^ "_def";
wenzelm@6368
   484
fun get_def thy = get_axiom thy o def_name;
wenzelm@4847
   485
paulson@1529
   486
wenzelm@776
   487
(*return additional axioms of this theory node*)
wenzelm@776
   488
fun axioms_of thy =
wenzelm@776
   489
  map (fn (s, _) => (s, get_axiom thy s))
wenzelm@6390
   490
    (Symtab.dest (#axioms (Theory.rep_theory thy)));
wenzelm@776
   491
wenzelm@6089
   492
wenzelm@6089
   493
(* name and tags -- make proof objects more readable *)
wenzelm@6089
   494
berghofe@11518
   495
fun get_name_tags (Thm {prop, der = (_, prf), ...}) = Pt.get_name_tags prop prf;
wenzelm@4018
   496
berghofe@11518
   497
fun put_name_tags x (Thm {sign_ref, der = (ora, prf), maxidx, shyps, hyps, prop}) =
berghofe@11518
   498
  Thm {sign_ref = sign_ref,
berghofe@11518
   499
    der = (ora, Pt.thm_proof (Sign.deref sign_ref) x hyps prop prf),
berghofe@11518
   500
    maxidx = maxidx, shyps = shyps, hyps = hyps, prop = prop};
wenzelm@6089
   501
wenzelm@6089
   502
val name_of_thm = #1 o get_name_tags;
wenzelm@6089
   503
val tags_of_thm = #2 o get_name_tags;
wenzelm@6089
   504
wenzelm@6089
   505
fun name_thm (name, thm) = put_name_tags (name, tags_of_thm thm) thm;
clasohm@0
   506
clasohm@0
   507
paulson@1529
   508
(*Compression of theorems -- a separate rule, not integrated with the others,
paulson@1529
   509
  as it could be slow.*)
wenzelm@3967
   510
fun compress (Thm {sign_ref, der, maxidx, shyps, hyps, prop}) = 
wenzelm@3967
   511
    Thm {sign_ref = sign_ref, 
wenzelm@2386
   512
         der = der,     (*No derivation recorded!*)
wenzelm@2386
   513
         maxidx = maxidx,
wenzelm@2386
   514
         shyps = shyps, 
wenzelm@2386
   515
         hyps = map Term.compress_term hyps, 
wenzelm@2386
   516
         prop = Term.compress_term prop};
wenzelm@564
   517
wenzelm@387
   518
wenzelm@2509
   519
paulson@1529
   520
(*** Meta rules ***)
clasohm@0
   521
paulson@2147
   522
(*Check that term does not contain same var with different typing/sorting.
paulson@2147
   523
  If this check must be made, recalculate maxidx in hope of preventing its
paulson@2147
   524
  recurrence.*)
wenzelm@8291
   525
fun nodup_vars (thm as Thm{sign_ref, der, maxidx, shyps, hyps, prop}) s =
wenzelm@8296
   526
  Thm {sign_ref = sign_ref, 
wenzelm@2386
   527
         der = der,     
wenzelm@2386
   528
         maxidx = maxidx_of_term prop,
wenzelm@2386
   529
         shyps = shyps, 
wenzelm@2386
   530
         hyps = hyps, 
wenzelm@8296
   531
         prop = Sign.nodup_vars prop}
paulson@2147
   532
  handle TYPE(msg,Ts,ts) => raise TYPE(s^": "^msg,Ts,ts);
nipkow@1495
   533
wenzelm@8291
   534
wenzelm@1220
   535
(** 'primitive' rules **)
wenzelm@1220
   536
wenzelm@1220
   537
(*discharge all assumptions t from ts*)
clasohm@0
   538
val disch = gen_rem (op aconv);
clasohm@0
   539
wenzelm@1220
   540
(*The assumption rule A|-A in a theory*)
wenzelm@5344
   541
fun assume raw_ct : thm =
wenzelm@5344
   542
  let val ct as Cterm {sign_ref, t=prop, T, maxidx} = adjust_maxidx raw_ct
wenzelm@250
   543
  in  if T<>propT then
wenzelm@250
   544
        raise THM("assume: assumptions must have type prop", 0, [])
clasohm@0
   545
      else if maxidx <> ~1 then
wenzelm@250
   546
        raise THM("assume: assumptions may not contain scheme variables",
wenzelm@250
   547
                  maxidx, [])
wenzelm@3967
   548
      else Thm{sign_ref   = sign_ref,
berghofe@11518
   549
               der    = Pt.infer_derivs' I (false, Pt.Hyp prop),
wenzelm@2386
   550
               maxidx = ~1, 
wenzelm@2386
   551
               shyps  = add_term_sorts(prop,[]), 
wenzelm@2386
   552
               hyps   = [prop], 
wenzelm@2386
   553
               prop   = prop}
clasohm@0
   554
  end;
clasohm@0
   555
wenzelm@1220
   556
(*Implication introduction
wenzelm@3529
   557
    [A]
wenzelm@3529
   558
     :
wenzelm@3529
   559
     B
wenzelm@1220
   560
  -------
wenzelm@1220
   561
  A ==> B
wenzelm@1220
   562
*)
berghofe@10416
   563
fun implies_intr cA (thB as Thm{sign_ref,der,maxidx,hyps,shyps,prop}) : thm =
wenzelm@3967
   564
  let val Cterm {sign_ref=sign_refA, t=A, T, maxidx=maxidxA} = cA
clasohm@0
   565
  in  if T<>propT then
wenzelm@250
   566
        raise THM("implies_intr: assumptions must have type prop", 0, [thB])
berghofe@10416
   567
      else
berghofe@10416
   568
         Thm{sign_ref = Sign.merge_refs (sign_ref,sign_refA),  
berghofe@11518
   569
             der = Pt.infer_derivs' (Pt.implies_intr_proof A) der,
wenzelm@2386
   570
             maxidx = Int.max(maxidxA, maxidx),
berghofe@10416
   571
             shyps = add_term_sorts (A, shyps),
wenzelm@2386
   572
             hyps = disch(hyps,A),
berghofe@10416
   573
             prop = implies$A$prop}
clasohm@0
   574
      handle TERM _ =>
clasohm@0
   575
        raise THM("implies_intr: incompatible signatures", 0, [thB])
clasohm@0
   576
  end;
clasohm@0
   577
paulson@1529
   578
wenzelm@1220
   579
(*Implication elimination
wenzelm@1220
   580
  A ==> B    A
wenzelm@1220
   581
  ------------
wenzelm@1220
   582
        B
wenzelm@1220
   583
*)
clasohm@0
   584
fun implies_elim thAB thA : thm =
berghofe@10416
   585
    let val Thm{maxidx=maxA, der=derA, hyps=hypsA, shyps=shypsA, prop=propA, ...} = thA
berghofe@10416
   586
        and Thm{der, maxidx, hyps, shyps, prop, ...} = thAB;
wenzelm@250
   587
        fun err(a) = raise THM("implies_elim: "^a, 0, [thAB,thA])
clasohm@0
   588
    in  case prop of
wenzelm@250
   589
            imp$A$B =>
wenzelm@250
   590
                if imp=implies andalso  A aconv propA
berghofe@10416
   591
                then
berghofe@10416
   592
                  Thm{sign_ref= merge_thm_sgs(thAB,thA),
berghofe@11612
   593
                      der = Pt.infer_derivs (curry Pt.%%) der derA,
berghofe@10416
   594
                      maxidx = Int.max(maxA,maxidx),
berghofe@10416
   595
                      shyps = union_sort (shypsA, shyps),
berghofe@10416
   596
                      hyps = union_term(hypsA,hyps),  (*dups suppressed*)
berghofe@10416
   597
                      prop = B}
wenzelm@250
   598
                else err("major premise")
wenzelm@250
   599
          | _ => err("major premise")
clasohm@0
   600
    end;
wenzelm@250
   601
wenzelm@1220
   602
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@1220
   603
    A
wenzelm@1220
   604
  -----
wenzelm@1220
   605
  !!x.A
wenzelm@1220
   606
*)
wenzelm@3967
   607
fun forall_intr cx (th as Thm{sign_ref,der,maxidx,hyps,prop,...}) =
lcp@229
   608
  let val x = term_of cx;
wenzelm@1238
   609
      fun result(a,T) = fix_shyps [th] []
wenzelm@3967
   610
        (Thm{sign_ref = sign_ref, 
berghofe@11518
   611
             der = Pt.infer_derivs' (Pt.forall_intr_proof x a) der,
wenzelm@2386
   612
             maxidx = maxidx,
wenzelm@2386
   613
             shyps = [],
wenzelm@2386
   614
             hyps = hyps,
wenzelm@2386
   615
             prop = all(T) $ Abs(a, T, abstract_over (x,prop))})
clasohm@0
   616
  in  case x of
wenzelm@250
   617
        Free(a,T) =>
wenzelm@250
   618
          if exists (apl(x, Logic.occs)) hyps
wenzelm@250
   619
          then  raise THM("forall_intr: variable free in assumptions", 0, [th])
wenzelm@250
   620
          else  result(a,T)
clasohm@0
   621
      | Var((a,_),T) => result(a,T)
clasohm@0
   622
      | _ => raise THM("forall_intr: not a variable", 0, [th])
clasohm@0
   623
  end;
clasohm@0
   624
wenzelm@1220
   625
(*Forall elimination
wenzelm@1220
   626
  !!x.A
wenzelm@1220
   627
  ------
wenzelm@1220
   628
  A[t/x]
wenzelm@1220
   629
*)
wenzelm@3967
   630
fun forall_elim ct (th as Thm{sign_ref,der,maxidx,hyps,prop,...}) : thm =
wenzelm@3967
   631
  let val Cterm {sign_ref=sign_reft, t, T, maxidx=maxt} = ct
clasohm@0
   632
  in  case prop of
wenzelm@2386
   633
        Const("all",Type("fun",[Type("fun",[qary,_]),_])) $ A =>
wenzelm@2386
   634
          if T<>qary then
wenzelm@2386
   635
              raise THM("forall_elim: type mismatch", 0, [th])
wenzelm@2386
   636
          else let val thm = fix_shyps [th] []
wenzelm@3967
   637
                    (Thm{sign_ref= Sign.merge_refs(sign_ref,sign_reft),
berghofe@11612
   638
                         der = Pt.infer_derivs' (Pt.% o rpair (Some t)) der,
wenzelm@2386
   639
                         maxidx = Int.max(maxidx, maxt),
wenzelm@2386
   640
                         shyps = [],
wenzelm@2386
   641
                         hyps = hyps,  
wenzelm@2386
   642
                         prop = betapply(A,t)})
wenzelm@2386
   643
               in if maxt >= 0 andalso maxidx >= 0
wenzelm@8291
   644
                  then nodup_vars thm "forall_elim" 
wenzelm@2386
   645
                  else thm (*no new Vars: no expensive check!*)
wenzelm@2386
   646
               end
paulson@2147
   647
      | _ => raise THM("forall_elim: not quantified", 0, [th])
clasohm@0
   648
  end
clasohm@0
   649
  handle TERM _ =>
wenzelm@250
   650
         raise THM("forall_elim: incompatible signatures", 0, [th]);
clasohm@0
   651
clasohm@0
   652
wenzelm@1220
   653
(* Equality *)
clasohm@0
   654
clasohm@0
   655
(*The reflexivity rule: maps  t   to the theorem   t==t   *)
wenzelm@250
   656
fun reflexive ct =
wenzelm@3967
   657
  let val Cterm {sign_ref, t, T, maxidx} = ct
berghofe@10416
   658
  in Thm{sign_ref= sign_ref, 
berghofe@11518
   659
         der = Pt.infer_derivs' I (false, Pt.reflexive),
berghofe@10416
   660
         shyps = add_term_sorts (t, []),
berghofe@10416
   661
         hyps = [], 
berghofe@10416
   662
         maxidx = maxidx,
berghofe@10416
   663
         prop = Logic.mk_equals(t,t)}
clasohm@0
   664
  end;
clasohm@0
   665
clasohm@0
   666
(*The symmetry rule
wenzelm@1220
   667
  t==u
wenzelm@1220
   668
  ----
wenzelm@1220
   669
  u==t
wenzelm@1220
   670
*)
wenzelm@3967
   671
fun symmetric (th as Thm{sign_ref,der,maxidx,shyps,hyps,prop}) =
clasohm@0
   672
  case prop of
berghofe@11518
   673
      (eq as Const("==", Type (_, [T, _]))) $ t $ u =>
wenzelm@1238
   674
        (*no fix_shyps*)
wenzelm@3967
   675
          Thm{sign_ref = sign_ref,
berghofe@11518
   676
              der = Pt.infer_derivs' Pt.symmetric der,
wenzelm@2386
   677
              maxidx = maxidx,
wenzelm@2386
   678
              shyps = shyps,
wenzelm@2386
   679
              hyps = hyps,
wenzelm@2386
   680
              prop = eq$u$t}
clasohm@0
   681
    | _ => raise THM("symmetric", 0, [th]);
clasohm@0
   682
clasohm@0
   683
(*The transitive rule
wenzelm@1220
   684
  t1==u    u==t2
wenzelm@1220
   685
  --------------
wenzelm@1220
   686
      t1==t2
wenzelm@1220
   687
*)
clasohm@0
   688
fun transitive th1 th2 =
berghofe@10416
   689
  let val Thm{der=der1, maxidx=max1, hyps=hyps1, shyps=shyps1, prop=prop1,...} = th1
berghofe@10416
   690
      and Thm{der=der2, maxidx=max2, hyps=hyps2, shyps=shyps2, prop=prop2,...} = th2;
clasohm@0
   691
      fun err(msg) = raise THM("transitive: "^msg, 0, [th1,th2])
clasohm@0
   692
  in case (prop1,prop2) of
berghofe@11518
   693
       ((eq as Const("==", Type (_, [T, _]))) $ t1 $ u, Const("==",_) $ u' $ t2) =>
nipkow@1634
   694
          if not (u aconv u') then err"middle term"
nipkow@1634
   695
          else let val thm =      
berghofe@10416
   696
                 Thm{sign_ref= merge_thm_sgs(th1,th2), 
berghofe@11518
   697
                     der = Pt.infer_derivs (Pt.transitive u T) der1 der2,
paulson@2147
   698
                     maxidx = Int.max(max1,max2), 
berghofe@10416
   699
                     shyps = union_sort (shyps1, shyps2),
wenzelm@2386
   700
                     hyps = union_term(hyps1,hyps2),
berghofe@10416
   701
                     prop = eq$t1$t2}
paulson@2139
   702
                 in if max1 >= 0 andalso max2 >= 0
wenzelm@8291
   703
                    then nodup_vars thm "transitive" 
paulson@2147
   704
                    else thm (*no new Vars: no expensive check!*)
paulson@2139
   705
                 end
clasohm@0
   706
     | _ =>  err"premises"
clasohm@0
   707
  end;
clasohm@0
   708
berghofe@10416
   709
(*Beta-conversion: maps (%x.t)(u) to the theorem (%x.t)(u) == t[u/x]
berghofe@10416
   710
  Fully beta-reduces the term if full=true
berghofe@10416
   711
*)
berghofe@10416
   712
fun beta_conversion full ct =
wenzelm@3967
   713
  let val Cterm {sign_ref, t, T, maxidx} = ct
berghofe@10416
   714
  in Thm
berghofe@10416
   715
    {sign_ref = sign_ref,  
berghofe@11518
   716
     der = Pt.infer_derivs' I (false, Pt.reflexive),
berghofe@10416
   717
     maxidx = maxidx,
berghofe@10416
   718
     shyps = add_term_sorts (t, []),
berghofe@10416
   719
     hyps = [],
wenzelm@10486
   720
     prop = Logic.mk_equals (t, if full then Envir.beta_norm t
berghofe@10416
   721
       else case t of
berghofe@10416
   722
          Abs(_, _, bodt) $ u => subst_bound (u, bodt)
berghofe@10416
   723
        | _ => raise THM ("beta_conversion: not a redex", 0, []))}
berghofe@10416
   724
  end;
berghofe@10416
   725
berghofe@10416
   726
fun eta_conversion ct =
berghofe@10416
   727
  let val Cterm {sign_ref, t, T, maxidx} = ct
berghofe@10416
   728
  in Thm
berghofe@10416
   729
    {sign_ref = sign_ref,  
berghofe@11518
   730
     der = Pt.infer_derivs' I (false, Pt.reflexive),
berghofe@10416
   731
     maxidx = maxidx,
berghofe@10416
   732
     shyps = add_term_sorts (t, []),
berghofe@10416
   733
     hyps = [],
berghofe@10416
   734
     prop = Logic.mk_equals (t, Pattern.eta_contract t)}
clasohm@0
   735
  end;
clasohm@0
   736
clasohm@0
   737
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   738
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@1220
   739
     t == u
wenzelm@1220
   740
  ------------
wenzelm@1220
   741
  %x.t == %x.u
wenzelm@1220
   742
*)
berghofe@10416
   743
fun abstract_rule a cx (th as Thm{sign_ref,der,maxidx,hyps,shyps,prop}) =
lcp@229
   744
  let val x = term_of cx;
wenzelm@250
   745
      val (t,u) = Logic.dest_equals prop
wenzelm@250
   746
            handle TERM _ =>
wenzelm@250
   747
                raise THM("abstract_rule: premise not an equality", 0, [th])
berghofe@10416
   748
      fun result T =
berghofe@10416
   749
           Thm{sign_ref = sign_ref,
berghofe@11518
   750
               der = Pt.infer_derivs' (Pt.abstract_rule x a) der,
wenzelm@2386
   751
               maxidx = maxidx, 
berghofe@10416
   752
               shyps = add_typ_sorts (T, shyps), 
wenzelm@2386
   753
               hyps = hyps,
wenzelm@2386
   754
               prop = Logic.mk_equals(Abs(a, T, abstract_over (x,t)),
berghofe@10416
   755
                                      Abs(a, T, abstract_over (x,u)))}
clasohm@0
   756
  in  case x of
wenzelm@250
   757
        Free(_,T) =>
wenzelm@250
   758
         if exists (apl(x, Logic.occs)) hyps
wenzelm@250
   759
         then raise THM("abstract_rule: variable free in assumptions", 0, [th])
wenzelm@250
   760
         else result T
clasohm@0
   761
      | Var(_,T) => result T
clasohm@0
   762
      | _ => raise THM("abstract_rule: not a variable", 0, [th])
clasohm@0
   763
  end;
clasohm@0
   764
clasohm@0
   765
(*The combination rule
wenzelm@3529
   766
  f == g  t == u
wenzelm@3529
   767
  --------------
wenzelm@3529
   768
   f(t) == g(u)
wenzelm@1220
   769
*)
clasohm@0
   770
fun combination th1 th2 =
paulson@1529
   771
  let val Thm{der=der1, maxidx=max1, shyps=shyps1, hyps=hyps1, 
wenzelm@2386
   772
              prop=prop1,...} = th1
paulson@1529
   773
      and Thm{der=der2, maxidx=max2, shyps=shyps2, hyps=hyps2, 
wenzelm@2386
   774
              prop=prop2,...} = th2
berghofe@10416
   775
      fun chktypes fT tT =
berghofe@10416
   776
            (case fT of
wenzelm@2386
   777
                Type("fun",[T1,T2]) => 
berghofe@10416
   778
                    if T1 <> tT then
wenzelm@2386
   779
                         raise THM("combination: types", 0, [th1,th2])
wenzelm@2386
   780
                    else ()
wenzelm@2386
   781
                | _ => raise THM("combination: not function type", 0, 
wenzelm@2386
   782
                                 [th1,th2]))
nipkow@1495
   783
  in case (prop1,prop2)  of
berghofe@10416
   784
       (Const ("==", Type ("fun", [fT, _])) $ f $ g,
berghofe@10416
   785
        Const ("==", Type ("fun", [tT, _])) $ t $ u) =>
berghofe@10416
   786
          let val _   = chktypes fT tT
wenzelm@2386
   787
              val thm = (*no fix_shyps*)
wenzelm@3967
   788
                        Thm{sign_ref = merge_thm_sgs(th1,th2), 
berghofe@11518
   789
                            der = Pt.infer_derivs
berghofe@11518
   790
                              (Pt.combination f g t u fT) der1 der2,
wenzelm@2386
   791
                            maxidx = Int.max(max1,max2), 
wenzelm@2386
   792
                            shyps = union_sort(shyps1,shyps2),
wenzelm@2386
   793
                            hyps = union_term(hyps1,hyps2),
wenzelm@2386
   794
                            prop = Logic.mk_equals(f$t, g$u)}
paulson@2139
   795
          in if max1 >= 0 andalso max2 >= 0
wenzelm@8291
   796
             then nodup_vars thm "combination" 
wenzelm@2386
   797
             else thm (*no new Vars: no expensive check!*)  
paulson@2139
   798
          end
clasohm@0
   799
     | _ =>  raise THM("combination: premises", 0, [th1,th2])
clasohm@0
   800
  end;
clasohm@0
   801
clasohm@0
   802
clasohm@0
   803
(* Equality introduction
wenzelm@3529
   804
  A ==> B  B ==> A
wenzelm@3529
   805
  ----------------
wenzelm@3529
   806
       A == B
wenzelm@1220
   807
*)
clasohm@0
   808
fun equal_intr th1 th2 =
berghofe@11518
   809
  let val Thm{der=der1, maxidx=max1, shyps=shyps1, hyps=hyps1, 
wenzelm@2386
   810
              prop=prop1,...} = th1
paulson@1529
   811
      and Thm{der=der2, maxidx=max2, shyps=shyps2, hyps=hyps2, 
wenzelm@2386
   812
              prop=prop2,...} = th2;
paulson@1529
   813
      fun err(msg) = raise THM("equal_intr: "^msg, 0, [th1,th2])
paulson@1529
   814
  in case (prop1,prop2) of
paulson@1529
   815
       (Const("==>",_) $ A $ B, Const("==>",_) $ B' $ A')  =>
wenzelm@2386
   816
          if A aconv A' andalso B aconv B'
wenzelm@2386
   817
          then
wenzelm@2386
   818
            (*no fix_shyps*)
wenzelm@3967
   819
              Thm{sign_ref = merge_thm_sgs(th1,th2),
berghofe@11518
   820
                  der = Pt.infer_derivs (Pt.equal_intr A B) der1 der2,
wenzelm@2386
   821
                  maxidx = Int.max(max1,max2),
wenzelm@2386
   822
                  shyps = union_sort(shyps1,shyps2),
wenzelm@2386
   823
                  hyps = union_term(hyps1,hyps2),
wenzelm@2386
   824
                  prop = Logic.mk_equals(A,B)}
wenzelm@2386
   825
          else err"not equal"
paulson@1529
   826
     | _ =>  err"premises"
paulson@1529
   827
  end;
paulson@1529
   828
paulson@1529
   829
paulson@1529
   830
(*The equal propositions rule
wenzelm@3529
   831
  A == B  A
paulson@1529
   832
  ---------
paulson@1529
   833
      B
paulson@1529
   834
*)
paulson@1529
   835
fun equal_elim th1 th2 =
paulson@1529
   836
  let val Thm{der=der1, maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
paulson@1529
   837
      and Thm{der=der2, maxidx=max2, hyps=hyps2, prop=prop2,...} = th2;
paulson@1529
   838
      fun err(msg) = raise THM("equal_elim: "^msg, 0, [th1,th2])
paulson@1529
   839
  in  case prop1  of
paulson@1529
   840
       Const("==",_) $ A $ B =>
paulson@1529
   841
          if not (prop2 aconv A) then err"not equal"  else
paulson@1529
   842
            fix_shyps [th1, th2] []
wenzelm@3967
   843
              (Thm{sign_ref= merge_thm_sgs(th1,th2), 
berghofe@11518
   844
                   der = Pt.infer_derivs (Pt.equal_elim A B) der1 der2,
wenzelm@2386
   845
                   maxidx = Int.max(max1,max2),
wenzelm@2386
   846
                   shyps = [],
wenzelm@2386
   847
                   hyps = union_term(hyps1,hyps2),
wenzelm@2386
   848
                   prop = B})
paulson@1529
   849
     | _ =>  err"major premise"
paulson@1529
   850
  end;
clasohm@0
   851
wenzelm@1220
   852
wenzelm@1220
   853
clasohm@0
   854
(**** Derived rules ****)
clasohm@0
   855
paulson@1503
   856
(*Discharge all hypotheses.  Need not verify cterms or call fix_shyps.
clasohm@0
   857
  Repeated hypotheses are discharged only once;  fold cannot do this*)
wenzelm@3967
   858
fun implies_intr_hyps (Thm{sign_ref, der, maxidx, shyps, hyps=A::As, prop}) =
wenzelm@1238
   859
      implies_intr_hyps (*no fix_shyps*)
wenzelm@3967
   860
            (Thm{sign_ref = sign_ref, 
berghofe@11518
   861
                 der = Pt.infer_derivs' (Pt.implies_intr_proof A) der,
wenzelm@2386
   862
                 maxidx = maxidx, 
wenzelm@2386
   863
                 shyps = shyps,
paulson@1529
   864
                 hyps = disch(As,A),  
wenzelm@2386
   865
                 prop = implies$A$prop})
clasohm@0
   866
  | implies_intr_hyps th = th;
clasohm@0
   867
clasohm@0
   868
(*Smash" unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@250
   869
  Instantiates the theorem and deletes trivial tpairs.
clasohm@0
   870
  Resulting sequence may contain multiple elements if the tpairs are
clasohm@0
   871
    not all flex-flex. *)
wenzelm@3967
   872
fun flexflex_rule (th as Thm{sign_ref, der, maxidx, hyps, prop,...}) =
wenzelm@250
   873
  let fun newthm env =
paulson@1529
   874
          if Envir.is_empty env then th
paulson@1529
   875
          else
wenzelm@250
   876
          let val (tpairs,horn) =
wenzelm@250
   877
                        Logic.strip_flexpairs (Envir.norm_term env prop)
wenzelm@250
   878
                (*Remove trivial tpairs, of the form t=t*)
wenzelm@250
   879
              val distpairs = filter (not o op aconv) tpairs
wenzelm@250
   880
              val newprop = Logic.list_flexpairs(distpairs, horn)
wenzelm@1220
   881
          in  fix_shyps [th] (env_codT env)
wenzelm@3967
   882
                (Thm{sign_ref = sign_ref, 
berghofe@11518
   883
                     der = Pt.infer_derivs' (Pt.norm_proof' env) der,
wenzelm@2386
   884
                     maxidx = maxidx_of_term newprop, 
wenzelm@2386
   885
                     shyps = [], 
wenzelm@2386
   886
                     hyps = hyps,
wenzelm@2386
   887
                     prop = newprop})
wenzelm@250
   888
          end;
clasohm@0
   889
      val (tpairs,_) = Logic.strip_flexpairs prop
wenzelm@4270
   890
  in Seq.map newthm
wenzelm@3967
   891
            (Unify.smash_unifiers(Sign.deref sign_ref, Envir.empty maxidx, tpairs))
clasohm@0
   892
  end;
clasohm@0
   893
clasohm@0
   894
(*Instantiation of Vars
wenzelm@1220
   895
           A
wenzelm@1220
   896
  -------------------
wenzelm@1220
   897
  A[t1/v1,....,tn/vn]
wenzelm@1220
   898
*)
clasohm@0
   899
wenzelm@6928
   900
local
wenzelm@6928
   901
clasohm@0
   902
(*Check that all the terms are Vars and are distinct*)
clasohm@0
   903
fun instl_ok ts = forall is_Var ts andalso null(findrep ts);
clasohm@0
   904
wenzelm@6928
   905
fun prt_typing sg_ref t T =
wenzelm@6928
   906
  let val sg = Sign.deref sg_ref in
wenzelm@6928
   907
    Pretty.block [Sign.pretty_term sg t, Pretty.str " ::", Pretty.brk 1, Sign.pretty_typ sg T]
wenzelm@6928
   908
  end;
wenzelm@6928
   909
clasohm@0
   910
(*For instantiate: process pair of cterms, merge theories*)
wenzelm@3967
   911
fun add_ctpair ((ct,cu), (sign_ref,tpairs)) =
wenzelm@6928
   912
  let
wenzelm@6928
   913
    val Cterm {sign_ref=sign_reft, t=t, T= T, ...} = ct
wenzelm@6928
   914
    and Cterm {sign_ref=sign_refu, t=u, T= U, ...} = cu;
wenzelm@6928
   915
    val sign_ref_merged = Sign.merge_refs (sign_ref, Sign.merge_refs (sign_reft, sign_refu));
wenzelm@3967
   916
  in
wenzelm@6928
   917
    if T=U then (sign_ref_merged, (t,u)::tpairs)
wenzelm@6928
   918
    else raise TYPE (Pretty.string_of (Pretty.block [Pretty.str "instantiate: type conflict",
wenzelm@6928
   919
      Pretty.fbrk, prt_typing sign_ref_merged t T,
wenzelm@6928
   920
      Pretty.fbrk, prt_typing sign_ref_merged u U]), [T,U], [t,u])
clasohm@0
   921
  end;
clasohm@0
   922
wenzelm@3967
   923
fun add_ctyp ((v,ctyp), (sign_ref',vTs)) =
wenzelm@3967
   924
  let val Ctyp {T,sign_ref} = ctyp
wenzelm@3967
   925
  in (Sign.merge_refs(sign_ref,sign_ref'), (v,T)::vTs) end;
clasohm@0
   926
wenzelm@6928
   927
in
wenzelm@6928
   928
clasohm@0
   929
(*Left-to-right replacements: ctpairs = [...,(vi,ti),...].
clasohm@0
   930
  Instantiates distinct Vars by terms of same type.
paulson@8129
   931
  No longer normalizes the new theorem! *)
paulson@1529
   932
fun instantiate ([], []) th = th
berghofe@10416
   933
  | instantiate (vcTs,ctpairs) (th as Thm{sign_ref,der,maxidx,hyps,shyps,prop}) =
wenzelm@3967
   934
  let val (newsign_ref,tpairs) = foldr add_ctpair (ctpairs, (sign_ref,[]));
wenzelm@3967
   935
      val (newsign_ref,vTs) = foldr add_ctyp (vcTs, (newsign_ref,[]));
paulson@8129
   936
      val newprop = subst_atomic tpairs
paulson@8129
   937
	             (Type.inst_term_tvars
paulson@8129
   938
		      (Sign.tsig_of (Sign.deref newsign_ref),vTs) prop)
wenzelm@1220
   939
      val newth =
berghofe@10416
   940
            (Thm{sign_ref = newsign_ref, 
berghofe@11518
   941
                 der = Pt.infer_derivs' (Pt.instantiate vTs tpairs) der,
berghofe@10416
   942
                 maxidx = maxidx_of_term newprop, 
berghofe@10416
   943
                 shyps = add_insts_sorts ((vTs, tpairs), shyps),
berghofe@10416
   944
                 hyps = hyps,
berghofe@10416
   945
                 prop = newprop})
wenzelm@250
   946
  in  if not(instl_ok(map #1 tpairs))
nipkow@193
   947
      then raise THM("instantiate: variables not distinct", 0, [th])
nipkow@193
   948
      else if not(null(findrep(map #1 vTs)))
nipkow@193
   949
      then raise THM("instantiate: type variables not distinct", 0, [th])
wenzelm@8291
   950
      else nodup_vars newth "instantiate"
clasohm@0
   951
  end
wenzelm@6928
   952
  handle TERM _ => raise THM("instantiate: incompatible signatures", 0, [th])
wenzelm@6928
   953
       | TYPE (msg, _, _) => raise THM (msg, 0, [th]);
wenzelm@6928
   954
wenzelm@6928
   955
end;
wenzelm@6928
   956
clasohm@0
   957
clasohm@0
   958
(*The trivial implication A==>A, justified by assume and forall rules.
clasohm@0
   959
  A can contain Vars, not so for assume!   *)
wenzelm@250
   960
fun trivial ct : thm =
wenzelm@3967
   961
  let val Cterm {sign_ref, t=A, T, maxidx} = ct
wenzelm@250
   962
  in  if T<>propT then
wenzelm@250
   963
            raise THM("trivial: the term must have type prop", 0, [])
wenzelm@1238
   964
      else fix_shyps [] []
wenzelm@3967
   965
        (Thm{sign_ref = sign_ref, 
berghofe@11518
   966
             der = Pt.infer_derivs' I (false, Pt.AbsP ("H", None, Pt.PBound 0)),
wenzelm@2386
   967
             maxidx = maxidx, 
wenzelm@2386
   968
             shyps = [], 
wenzelm@2386
   969
             hyps = [],
wenzelm@2386
   970
             prop = implies$A$A})
clasohm@0
   971
  end;
clasohm@0
   972
paulson@1503
   973
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)" *)
wenzelm@6368
   974
fun class_triv sign c =
wenzelm@6368
   975
  let val Cterm {sign_ref, t, maxidx, ...} =
wenzelm@6368
   976
    cterm_of sign (Logic.mk_inclass (TVar (("'a", 0), [c]), c))
wenzelm@6368
   977
      handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@399
   978
  in
wenzelm@1238
   979
    fix_shyps [] []
wenzelm@3967
   980
      (Thm {sign_ref = sign_ref, 
berghofe@11518
   981
            der = Pt.infer_derivs' I
berghofe@11518
   982
              (false, Pt.PAxm ("ProtoPure.class_triv:" ^ c, t, Some [])),
wenzelm@2386
   983
            maxidx = maxidx, 
wenzelm@2386
   984
            shyps = [], 
wenzelm@2386
   985
            hyps = [], 
wenzelm@2386
   986
            prop = t})
wenzelm@399
   987
  end;
wenzelm@399
   988
wenzelm@399
   989
wenzelm@6786
   990
(* Replace all TFrees not fixed or in the hyps by new TVars *)
wenzelm@6786
   991
fun varifyT' fixed (Thm{sign_ref,der,maxidx,shyps,hyps,prop}) =
wenzelm@6786
   992
  let val tfrees = foldr add_term_tfree_names (hyps,fixed)
nipkow@1634
   993
  in let val thm = (*no fix_shyps*)
wenzelm@3967
   994
    Thm{sign_ref = sign_ref, 
berghofe@11518
   995
        der = Pt.infer_derivs' (Pt.varify_proof prop tfrees) der,
wenzelm@2386
   996
        maxidx = Int.max(0,maxidx), 
wenzelm@2386
   997
        shyps = shyps, 
wenzelm@2386
   998
        hyps = hyps,
paulson@1529
   999
        prop = Type.varify(prop,tfrees)}
wenzelm@8291
  1000
     in nodup_vars thm "varifyT" end
wenzelm@8291
  1001
(* this nodup_vars check can be removed if thms are guaranteed not to contain
wenzelm@8291
  1002
duplicate TVars with different sorts *)
clasohm@0
  1003
  end;
clasohm@0
  1004
wenzelm@6786
  1005
val varifyT = varifyT' [];
wenzelm@6786
  1006
clasohm@0
  1007
(* Replace all TVars by new TFrees *)
wenzelm@3967
  1008
fun freezeT(Thm{sign_ref,der,maxidx,shyps,hyps,prop}) =
paulson@3410
  1009
  let val (prop',_) = Type.freeze_thaw prop
wenzelm@1238
  1010
  in (*no fix_shyps*)
wenzelm@3967
  1011
    Thm{sign_ref = sign_ref, 
berghofe@11518
  1012
        der = Pt.infer_derivs' (Pt.freezeT prop) der,
wenzelm@2386
  1013
        maxidx = maxidx_of_term prop',
wenzelm@2386
  1014
        shyps = shyps,
wenzelm@2386
  1015
        hyps = hyps,
paulson@1529
  1016
        prop = prop'}
wenzelm@1220
  1017
  end;
clasohm@0
  1018
clasohm@0
  1019
clasohm@0
  1020
(*** Inference rules for tactics ***)
clasohm@0
  1021
clasohm@0
  1022
(*Destruct proof state into constraints, other goals, goal(i), rest *)
clasohm@0
  1023
fun dest_state (state as Thm{prop,...}, i) =
clasohm@0
  1024
  let val (tpairs,horn) = Logic.strip_flexpairs prop
clasohm@0
  1025
  in  case  Logic.strip_prems(i, [], horn) of
clasohm@0
  1026
          (B::rBs, C) => (tpairs, rev rBs, B, C)
clasohm@0
  1027
        | _ => raise THM("dest_state", i, [state])
clasohm@0
  1028
  end
clasohm@0
  1029
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1030
lcp@309
  1031
(*Increment variables and parameters of orule as required for
clasohm@0
  1032
  resolution with goal i of state. *)
clasohm@0
  1033
fun lift_rule (state, i) orule =
wenzelm@3967
  1034
  let val Thm{shyps=sshyps, prop=sprop, maxidx=smax, sign_ref=ssign_ref,...} = state
clasohm@0
  1035
      val (Bi::_, _) = Logic.strip_prems(i, [], Logic.skip_flexpairs sprop)
paulson@1529
  1036
        handle TERM _ => raise THM("lift_rule", i, [orule,state])
wenzelm@3967
  1037
      val ct_Bi = Cterm {sign_ref=ssign_ref, maxidx=smax, T=propT, t=Bi}
paulson@1529
  1038
      val (lift_abs,lift_all) = Logic.lift_fns(Bi,smax+1)
wenzelm@3967
  1039
      val (Thm{sign_ref, der, maxidx,shyps,hyps,prop}) = orule
clasohm@0
  1040
      val (tpairs,As,B) = Logic.strip_horn prop
wenzelm@1238
  1041
  in  (*no fix_shyps*)
wenzelm@3967
  1042
      Thm{sign_ref = merge_thm_sgs(state,orule),
berghofe@11518
  1043
          der = Pt.infer_derivs' (Pt.lift_proof Bi (smax+1) prop) der,
wenzelm@2386
  1044
          maxidx = maxidx+smax+1,
paulson@2177
  1045
          shyps=union_sort(sshyps,shyps), 
wenzelm@2386
  1046
          hyps=hyps, 
paulson@1529
  1047
          prop = Logic.rule_of (map (pairself lift_abs) tpairs,
wenzelm@2386
  1048
                                map lift_all As,    
wenzelm@2386
  1049
                                lift_all B)}
clasohm@0
  1050
  end;
clasohm@0
  1051
berghofe@10416
  1052
fun incr_indexes i (thm as Thm {sign_ref, der, maxidx, shyps, hyps, prop}) =
berghofe@10416
  1053
  if i < 0 then raise THM ("negative increment", 0, [thm]) else
berghofe@10416
  1054
  if i = 0 then thm else
berghofe@10416
  1055
    Thm {sign_ref = sign_ref,
berghofe@11518
  1056
         der = Pt.infer_derivs' (Pt.map_proof_terms
berghofe@11518
  1057
           (Logic.incr_indexes ([], i)) (incr_tvar i)) der,
berghofe@10416
  1058
         maxidx = maxidx + i,
berghofe@10416
  1059
         shyps = shyps,
berghofe@10416
  1060
         hyps = hyps,
berghofe@10416
  1061
         prop = Logic.incr_indexes ([], i) prop};
berghofe@10416
  1062
clasohm@0
  1063
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1064
fun assumption i state =
wenzelm@3967
  1065
  let val Thm{sign_ref,der,maxidx,hyps,prop,...} = state;
clasohm@0
  1066
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
berghofe@11518
  1067
      fun newth n (env as Envir.Envir{maxidx, ...}, tpairs) =
wenzelm@1220
  1068
        fix_shyps [state] (env_codT env)
wenzelm@3967
  1069
          (Thm{sign_ref = sign_ref, 
berghofe@11518
  1070
               der = Pt.infer_derivs'
berghofe@11518
  1071
                 ((if Envir.is_empty env then I else (Pt.norm_proof' env)) o
berghofe@11518
  1072
                   Pt.assumption_proof Bs Bi n) der,
wenzelm@2386
  1073
               maxidx = maxidx,
wenzelm@2386
  1074
               shyps = [],
wenzelm@2386
  1075
               hyps = hyps,
wenzelm@2386
  1076
               prop = 
wenzelm@2386
  1077
               if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@2386
  1078
                   Logic.rule_of (tpairs, Bs, C)
wenzelm@2386
  1079
               else (*normalize the new rule fully*)
wenzelm@2386
  1080
                   Envir.norm_term env (Logic.rule_of (tpairs, Bs, C))});
berghofe@11518
  1081
      fun addprfs [] _ = Seq.empty
berghofe@11518
  1082
        | addprfs ((t,u)::apairs) n = Seq.make (fn()=> Seq.pull
berghofe@11518
  1083
             (Seq.mapp (newth n)
wenzelm@3967
  1084
                (Unify.unifiers(Sign.deref sign_ref,Envir.empty maxidx, (t,u)::tpairs))
berghofe@11518
  1085
                (addprfs apairs (n+1))))
berghofe@11518
  1086
  in  addprfs (Logic.assum_pairs Bi) 1 end;
clasohm@0
  1087
wenzelm@250
  1088
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1089
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1090
fun eq_assumption i state =
wenzelm@3967
  1091
  let val Thm{sign_ref,der,maxidx,hyps,prop,...} = state;
clasohm@0
  1092
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
berghofe@11518
  1093
  in  (case find_index (op aconv) (Logic.assum_pairs Bi) of
berghofe@11518
  1094
         (~1) => raise THM("eq_assumption", 0, [state])
berghofe@11518
  1095
       | n => fix_shyps [state] []
berghofe@11518
  1096
                (Thm{sign_ref = sign_ref, 
berghofe@11518
  1097
                     der = Pt.infer_derivs'
berghofe@11518
  1098
                       (Pt.assumption_proof Bs Bi (n+1)) der,
berghofe@11518
  1099
                     maxidx = maxidx,
berghofe@11518
  1100
                     shyps = [],
berghofe@11518
  1101
                     hyps = hyps,
berghofe@11518
  1102
                     prop = Logic.rule_of(tpairs, Bs, C)}))
clasohm@0
  1103
  end;
clasohm@0
  1104
clasohm@0
  1105
paulson@2671
  1106
(*For rotate_tac: fast rotation of assumptions of subgoal i*)
paulson@2671
  1107
fun rotate_rule k i state =
wenzelm@3967
  1108
  let val Thm{sign_ref,der,maxidx,hyps,prop,shyps} = state;
paulson@2671
  1109
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
paulson@8066
  1110
      val params = Term.strip_all_vars Bi
paulson@8066
  1111
      and rest   = Term.strip_all_body Bi
paulson@8066
  1112
      val asms   = Logic.strip_imp_prems rest
paulson@8066
  1113
      and concl  = Logic.strip_imp_concl rest
paulson@2671
  1114
      val n      = length asms
berghofe@11563
  1115
      val m      = if k<0 then n+k else k
berghofe@11563
  1116
      val Bi'    = if 0=m orelse m=n then Bi
paulson@2671
  1117
		   else if 0<m andalso m<n 
paulson@2671
  1118
		   then list_all 
paulson@2671
  1119
			   (params, 
paulson@2671
  1120
			    Logic.list_implies(List.drop(asms, m) @ 
paulson@2671
  1121
					       List.take(asms, m),
paulson@2671
  1122
					       concl))
paulson@7248
  1123
		   else raise THM("rotate_rule", k, [state])
wenzelm@7264
  1124
  in  (*no fix_shyps*)
wenzelm@7264
  1125
      Thm{sign_ref = sign_ref, 
berghofe@11563
  1126
          der = Pt.infer_derivs' (Pt.rotate_proof Bs Bi m) der,
paulson@2671
  1127
	  maxidx = maxidx,
paulson@2671
  1128
	  shyps = shyps,
paulson@2671
  1129
	  hyps = hyps,
berghofe@11563
  1130
	  prop = Logic.rule_of (tpairs, Bs @ [Bi'], C)}
paulson@2671
  1131
  end;
paulson@2671
  1132
paulson@2671
  1133
paulson@7248
  1134
(*Rotates a rule's premises to the left by k, leaving the first j premises
paulson@7248
  1135
  unchanged.  Does nothing if k=0 or if k equals n-j, where n is the
paulson@7248
  1136
  number of premises.  Useful with etac and underlies tactic/defer_tac*)
paulson@7248
  1137
fun permute_prems j k rl =
paulson@7248
  1138
  let val Thm{sign_ref,der,maxidx,hyps,prop,shyps} = rl
paulson@7248
  1139
      val prems  = Logic.strip_imp_prems prop
paulson@7248
  1140
      and concl  = Logic.strip_imp_concl prop
paulson@7248
  1141
      val moved_prems = List.drop(prems, j)
paulson@7248
  1142
      and fixed_prems = List.take(prems, j)
paulson@7248
  1143
        handle Subscript => raise THM("permute_prems:j", j, [rl])
paulson@7248
  1144
      val n_j    = length moved_prems
berghofe@11563
  1145
      val m = if k<0 then n_j + k else k
berghofe@11563
  1146
      val prop'  = if 0 = m orelse m = n_j then prop
paulson@7248
  1147
		   else if 0<m andalso m<n_j 
paulson@7248
  1148
		   then Logic.list_implies(fixed_prems @
paulson@7248
  1149
					   List.drop(moved_prems, m) @ 
paulson@7248
  1150
					   List.take(moved_prems, m),
paulson@7248
  1151
					   concl)
paulson@7248
  1152
		   else raise THM("permute_prems:k", k, [rl])
wenzelm@7264
  1153
  in  (*no fix_shyps*)
wenzelm@7264
  1154
      Thm{sign_ref = sign_ref, 
berghofe@11563
  1155
          der = Pt.infer_derivs' (Pt.permute_prems_prf prems j m) der,
paulson@7248
  1156
	  maxidx = maxidx,
paulson@7248
  1157
	  shyps = shyps,
paulson@7248
  1158
	  hyps = hyps,
berghofe@11563
  1159
	  prop = prop'}
paulson@7248
  1160
  end;
paulson@7248
  1161
paulson@7248
  1162
clasohm@0
  1163
(** User renaming of parameters in a subgoal **)
clasohm@0
  1164
clasohm@0
  1165
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1166
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1167
  The names in cs, if distinct, are used for the innermost parameters;
clasohm@0
  1168
   preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1169
fun rename_params_rule (cs, i) state =
wenzelm@3967
  1170
  let val Thm{sign_ref,der,maxidx,hyps,...} = state
clasohm@0
  1171
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
clasohm@0
  1172
      val iparams = map #1 (Logic.strip_params Bi)
clasohm@0
  1173
      val short = length iparams - length cs
wenzelm@250
  1174
      val newnames =
wenzelm@250
  1175
            if short<0 then error"More names than abstractions!"
wenzelm@250
  1176
            else variantlist(take (short,iparams), cs) @ cs
nipkow@3037
  1177
      val freenames = map (#1 o dest_Free) (term_frees Bi)
clasohm@0
  1178
      val newBi = Logic.list_rename_params (newnames, Bi)
wenzelm@250
  1179
  in
clasohm@0
  1180
  case findrep cs of
paulson@3565
  1181
     c::_ => (warning ("Can't rename.  Bound variables not distinct: " ^ c); 
paulson@3565
  1182
	      state)
berghofe@1576
  1183
   | [] => (case cs inter_string freenames of
paulson@3565
  1184
       a::_ => (warning ("Can't rename.  Bound/Free variable clash: " ^ a); 
paulson@3565
  1185
		state)
wenzelm@1220
  1186
     | [] => fix_shyps [state] []
wenzelm@3967
  1187
                (Thm{sign_ref = sign_ref,
berghofe@11518
  1188
                     der = der,
wenzelm@2386
  1189
                     maxidx = maxidx,
wenzelm@2386
  1190
                     shyps = [],
wenzelm@2386
  1191
                     hyps = hyps,
wenzelm@2386
  1192
                     prop = Logic.rule_of(tpairs, Bs@[newBi], C)}))
clasohm@0
  1193
  end;
clasohm@0
  1194
clasohm@0
  1195
(*** Preservation of bound variable names ***)
clasohm@0
  1196
wenzelm@250
  1197
(*Scan a pair of terms; while they are similar,
clasohm@0
  1198
  accumulate corresponding bound vars in "al"*)
wenzelm@1238
  1199
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
lcp@1195
  1200
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@1238
  1201
                                          else (x,y)::al)
clasohm@0
  1202
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
clasohm@0
  1203
  | match_bvs(_,_,al) = al;
clasohm@0
  1204
clasohm@0
  1205
(* strip abstractions created by parameters *)
clasohm@0
  1206
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
clasohm@0
  1207
berghofe@10416
  1208
fun rename_boundvars pat obj (thm as Thm {sign_ref,der,maxidx,hyps,shyps,prop}) =
berghofe@10416
  1209
  let val ren = match_bvs (pat, obj, [])
berghofe@10416
  1210
      fun renAbs (Abs (x, T, b)) =
berghofe@10416
  1211
            Abs (if_none (assoc_string (ren, x)) x, T, renAbs b)
berghofe@10416
  1212
        | renAbs (f $ t) = renAbs f $ renAbs t
berghofe@10416
  1213
        | renAbs t = t
berghofe@10416
  1214
  in if null ren then thm else Thm
berghofe@10416
  1215
    {sign_ref = sign_ref,
berghofe@10416
  1216
     der = der,
berghofe@10416
  1217
     maxidx = maxidx,
berghofe@10416
  1218
     hyps = hyps,
berghofe@10416
  1219
     shyps = shyps,
berghofe@10416
  1220
     prop = renAbs prop}
berghofe@10416
  1221
  end;
berghofe@10416
  1222
clasohm@0
  1223
wenzelm@250
  1224
(* strip_apply f A(,B) strips off all assumptions/parameters from A
clasohm@0
  1225
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
  1226
fun strip_apply f =
clasohm@0
  1227
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@250
  1228
                Const("==>",_)$ _  $ B2) = implies $ A1 $ strip(B1,B2)
wenzelm@250
  1229
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
  1230
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
  1231
        | strip(A,_) = f A
clasohm@0
  1232
  in strip end;
clasohm@0
  1233
clasohm@0
  1234
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1235
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1236
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1237
fun rename_bvs([],_,_,_) = I
clasohm@0
  1238
  | rename_bvs(al,dpairs,tpairs,B) =
wenzelm@250
  1239
    let val vars = foldr add_term_vars
wenzelm@250
  1240
                        (map fst dpairs @ map fst tpairs @ map snd tpairs, [])
wenzelm@250
  1241
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1242
        val vids = map (#1 o #1 o dest_Var) vars;
wenzelm@250
  1243
        fun rename(t as Var((x,i),T)) =
wenzelm@250
  1244
                (case assoc(al,x) of
berghofe@1576
  1245
                   Some(y) => if x mem_string vids orelse y mem_string vids then t
wenzelm@250
  1246
                              else Var((y,i),T)
wenzelm@250
  1247
                 | None=> t)
clasohm@0
  1248
          | rename(Abs(x,T,t)) =
nipkow@9721
  1249
              Abs(if_none(assoc_string(al,x)) x, T, rename t)
clasohm@0
  1250
          | rename(f$t) = rename f $ rename t
clasohm@0
  1251
          | rename(t) = t;
wenzelm@250
  1252
        fun strip_ren Ai = strip_apply rename (Ai,B)
clasohm@0
  1253
    in strip_ren end;
clasohm@0
  1254
clasohm@0
  1255
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
  1256
fun rename_bvars(dpairs, tpairs, B) =
wenzelm@250
  1257
        rename_bvs(foldr match_bvars (dpairs,[]), dpairs, tpairs, B);
clasohm@0
  1258
clasohm@0
  1259
clasohm@0
  1260
(*** RESOLUTION ***)
clasohm@0
  1261
lcp@721
  1262
(** Lifting optimizations **)
lcp@721
  1263
clasohm@0
  1264
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
  1265
  identical because of lifting*)
wenzelm@250
  1266
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
  1267
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
  1268
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
  1269
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
  1270
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
  1271
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
  1272
  | strip_assums2 BB = BB;
clasohm@0
  1273
clasohm@0
  1274
lcp@721
  1275
(*Faster normalization: skip assumptions that were lifted over*)
lcp@721
  1276
fun norm_term_skip env 0 t = Envir.norm_term env t
lcp@721
  1277
  | norm_term_skip env n (Const("all",_)$Abs(a,T,t)) =
lcp@721
  1278
        let val Envir.Envir{iTs, ...} = env
berghofe@8407
  1279
            val T' = typ_subst_TVars_Vartab iTs T
wenzelm@1238
  1280
            (*Must instantiate types of parameters because they are flattened;
lcp@721
  1281
              this could be a NEW parameter*)
lcp@721
  1282
        in  all T' $ Abs(a, T', norm_term_skip env n t)  end
lcp@721
  1283
  | norm_term_skip env n (Const("==>", _) $ A $ B) =
wenzelm@1238
  1284
        implies $ A $ norm_term_skip env (n-1) B
lcp@721
  1285
  | norm_term_skip env n t = error"norm_term_skip: too few assumptions??";
lcp@721
  1286
lcp@721
  1287
clasohm@0
  1288
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
  1289
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
  1290
  If match then forbid instantiations in proof state
clasohm@0
  1291
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
  1292
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
  1293
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
  1294
  Curried so that resolution calls dest_state only once.
clasohm@0
  1295
*)
wenzelm@4270
  1296
local exception COMPOSE
clasohm@0
  1297
in
wenzelm@250
  1298
fun bicompose_aux match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
  1299
                        (eres_flg, orule, nsubgoal) =
paulson@1529
  1300
 let val Thm{der=sder, maxidx=smax, shyps=sshyps, hyps=shyps, ...} = state
paulson@1529
  1301
     and Thm{der=rder, maxidx=rmax, shyps=rshyps, hyps=rhyps, 
wenzelm@2386
  1302
             prop=rprop,...} = orule
paulson@1529
  1303
         (*How many hyps to skip over during normalization*)
wenzelm@1238
  1304
     and nlift = Logic.count_prems(strip_all_body Bi,
wenzelm@1238
  1305
                                   if eres_flg then ~1 else 0)
wenzelm@3967
  1306
     val sign_ref = merge_thm_sgs(state,orule);
wenzelm@3967
  1307
     val sign = Sign.deref sign_ref;
clasohm@0
  1308
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
berghofe@11518
  1309
     fun addth A (As, oldAs, rder', n) ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
  1310
       let val normt = Envir.norm_term env;
wenzelm@250
  1311
           (*perform minimal copying here by examining env*)
wenzelm@250
  1312
           val normp =
wenzelm@250
  1313
             if Envir.is_empty env then (tpairs, Bs @ As, C)
wenzelm@250
  1314
             else
wenzelm@250
  1315
             let val ntps = map (pairself normt) tpairs
paulson@2147
  1316
             in if Envir.above (smax, env) then
wenzelm@1238
  1317
                  (*no assignments in state; normalize the rule only*)
wenzelm@1238
  1318
                  if lifted
wenzelm@1238
  1319
                  then (ntps, Bs @ map (norm_term_skip env nlift) As, C)
wenzelm@1238
  1320
                  else (ntps, Bs @ map normt As, C)
paulson@1529
  1321
                else if match then raise COMPOSE
wenzelm@250
  1322
                else (*normalize the new rule fully*)
wenzelm@250
  1323
                  (ntps, map normt (Bs @ As), normt C)
wenzelm@250
  1324
             end
wenzelm@1258
  1325
           val th = (*tuned fix_shyps*)
wenzelm@3967
  1326
             Thm{sign_ref = sign_ref,
berghofe@11518
  1327
                 der = Pt.infer_derivs
berghofe@11518
  1328
                   ((if Envir.is_empty env then I
berghofe@11518
  1329
                     else if Envir.above (smax, env) then
berghofe@11518
  1330
                       (fn f => fn der => f (Pt.norm_proof' env der))
berghofe@11518
  1331
                     else
berghofe@11518
  1332
                       curry op oo (Pt.norm_proof' env))
berghofe@11518
  1333
                    (Pt.bicompose_proof Bs oldAs As A n)) rder' sder,
wenzelm@2386
  1334
                 maxidx = maxidx,
wenzelm@2386
  1335
                 shyps = add_env_sorts (env, union_sort(rshyps,sshyps)),
wenzelm@2386
  1336
                 hyps = union_term(rhyps,shyps),
wenzelm@2386
  1337
                 prop = Logic.rule_of normp}
berghofe@11518
  1338
        in  Seq.cons(th, thq)  end  handle COMPOSE => thq;
clasohm@0
  1339
     val (rtpairs,rhorn) = Logic.strip_flexpairs(rprop);
clasohm@0
  1340
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rhorn)
clasohm@0
  1341
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
  1342
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
  1343
     fun newAs(As0, n, dpairs, tpairs) =
berghofe@11518
  1344
       let val (As1, rder') =
berghofe@11518
  1345
         if !Logic.auto_rename orelse not lifted then (As0, rder)
berghofe@11518
  1346
         else (map (rename_bvars(dpairs,tpairs,B)) As0,
berghofe@11518
  1347
           Pt.infer_derivs' (Pt.map_proof_terms
berghofe@11518
  1348
             (rename_bvars (dpairs, tpairs, Bound 0)) I) rder);
berghofe@11518
  1349
       in (map (Logic.flatten_params n) As1, As1, rder', n)
wenzelm@250
  1350
          handle TERM _ =>
wenzelm@250
  1351
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
  1352
       end;
paulson@2147
  1353
     val env = Envir.empty(Int.max(rmax,smax));
clasohm@0
  1354
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
  1355
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
  1356
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
berghofe@11518
  1357
     fun tryasms (_, _, _, []) = Seq.empty
berghofe@11518
  1358
       | tryasms (A, As, n, (t,u)::apairs) =
wenzelm@4270
  1359
          (case Seq.pull(Unify.unifiers(sign, env, (t,u)::dpairs))  of
berghofe@11518
  1360
               None                   => tryasms (A, As, n+1, apairs)
wenzelm@250
  1361
             | cell as Some((_,tpairs),_) =>
berghofe@11518
  1362
                   Seq.it_right (addth A (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@4270
  1363
                       (Seq.make (fn()=> cell),
berghofe@11518
  1364
                        Seq.make (fn()=> Seq.pull (tryasms (A, As, n+1, apairs)))));
clasohm@0
  1365
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
berghofe@11518
  1366
       | eres (A1::As) = tryasms (Some A1, As, 1, Logic.assum_pairs A1);
clasohm@0
  1367
     (*ordinary resolution*)
wenzelm@4270
  1368
     fun res(None) = Seq.empty
wenzelm@250
  1369
       | res(cell as Some((_,tpairs),_)) =
berghofe@11518
  1370
             Seq.it_right (addth None (newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@4270
  1371
                       (Seq.make (fn()=> cell), Seq.empty)
clasohm@0
  1372
 in  if eres_flg then eres(rev rAs)
wenzelm@4270
  1373
     else res(Seq.pull(Unify.unifiers(sign, env, dpairs)))
clasohm@0
  1374
 end;
wenzelm@7528
  1375
end;
clasohm@0
  1376
clasohm@0
  1377
clasohm@0
  1378
fun bicompose match arg i state =
clasohm@0
  1379
    bicompose_aux match (state, dest_state(state,i), false) arg;
clasohm@0
  1380
clasohm@0
  1381
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1382
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1383
fun could_bires (Hs, B, eres_flg, rule) =
clasohm@0
  1384
    let fun could_reshyp (A1::_) = exists (apl(A1,could_unify)) Hs
wenzelm@250
  1385
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@250
  1386
    in  could_unify(concl_of rule, B) andalso
wenzelm@250
  1387
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1388
    end;
clasohm@0
  1389
clasohm@0
  1390
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1391
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1392
fun biresolution match brules i state =
clasohm@0
  1393
    let val lift = lift_rule(state, i);
wenzelm@250
  1394
        val (stpairs, Bs, Bi, C) = dest_state(state,i)
wenzelm@250
  1395
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1396
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@250
  1397
        val comp = bicompose_aux match (state, (stpairs, Bs, Bi, C), true);
wenzelm@4270
  1398
        fun res [] = Seq.empty
wenzelm@250
  1399
          | res ((eres_flg, rule)::brules) =
wenzelm@250
  1400
              if could_bires (Hs, B, eres_flg, rule)
wenzelm@4270
  1401
              then Seq.make (*delay processing remainder till needed*)
wenzelm@250
  1402
                  (fn()=> Some(comp (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1403
                               res brules))
wenzelm@250
  1404
              else res brules
wenzelm@4270
  1405
    in  Seq.flat (res brules)  end;
clasohm@0
  1406
clasohm@0
  1407
wenzelm@2509
  1408
(*** Oracles ***)
wenzelm@2509
  1409
wenzelm@3812
  1410
fun invoke_oracle thy raw_name =
wenzelm@3812
  1411
  let
wenzelm@6390
  1412
    val {sign = sg, oracles, ...} = Theory.rep_theory thy;
wenzelm@3812
  1413
    val name = Sign.intern sg Theory.oracleK raw_name;
wenzelm@3812
  1414
    val oracle =
wenzelm@3812
  1415
      (case Symtab.lookup (oracles, name) of
wenzelm@3812
  1416
        None => raise THM ("Unknown oracle: " ^ name, 0, [])
wenzelm@3812
  1417
      | Some (f, _) => f);
wenzelm@3812
  1418
  in
wenzelm@3812
  1419
    fn (sign, exn) =>
wenzelm@3812
  1420
      let
wenzelm@3967
  1421
        val sign_ref' = Sign.merge_refs (Sign.self_ref sg, Sign.self_ref sign);
wenzelm@3967
  1422
        val sign' = Sign.deref sign_ref';
wenzelm@3812
  1423
        val (prop, T, maxidx) = Sign.certify_term sign' (oracle (sign', exn));
wenzelm@3812
  1424
      in
wenzelm@3812
  1425
        if T <> propT then
wenzelm@3812
  1426
          raise THM ("Oracle's result must have type prop: " ^ name, 0, [])
wenzelm@3812
  1427
        else fix_shyps [] []
wenzelm@3967
  1428
          (Thm {sign_ref = sign_ref', 
berghofe@11518
  1429
            der = (true, Pt.oracle_proof name prop),
wenzelm@3812
  1430
            maxidx = maxidx,
wenzelm@3812
  1431
            shyps = [], 
wenzelm@3812
  1432
            hyps = [], 
wenzelm@3812
  1433
            prop = prop})
wenzelm@3812
  1434
      end
wenzelm@3812
  1435
  end;
wenzelm@3812
  1436
paulson@1539
  1437
clasohm@0
  1438
end;
paulson@1503
  1439
wenzelm@6089
  1440
wenzelm@6089
  1441
structure BasicThm: BASIC_THM = Thm;
wenzelm@6089
  1442
open BasicThm;