src/Pure/thm.ML
author berghofe
Thu Apr 21 19:12:03 2005 +0200 (2005-04-21)
changeset 15797 a63605582573
parent 15672 32aea1e31eb8
child 16024 ffe25459c72a
permissions -rw-r--r--
- Eliminated nodup_vars check.
- Unification and matching functions now check types of term variables / sorts
of type variables when applying a substitution.
- Thm.instantiate now takes (ctyp * ctyp) list instead of (indexname * ctyp) list
as argument, to allow for proper instantiation of theorems containing
type variables with same name but different sorts.
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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 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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                                  tpairs: (term * term) list, 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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                                  tpairs: (cterm * cterm) list, 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 prop_of           : thm -> term
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  val proof_of		: thm -> Proofterm.proof
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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_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 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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    (ctyp * 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 * 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 ->
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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_i   : theory -> string -> Sign.sg * Object.T -> thm
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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_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 ->
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    (ctyp * ctyp) list * (cterm * cterm) list
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  val cterm_first_order_match : cterm * cterm ->
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    (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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(** 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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fun dest_ctyp (Ctyp {sign_ref, T = Type (s, Ts)}) =
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      map (fn T => Ctyp {sign_ref = sign_ref, T = T}) Ts
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  | dest_ctyp ct = [ct];
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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.pp sign) 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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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 (getOpt (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 = f $ x,
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          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=t1, 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 = lambda t1 t2, sign_ref = Sign.merge_refs (sign_ref1,sign_ref2),
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             T = T1 --> T2, maxidx=Int.max(maxidx1, maxidx2)}
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      handle TERM _ => raise CTERM "cabs: first arg is not a 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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    fun mk_cTinsts (ixn, (S, T)) =
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      (Ctyp {sign_ref = sign_ref, T = TVar (ixn, S)},
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       Ctyp {sign_ref = sign_ref, T = T});
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    fun mk_ctinsts (ixn, (T, t)) =
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      let val T = Envir.typ_subst_TVars Tinsts T
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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 (Vartab.dest Tinsts),
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    map mk_ctinsts (Vartab.dest tinsts))
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  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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   300
  tpairs: (term * term) list,  (*flex-flex pairs*)
wenzelm@3967
   301
  prop: term};                 (*conclusion*)
clasohm@0
   302
skalberg@15570
   303
fun terms_of_tpairs tpairs = List.concat (map (op @ o pairself single) tpairs);
berghofe@13658
   304
berghofe@13658
   305
fun attach_tpairs tpairs prop =
berghofe@13658
   306
  Logic.list_implies (map Logic.mk_equals tpairs, prop);
berghofe@13658
   307
berghofe@13658
   308
fun rep_thm (Thm {sign_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@3967
   309
  {sign = Sign.deref sign_ref, der = der, maxidx = maxidx,
berghofe@13658
   310
    shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop};
clasohm@0
   311
paulson@1529
   312
(*Version of rep_thm returning cterms instead of terms*)
berghofe@13658
   313
fun crep_thm (Thm {sign_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@3967
   314
  let fun ctermf max t = Cterm{sign_ref=sign_ref, t=t, T=propT, maxidx=max};
wenzelm@3967
   315
  in {sign = Sign.deref sign_ref, der = der, maxidx = maxidx, shyps = shyps,
paulson@1529
   316
      hyps = map (ctermf ~1) hyps,
berghofe@13658
   317
      tpairs = map (pairself (ctermf maxidx)) tpairs,
paulson@1529
   318
      prop = ctermf maxidx prop}
clasohm@1517
   319
  end;
clasohm@1517
   320
wenzelm@387
   321
(*errors involving theorems*)
clasohm@0
   322
exception THM of string * int * thm list;
clasohm@0
   323
wenzelm@6089
   324
(*attributes subsume any kind of rules or addXXXs modifiers*)
wenzelm@6089
   325
type 'a attribute = 'a * thm -> 'a * thm;
wenzelm@6089
   326
wenzelm@6089
   327
fun no_attributes x = (x, []);
wenzelm@6089
   328
fun apply_attributes (x_th, atts) = Library.apply atts x_th;
wenzelm@6089
   329
fun applys_attributes (x_ths, atts) = foldl_map (Library.apply atts) x_ths;
wenzelm@6089
   330
wenzelm@3994
   331
fun eq_thm (th1, th2) =
wenzelm@3994
   332
  let
berghofe@13658
   333
    val {sign = sg1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1, prop = prop1, ...} =
wenzelm@9031
   334
      rep_thm th1;
berghofe@13658
   335
    val {sign = sg2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2, prop = prop2, ...} =
wenzelm@9031
   336
      rep_thm th2;
wenzelm@3994
   337
  in
wenzelm@9031
   338
    Sign.joinable (sg1, sg2) andalso
wenzelm@14791
   339
    Sorts.eq_set_sort (shyps1, shyps2) andalso
wenzelm@3994
   340
    aconvs (hyps1, hyps2) andalso
berghofe@13658
   341
    aconvs (terms_of_tpairs tpairs1, terms_of_tpairs tpairs2) andalso
wenzelm@3994
   342
    prop1 aconv prop2
wenzelm@3994
   343
  end;
wenzelm@387
   344
wenzelm@3967
   345
fun sign_of_thm (Thm {sign_ref, ...}) = Sign.deref sign_ref;
wenzelm@12803
   346
fun prop_of (Thm {prop, ...}) = prop;
wenzelm@13528
   347
fun proof_of (Thm {der = (_, proof), ...}) = proof;
clasohm@0
   348
wenzelm@387
   349
(*merge signatures of two theorems; raise exception if incompatible*)
wenzelm@3967
   350
fun merge_thm_sgs
wenzelm@3967
   351
    (th1 as Thm {sign_ref = sgr1, ...}, th2 as Thm {sign_ref = sgr2, ...}) =
wenzelm@3967
   352
  Sign.merge_refs (sgr1, sgr2) handle TERM (msg, _) => raise THM (msg, 0, [th1, th2]);
wenzelm@387
   353
wenzelm@3967
   354
(*transfer thm to super theory (non-destructive)*)
wenzelm@4254
   355
fun transfer_sg sign' thm =
wenzelm@3895
   356
  let
berghofe@13658
   357
    val Thm {sign_ref, der, maxidx, shyps, hyps, tpairs, prop} = thm;
wenzelm@3967
   358
    val sign = Sign.deref sign_ref;
wenzelm@3895
   359
  in
wenzelm@4254
   360
    if Sign.eq_sg (sign, sign') then thm
wenzelm@4254
   361
    else if Sign.subsig (sign, sign') then
wenzelm@3967
   362
      Thm {sign_ref = Sign.self_ref sign', der = der, maxidx = maxidx,
berghofe@13658
   363
        shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@3895
   364
    else raise THM ("transfer: not a super theory", 0, [thm])
wenzelm@3895
   365
  end;
wenzelm@387
   366
wenzelm@6390
   367
val transfer = transfer_sg o Theory.sign_of;
wenzelm@4254
   368
wenzelm@387
   369
(*maps object-rule to tpairs*)
berghofe@13658
   370
fun tpairs_of (Thm {tpairs, ...}) = tpairs;
wenzelm@387
   371
wenzelm@387
   372
(*maps object-rule to premises*)
wenzelm@387
   373
fun prems_of (Thm {prop, ...}) =
berghofe@13658
   374
  Logic.strip_imp_prems prop;
clasohm@0
   375
clasohm@0
   376
(*counts premises in a rule*)
wenzelm@387
   377
fun nprems_of (Thm {prop, ...}) =
berghofe@13658
   378
  Logic.count_prems (prop, 0);
clasohm@0
   379
wenzelm@8299
   380
fun major_prem_of thm =
wenzelm@8299
   381
  (case prems_of thm of
wenzelm@11692
   382
    prem :: _ => Logic.strip_assums_concl prem
wenzelm@8299
   383
  | [] => raise THM ("major_prem_of: rule with no premises", 0, [thm]));
wenzelm@8299
   384
wenzelm@7534
   385
fun no_prems thm = nprems_of thm = 0;
wenzelm@7534
   386
wenzelm@387
   387
(*maps object-rule to conclusion*)
wenzelm@387
   388
fun concl_of (Thm {prop, ...}) = Logic.strip_imp_concl prop;
clasohm@0
   389
wenzelm@387
   390
(*the statement of any thm is a cterm*)
wenzelm@3967
   391
fun cprop_of (Thm {sign_ref, maxidx, prop, ...}) =
wenzelm@3967
   392
  Cterm {sign_ref = sign_ref, maxidx = maxidx, T = propT, t = prop};
lcp@229
   393
wenzelm@387
   394
clasohm@0
   395
wenzelm@1238
   396
(** sort contexts of theorems **)
wenzelm@1238
   397
wenzelm@1238
   398
(* basic utils *)
wenzelm@1238
   399
wenzelm@2163
   400
(*accumulate sorts suppressing duplicates; these are coded low levelly
wenzelm@1238
   401
  to improve efficiency a bit*)
wenzelm@1238
   402
wenzelm@1238
   403
fun add_typ_sorts (Type (_, Ts), Ss) = add_typs_sorts (Ts, Ss)
wenzelm@14791
   404
  | add_typ_sorts (TFree (_, S), Ss) = Sorts.ins_sort(S,Ss)
wenzelm@14791
   405
  | add_typ_sorts (TVar (_, S), Ss) = Sorts.ins_sort(S,Ss)
wenzelm@1238
   406
and add_typs_sorts ([], Ss) = Ss
wenzelm@1238
   407
  | add_typs_sorts (T :: Ts, Ss) = add_typs_sorts (Ts, add_typ_sorts (T, Ss));
wenzelm@1238
   408
wenzelm@1238
   409
fun add_term_sorts (Const (_, T), Ss) = add_typ_sorts (T, Ss)
wenzelm@1238
   410
  | add_term_sorts (Free (_, T), Ss) = add_typ_sorts (T, Ss)
wenzelm@1238
   411
  | add_term_sorts (Var (_, T), Ss) = add_typ_sorts (T, Ss)
wenzelm@1238
   412
  | add_term_sorts (Bound _, Ss) = Ss
paulson@2177
   413
  | add_term_sorts (Abs (_,T,t), Ss) = add_term_sorts (t, add_typ_sorts (T,Ss))
wenzelm@1238
   414
  | add_term_sorts (t $ u, Ss) = add_term_sorts (t, add_term_sorts (u, Ss));
wenzelm@1238
   415
wenzelm@1238
   416
fun add_terms_sorts ([], Ss) = Ss
paulson@2177
   417
  | add_terms_sorts (t::ts, Ss) = add_terms_sorts (ts, add_term_sorts (t,Ss));
wenzelm@1238
   418
berghofe@15797
   419
fun env_codT (Envir.Envir {iTs, ...}) = map (snd o snd) (Vartab.dest iTs);
wenzelm@1258
   420
berghofe@8407
   421
fun add_env_sorts (Envir.Envir {iTs, asol, ...}, Ss) =
berghofe@15797
   422
  Vartab.foldl (add_term_sorts o swap o apsnd (snd o snd))
berghofe@15797
   423
    (Vartab.foldl (add_typ_sorts o swap o apsnd (snd o snd)) (Ss, iTs), asol);
wenzelm@1258
   424
berghofe@10416
   425
fun add_insts_sorts ((iTs, is), Ss) =
berghofe@10416
   426
  add_typs_sorts (map snd iTs, add_terms_sorts (map snd is, Ss));
berghofe@10416
   427
berghofe@13658
   428
fun add_thm_sorts (Thm {hyps, tpairs, prop, ...}, Ss) =
berghofe@13658
   429
  add_terms_sorts (hyps @ terms_of_tpairs tpairs, add_term_sorts (prop, Ss));
wenzelm@1238
   430
wenzelm@1238
   431
fun add_thms_shyps ([], Ss) = Ss
wenzelm@1238
   432
  | add_thms_shyps (Thm {shyps, ...} :: ths, Ss) =
wenzelm@14791
   433
      add_thms_shyps (ths, Sorts.union_sort (shyps, Ss));
wenzelm@1238
   434
wenzelm@1238
   435
wenzelm@1238
   436
(*get 'dangling' sort constraints of a thm*)
wenzelm@1238
   437
fun extra_shyps (th as Thm {shyps, ...}) =
wenzelm@14791
   438
  Sorts.rems_sort (shyps, add_thm_sorts (th, []));
wenzelm@1238
   439
wenzelm@1238
   440
wenzelm@1238
   441
(* fix_shyps *)
wenzelm@1238
   442
skalberg@15570
   443
fun all_sorts_nonempty sign_ref = isSome (Sign.universal_witness (Sign.deref sign_ref));
wenzelm@7642
   444
wenzelm@1238
   445
(*preserve sort contexts of rule premises and substituted types*)
berghofe@13658
   446
fun fix_shyps thms Ts (thm as Thm {sign_ref, der, maxidx, hyps, tpairs, prop, ...}) =
wenzelm@7642
   447
  Thm
wenzelm@7642
   448
   {sign_ref = sign_ref,
wenzelm@7642
   449
    der = der,             (*no new derivation, as other rules call this*)
wenzelm@7642
   450
    maxidx = maxidx,
wenzelm@7642
   451
    shyps =
wenzelm@7642
   452
      if all_sorts_nonempty sign_ref then []
wenzelm@7642
   453
      else add_thm_sorts (thm, add_typs_sorts (Ts, add_thms_shyps (thms, []))),
berghofe@13658
   454
    hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@1238
   455
wenzelm@1238
   456
wenzelm@7642
   457
(* strip_shyps *)
wenzelm@1238
   458
wenzelm@7642
   459
(*remove extra sorts that are non-empty by virtue of type signature information*)
wenzelm@7642
   460
fun strip_shyps (thm as Thm {shyps = [], ...}) = thm
berghofe@13658
   461
  | strip_shyps (thm as Thm {sign_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@7642
   462
      let
wenzelm@7642
   463
        val sign = Sign.deref sign_ref;
wenzelm@1238
   464
wenzelm@7642
   465
        val present_sorts = add_thm_sorts (thm, []);
wenzelm@14791
   466
        val extra_shyps = Sorts.rems_sort (shyps, present_sorts);
wenzelm@7642
   467
        val witnessed_shyps = Sign.witness_sorts sign present_sorts extra_shyps;
wenzelm@7642
   468
      in
wenzelm@7642
   469
        Thm {sign_ref = sign_ref, der = der, maxidx = maxidx,
wenzelm@14791
   470
             shyps = Sorts.rems_sort (shyps, map #2 witnessed_shyps),
berghofe@13658
   471
             hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@7642
   472
      end;
wenzelm@1238
   473
wenzelm@1238
   474
wenzelm@1238
   475
paulson@1529
   476
(** Axioms **)
wenzelm@387
   477
wenzelm@387
   478
(*look up the named axiom in the theory*)
wenzelm@15672
   479
fun get_axiom_i theory name =
wenzelm@387
   480
  let
skalberg@15531
   481
    fun get_ax [] = NONE
paulson@1529
   482
      | get_ax (thy :: thys) =
wenzelm@4847
   483
          let val {sign, axioms, ...} = Theory.rep_theory thy in
wenzelm@4847
   484
            (case Symtab.lookup (axioms, name) of
skalberg@15531
   485
              SOME t =>
skalberg@15531
   486
                SOME (fix_shyps [] []
wenzelm@4847
   487
                  (Thm {sign_ref = Sign.self_ref sign,
berghofe@11518
   488
                    der = Pt.infer_derivs' I
berghofe@11518
   489
                      (false, Pt.axm_proof name t),
wenzelm@4847
   490
                    maxidx = maxidx_of_term t,
wenzelm@4847
   491
                    shyps = [], 
wenzelm@4847
   492
                    hyps = [], 
berghofe@13658
   493
                    tpairs = [],
wenzelm@4847
   494
                    prop = t}))
skalberg@15531
   495
            | NONE => get_ax thys)
paulson@1529
   496
          end;
wenzelm@387
   497
  in
wenzelm@4847
   498
    (case get_ax (theory :: Theory.ancestors_of theory) of
skalberg@15531
   499
      SOME thm => thm
skalberg@15531
   500
    | NONE => raise THEORY ("No axiom " ^ quote name, [theory]))
wenzelm@387
   501
  end;
wenzelm@387
   502
wenzelm@15672
   503
fun get_axiom thy = get_axiom_i thy o Sign.intern (Theory.sign_of thy) Theory.axiomK;
wenzelm@15672
   504
wenzelm@6368
   505
fun def_name name = name ^ "_def";
wenzelm@6368
   506
fun get_def thy = get_axiom thy o def_name;
wenzelm@4847
   507
paulson@1529
   508
wenzelm@776
   509
(*return additional axioms of this theory node*)
wenzelm@776
   510
fun axioms_of thy =
wenzelm@776
   511
  map (fn (s, _) => (s, get_axiom thy s))
wenzelm@6390
   512
    (Symtab.dest (#axioms (Theory.rep_theory thy)));
wenzelm@776
   513
wenzelm@6089
   514
wenzelm@6089
   515
(* name and tags -- make proof objects more readable *)
wenzelm@6089
   516
wenzelm@12923
   517
fun get_name_tags (Thm {hyps, prop, der = (_, prf), ...}) =
wenzelm@12923
   518
  Pt.get_name_tags hyps prop prf;
wenzelm@4018
   519
berghofe@13658
   520
fun put_name_tags x (Thm {sign_ref, der = (ora, prf), maxidx,
berghofe@13658
   521
      shyps, hyps, tpairs = [], prop}) = Thm {sign_ref = sign_ref,
berghofe@13658
   522
        der = (ora, Pt.thm_proof (Sign.deref sign_ref) x hyps prop prf),
berghofe@13658
   523
        maxidx = maxidx, shyps = shyps, hyps = hyps, tpairs = [], prop = prop}
berghofe@13658
   524
  | put_name_tags _ thm =
berghofe@13658
   525
      raise THM ("put_name_tags: unsolved flex-flex constraints", 0, [thm]);
wenzelm@6089
   526
wenzelm@6089
   527
val name_of_thm = #1 o get_name_tags;
wenzelm@6089
   528
val tags_of_thm = #2 o get_name_tags;
wenzelm@6089
   529
wenzelm@6089
   530
fun name_thm (name, thm) = put_name_tags (name, tags_of_thm thm) thm;
clasohm@0
   531
clasohm@0
   532
paulson@1529
   533
(*Compression of theorems -- a separate rule, not integrated with the others,
paulson@1529
   534
  as it could be slow.*)
berghofe@13658
   535
fun compress (Thm {sign_ref, der, maxidx, shyps, hyps, tpairs, prop}) = 
wenzelm@3967
   536
    Thm {sign_ref = sign_ref, 
wenzelm@2386
   537
         der = der,     (*No derivation recorded!*)
wenzelm@2386
   538
         maxidx = maxidx,
wenzelm@2386
   539
         shyps = shyps, 
wenzelm@2386
   540
         hyps = map Term.compress_term hyps, 
berghofe@13658
   541
         tpairs = map (pairself Term.compress_term) tpairs,
wenzelm@2386
   542
         prop = Term.compress_term prop};
wenzelm@564
   543
wenzelm@387
   544
wenzelm@2509
   545
paulson@1529
   546
(*** Meta rules ***)
clasohm@0
   547
wenzelm@1220
   548
(** 'primitive' rules **)
wenzelm@1220
   549
wenzelm@1220
   550
(*discharge all assumptions t from ts*)
clasohm@0
   551
val disch = gen_rem (op aconv);
clasohm@0
   552
wenzelm@1220
   553
(*The assumption rule A|-A in a theory*)
wenzelm@5344
   554
fun assume raw_ct : thm =
wenzelm@5344
   555
  let val ct as Cterm {sign_ref, t=prop, T, maxidx} = adjust_maxidx raw_ct
wenzelm@250
   556
  in  if T<>propT then
wenzelm@250
   557
        raise THM("assume: assumptions must have type prop", 0, [])
clasohm@0
   558
      else if maxidx <> ~1 then
wenzelm@250
   559
        raise THM("assume: assumptions may not contain scheme variables",
wenzelm@250
   560
                  maxidx, [])
wenzelm@3967
   561
      else Thm{sign_ref   = sign_ref,
berghofe@11518
   562
               der    = Pt.infer_derivs' I (false, Pt.Hyp prop),
wenzelm@2386
   563
               maxidx = ~1, 
wenzelm@2386
   564
               shyps  = add_term_sorts(prop,[]), 
wenzelm@2386
   565
               hyps   = [prop], 
berghofe@13658
   566
               tpairs = [],
wenzelm@2386
   567
               prop   = prop}
clasohm@0
   568
  end;
clasohm@0
   569
wenzelm@1220
   570
(*Implication introduction
wenzelm@3529
   571
    [A]
wenzelm@3529
   572
     :
wenzelm@3529
   573
     B
wenzelm@1220
   574
  -------
wenzelm@1220
   575
  A ==> B
wenzelm@1220
   576
*)
berghofe@13658
   577
fun implies_intr cA (thB as Thm{sign_ref,der,maxidx,hyps,shyps,tpairs,prop}) : thm =
wenzelm@3967
   578
  let val Cterm {sign_ref=sign_refA, t=A, T, maxidx=maxidxA} = cA
clasohm@0
   579
  in  if T<>propT then
wenzelm@250
   580
        raise THM("implies_intr: assumptions must have type prop", 0, [thB])
berghofe@10416
   581
      else
berghofe@10416
   582
         Thm{sign_ref = Sign.merge_refs (sign_ref,sign_refA),  
berghofe@11518
   583
             der = Pt.infer_derivs' (Pt.implies_intr_proof A) der,
wenzelm@2386
   584
             maxidx = Int.max(maxidxA, maxidx),
berghofe@10416
   585
             shyps = add_term_sorts (A, shyps),
wenzelm@2386
   586
             hyps = disch(hyps,A),
berghofe@13658
   587
             tpairs = tpairs,
berghofe@10416
   588
             prop = implies$A$prop}
clasohm@0
   589
      handle TERM _ =>
clasohm@0
   590
        raise THM("implies_intr: incompatible signatures", 0, [thB])
clasohm@0
   591
  end;
clasohm@0
   592
paulson@1529
   593
wenzelm@1220
   594
(*Implication elimination
wenzelm@1220
   595
  A ==> B    A
wenzelm@1220
   596
  ------------
wenzelm@1220
   597
        B
wenzelm@1220
   598
*)
clasohm@0
   599
fun implies_elim thAB thA : thm =
berghofe@13658
   600
    let val Thm{maxidx=maxA, der=derA, hyps=hypsA, shyps=shypsA, tpairs=tpairsA, prop=propA, ...} = thA
berghofe@13658
   601
        and Thm{der, maxidx, hyps, shyps, tpairs, prop, ...} = thAB;
wenzelm@250
   602
        fun err(a) = raise THM("implies_elim: "^a, 0, [thAB,thA])
clasohm@0
   603
    in  case prop of
wenzelm@250
   604
            imp$A$B =>
wenzelm@250
   605
                if imp=implies andalso  A aconv propA
berghofe@10416
   606
                then
berghofe@10416
   607
                  Thm{sign_ref= merge_thm_sgs(thAB,thA),
berghofe@11612
   608
                      der = Pt.infer_derivs (curry Pt.%%) der derA,
berghofe@10416
   609
                      maxidx = Int.max(maxA,maxidx),
wenzelm@14791
   610
                      shyps = Sorts.union_sort (shypsA, shyps),
berghofe@10416
   611
                      hyps = union_term(hypsA,hyps),  (*dups suppressed*)
berghofe@13658
   612
                      tpairs = tpairsA @ tpairs,
berghofe@10416
   613
                      prop = B}
wenzelm@250
   614
                else err("major premise")
wenzelm@250
   615
          | _ => err("major premise")
clasohm@0
   616
    end;
wenzelm@250
   617
wenzelm@1220
   618
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@1220
   619
    A
wenzelm@1220
   620
  -----
wenzelm@1220
   621
  !!x.A
wenzelm@1220
   622
*)
berghofe@13658
   623
fun forall_intr cx (th as Thm{sign_ref,der,maxidx,hyps,tpairs,prop,...}) =
lcp@229
   624
  let val x = term_of cx;
berghofe@13658
   625
      fun result a T = fix_shyps [th] []
wenzelm@3967
   626
        (Thm{sign_ref = sign_ref, 
berghofe@11518
   627
             der = Pt.infer_derivs' (Pt.forall_intr_proof x a) der,
wenzelm@2386
   628
             maxidx = maxidx,
wenzelm@2386
   629
             shyps = [],
wenzelm@2386
   630
             hyps = hyps,
berghofe@13658
   631
             tpairs = tpairs,
wenzelm@2386
   632
             prop = all(T) $ Abs(a, T, abstract_over (x,prop))})
berghofe@13658
   633
      fun check_occs x ts =
berghofe@13658
   634
        if exists (apl(x, Logic.occs)) ts
berghofe@13658
   635
        then raise THM("forall_intr: variable free in assumptions", 0, [th])
berghofe@13658
   636
        else ()
clasohm@0
   637
  in  case x of
berghofe@13658
   638
        Free(a,T) => (check_occs x (hyps @ terms_of_tpairs tpairs); result a T)
berghofe@13658
   639
      | Var((a,_),T) => (check_occs x (terms_of_tpairs tpairs); result a T)
clasohm@0
   640
      | _ => raise THM("forall_intr: not a variable", 0, [th])
clasohm@0
   641
  end;
clasohm@0
   642
wenzelm@1220
   643
(*Forall elimination
wenzelm@1220
   644
  !!x.A
wenzelm@1220
   645
  ------
wenzelm@1220
   646
  A[t/x]
wenzelm@1220
   647
*)
berghofe@13658
   648
fun forall_elim ct (th as Thm{sign_ref,der,maxidx,hyps,tpairs,prop,...}) : thm =
wenzelm@3967
   649
  let val Cterm {sign_ref=sign_reft, t, T, maxidx=maxt} = ct
clasohm@0
   650
  in  case prop of
wenzelm@2386
   651
        Const("all",Type("fun",[Type("fun",[qary,_]),_])) $ A =>
wenzelm@2386
   652
          if T<>qary then
wenzelm@2386
   653
              raise THM("forall_elim: type mismatch", 0, [th])
berghofe@15797
   654
          else fix_shyps [th] []
wenzelm@3967
   655
                    (Thm{sign_ref= Sign.merge_refs(sign_ref,sign_reft),
skalberg@15531
   656
                         der = Pt.infer_derivs' (Pt.% o rpair (SOME t)) der,
wenzelm@2386
   657
                         maxidx = Int.max(maxidx, maxt),
wenzelm@2386
   658
                         shyps = [],
wenzelm@2386
   659
                         hyps = hyps,  
berghofe@13658
   660
                         tpairs = tpairs,
wenzelm@2386
   661
                         prop = betapply(A,t)})
paulson@2147
   662
      | _ => raise THM("forall_elim: not quantified", 0, [th])
clasohm@0
   663
  end
clasohm@0
   664
  handle TERM _ =>
wenzelm@250
   665
         raise THM("forall_elim: incompatible signatures", 0, [th]);
clasohm@0
   666
clasohm@0
   667
wenzelm@1220
   668
(* Equality *)
clasohm@0
   669
clasohm@0
   670
(*The reflexivity rule: maps  t   to the theorem   t==t   *)
wenzelm@250
   671
fun reflexive ct =
wenzelm@3967
   672
  let val Cterm {sign_ref, t, T, maxidx} = ct
berghofe@10416
   673
  in Thm{sign_ref= sign_ref, 
berghofe@11518
   674
         der = Pt.infer_derivs' I (false, Pt.reflexive),
berghofe@10416
   675
         shyps = add_term_sorts (t, []),
berghofe@10416
   676
         hyps = [], 
berghofe@10416
   677
         maxidx = maxidx,
berghofe@13658
   678
         tpairs = [],
berghofe@10416
   679
         prop = Logic.mk_equals(t,t)}
clasohm@0
   680
  end;
clasohm@0
   681
clasohm@0
   682
(*The symmetry rule
wenzelm@1220
   683
  t==u
wenzelm@1220
   684
  ----
wenzelm@1220
   685
  u==t
wenzelm@1220
   686
*)
berghofe@13658
   687
fun symmetric (th as Thm{sign_ref,der,maxidx,shyps,hyps,tpairs,prop}) =
clasohm@0
   688
  case prop of
berghofe@11518
   689
      (eq as Const("==", Type (_, [T, _]))) $ t $ u =>
wenzelm@1238
   690
        (*no fix_shyps*)
wenzelm@3967
   691
          Thm{sign_ref = sign_ref,
berghofe@11518
   692
              der = Pt.infer_derivs' Pt.symmetric der,
wenzelm@2386
   693
              maxidx = maxidx,
wenzelm@2386
   694
              shyps = shyps,
wenzelm@2386
   695
              hyps = hyps,
berghofe@13658
   696
              tpairs = tpairs,
wenzelm@2386
   697
              prop = eq$u$t}
clasohm@0
   698
    | _ => raise THM("symmetric", 0, [th]);
clasohm@0
   699
clasohm@0
   700
(*The transitive rule
wenzelm@1220
   701
  t1==u    u==t2
wenzelm@1220
   702
  --------------
wenzelm@1220
   703
      t1==t2
wenzelm@1220
   704
*)
clasohm@0
   705
fun transitive th1 th2 =
berghofe@13658
   706
  let val Thm{der=der1, maxidx=max1, hyps=hyps1, shyps=shyps1, tpairs=tpairs1, prop=prop1,...} = th1
berghofe@13658
   707
      and Thm{der=der2, maxidx=max2, hyps=hyps2, shyps=shyps2, tpairs=tpairs2, prop=prop2,...} = th2;
clasohm@0
   708
      fun err(msg) = raise THM("transitive: "^msg, 0, [th1,th2])
clasohm@0
   709
  in case (prop1,prop2) of
berghofe@11518
   710
       ((eq as Const("==", Type (_, [T, _]))) $ t1 $ u, Const("==",_) $ u' $ t2) =>
nipkow@1634
   711
          if not (u aconv u') then err"middle term"
berghofe@15797
   712
          else
berghofe@10416
   713
                 Thm{sign_ref= merge_thm_sgs(th1,th2), 
berghofe@11518
   714
                     der = Pt.infer_derivs (Pt.transitive u T) der1 der2,
paulson@2147
   715
                     maxidx = Int.max(max1,max2), 
wenzelm@14791
   716
                     shyps = Sorts.union_sort (shyps1, shyps2),
wenzelm@2386
   717
                     hyps = union_term(hyps1,hyps2),
berghofe@13658
   718
                     tpairs = tpairs1 @ tpairs2,
berghofe@10416
   719
                     prop = eq$t1$t2}
clasohm@0
   720
     | _ =>  err"premises"
clasohm@0
   721
  end;
clasohm@0
   722
berghofe@10416
   723
(*Beta-conversion: maps (%x.t)(u) to the theorem (%x.t)(u) == t[u/x]
berghofe@10416
   724
  Fully beta-reduces the term if full=true
berghofe@10416
   725
*)
berghofe@10416
   726
fun beta_conversion full ct =
wenzelm@3967
   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@13658
   734
     tpairs = [],
wenzelm@10486
   735
     prop = Logic.mk_equals (t, if full then Envir.beta_norm t
berghofe@10416
   736
       else case t of
berghofe@10416
   737
          Abs(_, _, bodt) $ u => subst_bound (u, bodt)
berghofe@10416
   738
        | _ => raise THM ("beta_conversion: not a redex", 0, []))}
berghofe@10416
   739
  end;
berghofe@10416
   740
berghofe@10416
   741
fun eta_conversion ct =
berghofe@10416
   742
  let val Cterm {sign_ref, t, T, maxidx} = ct
berghofe@10416
   743
  in Thm
berghofe@10416
   744
    {sign_ref = sign_ref,  
berghofe@11518
   745
     der = Pt.infer_derivs' I (false, Pt.reflexive),
berghofe@10416
   746
     maxidx = maxidx,
berghofe@10416
   747
     shyps = add_term_sorts (t, []),
berghofe@10416
   748
     hyps = [],
berghofe@13658
   749
     tpairs = [],
berghofe@10416
   750
     prop = Logic.mk_equals (t, Pattern.eta_contract t)}
clasohm@0
   751
  end;
clasohm@0
   752
clasohm@0
   753
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   754
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@1220
   755
     t == u
wenzelm@1220
   756
  ------------
wenzelm@1220
   757
  %x.t == %x.u
wenzelm@1220
   758
*)
berghofe@13658
   759
fun abstract_rule a cx (th as Thm{sign_ref,der,maxidx,hyps,shyps,tpairs,prop}) =
lcp@229
   760
  let val x = term_of cx;
wenzelm@250
   761
      val (t,u) = Logic.dest_equals prop
wenzelm@250
   762
            handle TERM _ =>
wenzelm@250
   763
                raise THM("abstract_rule: premise not an equality", 0, [th])
berghofe@10416
   764
      fun result T =
berghofe@10416
   765
           Thm{sign_ref = sign_ref,
berghofe@11518
   766
               der = Pt.infer_derivs' (Pt.abstract_rule x a) der,
wenzelm@2386
   767
               maxidx = maxidx, 
berghofe@10416
   768
               shyps = add_typ_sorts (T, shyps), 
wenzelm@2386
   769
               hyps = hyps,
berghofe@13658
   770
               tpairs = tpairs,
wenzelm@2386
   771
               prop = Logic.mk_equals(Abs(a, T, abstract_over (x,t)),
berghofe@10416
   772
                                      Abs(a, T, abstract_over (x,u)))}
berghofe@13658
   773
      fun check_occs x ts =
berghofe@13658
   774
         if exists (apl(x, Logic.occs)) ts
berghofe@13658
   775
         then raise THM("abstract_rule: variable free in assumptions", 0, [th])
berghofe@13658
   776
         else ()
clasohm@0
   777
  in  case x of
berghofe@13658
   778
        Free(_,T) => (check_occs x (hyps @ terms_of_tpairs tpairs); result T)
berghofe@13658
   779
      | Var(_,T) => (check_occs x (terms_of_tpairs tpairs); result T)
clasohm@0
   780
      | _ => raise THM("abstract_rule: not a variable", 0, [th])
clasohm@0
   781
  end;
clasohm@0
   782
clasohm@0
   783
(*The combination rule
wenzelm@3529
   784
  f == g  t == u
wenzelm@3529
   785
  --------------
wenzelm@3529
   786
   f(t) == g(u)
wenzelm@1220
   787
*)
clasohm@0
   788
fun combination th1 th2 =
paulson@1529
   789
  let val Thm{der=der1, maxidx=max1, shyps=shyps1, hyps=hyps1, 
berghofe@13658
   790
              tpairs=tpairs1, prop=prop1,...} = th1
paulson@1529
   791
      and Thm{der=der2, maxidx=max2, shyps=shyps2, hyps=hyps2, 
berghofe@13658
   792
              tpairs=tpairs2, prop=prop2,...} = th2
berghofe@10416
   793
      fun chktypes fT tT =
berghofe@10416
   794
            (case fT of
wenzelm@2386
   795
                Type("fun",[T1,T2]) => 
berghofe@10416
   796
                    if T1 <> tT then
wenzelm@2386
   797
                         raise THM("combination: types", 0, [th1,th2])
wenzelm@2386
   798
                    else ()
wenzelm@2386
   799
                | _ => raise THM("combination: not function type", 0, 
wenzelm@2386
   800
                                 [th1,th2]))
nipkow@1495
   801
  in case (prop1,prop2)  of
berghofe@10416
   802
       (Const ("==", Type ("fun", [fT, _])) $ f $ g,
berghofe@10416
   803
        Const ("==", Type ("fun", [tT, _])) $ t $ u) =>
berghofe@15797
   804
          (chktypes fT tT;
berghofe@15797
   805
                        (*no fix_shyps*)
wenzelm@3967
   806
                        Thm{sign_ref = merge_thm_sgs(th1,th2), 
berghofe@11518
   807
                            der = Pt.infer_derivs
berghofe@11518
   808
                              (Pt.combination f g t u fT) der1 der2,
wenzelm@2386
   809
                            maxidx = Int.max(max1,max2), 
wenzelm@14791
   810
                            shyps = Sorts.union_sort(shyps1,shyps2),
wenzelm@2386
   811
                            hyps = union_term(hyps1,hyps2),
berghofe@13658
   812
                            tpairs = tpairs1 @ tpairs2,
berghofe@15797
   813
                            prop = Logic.mk_equals(f$t, g$u)})
clasohm@0
   814
     | _ =>  raise THM("combination: premises", 0, [th1,th2])
clasohm@0
   815
  end;
clasohm@0
   816
clasohm@0
   817
clasohm@0
   818
(* Equality introduction
wenzelm@3529
   819
  A ==> B  B ==> A
wenzelm@3529
   820
  ----------------
wenzelm@3529
   821
       A == B
wenzelm@1220
   822
*)
clasohm@0
   823
fun equal_intr th1 th2 =
berghofe@11518
   824
  let val Thm{der=der1, maxidx=max1, shyps=shyps1, hyps=hyps1, 
berghofe@13658
   825
              tpairs=tpairs1, prop=prop1,...} = th1
paulson@1529
   826
      and Thm{der=der2, maxidx=max2, shyps=shyps2, hyps=hyps2, 
berghofe@13658
   827
              tpairs=tpairs2, prop=prop2,...} = th2;
paulson@1529
   828
      fun err(msg) = raise THM("equal_intr: "^msg, 0, [th1,th2])
paulson@1529
   829
  in case (prop1,prop2) of
paulson@1529
   830
       (Const("==>",_) $ A $ B, Const("==>",_) $ B' $ A')  =>
wenzelm@2386
   831
          if A aconv A' andalso B aconv B'
wenzelm@2386
   832
          then
wenzelm@2386
   833
            (*no fix_shyps*)
wenzelm@3967
   834
              Thm{sign_ref = merge_thm_sgs(th1,th2),
berghofe@11518
   835
                  der = Pt.infer_derivs (Pt.equal_intr A B) der1 der2,
wenzelm@2386
   836
                  maxidx = Int.max(max1,max2),
wenzelm@14791
   837
                  shyps = Sorts.union_sort(shyps1,shyps2),
wenzelm@2386
   838
                  hyps = union_term(hyps1,hyps2),
berghofe@13658
   839
                  tpairs = tpairs1 @ tpairs2,
wenzelm@2386
   840
                  prop = Logic.mk_equals(A,B)}
wenzelm@2386
   841
          else err"not equal"
paulson@1529
   842
     | _ =>  err"premises"
paulson@1529
   843
  end;
paulson@1529
   844
paulson@1529
   845
paulson@1529
   846
(*The equal propositions rule
wenzelm@3529
   847
  A == B  A
paulson@1529
   848
  ---------
paulson@1529
   849
      B
paulson@1529
   850
*)
paulson@1529
   851
fun equal_elim th1 th2 =
berghofe@13658
   852
  let val Thm{der=der1, maxidx=max1, hyps=hyps1, tpairs=tpairs1, prop=prop1,...} = th1
berghofe@13658
   853
      and Thm{der=der2, maxidx=max2, hyps=hyps2, tpairs=tpairs2, prop=prop2,...} = th2;
paulson@1529
   854
      fun err(msg) = raise THM("equal_elim: "^msg, 0, [th1,th2])
paulson@1529
   855
  in  case prop1  of
paulson@1529
   856
       Const("==",_) $ A $ B =>
paulson@1529
   857
          if not (prop2 aconv A) then err"not equal"  else
paulson@1529
   858
            fix_shyps [th1, th2] []
wenzelm@3967
   859
              (Thm{sign_ref= merge_thm_sgs(th1,th2), 
berghofe@11518
   860
                   der = Pt.infer_derivs (Pt.equal_elim A B) der1 der2,
wenzelm@2386
   861
                   maxidx = Int.max(max1,max2),
wenzelm@2386
   862
                   shyps = [],
wenzelm@2386
   863
                   hyps = union_term(hyps1,hyps2),
berghofe@13658
   864
                   tpairs = tpairs1 @ tpairs2,
wenzelm@2386
   865
                   prop = B})
paulson@1529
   866
     | _ =>  err"major premise"
paulson@1529
   867
  end;
clasohm@0
   868
wenzelm@1220
   869
wenzelm@1220
   870
clasohm@0
   871
(**** Derived rules ****)
clasohm@0
   872
paulson@1503
   873
(*Discharge all hypotheses.  Need not verify cterms or call fix_shyps.
clasohm@0
   874
  Repeated hypotheses are discharged only once;  fold cannot do this*)
berghofe@13658
   875
fun implies_intr_hyps (Thm{sign_ref, der, maxidx, shyps, hyps=A::As, tpairs, prop}) =
wenzelm@1238
   876
      implies_intr_hyps (*no fix_shyps*)
wenzelm@3967
   877
            (Thm{sign_ref = sign_ref, 
berghofe@11518
   878
                 der = Pt.infer_derivs' (Pt.implies_intr_proof A) der,
wenzelm@2386
   879
                 maxidx = maxidx, 
wenzelm@2386
   880
                 shyps = shyps,
paulson@1529
   881
                 hyps = disch(As,A),  
berghofe@13658
   882
                 tpairs = tpairs,
wenzelm@2386
   883
                 prop = implies$A$prop})
clasohm@0
   884
  | implies_intr_hyps th = th;
clasohm@0
   885
clasohm@0
   886
(*Smash" unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@250
   887
  Instantiates the theorem and deletes trivial tpairs.
clasohm@0
   888
  Resulting sequence may contain multiple elements if the tpairs are
clasohm@0
   889
    not all flex-flex. *)
berghofe@13658
   890
fun flexflex_rule (th as Thm{sign_ref, der, maxidx, hyps, tpairs, prop, ...}) =
wenzelm@250
   891
  let fun newthm env =
paulson@1529
   892
          if Envir.is_empty env then th
paulson@1529
   893
          else
berghofe@13658
   894
          let val ntpairs = map (pairself (Envir.norm_term env)) tpairs;
berghofe@13658
   895
              val newprop = Envir.norm_term env prop;
wenzelm@250
   896
                (*Remove trivial tpairs, of the form t=t*)
skalberg@15570
   897
              val distpairs = List.filter (not o op aconv) ntpairs
wenzelm@1220
   898
          in  fix_shyps [th] (env_codT env)
wenzelm@3967
   899
                (Thm{sign_ref = sign_ref, 
berghofe@11518
   900
                     der = Pt.infer_derivs' (Pt.norm_proof' env) der,
berghofe@13658
   901
                     maxidx = maxidx_of_terms (newprop ::
berghofe@13658
   902
                       terms_of_tpairs distpairs),
wenzelm@2386
   903
                     shyps = [], 
wenzelm@2386
   904
                     hyps = hyps,
berghofe@13658
   905
                     tpairs = distpairs,
wenzelm@2386
   906
                     prop = newprop})
wenzelm@250
   907
          end;
wenzelm@4270
   908
  in Seq.map newthm
wenzelm@3967
   909
            (Unify.smash_unifiers(Sign.deref sign_ref, Envir.empty maxidx, tpairs))
clasohm@0
   910
  end;
clasohm@0
   911
clasohm@0
   912
(*Instantiation of Vars
wenzelm@1220
   913
           A
wenzelm@1220
   914
  -------------------
wenzelm@1220
   915
  A[t1/v1,....,tn/vn]
wenzelm@1220
   916
*)
clasohm@0
   917
wenzelm@6928
   918
local
wenzelm@6928
   919
clasohm@0
   920
(*Check that all the terms are Vars and are distinct*)
clasohm@0
   921
fun instl_ok ts = forall is_Var ts andalso null(findrep ts);
clasohm@0
   922
wenzelm@6928
   923
fun prt_typing sg_ref t T =
wenzelm@6928
   924
  let val sg = Sign.deref sg_ref in
wenzelm@6928
   925
    Pretty.block [Sign.pretty_term sg t, Pretty.str " ::", Pretty.brk 1, Sign.pretty_typ sg T]
wenzelm@6928
   926
  end;
wenzelm@6928
   927
berghofe@15797
   928
fun prt_type sg_ref T = Sign.pretty_typ (Sign.deref sg_ref) T;
berghofe@15797
   929
clasohm@0
   930
(*For instantiate: process pair of cterms, merge theories*)
wenzelm@3967
   931
fun add_ctpair ((ct,cu), (sign_ref,tpairs)) =
wenzelm@6928
   932
  let
wenzelm@6928
   933
    val Cterm {sign_ref=sign_reft, t=t, T= T, ...} = ct
wenzelm@6928
   934
    and Cterm {sign_ref=sign_refu, t=u, T= U, ...} = cu;
wenzelm@6928
   935
    val sign_ref_merged = Sign.merge_refs (sign_ref, Sign.merge_refs (sign_reft, sign_refu));
wenzelm@3967
   936
  in
wenzelm@6928
   937
    if T=U then (sign_ref_merged, (t,u)::tpairs)
wenzelm@6928
   938
    else raise TYPE (Pretty.string_of (Pretty.block [Pretty.str "instantiate: type conflict",
wenzelm@6928
   939
      Pretty.fbrk, prt_typing sign_ref_merged t T,
wenzelm@6928
   940
      Pretty.fbrk, prt_typing sign_ref_merged u U]), [T,U], [t,u])
clasohm@0
   941
  end;
clasohm@0
   942
berghofe@15797
   943
fun add_ctyp ((Ctyp {T = T as TVar (_, S), sign_ref = sign_refT},
berghofe@15797
   944
      Ctyp {T = U, sign_ref = sign_refU}), (sign_ref, vTs)) =
berghofe@15797
   945
      let
berghofe@15797
   946
        val sign_ref_merged = Sign.merge_refs
berghofe@15797
   947
          (sign_ref, Sign.merge_refs (sign_refT, sign_refU));
berghofe@15797
   948
        val sign = Sign.deref sign_ref_merged
berghofe@15797
   949
      in
berghofe@15797
   950
        if Type.of_sort (Sign.tsig_of sign) (U, S) then
berghofe@15797
   951
          (sign_ref_merged, (T, U) :: vTs)
berghofe@15797
   952
        else raise TYPE ("Type not of sort " ^
berghofe@15797
   953
          Sign.string_of_sort sign S, [U], [])
berghofe@15797
   954
      end
berghofe@15797
   955
  | add_ctyp ((Ctyp {T, sign_ref}, _), _) =
berghofe@15797
   956
      raise TYPE (Pretty.string_of (Pretty.block
berghofe@15797
   957
        [Pretty.str "instantiate: not a type variable",
berghofe@15797
   958
         Pretty.fbrk, prt_type sign_ref T]), [T], []);
clasohm@0
   959
wenzelm@6928
   960
in
wenzelm@6928
   961
clasohm@0
   962
(*Left-to-right replacements: ctpairs = [...,(vi,ti),...].
clasohm@0
   963
  Instantiates distinct Vars by terms of same type.
paulson@8129
   964
  No longer normalizes the new theorem! *)
paulson@1529
   965
fun instantiate ([], []) th = th
berghofe@13658
   966
  | instantiate (vcTs,ctpairs) (th as Thm{sign_ref,der,maxidx,hyps,shyps,tpairs=dpairs,prop}) =
skalberg@15574
   967
  let val (newsign_ref,tpairs) = foldr add_ctpair (sign_ref,[]) ctpairs;
skalberg@15574
   968
      val (newsign_ref,vTs) = foldr add_ctyp (newsign_ref,[]) vcTs;
wenzelm@14828
   969
      fun subst t =
berghofe@15797
   970
        subst_atomic tpairs (map_term_types (typ_subst_atomic vTs) t);
berghofe@13658
   971
      val newprop = subst prop;
berghofe@13658
   972
      val newdpairs = map (pairself subst) dpairs;
wenzelm@1220
   973
      val newth =
berghofe@10416
   974
            (Thm{sign_ref = newsign_ref, 
berghofe@11518
   975
                 der = Pt.infer_derivs' (Pt.instantiate vTs tpairs) der,
berghofe@13658
   976
                 maxidx = maxidx_of_terms (newprop ::
berghofe@13658
   977
                   terms_of_tpairs newdpairs), 
berghofe@10416
   978
                 shyps = add_insts_sorts ((vTs, tpairs), shyps),
berghofe@10416
   979
                 hyps = hyps,
berghofe@13658
   980
                 tpairs = newdpairs,
berghofe@10416
   981
                 prop = newprop})
wenzelm@250
   982
  in  if not(instl_ok(map #1 tpairs))
nipkow@193
   983
      then raise THM("instantiate: variables not distinct", 0, [th])
nipkow@193
   984
      else if not(null(findrep(map #1 vTs)))
nipkow@193
   985
      then raise THM("instantiate: type variables not distinct", 0, [th])
berghofe@15797
   986
      else newth
clasohm@0
   987
  end
wenzelm@6928
   988
  handle TERM _ => raise THM("instantiate: incompatible signatures", 0, [th])
wenzelm@6928
   989
       | TYPE (msg, _, _) => raise THM (msg, 0, [th]);
wenzelm@6928
   990
wenzelm@6928
   991
end;
wenzelm@6928
   992
clasohm@0
   993
clasohm@0
   994
(*The trivial implication A==>A, justified by assume and forall rules.
clasohm@0
   995
  A can contain Vars, not so for assume!   *)
wenzelm@250
   996
fun trivial ct : thm =
wenzelm@3967
   997
  let val Cterm {sign_ref, t=A, T, maxidx} = ct
wenzelm@250
   998
  in  if T<>propT then
wenzelm@250
   999
            raise THM("trivial: the term must have type prop", 0, [])
wenzelm@1238
  1000
      else fix_shyps [] []
wenzelm@3967
  1001
        (Thm{sign_ref = sign_ref, 
skalberg@15531
  1002
             der = Pt.infer_derivs' I (false, Pt.AbsP ("H", NONE, Pt.PBound 0)),
wenzelm@2386
  1003
             maxidx = maxidx, 
wenzelm@2386
  1004
             shyps = [], 
wenzelm@2386
  1005
             hyps = [],
berghofe@13658
  1006
             tpairs = [],
wenzelm@2386
  1007
             prop = implies$A$A})
clasohm@0
  1008
  end;
clasohm@0
  1009
paulson@1503
  1010
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)" *)
wenzelm@6368
  1011
fun class_triv sign c =
wenzelm@6368
  1012
  let val Cterm {sign_ref, t, maxidx, ...} =
wenzelm@6368
  1013
    cterm_of sign (Logic.mk_inclass (TVar (("'a", 0), [c]), c))
wenzelm@6368
  1014
      handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@399
  1015
  in
wenzelm@1238
  1016
    fix_shyps [] []
wenzelm@3967
  1017
      (Thm {sign_ref = sign_ref, 
berghofe@11518
  1018
            der = Pt.infer_derivs' I
skalberg@15531
  1019
              (false, Pt.PAxm ("ProtoPure.class_triv:" ^ c, t, SOME [])),
wenzelm@2386
  1020
            maxidx = maxidx, 
wenzelm@2386
  1021
            shyps = [], 
wenzelm@2386
  1022
            hyps = [], 
berghofe@13658
  1023
            tpairs = [],
wenzelm@2386
  1024
            prop = t})
wenzelm@399
  1025
  end;
wenzelm@399
  1026
wenzelm@399
  1027
wenzelm@6786
  1028
(* Replace all TFrees not fixed or in the hyps by new TVars *)
berghofe@13658
  1029
fun varifyT' fixed (Thm{sign_ref,der,maxidx,shyps,hyps,tpairs,prop}) =
wenzelm@12500
  1030
  let
berghofe@15797
  1031
    val tfrees = foldr add_term_tfrees fixed hyps;
berghofe@13658
  1032
    val prop1 = attach_tpairs tpairs prop;
berghofe@13658
  1033
    val (prop2, al) = Type.varify (prop1, tfrees);
berghofe@13658
  1034
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2)
berghofe@15797
  1035
  in (*no fix_shyps*)
berghofe@15797
  1036
   (Thm{sign_ref = sign_ref, 
berghofe@11518
  1037
        der = Pt.infer_derivs' (Pt.varify_proof prop tfrees) der,
wenzelm@2386
  1038
        maxidx = Int.max(0,maxidx), 
wenzelm@2386
  1039
        shyps = shyps, 
wenzelm@2386
  1040
        hyps = hyps,
berghofe@13658
  1041
        tpairs = rev (map Logic.dest_equals ts),
berghofe@15797
  1042
        prop = prop3}, al)
clasohm@0
  1043
  end;
clasohm@0
  1044
wenzelm@12500
  1045
val varifyT = #1 o varifyT' [];
wenzelm@6786
  1046
clasohm@0
  1047
(* Replace all TVars by new TFrees *)
berghofe@13658
  1048
fun freezeT(Thm{sign_ref,der,maxidx,shyps,hyps,tpairs,prop}) =
berghofe@13658
  1049
  let
berghofe@13658
  1050
    val prop1 = attach_tpairs tpairs prop;
berghofe@13658
  1051
    val (prop2, _) = Type.freeze_thaw prop1;
berghofe@13658
  1052
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2)
wenzelm@1238
  1053
  in (*no fix_shyps*)
wenzelm@3967
  1054
    Thm{sign_ref = sign_ref, 
berghofe@13658
  1055
        der = Pt.infer_derivs' (Pt.freezeT prop1) der,
berghofe@13658
  1056
        maxidx = maxidx_of_term prop2,
wenzelm@2386
  1057
        shyps = shyps,
wenzelm@2386
  1058
        hyps = hyps,
berghofe@13658
  1059
        tpairs = rev (map Logic.dest_equals ts),
berghofe@13658
  1060
        prop = prop3}
wenzelm@1220
  1061
  end;
clasohm@0
  1062
clasohm@0
  1063
clasohm@0
  1064
(*** Inference rules for tactics ***)
clasohm@0
  1065
clasohm@0
  1066
(*Destruct proof state into constraints, other goals, goal(i), rest *)
berghofe@13658
  1067
fun dest_state (state as Thm{prop,tpairs,...}, i) =
berghofe@13658
  1068
  (case  Logic.strip_prems(i, [], prop) of
berghofe@13658
  1069
      (B::rBs, C) => (tpairs, rev rBs, B, C)
berghofe@13658
  1070
    | _ => raise THM("dest_state", i, [state]))
clasohm@0
  1071
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1072
lcp@309
  1073
(*Increment variables and parameters of orule as required for
clasohm@0
  1074
  resolution with goal i of state. *)
clasohm@0
  1075
fun lift_rule (state, i) orule =
wenzelm@3967
  1076
  let val Thm{shyps=sshyps, prop=sprop, maxidx=smax, sign_ref=ssign_ref,...} = state
berghofe@13658
  1077
      val (Bi::_, _) = Logic.strip_prems(i, [], sprop)
paulson@1529
  1078
        handle TERM _ => raise THM("lift_rule", i, [orule,state])
wenzelm@3967
  1079
      val ct_Bi = Cterm {sign_ref=ssign_ref, maxidx=smax, T=propT, t=Bi}
paulson@1529
  1080
      val (lift_abs,lift_all) = Logic.lift_fns(Bi,smax+1)
berghofe@13658
  1081
      val (Thm{sign_ref, der, maxidx,shyps,hyps,tpairs,prop}) = orule
berghofe@13658
  1082
      val (As, B) = Logic.strip_horn prop
wenzelm@1238
  1083
  in  (*no fix_shyps*)
wenzelm@3967
  1084
      Thm{sign_ref = merge_thm_sgs(state,orule),
berghofe@11518
  1085
          der = Pt.infer_derivs' (Pt.lift_proof Bi (smax+1) prop) der,
wenzelm@2386
  1086
          maxidx = maxidx+smax+1,
wenzelm@14791
  1087
          shyps = Sorts.union_sort(sshyps,shyps), 
wenzelm@14791
  1088
          hyps = hyps, 
berghofe@13658
  1089
          tpairs = map (pairself lift_abs) tpairs,
berghofe@13658
  1090
          prop = Logic.list_implies (map lift_all As, lift_all B)}
clasohm@0
  1091
  end;
clasohm@0
  1092
berghofe@13658
  1093
fun incr_indexes i (thm as Thm {sign_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
berghofe@10416
  1094
  if i < 0 then raise THM ("negative increment", 0, [thm]) else
berghofe@10416
  1095
  if i = 0 then thm else
berghofe@10416
  1096
    Thm {sign_ref = sign_ref,
berghofe@11518
  1097
         der = Pt.infer_derivs' (Pt.map_proof_terms
berghofe@11518
  1098
           (Logic.incr_indexes ([], i)) (incr_tvar i)) der,
berghofe@10416
  1099
         maxidx = maxidx + i,
berghofe@10416
  1100
         shyps = shyps,
berghofe@10416
  1101
         hyps = hyps,
berghofe@13658
  1102
         tpairs = map (pairself (Logic.incr_indexes ([], i))) tpairs,
berghofe@10416
  1103
         prop = Logic.incr_indexes ([], i) prop};
berghofe@10416
  1104
clasohm@0
  1105
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1106
fun assumption i state =
wenzelm@3967
  1107
  let val Thm{sign_ref,der,maxidx,hyps,prop,...} = state;
clasohm@0
  1108
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
berghofe@11518
  1109
      fun newth n (env as Envir.Envir{maxidx, ...}, tpairs) =
wenzelm@1220
  1110
        fix_shyps [state] (env_codT env)
wenzelm@3967
  1111
          (Thm{sign_ref = sign_ref, 
berghofe@11518
  1112
               der = Pt.infer_derivs'
berghofe@11518
  1113
                 ((if Envir.is_empty env then I else (Pt.norm_proof' env)) o
berghofe@11518
  1114
                   Pt.assumption_proof Bs Bi n) der,
wenzelm@2386
  1115
               maxidx = maxidx,
wenzelm@2386
  1116
               shyps = [],
wenzelm@2386
  1117
               hyps = hyps,
berghofe@13658
  1118
               tpairs = if Envir.is_empty env then tpairs else
berghofe@13658
  1119
                 map (pairself (Envir.norm_term env)) tpairs,
wenzelm@2386
  1120
               prop = 
wenzelm@2386
  1121
               if Envir.is_empty env then (*avoid wasted normalizations*)
berghofe@13658
  1122
                   Logic.list_implies (Bs, C)
wenzelm@2386
  1123
               else (*normalize the new rule fully*)
berghofe@13658
  1124
                   Envir.norm_term env (Logic.list_implies (Bs, C))});
berghofe@11518
  1125
      fun addprfs [] _ = Seq.empty
berghofe@11518
  1126
        | addprfs ((t,u)::apairs) n = Seq.make (fn()=> Seq.pull
berghofe@11518
  1127
             (Seq.mapp (newth n)
wenzelm@3967
  1128
                (Unify.unifiers(Sign.deref sign_ref,Envir.empty maxidx, (t,u)::tpairs))
berghofe@11518
  1129
                (addprfs apairs (n+1))))
paulson@15454
  1130
  in  addprfs (Logic.assum_pairs (~1,Bi)) 1 end;
clasohm@0
  1131
wenzelm@250
  1132
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1133
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1134
fun eq_assumption i state =
wenzelm@3967
  1135
  let val Thm{sign_ref,der,maxidx,hyps,prop,...} = state;
clasohm@0
  1136
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
paulson@15454
  1137
  in  (case find_index (op aconv) (Logic.assum_pairs (~1,Bi)) of
berghofe@11518
  1138
         (~1) => raise THM("eq_assumption", 0, [state])
berghofe@11518
  1139
       | n => fix_shyps [state] []
berghofe@11518
  1140
                (Thm{sign_ref = sign_ref, 
berghofe@11518
  1141
                     der = Pt.infer_derivs'
berghofe@11518
  1142
                       (Pt.assumption_proof Bs Bi (n+1)) der,
berghofe@11518
  1143
                     maxidx = maxidx,
berghofe@11518
  1144
                     shyps = [],
berghofe@11518
  1145
                     hyps = hyps,
berghofe@13658
  1146
                     tpairs = tpairs,
berghofe@13658
  1147
                     prop = Logic.list_implies (Bs, C)}))
clasohm@0
  1148
  end;
clasohm@0
  1149
clasohm@0
  1150
paulson@2671
  1151
(*For rotate_tac: fast rotation of assumptions of subgoal i*)
paulson@2671
  1152
fun rotate_rule k i state =
berghofe@13658
  1153
  let val Thm{sign_ref,der,maxidx,hyps,prop,shyps,...} = state;
paulson@2671
  1154
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
paulson@8066
  1155
      val params = Term.strip_all_vars Bi
paulson@8066
  1156
      and rest   = Term.strip_all_body Bi
paulson@8066
  1157
      val asms   = Logic.strip_imp_prems rest
paulson@8066
  1158
      and concl  = Logic.strip_imp_concl rest
paulson@2671
  1159
      val n      = length asms
berghofe@11563
  1160
      val m      = if k<0 then n+k else k
berghofe@11563
  1161
      val Bi'    = if 0=m orelse m=n then Bi
paulson@2671
  1162
		   else if 0<m andalso m<n 
nipkow@13629
  1163
		   then let val (ps,qs) = splitAt(m,asms)
nipkow@13629
  1164
                        in list_all(params, Logic.list_implies(qs @ ps, concl))
nipkow@13629
  1165
			end
paulson@7248
  1166
		   else raise THM("rotate_rule", k, [state])
wenzelm@7264
  1167
  in  (*no fix_shyps*)
wenzelm@7264
  1168
      Thm{sign_ref = sign_ref, 
berghofe@11563
  1169
          der = Pt.infer_derivs' (Pt.rotate_proof Bs Bi m) der,
paulson@2671
  1170
	  maxidx = maxidx,
paulson@2671
  1171
	  shyps = shyps,
paulson@2671
  1172
	  hyps = hyps,
berghofe@13658
  1173
          tpairs = tpairs,
berghofe@13658
  1174
	  prop = Logic.list_implies (Bs @ [Bi'], C)}
paulson@2671
  1175
  end;
paulson@2671
  1176
paulson@2671
  1177
paulson@7248
  1178
(*Rotates a rule's premises to the left by k, leaving the first j premises
paulson@7248
  1179
  unchanged.  Does nothing if k=0 or if k equals n-j, where n is the
paulson@7248
  1180
  number of premises.  Useful with etac and underlies tactic/defer_tac*)
paulson@7248
  1181
fun permute_prems j k rl =
berghofe@13658
  1182
  let val Thm{sign_ref,der,maxidx,hyps,tpairs,prop,shyps} = rl
paulson@7248
  1183
      val prems  = Logic.strip_imp_prems prop
paulson@7248
  1184
      and concl  = Logic.strip_imp_concl prop
paulson@7248
  1185
      val moved_prems = List.drop(prems, j)
paulson@7248
  1186
      and fixed_prems = List.take(prems, j)
paulson@7248
  1187
        handle Subscript => raise THM("permute_prems:j", j, [rl])
paulson@7248
  1188
      val n_j    = length moved_prems
berghofe@11563
  1189
      val m = if k<0 then n_j + k else k
berghofe@11563
  1190
      val prop'  = if 0 = m orelse m = n_j then prop
paulson@7248
  1191
		   else if 0<m andalso m<n_j 
nipkow@13629
  1192
		   then let val (ps,qs) = splitAt(m,moved_prems)
nipkow@13629
  1193
			in Logic.list_implies(fixed_prems @ qs @ ps, concl) end
paulson@7248
  1194
		   else raise THM("permute_prems:k", k, [rl])
wenzelm@7264
  1195
  in  (*no fix_shyps*)
wenzelm@7264
  1196
      Thm{sign_ref = sign_ref, 
berghofe@11563
  1197
          der = Pt.infer_derivs' (Pt.permute_prems_prf prems j m) der,
paulson@7248
  1198
	  maxidx = maxidx,
paulson@7248
  1199
	  shyps = shyps,
paulson@7248
  1200
	  hyps = hyps,
berghofe@13658
  1201
          tpairs = tpairs,
berghofe@11563
  1202
	  prop = prop'}
paulson@7248
  1203
  end;
paulson@7248
  1204
paulson@7248
  1205
clasohm@0
  1206
(** User renaming of parameters in a subgoal **)
clasohm@0
  1207
clasohm@0
  1208
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1209
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1210
  The names in cs, if distinct, are used for the innermost parameters;
clasohm@0
  1211
   preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1212
fun rename_params_rule (cs, i) state =
berghofe@13658
  1213
  let val Thm{sign_ref,der,maxidx,hyps,shyps,...} = state
clasohm@0
  1214
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
clasohm@0
  1215
      val iparams = map #1 (Logic.strip_params Bi)
clasohm@0
  1216
      val short = length iparams - length cs
wenzelm@250
  1217
      val newnames =
wenzelm@250
  1218
            if short<0 then error"More names than abstractions!"
skalberg@15570
  1219
            else variantlist(Library.take (short,iparams), cs) @ cs
nipkow@3037
  1220
      val freenames = map (#1 o dest_Free) (term_frees Bi)
clasohm@0
  1221
      val newBi = Logic.list_rename_params (newnames, Bi)
wenzelm@250
  1222
  in
clasohm@0
  1223
  case findrep cs of
paulson@3565
  1224
     c::_ => (warning ("Can't rename.  Bound variables not distinct: " ^ c); 
paulson@3565
  1225
	      state)
berghofe@1576
  1226
   | [] => (case cs inter_string freenames of
paulson@3565
  1227
       a::_ => (warning ("Can't rename.  Bound/Free variable clash: " ^ a); 
paulson@3565
  1228
		state)
berghofe@13658
  1229
     | [] => Thm{sign_ref = sign_ref,
berghofe@13658
  1230
                 der = der,
berghofe@13658
  1231
                 maxidx = maxidx,
berghofe@13658
  1232
                 shyps = shyps,
berghofe@13658
  1233
                 hyps = hyps,
berghofe@13658
  1234
                 tpairs = tpairs,
berghofe@13658
  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
berghofe@13658
  1241
fun rename_boundvars pat obj (thm as Thm {sign_ref, der, maxidx, hyps, shyps, 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@12982
  1245
      {sign_ref = sign_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@250
  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$Abs(a,T,strip(t1,t2))
wenzelm@250
  1261
        | strip(A,_) = f A
clasohm@0
  1262
  in strip end;
clasohm@0
  1263
clasohm@0
  1264
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1265
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1266
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1267
fun rename_bvs([],_,_,_) = I
clasohm@0
  1268
  | rename_bvs(al,dpairs,tpairs,B) =
skalberg@15574
  1269
    let val vars = foldr add_term_vars []
skalberg@15574
  1270
                        (map fst dpairs @ map fst tpairs @ map snd tpairs)
wenzelm@250
  1271
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1272
        val vids = map (#1 o #1 o dest_Var) vars;
wenzelm@250
  1273
        fun rename(t as Var((x,i),T)) =
wenzelm@250
  1274
                (case assoc(al,x) of
skalberg@15531
  1275
                   SOME(y) => if x mem_string vids orelse y mem_string vids then t
wenzelm@250
  1276
                              else Var((y,i),T)
skalberg@15531
  1277
                 | NONE=> t)
clasohm@0
  1278
          | rename(Abs(x,T,t)) =
skalberg@15570
  1279
              Abs(getOpt(assoc_string(al,x),x), T, rename t)
clasohm@0
  1280
          | rename(f$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
paulson@1529
  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@3967
  1336
     val sign_ref = merge_thm_sgs(state,orule);
wenzelm@3967
  1337
     val sign = Sign.deref sign_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@1258
  1355
           val th = (*tuned fix_shyps*)
wenzelm@3967
  1356
             Thm{sign_ref = sign_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@14791
  1365
                 shyps = add_env_sorts (env, Sorts.union_sort(rshyps,sshyps)),
wenzelm@2386
  1366
                 hyps = union_term(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@4270
  1389
          (case Seq.pull(Unify.unifiers(sign, env, (t,u)::dpairs))  of
skalberg@15531
  1390
	      NONE                   => tryasms (A, As, n+1, apairs)
skalberg@15531
  1391
	    | cell as SOME((_,tpairs),_) =>
paulson@15454
  1392
		Seq.it_right (addth A (newAs(As, n, [BBi,(u,t)], tpairs)))
paulson@15454
  1393
		    (Seq.make(fn()=> cell),
paulson@15454
  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@4270
  1403
     else res(Seq.pull(Unify.unifiers(sign, 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@15672
  1441
fun invoke_oracle_i thy name =
wenzelm@3812
  1442
  let
wenzelm@6390
  1443
    val {sign = sg, oracles, ...} = Theory.rep_theory thy;
wenzelm@3812
  1444
    val oracle =
wenzelm@3812
  1445
      (case Symtab.lookup (oracles, name) of
skalberg@15531
  1446
        NONE => raise THM ("Unknown oracle: " ^ name, 0, [])
skalberg@15531
  1447
      | SOME (f, _) => f);
wenzelm@3812
  1448
  in
wenzelm@3812
  1449
    fn (sign, exn) =>
wenzelm@3812
  1450
      let
wenzelm@3967
  1451
        val sign_ref' = Sign.merge_refs (Sign.self_ref sg, Sign.self_ref sign);
wenzelm@3967
  1452
        val sign' = Sign.deref sign_ref';
wenzelm@14828
  1453
        val (prop, T, maxidx) =
wenzelm@14828
  1454
          Sign.certify_term (Sign.pp sign') sign' (oracle (sign', exn));
wenzelm@3812
  1455
      in
wenzelm@3812
  1456
        if T <> propT then
wenzelm@3812
  1457
          raise THM ("Oracle's result must have type prop: " ^ name, 0, [])
wenzelm@3812
  1458
        else fix_shyps [] []
wenzelm@3967
  1459
          (Thm {sign_ref = sign_ref', 
berghofe@11518
  1460
            der = (true, Pt.oracle_proof name prop),
wenzelm@3812
  1461
            maxidx = maxidx,
wenzelm@3812
  1462
            shyps = [], 
wenzelm@3812
  1463
            hyps = [], 
berghofe@13658
  1464
            tpairs = [],
wenzelm@3812
  1465
            prop = prop})
wenzelm@3812
  1466
      end
wenzelm@3812
  1467
  end;
wenzelm@3812
  1468
wenzelm@15672
  1469
fun invoke_oracle thy =
wenzelm@15672
  1470
  invoke_oracle_i thy o Sign.intern (Theory.sign_of thy) Theory.oracleK;
wenzelm@15672
  1471
paulson@1539
  1472
clasohm@0
  1473
end;
paulson@1503
  1474
wenzelm@6089
  1475
wenzelm@6089
  1476
structure BasicThm: BASIC_THM = Thm;
wenzelm@6089
  1477
open BasicThm;