src/Pure/thm.ML
author wenzelm
Thu Mar 05 19:48:02 2009 +0100 (2009-03-05)
changeset 30288 a32700e45ab3
parent 29636 d01bada1df33
child 30342 d32daa6aba3c
permissions -rw-r--r--
Thm.add_oracle interface: replaced old bstring by binding;
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(*  Title:      Pure/thm.ML
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Author:     Makarius
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The very core of Isabelle's Meta Logic: certified types and terms,
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derivations, theorems, framework rules (including lifting and
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resolution), oracles.
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*)
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signature BASIC_THM =
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  sig
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  (*certified types*)
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  type ctyp
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  val rep_ctyp: ctyp ->
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   {thy_ref: theory_ref,
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    T: typ,
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    maxidx: int,
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    sorts: sort OrdList.T}
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  val theory_of_ctyp: ctyp -> theory
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  val typ_of: ctyp -> typ
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  val ctyp_of: theory -> typ -> ctyp
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  (*certified terms*)
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  type cterm
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  exception CTERM of string * cterm list
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  val rep_cterm: cterm ->
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   {thy_ref: theory_ref,
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    t: term,
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    T: typ,
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    maxidx: int,
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    sorts: sort OrdList.T}
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  val crep_cterm: cterm ->
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    {thy_ref: theory_ref, t: term, T: ctyp, maxidx: int, sorts: sort OrdList.T}
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  val theory_of_cterm: cterm -> theory
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  val term_of: cterm -> term
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  val cterm_of: theory -> term -> cterm
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  val ctyp_of_term: cterm -> ctyp
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  (*theorems*)
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  type thm
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  type conv = cterm -> thm
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  type attribute = Context.generic * thm -> Context.generic * thm
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  val rep_thm: thm ->
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   {thy_ref: theory_ref,
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    tags: Properties.T,
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    maxidx: int,
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    shyps: sort OrdList.T,
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    hyps: term OrdList.T,
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    tpairs: (term * term) list,
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    prop: term}
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  val crep_thm: thm ->
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   {thy_ref: theory_ref,
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    tags: Properties.T,
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    maxidx: int,
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    shyps: sort OrdList.T,
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    hyps: cterm OrdList.T,
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    tpairs: (cterm * cterm) list,
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    prop: cterm}
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  exception THM of string * int * thm list
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  val theory_of_thm: thm -> theory
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  val prop_of: thm -> term
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  val tpairs_of: thm -> (term * term) list
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  val concl_of: thm -> term
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  val prems_of: thm -> term list
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  val nprems_of: thm -> int
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  val cprop_of: thm -> cterm
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  val cprem_of: thm -> int -> cterm
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  val transfer: theory -> thm -> thm
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  val weaken: cterm -> thm -> thm
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  val weaken_sorts: sort list -> cterm -> cterm
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  val extra_shyps: thm -> sort list
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  val strip_shyps: thm -> thm
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  (*meta rules*)
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  val assume: cterm -> 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 -> conv
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  val eta_conversion: conv
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  val eta_long_conversion: conv
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  val abstract_rule: string -> cterm -> thm -> thm
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  val combination: thm -> thm -> thm
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  val equal_intr: thm -> thm -> thm
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  val equal_elim: thm -> thm -> thm
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  val flexflex_rule: thm -> thm Seq.seq
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  val generalize: string list * string list -> int -> thm -> thm
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  val instantiate: (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm
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  val instantiate_cterm: (ctyp * ctyp) list * (cterm * cterm) list -> cterm -> cterm
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  val trivial: cterm -> thm
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  val class_triv: theory -> class -> thm
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  val unconstrainT: ctyp -> thm -> thm
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  val dest_state: thm * int -> (term * term) list * term list * term * term
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  val lift_rule: cterm -> 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 compose_no_flatten: bool -> thm * int -> int -> thm -> thm Seq.seq
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  val bicompose: bool -> bool * thm * int -> int -> thm -> thm Seq.seq
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  val biresolution: bool -> (bool * thm) list -> int -> thm -> thm Seq.seq
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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_fun: cterm -> cterm
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  val dest_arg: cterm -> cterm
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  val dest_fun2: cterm -> cterm
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  val dest_arg1: cterm -> cterm
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  val dest_abs: string option -> cterm -> cterm * cterm
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  val adjust_maxidx_cterm: int -> 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 terms_of_tpairs: (term * term) list -> term list
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  val maxidx_of: thm -> int
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  val maxidx_thm: thm -> int -> int
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  val hyps_of: thm -> term list
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  val full_prop_of: thm -> term
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  val axiom: theory -> string -> thm
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  val def_name: string -> string
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  val def_name_optional: string -> 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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  val get_name: thm -> string
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  val put_name: string -> thm -> thm
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  val get_tags: thm -> Properties.T
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  val map_tags: (Properties.T -> Properties.T) -> thm -> thm
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  val norm_proof: thm -> thm
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  val adjust_maxidx_thm: int -> thm -> thm
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  val rename_boundvars: term -> term -> thm -> thm
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  val match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
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  val first_order_match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
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  val incr_indexes_cterm: int -> cterm -> cterm
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  val varifyT: thm -> thm
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  val varifyT': (string * sort) list -> thm -> ((string * sort) * indexname) list * thm
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  val freezeT: thm -> thm
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  val future: thm future -> cterm -> thm
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  val pending_groups: thm -> Task_Queue.group list -> Task_Queue.group list
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  val proof_body_of: thm -> proof_body
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  val proof_of: thm -> proof
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  val join_proof: thm -> unit
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  val extern_oracles: theory -> xstring list
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  val add_oracle: binding * ('a -> cterm) -> theory -> (string * ('a -> thm)) * theory
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end;
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structure Thm:> THM =
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struct
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structure Pt = Proofterm;
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(*** Certified terms and types ***)
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(** certified types **)
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datatype ctyp = Ctyp of
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 {thy_ref: theory_ref,
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  T: typ,
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  maxidx: int,
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  sorts: sort OrdList.T};
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fun rep_ctyp (Ctyp args) = args;
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fun theory_of_ctyp (Ctyp {thy_ref, ...}) = Theory.deref thy_ref;
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fun typ_of (Ctyp {T, ...}) = T;
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fun ctyp_of thy raw_T =
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  let
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    val T = Sign.certify_typ thy raw_T;
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    val maxidx = Term.maxidx_of_typ T;
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    val sorts = Sorts.insert_typ T [];
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  in Ctyp {thy_ref = Theory.check_thy thy, T = T, maxidx = maxidx, sorts = sorts} end;
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fun dest_ctyp (Ctyp {thy_ref, T = Type (s, Ts), maxidx, sorts}) =
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      map (fn T => Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts}) Ts
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  | dest_ctyp cT = raise TYPE ("dest_ctyp", [typ_of cT], []);
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(** certified terms **)
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(*certified terms with checked typ, maxidx, and sorts*)
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datatype cterm = Cterm of
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 {thy_ref: theory_ref,
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  t: term,
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  T: typ,
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  maxidx: int,
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  sorts: sort OrdList.T};
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exception CTERM of string * cterm list;
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fun rep_cterm (Cterm args) = args;
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fun crep_cterm (Cterm {thy_ref, t, T, maxidx, sorts}) =
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  {thy_ref = thy_ref, t = t, maxidx = maxidx, sorts = sorts,
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    T = Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts}};
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fun theory_of_cterm (Cterm {thy_ref, ...}) = Theory.deref thy_ref;
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fun term_of (Cterm {t, ...}) = t;
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fun ctyp_of_term (Cterm {thy_ref, T, maxidx, sorts, ...}) =
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  Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts};
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fun cterm_of thy tm =
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  let
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    val (t, T, maxidx) = Sign.certify_term thy tm;
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    val sorts = Sorts.insert_term t [];
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  in Cterm {thy_ref = Theory.check_thy thy, t = t, T = T, maxidx = maxidx, sorts = sorts} end;
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fun merge_thys0 (Cterm {thy_ref = r1, t = t1, ...}) (Cterm {thy_ref = r2, t = t2, ...}) =
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  Theory.merge_refs (r1, r2);
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(* destructors *)
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fun dest_comb (ct as Cterm {t = c $ a, T, thy_ref, maxidx, sorts}) =
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      let val A = Term.argument_type_of c 0 in
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        (Cterm {t = c, T = A --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
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         Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
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      end
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  | dest_comb ct = raise CTERM ("dest_comb", [ct]);
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fun dest_fun (ct as Cterm {t = c $ _, T, thy_ref, maxidx, sorts}) =
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      let val A = Term.argument_type_of c 0
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      in Cterm {t = c, T = A --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
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  | dest_fun ct = raise CTERM ("dest_fun", [ct]);
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fun dest_arg (ct as Cterm {t = c $ a, T = _, thy_ref, maxidx, sorts}) =
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      let val A = Term.argument_type_of c 0
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      in Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
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  | dest_arg ct = raise CTERM ("dest_arg", [ct]);
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fun dest_fun2 (Cterm {t = c $ a $ b, T, thy_ref, maxidx, sorts}) =
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      let
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        val A = Term.argument_type_of c 0;
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        val B = Term.argument_type_of c 1;
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      in Cterm {t = c, T = A --> B --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
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  | dest_fun2 ct = raise CTERM ("dest_fun2", [ct]);
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fun dest_arg1 (Cterm {t = c $ a $ _, T = _, thy_ref, maxidx, sorts}) =
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      let val A = Term.argument_type_of c 0
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      in Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
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  | dest_arg1 ct = raise CTERM ("dest_arg1", [ct]);
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fun dest_abs a (ct as
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        Cterm {t = Abs (x, T, t), T = Type ("fun", [_, U]), thy_ref, maxidx, sorts}) =
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      let val (y', t') = Term.dest_abs (the_default x a, T, t) in
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        (Cterm {t = Free (y', T), T = T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
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          Cterm {t = t', T = U, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
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      end
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  | dest_abs _ ct = raise CTERM ("dest_abs", [ct]);
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(* constructors *)
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fun capply
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  (cf as Cterm {t = f, T = Type ("fun", [dty, rty]), maxidx = maxidx1, sorts = sorts1, ...})
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  (cx as Cterm {t = x, T, maxidx = maxidx2, sorts = sorts2, ...}) =
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    if T = dty then
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      Cterm {thy_ref = merge_thys0 cf cx,
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        t = f $ x,
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        T = rty,
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        maxidx = Int.max (maxidx1, maxidx2),
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        sorts = Sorts.union sorts1 sorts2}
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      else raise CTERM ("capply: types don't agree", [cf, cx])
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  | capply cf cx = raise CTERM ("capply: first arg is not a function", [cf, cx]);
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fun cabs
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  (ct1 as Cterm {t = t1, T = T1, maxidx = maxidx1, sorts = sorts1, ...})
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  (ct2 as Cterm {t = t2, T = T2, maxidx = maxidx2, sorts = sorts2, ...}) =
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    let val t = Term.lambda t1 t2 in
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      Cterm {thy_ref = merge_thys0 ct1 ct2,
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        t = t, T = T1 --> T2,
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        maxidx = Int.max (maxidx1, maxidx2),
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        sorts = Sorts.union sorts1 sorts2}
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    end;
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(* indexes *)
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fun adjust_maxidx_cterm i (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
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  if maxidx = i then ct
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  else if maxidx < i then
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    Cterm {maxidx = i, thy_ref = thy_ref, t = t, T = T, sorts = sorts}
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  else
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    Cterm {maxidx = Int.max (maxidx_of_term t, i), thy_ref = thy_ref, t = t, T = T, sorts = sorts};
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fun incr_indexes_cterm i (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
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  if i < 0 then raise CTERM ("negative increment", [ct])
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  else if i = 0 then ct
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  else Cterm {thy_ref = thy_ref, t = Logic.incr_indexes ([], i) t,
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    T = Logic.incr_tvar i T, maxidx = maxidx + i, sorts = sorts};
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(* matching *)
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local
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fun gen_match match
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    (ct1 as Cterm {t = t1, sorts = sorts1, ...},
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     ct2 as Cterm {t = t2, sorts = sorts2, maxidx = maxidx2, ...}) =
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   313
  let
wenzelm@24143
   314
    val thy = Theory.deref (merge_thys0 ct1 ct2);
wenzelm@24143
   315
    val (Tinsts, tinsts) = match thy (t1, t2) (Vartab.empty, Vartab.empty);
wenzelm@16601
   316
    val sorts = Sorts.union sorts1 sorts2;
wenzelm@20512
   317
    fun mk_cTinst ((a, i), (S, T)) =
wenzelm@24143
   318
      (Ctyp {T = TVar ((a, i), S), thy_ref = Theory.check_thy thy, maxidx = i, sorts = sorts},
wenzelm@24143
   319
       Ctyp {T = T, thy_ref = Theory.check_thy thy, maxidx = maxidx2, sorts = sorts});
wenzelm@20512
   320
    fun mk_ctinst ((x, i), (T, t)) =
wenzelm@16601
   321
      let val T = Envir.typ_subst_TVars Tinsts T in
wenzelm@24143
   322
        (Cterm {t = Var ((x, i), T), T = T, thy_ref = Theory.check_thy thy,
wenzelm@24143
   323
          maxidx = i, sorts = sorts},
wenzelm@24143
   324
         Cterm {t = t, T = T, thy_ref = Theory.check_thy thy, maxidx = maxidx2, sorts = sorts})
berghofe@10416
   325
      end;
wenzelm@16656
   326
  in (Vartab.fold (cons o mk_cTinst) Tinsts [], Vartab.fold (cons o mk_ctinst) tinsts []) end;
berghofe@10416
   327
wenzelm@22909
   328
in
berghofe@10416
   329
wenzelm@22909
   330
val match = gen_match Pattern.match;
wenzelm@22909
   331
val first_order_match = gen_match Pattern.first_order_match;
wenzelm@22909
   332
wenzelm@22909
   333
end;
berghofe@10416
   334
wenzelm@2509
   335
wenzelm@2509
   336
wenzelm@28321
   337
(*** Derivations and Theorems ***)
lcp@229
   338
wenzelm@28356
   339
datatype thm = Thm of
wenzelm@28378
   340
 deriv *                                        (*derivation*)
wenzelm@28378
   341
 {thy_ref: theory_ref,                          (*dynamic reference to theory*)
wenzelm@28378
   342
  tags: Properties.T,                           (*additional annotations/comments*)
wenzelm@28378
   343
  maxidx: int,                                  (*maximum index of any Var or TVar*)
wenzelm@28378
   344
  shyps: sort OrdList.T,                        (*sort hypotheses*)
wenzelm@28378
   345
  hyps: term OrdList.T,                         (*hypotheses*)
wenzelm@28378
   346
  tpairs: (term * term) list,                   (*flex-flex pairs*)
wenzelm@28378
   347
  prop: term}                                   (*conclusion*)
wenzelm@28624
   348
and deriv = Deriv of
wenzelm@28996
   349
 {max_promise: serial,
wenzelm@28996
   350
  open_promises: (serial * thm future) OrdList.T,
wenzelm@28978
   351
  promises: (serial * thm future) OrdList.T,
wenzelm@28804
   352
  body: Pt.proof_body};
clasohm@0
   353
wenzelm@23601
   354
type conv = cterm -> thm;
wenzelm@23601
   355
wenzelm@22365
   356
(*attributes subsume any kind of rules or context modifiers*)
wenzelm@22365
   357
type attribute = Context.generic * thm -> Context.generic * thm;
wenzelm@22365
   358
wenzelm@16725
   359
(*errors involving theorems*)
wenzelm@16725
   360
exception THM of string * int * thm list;
berghofe@13658
   361
wenzelm@28321
   362
fun rep_thm (Thm (_, args)) = args;
clasohm@0
   363
wenzelm@28321
   364
fun crep_thm (Thm (_, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@26631
   365
  let fun cterm max t = Cterm {thy_ref = thy_ref, t = t, T = propT, maxidx = max, sorts = shyps} in
wenzelm@28321
   366
   {thy_ref = thy_ref, tags = tags, maxidx = maxidx, shyps = shyps,
wenzelm@16425
   367
    hyps = map (cterm ~1) hyps,
wenzelm@16425
   368
    tpairs = map (pairself (cterm maxidx)) tpairs,
wenzelm@16425
   369
    prop = cterm maxidx prop}
clasohm@1517
   370
  end;
clasohm@1517
   371
wenzelm@16725
   372
fun terms_of_tpairs tpairs = fold_rev (fn (t, u) => cons t o cons u) tpairs [];
wenzelm@16725
   373
wenzelm@16725
   374
fun eq_tpairs ((t, u), (t', u')) = t aconv t' andalso u aconv u';
wenzelm@18944
   375
fun union_tpairs ts us = Library.merge eq_tpairs (ts, us);
wenzelm@16884
   376
val maxidx_tpairs = fold (fn (t, u) => Term.maxidx_term t #> Term.maxidx_term u);
wenzelm@16725
   377
wenzelm@16725
   378
fun attach_tpairs tpairs prop =
wenzelm@16725
   379
  Logic.list_implies (map Logic.mk_equals tpairs, prop);
wenzelm@16725
   380
wenzelm@28321
   381
fun full_prop_of (Thm (_, {tpairs, prop, ...})) = attach_tpairs tpairs prop;
wenzelm@16945
   382
wenzelm@29269
   383
val union_hyps = OrdList.union TermOrd.fast_term_ord;
wenzelm@29269
   384
val insert_hyps = OrdList.insert TermOrd.fast_term_ord;
wenzelm@29269
   385
val remove_hyps = OrdList.remove TermOrd.fast_term_ord;
wenzelm@22365
   386
wenzelm@16945
   387
wenzelm@24143
   388
(* merge theories of cterms/thms -- trivial absorption only *)
wenzelm@16945
   389
wenzelm@28321
   390
fun merge_thys1 (Cterm {thy_ref = r1, ...}) (th as Thm (_, {thy_ref = r2, ...})) =
wenzelm@23601
   391
  Theory.merge_refs (r1, r2);
wenzelm@16945
   392
wenzelm@28321
   393
fun merge_thys2 (th1 as Thm (_, {thy_ref = r1, ...})) (th2 as Thm (_, {thy_ref = r2, ...})) =
wenzelm@23601
   394
  Theory.merge_refs (r1, r2);
wenzelm@16945
   395
clasohm@0
   396
wenzelm@22365
   397
(* basic components *)
wenzelm@16135
   398
wenzelm@28321
   399
val theory_of_thm = Theory.deref o #thy_ref o rep_thm;
wenzelm@28321
   400
val maxidx_of = #maxidx o rep_thm;
wenzelm@19910
   401
fun maxidx_thm th i = Int.max (maxidx_of th, i);
wenzelm@28321
   402
val hyps_of = #hyps o rep_thm;
wenzelm@28321
   403
val prop_of = #prop o rep_thm;
wenzelm@28321
   404
val tpairs_of = #tpairs o rep_thm;
clasohm@0
   405
wenzelm@16601
   406
val concl_of = Logic.strip_imp_concl o prop_of;
wenzelm@16601
   407
val prems_of = Logic.strip_imp_prems o prop_of;
wenzelm@21576
   408
val nprems_of = Logic.count_prems o prop_of;
wenzelm@19305
   409
fun no_prems th = nprems_of th = 0;
wenzelm@16601
   410
wenzelm@16601
   411
fun major_prem_of th =
wenzelm@16601
   412
  (case prems_of th of
wenzelm@16601
   413
    prem :: _ => Logic.strip_assums_concl prem
wenzelm@16601
   414
  | [] => raise THM ("major_prem_of: rule with no premises", 0, [th]));
wenzelm@16601
   415
wenzelm@16601
   416
(*the statement of any thm is a cterm*)
wenzelm@28321
   417
fun cprop_of (Thm (_, {thy_ref, maxidx, shyps, prop, ...})) =
wenzelm@16601
   418
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, t = prop, sorts = shyps};
wenzelm@16601
   419
wenzelm@28321
   420
fun cprem_of (th as Thm (_, {thy_ref, maxidx, shyps, prop, ...})) i =
wenzelm@18035
   421
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, sorts = shyps,
wenzelm@18145
   422
    t = Logic.nth_prem (i, prop) handle TERM _ => raise THM ("cprem_of", i, [th])};
wenzelm@18035
   423
wenzelm@16656
   424
(*explicit transfer to a super theory*)
wenzelm@16425
   425
fun transfer thy' thm =
wenzelm@3895
   426
  let
wenzelm@28321
   427
    val Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop}) = thm;
wenzelm@16425
   428
    val thy = Theory.deref thy_ref;
wenzelm@26665
   429
    val _ = Theory.subthy (thy, thy') orelse raise THM ("transfer: not a super theory", 0, [thm]);
wenzelm@26665
   430
    val is_eq = Theory.eq_thy (thy, thy');
wenzelm@24143
   431
    val _ = Theory.check_thy thy;
wenzelm@3895
   432
  in
wenzelm@24143
   433
    if is_eq then thm
wenzelm@16945
   434
    else
wenzelm@28321
   435
      Thm (der,
wenzelm@28321
   436
       {thy_ref = Theory.check_thy thy',
wenzelm@21646
   437
        tags = tags,
wenzelm@16945
   438
        maxidx = maxidx,
wenzelm@16945
   439
        shyps = shyps,
wenzelm@16945
   440
        hyps = hyps,
wenzelm@16945
   441
        tpairs = tpairs,
wenzelm@28321
   442
        prop = prop})
wenzelm@3895
   443
  end;
wenzelm@387
   444
wenzelm@16945
   445
(*explicit weakening: maps |- B to A |- B*)
wenzelm@16945
   446
fun weaken raw_ct th =
wenzelm@16945
   447
  let
wenzelm@20261
   448
    val ct as Cterm {t = A, T, sorts, maxidx = maxidxA, ...} = adjust_maxidx_cterm ~1 raw_ct;
wenzelm@28321
   449
    val Thm (der, {tags, maxidx, shyps, hyps, tpairs, prop, ...}) = th;
wenzelm@16945
   450
  in
wenzelm@16945
   451
    if T <> propT then
wenzelm@16945
   452
      raise THM ("weaken: assumptions must have type prop", 0, [])
wenzelm@16945
   453
    else if maxidxA <> ~1 then
wenzelm@16945
   454
      raise THM ("weaken: assumptions may not contain schematic variables", maxidxA, [])
wenzelm@16945
   455
    else
wenzelm@28321
   456
      Thm (der,
wenzelm@28321
   457
       {thy_ref = merge_thys1 ct th,
wenzelm@21646
   458
        tags = tags,
wenzelm@16945
   459
        maxidx = maxidx,
wenzelm@16945
   460
        shyps = Sorts.union sorts shyps,
wenzelm@28354
   461
        hyps = insert_hyps A hyps,
wenzelm@16945
   462
        tpairs = tpairs,
wenzelm@28321
   463
        prop = prop})
wenzelm@16945
   464
  end;
wenzelm@16656
   465
wenzelm@28624
   466
fun weaken_sorts raw_sorts ct =
wenzelm@28624
   467
  let
wenzelm@28624
   468
    val Cterm {thy_ref, t, T, maxidx, sorts} = ct;
wenzelm@28624
   469
    val thy = Theory.deref thy_ref;
wenzelm@28624
   470
    val more_sorts = Sorts.make (map (Sign.certify_sort thy) raw_sorts);
wenzelm@28624
   471
    val sorts' = Sorts.union sorts more_sorts;
wenzelm@28624
   472
  in Cterm {thy_ref = Theory.check_thy thy, t = t, T = T, maxidx = maxidx, sorts = sorts'} end;
wenzelm@28624
   473
wenzelm@16656
   474
clasohm@0
   475
wenzelm@1238
   476
(** sort contexts of theorems **)
wenzelm@1238
   477
wenzelm@28321
   478
fun present_sorts (Thm (_, {hyps, tpairs, prop, ...})) =
wenzelm@16656
   479
  fold (fn (t, u) => Sorts.insert_term t o Sorts.insert_term u) tpairs
wenzelm@16656
   480
    (Sorts.insert_terms hyps (Sorts.insert_term prop []));
wenzelm@1238
   481
wenzelm@7642
   482
(*remove extra sorts that are non-empty by virtue of type signature information*)
wenzelm@28321
   483
fun strip_shyps (thm as Thm (_, {shyps = [], ...})) = thm
wenzelm@28321
   484
  | strip_shyps (thm as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@7642
   485
      let
wenzelm@16425
   486
        val thy = Theory.deref thy_ref;
wenzelm@26640
   487
        val present = present_sorts thm;
wenzelm@26640
   488
        val extra = Sorts.subtract present shyps;
wenzelm@28624
   489
        val extra' =
wenzelm@28624
   490
          Sorts.subtract (map #2 (Sign.witness_sorts thy present extra)) extra
wenzelm@28624
   491
          |> Sorts.minimal_sorts (Sign.classes_of thy);
wenzelm@28624
   492
        val shyps' = Sorts.union present extra';
wenzelm@7642
   493
      in
wenzelm@28321
   494
        Thm (der, {thy_ref = Theory.check_thy thy, tags = tags, maxidx = maxidx,
wenzelm@28321
   495
          shyps = shyps', hyps = hyps, tpairs = tpairs, prop = prop})
wenzelm@7642
   496
      end;
wenzelm@1238
   497
wenzelm@16656
   498
(*dangling sort constraints of a thm*)
wenzelm@28321
   499
fun extra_shyps (th as Thm (_, {shyps, ...})) = Sorts.subtract (present_sorts th) shyps;
wenzelm@28321
   500
wenzelm@28321
   501
wenzelm@28321
   502
wenzelm@28321
   503
(** derivations **)
wenzelm@28321
   504
wenzelm@28996
   505
fun make_deriv max_promise open_promises promises oracles thms proof =
wenzelm@28996
   506
  Deriv {max_promise = max_promise, open_promises = open_promises, promises = promises,
wenzelm@28804
   507
    body = PBody {oracles = oracles, thms = thms, proof = proof}};
wenzelm@28321
   508
wenzelm@28996
   509
val empty_deriv = make_deriv ~1 [] [] [] [] Pt.MinProof;
wenzelm@28321
   510
wenzelm@28330
   511
wenzelm@28354
   512
(* inference rules *)
wenzelm@28321
   513
wenzelm@28378
   514
fun promise_ord ((i, _), (j, _)) = int_ord (j, i);
wenzelm@28330
   515
wenzelm@28321
   516
fun deriv_rule2 f
wenzelm@28996
   517
    (Deriv {max_promise = max1, open_promises = open_ps1, promises = ps1,
wenzelm@28804
   518
      body = PBody {oracles = oras1, thms = thms1, proof = prf1}})
wenzelm@28996
   519
    (Deriv {max_promise = max2, open_promises = open_ps2, promises = ps2,
wenzelm@28804
   520
      body = PBody {oracles = oras2, thms = thms2, proof = prf2}}) =
wenzelm@28321
   521
  let
wenzelm@28996
   522
    val max = Int.max (max1, max2);
wenzelm@28996
   523
    val open_ps = OrdList.union promise_ord open_ps1 open_ps2;
wenzelm@28330
   524
    val ps = OrdList.union promise_ord ps1 ps2;
wenzelm@28804
   525
    val oras = Pt.merge_oracles oras1 oras2;
wenzelm@28804
   526
    val thms = Pt.merge_thms thms1 thms2;
wenzelm@28321
   527
    val prf =
wenzelm@28321
   528
      (case ! Pt.proofs of
wenzelm@28321
   529
        2 => f prf1 prf2
wenzelm@28804
   530
      | 1 => MinProof
wenzelm@28804
   531
      | 0 => MinProof
wenzelm@28321
   532
      | i => error ("Illegal level of detail for proof objects: " ^ string_of_int i));
wenzelm@28996
   533
  in make_deriv max open_ps ps oras thms prf end;
wenzelm@28321
   534
wenzelm@28321
   535
fun deriv_rule1 f = deriv_rule2 (K f) empty_deriv;
wenzelm@28996
   536
fun deriv_rule0 prf = deriv_rule1 I (make_deriv ~1 [] [] [] [] prf);
wenzelm@28321
   537
wenzelm@1238
   538
wenzelm@1238
   539
paulson@1529
   540
(** Axioms **)
wenzelm@387
   541
wenzelm@28675
   542
fun axiom theory name =
wenzelm@387
   543
  let
wenzelm@16425
   544
    fun get_ax thy =
wenzelm@22685
   545
      Symtab.lookup (Theory.axiom_table thy) name
wenzelm@16601
   546
      |> Option.map (fn prop =>
wenzelm@24143
   547
           let
wenzelm@28321
   548
             val der = deriv_rule0 (Pt.axm_proof name prop);
wenzelm@24143
   549
             val maxidx = maxidx_of_term prop;
wenzelm@26640
   550
             val shyps = Sorts.insert_term prop [];
wenzelm@24143
   551
           in
wenzelm@28321
   552
             Thm (der, {thy_ref = Theory.check_thy thy, tags = [],
wenzelm@28321
   553
               maxidx = maxidx, shyps = shyps, hyps = [], tpairs = [], prop = prop})
wenzelm@24143
   554
           end);
wenzelm@387
   555
  in
wenzelm@16425
   556
    (case get_first get_ax (theory :: Theory.ancestors_of theory) of
skalberg@15531
   557
      SOME thm => thm
skalberg@15531
   558
    | NONE => raise THEORY ("No axiom " ^ quote name, [theory]))
wenzelm@387
   559
  end;
wenzelm@387
   560
wenzelm@20884
   561
fun def_name c = c ^ "_def";
wenzelm@20884
   562
wenzelm@20884
   563
fun def_name_optional c "" = def_name c
wenzelm@20884
   564
  | def_name_optional _ name = name;
wenzelm@20884
   565
wenzelm@28675
   566
fun get_def thy = axiom thy o NameSpace.intern (Theory.axiom_space thy) o def_name;
wenzelm@4847
   567
paulson@1529
   568
wenzelm@776
   569
(*return additional axioms of this theory node*)
wenzelm@776
   570
fun axioms_of thy =
wenzelm@28675
   571
  map (fn s => (s, axiom thy s)) (Symtab.keys (Theory.axiom_table thy));
wenzelm@776
   572
wenzelm@6089
   573
wenzelm@28804
   574
(* tags *)
wenzelm@6089
   575
wenzelm@21646
   576
val get_tags = #tags o rep_thm;
wenzelm@6089
   577
wenzelm@28321
   578
fun map_tags f (Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@28321
   579
  Thm (der, {thy_ref = thy_ref, tags = f tags, maxidx = maxidx,
wenzelm@28321
   580
    shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop});
clasohm@0
   581
clasohm@0
   582
wenzelm@28321
   583
fun norm_proof (Thm (der, args as {thy_ref, ...})) =
wenzelm@24143
   584
  let
wenzelm@24143
   585
    val thy = Theory.deref thy_ref;
wenzelm@28321
   586
    val der' = deriv_rule1 (Pt.rew_proof thy) der;
wenzelm@28321
   587
    val _ = Theory.check_thy thy;
wenzelm@28321
   588
  in Thm (der', args) end;
berghofe@23781
   589
wenzelm@28321
   590
fun adjust_maxidx_thm i (th as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@20261
   591
  if maxidx = i then th
wenzelm@20261
   592
  else if maxidx < i then
wenzelm@28321
   593
    Thm (der, {maxidx = i, thy_ref = thy_ref, tags = tags, shyps = shyps,
wenzelm@28321
   594
      hyps = hyps, tpairs = tpairs, prop = prop})
wenzelm@20261
   595
  else
wenzelm@28321
   596
    Thm (der, {maxidx = Int.max (maxidx_tpairs tpairs (maxidx_of_term prop), i), thy_ref = thy_ref,
wenzelm@28321
   597
      tags = tags, shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop});
wenzelm@564
   598
wenzelm@387
   599
wenzelm@2509
   600
paulson@1529
   601
(*** Meta rules ***)
clasohm@0
   602
wenzelm@16601
   603
(** primitive rules **)
clasohm@0
   604
wenzelm@16656
   605
(*The assumption rule A |- A*)
wenzelm@16601
   606
fun assume raw_ct =
wenzelm@20261
   607
  let val Cterm {thy_ref, t = prop, T, maxidx, sorts} = adjust_maxidx_cterm ~1 raw_ct in
wenzelm@16601
   608
    if T <> propT then
mengj@19230
   609
      raise THM ("assume: prop", 0, [])
wenzelm@16601
   610
    else if maxidx <> ~1 then
mengj@19230
   611
      raise THM ("assume: variables", maxidx, [])
wenzelm@28321
   612
    else Thm (deriv_rule0 (Pt.Hyp prop),
wenzelm@28321
   613
     {thy_ref = thy_ref,
wenzelm@21646
   614
      tags = [],
wenzelm@16601
   615
      maxidx = ~1,
wenzelm@16601
   616
      shyps = sorts,
wenzelm@16601
   617
      hyps = [prop],
wenzelm@16601
   618
      tpairs = [],
wenzelm@28321
   619
      prop = prop})
clasohm@0
   620
  end;
clasohm@0
   621
wenzelm@1220
   622
(*Implication introduction
wenzelm@3529
   623
    [A]
wenzelm@3529
   624
     :
wenzelm@3529
   625
     B
wenzelm@1220
   626
  -------
wenzelm@1220
   627
  A ==> B
wenzelm@1220
   628
*)
wenzelm@16601
   629
fun implies_intr
wenzelm@16679
   630
    (ct as Cterm {t = A, T, maxidx = maxidxA, sorts, ...})
wenzelm@28321
   631
    (th as Thm (der, {maxidx, hyps, shyps, tpairs, prop, ...})) =
wenzelm@16601
   632
  if T <> propT then
wenzelm@16601
   633
    raise THM ("implies_intr: assumptions must have type prop", 0, [th])
wenzelm@16601
   634
  else
wenzelm@28321
   635
    Thm (deriv_rule1 (Pt.implies_intr_proof A) der,
wenzelm@28321
   636
     {thy_ref = merge_thys1 ct th,
wenzelm@21646
   637
      tags = [],
wenzelm@16601
   638
      maxidx = Int.max (maxidxA, maxidx),
wenzelm@16601
   639
      shyps = Sorts.union sorts shyps,
wenzelm@28354
   640
      hyps = remove_hyps A hyps,
wenzelm@16601
   641
      tpairs = tpairs,
wenzelm@28321
   642
      prop = Logic.mk_implies (A, prop)});
clasohm@0
   643
paulson@1529
   644
wenzelm@1220
   645
(*Implication elimination
wenzelm@1220
   646
  A ==> B    A
wenzelm@1220
   647
  ------------
wenzelm@1220
   648
        B
wenzelm@1220
   649
*)
wenzelm@16601
   650
fun implies_elim thAB thA =
wenzelm@16601
   651
  let
wenzelm@28321
   652
    val Thm (derA, {maxidx = maxA, hyps = hypsA, shyps = shypsA, tpairs = tpairsA,
wenzelm@28321
   653
      prop = propA, ...}) = thA
wenzelm@28321
   654
    and Thm (der, {maxidx, hyps, shyps, tpairs, prop, ...}) = thAB;
wenzelm@16601
   655
    fun err () = raise THM ("implies_elim: major premise", 0, [thAB, thA]);
wenzelm@16601
   656
  in
wenzelm@16601
   657
    case prop of
wenzelm@20512
   658
      Const ("==>", _) $ A $ B =>
wenzelm@20512
   659
        if A aconv propA then
wenzelm@28321
   660
          Thm (deriv_rule2 (curry Pt.%%) der derA,
wenzelm@28321
   661
           {thy_ref = merge_thys2 thAB thA,
wenzelm@21646
   662
            tags = [],
wenzelm@16601
   663
            maxidx = Int.max (maxA, maxidx),
wenzelm@16601
   664
            shyps = Sorts.union shypsA shyps,
wenzelm@16601
   665
            hyps = union_hyps hypsA hyps,
wenzelm@16601
   666
            tpairs = union_tpairs tpairsA tpairs,
wenzelm@28321
   667
            prop = B})
wenzelm@16601
   668
        else err ()
wenzelm@16601
   669
    | _ => err ()
wenzelm@16601
   670
  end;
wenzelm@250
   671
wenzelm@1220
   672
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@16656
   673
    [x]
wenzelm@16656
   674
     :
wenzelm@16656
   675
     A
wenzelm@16656
   676
  ------
wenzelm@16656
   677
  !!x. A
wenzelm@1220
   678
*)
wenzelm@16601
   679
fun forall_intr
wenzelm@16601
   680
    (ct as Cterm {t = x, T, sorts, ...})
wenzelm@28321
   681
    (th as Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   682
  let
wenzelm@16601
   683
    fun result a =
wenzelm@28321
   684
      Thm (deriv_rule1 (Pt.forall_intr_proof x a) der,
wenzelm@28321
   685
       {thy_ref = merge_thys1 ct th,
wenzelm@21646
   686
        tags = [],
wenzelm@16601
   687
        maxidx = maxidx,
wenzelm@16601
   688
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   689
        hyps = hyps,
wenzelm@16601
   690
        tpairs = tpairs,
wenzelm@28321
   691
        prop = Term.all T $ Abs (a, T, abstract_over (x, prop))});
wenzelm@21798
   692
    fun check_occs a x ts =
wenzelm@16847
   693
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@21798
   694
        raise THM ("forall_intr: variable " ^ quote a ^ " free in assumptions", 0, [th])
wenzelm@16601
   695
      else ();
wenzelm@16601
   696
  in
wenzelm@16601
   697
    case x of
wenzelm@21798
   698
      Free (a, _) => (check_occs a x hyps; check_occs a x (terms_of_tpairs tpairs); result a)
wenzelm@21798
   699
    | Var ((a, _), _) => (check_occs a x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   700
    | _ => raise THM ("forall_intr: not a variable", 0, [th])
clasohm@0
   701
  end;
clasohm@0
   702
wenzelm@1220
   703
(*Forall elimination
wenzelm@16656
   704
  !!x. A
wenzelm@1220
   705
  ------
wenzelm@1220
   706
  A[t/x]
wenzelm@1220
   707
*)
wenzelm@16601
   708
fun forall_elim
wenzelm@16601
   709
    (ct as Cterm {t, T, maxidx = maxt, sorts, ...})
wenzelm@28321
   710
    (th as Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   711
  (case prop of
wenzelm@16601
   712
    Const ("all", Type ("fun", [Type ("fun", [qary, _]), _])) $ A =>
wenzelm@16601
   713
      if T <> qary then
wenzelm@16601
   714
        raise THM ("forall_elim: type mismatch", 0, [th])
wenzelm@16601
   715
      else
wenzelm@28321
   716
        Thm (deriv_rule1 (Pt.% o rpair (SOME t)) der,
wenzelm@28321
   717
         {thy_ref = merge_thys1 ct th,
wenzelm@21646
   718
          tags = [],
wenzelm@16601
   719
          maxidx = Int.max (maxidx, maxt),
wenzelm@16601
   720
          shyps = Sorts.union sorts shyps,
wenzelm@16601
   721
          hyps = hyps,
wenzelm@16601
   722
          tpairs = tpairs,
wenzelm@28321
   723
          prop = Term.betapply (A, t)})
wenzelm@16601
   724
  | _ => raise THM ("forall_elim: not quantified", 0, [th]));
clasohm@0
   725
clasohm@0
   726
wenzelm@1220
   727
(* Equality *)
clasohm@0
   728
wenzelm@16601
   729
(*Reflexivity
wenzelm@16601
   730
  t == t
wenzelm@16601
   731
*)
wenzelm@16601
   732
fun reflexive (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   733
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   734
   {thy_ref = thy_ref,
wenzelm@21646
   735
    tags = [],
wenzelm@16601
   736
    maxidx = maxidx,
wenzelm@16601
   737
    shyps = sorts,
wenzelm@16601
   738
    hyps = [],
wenzelm@16601
   739
    tpairs = [],
wenzelm@28321
   740
    prop = Logic.mk_equals (t, t)});
clasohm@0
   741
wenzelm@16601
   742
(*Symmetry
wenzelm@16601
   743
  t == u
wenzelm@16601
   744
  ------
wenzelm@16601
   745
  u == t
wenzelm@1220
   746
*)
wenzelm@28321
   747
fun symmetric (th as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   748
  (case prop of
wenzelm@16601
   749
    (eq as Const ("==", Type (_, [T, _]))) $ t $ u =>
wenzelm@28321
   750
      Thm (deriv_rule1 Pt.symmetric der,
wenzelm@28321
   751
       {thy_ref = thy_ref,
wenzelm@21646
   752
        tags = [],
wenzelm@16601
   753
        maxidx = maxidx,
wenzelm@16601
   754
        shyps = shyps,
wenzelm@16601
   755
        hyps = hyps,
wenzelm@16601
   756
        tpairs = tpairs,
wenzelm@28321
   757
        prop = eq $ u $ t})
wenzelm@16601
   758
    | _ => raise THM ("symmetric", 0, [th]));
clasohm@0
   759
wenzelm@16601
   760
(*Transitivity
wenzelm@16601
   761
  t1 == u    u == t2
wenzelm@16601
   762
  ------------------
wenzelm@16601
   763
       t1 == t2
wenzelm@1220
   764
*)
clasohm@0
   765
fun transitive th1 th2 =
wenzelm@16601
   766
  let
wenzelm@28321
   767
    val Thm (der1, {maxidx = max1, hyps = hyps1, shyps = shyps1, tpairs = tpairs1,
wenzelm@28321
   768
      prop = prop1, ...}) = th1
wenzelm@28321
   769
    and Thm (der2, {maxidx = max2, hyps = hyps2, shyps = shyps2, tpairs = tpairs2,
wenzelm@28321
   770
      prop = prop2, ...}) = th2;
wenzelm@16601
   771
    fun err msg = raise THM ("transitive: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   772
  in
wenzelm@16601
   773
    case (prop1, prop2) of
wenzelm@16601
   774
      ((eq as Const ("==", Type (_, [T, _]))) $ t1 $ u, Const ("==", _) $ u' $ t2) =>
wenzelm@16601
   775
        if not (u aconv u') then err "middle term"
wenzelm@16601
   776
        else
wenzelm@28321
   777
          Thm (deriv_rule2 (Pt.transitive u T) der1 der2,
wenzelm@28321
   778
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   779
            tags = [],
wenzelm@16601
   780
            maxidx = Int.max (max1, max2),
wenzelm@16601
   781
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   782
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   783
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   784
            prop = eq $ t1 $ t2})
wenzelm@16601
   785
     | _ =>  err "premises"
clasohm@0
   786
  end;
clasohm@0
   787
wenzelm@16601
   788
(*Beta-conversion
wenzelm@16656
   789
  (%x. t)(u) == t[u/x]
wenzelm@16601
   790
  fully beta-reduces the term if full = true
berghofe@10416
   791
*)
wenzelm@16601
   792
fun beta_conversion full (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   793
  let val t' =
wenzelm@16601
   794
    if full then Envir.beta_norm t
wenzelm@16601
   795
    else
wenzelm@16601
   796
      (case t of Abs (_, _, bodt) $ u => subst_bound (u, bodt)
wenzelm@16601
   797
      | _ => raise THM ("beta_conversion: not a redex", 0, []));
wenzelm@16601
   798
  in
wenzelm@28321
   799
    Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   800
     {thy_ref = thy_ref,
wenzelm@21646
   801
      tags = [],
wenzelm@16601
   802
      maxidx = maxidx,
wenzelm@16601
   803
      shyps = sorts,
wenzelm@16601
   804
      hyps = [],
wenzelm@16601
   805
      tpairs = [],
wenzelm@28321
   806
      prop = Logic.mk_equals (t, t')})
berghofe@10416
   807
  end;
berghofe@10416
   808
wenzelm@16601
   809
fun eta_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   810
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   811
   {thy_ref = thy_ref,
wenzelm@21646
   812
    tags = [],
wenzelm@16601
   813
    maxidx = maxidx,
wenzelm@16601
   814
    shyps = sorts,
wenzelm@16601
   815
    hyps = [],
wenzelm@16601
   816
    tpairs = [],
wenzelm@28321
   817
    prop = Logic.mk_equals (t, Envir.eta_contract t)});
clasohm@0
   818
wenzelm@23493
   819
fun eta_long_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   820
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   821
   {thy_ref = thy_ref,
wenzelm@23493
   822
    tags = [],
wenzelm@23493
   823
    maxidx = maxidx,
wenzelm@23493
   824
    shyps = sorts,
wenzelm@23493
   825
    hyps = [],
wenzelm@23493
   826
    tpairs = [],
wenzelm@28321
   827
    prop = Logic.mk_equals (t, Pattern.eta_long [] t)});
wenzelm@23493
   828
clasohm@0
   829
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   830
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@16601
   831
      t == u
wenzelm@16601
   832
  --------------
wenzelm@16601
   833
  %x. t == %x. u
wenzelm@1220
   834
*)
wenzelm@16601
   835
fun abstract_rule a
wenzelm@16601
   836
    (Cterm {t = x, T, sorts, ...})
wenzelm@28321
   837
    (th as Thm (der, {thy_ref, maxidx, hyps, shyps, tpairs, prop, ...})) =
wenzelm@16601
   838
  let
wenzelm@16601
   839
    val (t, u) = Logic.dest_equals prop
wenzelm@16601
   840
      handle TERM _ => raise THM ("abstract_rule: premise not an equality", 0, [th]);
wenzelm@16601
   841
    val result =
wenzelm@28321
   842
      Thm (deriv_rule1 (Pt.abstract_rule x a) der,
wenzelm@28321
   843
       {thy_ref = thy_ref,
wenzelm@21646
   844
        tags = [],
wenzelm@16601
   845
        maxidx = maxidx,
wenzelm@16601
   846
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   847
        hyps = hyps,
wenzelm@16601
   848
        tpairs = tpairs,
wenzelm@16601
   849
        prop = Logic.mk_equals
wenzelm@28321
   850
          (Abs (a, T, abstract_over (x, t)), Abs (a, T, abstract_over (x, u)))});
wenzelm@21798
   851
    fun check_occs a x ts =
wenzelm@16847
   852
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@21798
   853
        raise THM ("abstract_rule: variable " ^ quote a ^ " free in assumptions", 0, [th])
wenzelm@16601
   854
      else ();
wenzelm@16601
   855
  in
wenzelm@16601
   856
    case x of
wenzelm@21798
   857
      Free (a, _) => (check_occs a x hyps; check_occs a x (terms_of_tpairs tpairs); result)
wenzelm@21798
   858
    | Var ((a, _), _) => (check_occs a x (terms_of_tpairs tpairs); result)
wenzelm@21798
   859
    | _ => raise THM ("abstract_rule: not a variable", 0, [th])
clasohm@0
   860
  end;
clasohm@0
   861
clasohm@0
   862
(*The combination rule
wenzelm@3529
   863
  f == g  t == u
wenzelm@3529
   864
  --------------
wenzelm@16601
   865
    f t == g u
wenzelm@1220
   866
*)
clasohm@0
   867
fun combination th1 th2 =
wenzelm@16601
   868
  let
wenzelm@28321
   869
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@28321
   870
      prop = prop1, ...}) = th1
wenzelm@28321
   871
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@28321
   872
      prop = prop2, ...}) = th2;
wenzelm@16601
   873
    fun chktypes fT tT =
wenzelm@16601
   874
      (case fT of
wenzelm@16601
   875
        Type ("fun", [T1, T2]) =>
wenzelm@16601
   876
          if T1 <> tT then
wenzelm@16601
   877
            raise THM ("combination: types", 0, [th1, th2])
wenzelm@16601
   878
          else ()
wenzelm@16601
   879
      | _ => raise THM ("combination: not function type", 0, [th1, th2]));
wenzelm@16601
   880
  in
wenzelm@16601
   881
    case (prop1, prop2) of
wenzelm@16601
   882
      (Const ("==", Type ("fun", [fT, _])) $ f $ g,
wenzelm@16601
   883
       Const ("==", Type ("fun", [tT, _])) $ t $ u) =>
wenzelm@16601
   884
        (chktypes fT tT;
wenzelm@28321
   885
          Thm (deriv_rule2 (Pt.combination f g t u fT) der1 der2,
wenzelm@28321
   886
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   887
            tags = [],
wenzelm@16601
   888
            maxidx = Int.max (max1, max2),
wenzelm@16601
   889
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   890
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   891
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   892
            prop = Logic.mk_equals (f $ t, g $ u)}))
wenzelm@16601
   893
     | _ => raise THM ("combination: premises", 0, [th1, th2])
clasohm@0
   894
  end;
clasohm@0
   895
wenzelm@16601
   896
(*Equality introduction
wenzelm@3529
   897
  A ==> B  B ==> A
wenzelm@3529
   898
  ----------------
wenzelm@3529
   899
       A == B
wenzelm@1220
   900
*)
clasohm@0
   901
fun equal_intr th1 th2 =
wenzelm@16601
   902
  let
wenzelm@28321
   903
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@28321
   904
      prop = prop1, ...}) = th1
wenzelm@28321
   905
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@28321
   906
      prop = prop2, ...}) = th2;
wenzelm@16601
   907
    fun err msg = raise THM ("equal_intr: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   908
  in
wenzelm@16601
   909
    case (prop1, prop2) of
wenzelm@16601
   910
      (Const("==>", _) $ A $ B, Const("==>", _) $ B' $ A') =>
wenzelm@16601
   911
        if A aconv A' andalso B aconv B' then
wenzelm@28321
   912
          Thm (deriv_rule2 (Pt.equal_intr A B) der1 der2,
wenzelm@28321
   913
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   914
            tags = [],
wenzelm@16601
   915
            maxidx = Int.max (max1, max2),
wenzelm@16601
   916
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   917
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   918
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   919
            prop = Logic.mk_equals (A, B)})
wenzelm@16601
   920
        else err "not equal"
wenzelm@16601
   921
    | _ =>  err "premises"
paulson@1529
   922
  end;
paulson@1529
   923
paulson@1529
   924
(*The equal propositions rule
wenzelm@3529
   925
  A == B  A
paulson@1529
   926
  ---------
paulson@1529
   927
      B
paulson@1529
   928
*)
paulson@1529
   929
fun equal_elim th1 th2 =
wenzelm@16601
   930
  let
wenzelm@28321
   931
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1,
wenzelm@28321
   932
      tpairs = tpairs1, prop = prop1, ...}) = th1
wenzelm@28321
   933
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2,
wenzelm@28321
   934
      tpairs = tpairs2, prop = prop2, ...}) = th2;
wenzelm@16601
   935
    fun err msg = raise THM ("equal_elim: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   936
  in
wenzelm@16601
   937
    case prop1 of
wenzelm@16601
   938
      Const ("==", _) $ A $ B =>
wenzelm@16601
   939
        if prop2 aconv A then
wenzelm@28321
   940
          Thm (deriv_rule2 (Pt.equal_elim A B) der1 der2,
wenzelm@28321
   941
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   942
            tags = [],
wenzelm@16601
   943
            maxidx = Int.max (max1, max2),
wenzelm@16601
   944
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   945
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   946
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   947
            prop = B})
wenzelm@16601
   948
        else err "not equal"
paulson@1529
   949
     | _ =>  err"major premise"
paulson@1529
   950
  end;
clasohm@0
   951
wenzelm@1220
   952
wenzelm@1220
   953
clasohm@0
   954
(**** Derived rules ****)
clasohm@0
   955
wenzelm@16601
   956
(*Smash unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@24143
   957
  Instantiates the theorem and deletes trivial tpairs.  Resulting
wenzelm@24143
   958
  sequence may contain multiple elements if the tpairs are not all
wenzelm@24143
   959
  flex-flex.*)
wenzelm@28321
   960
fun flexflex_rule (th as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@24143
   961
  let val thy = Theory.deref thy_ref in
wenzelm@24143
   962
    Unify.smash_unifiers thy tpairs (Envir.empty maxidx)
wenzelm@24143
   963
    |> Seq.map (fn env =>
wenzelm@24143
   964
        if Envir.is_empty env then th
wenzelm@24143
   965
        else
wenzelm@24143
   966
          let
wenzelm@24143
   967
            val tpairs' = tpairs |> map (pairself (Envir.norm_term env))
wenzelm@24143
   968
              (*remove trivial tpairs, of the form t==t*)
wenzelm@24143
   969
              |> filter_out (op aconv);
wenzelm@28321
   970
            val der' = deriv_rule1 (Pt.norm_proof' env) der;
wenzelm@24143
   971
            val prop' = Envir.norm_term env prop;
wenzelm@24143
   972
            val maxidx = maxidx_tpairs tpairs' (maxidx_of_term prop');
wenzelm@26640
   973
            val shyps = Envir.insert_sorts env shyps;
wenzelm@24143
   974
          in
wenzelm@28321
   975
            Thm (der', {thy_ref = Theory.check_thy thy, tags = [], maxidx = maxidx,
wenzelm@28321
   976
              shyps = shyps, hyps = hyps, tpairs = tpairs', prop = prop'})
wenzelm@24143
   977
          end)
wenzelm@24143
   978
  end;
wenzelm@16601
   979
clasohm@0
   980
wenzelm@19910
   981
(*Generalization of fixed variables
wenzelm@19910
   982
           A
wenzelm@19910
   983
  --------------------
wenzelm@19910
   984
  A[?'a/'a, ?x/x, ...]
wenzelm@19910
   985
*)
wenzelm@19910
   986
wenzelm@19910
   987
fun generalize ([], []) _ th = th
wenzelm@19910
   988
  | generalize (tfrees, frees) idx th =
wenzelm@19910
   989
      let
wenzelm@28321
   990
        val Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...}) = th;
wenzelm@19910
   991
        val _ = idx <= maxidx andalso raise THM ("generalize: bad index", idx, [th]);
wenzelm@19910
   992
wenzelm@19910
   993
        val bad_type = if null tfrees then K false else
wenzelm@19910
   994
          Term.exists_subtype (fn TFree (a, _) => member (op =) tfrees a | _ => false);
wenzelm@19910
   995
        fun bad_term (Free (x, T)) = bad_type T orelse member (op =) frees x
wenzelm@19910
   996
          | bad_term (Var (_, T)) = bad_type T
wenzelm@19910
   997
          | bad_term (Const (_, T)) = bad_type T
wenzelm@19910
   998
          | bad_term (Abs (_, T, t)) = bad_type T orelse bad_term t
wenzelm@19910
   999
          | bad_term (t $ u) = bad_term t orelse bad_term u
wenzelm@19910
  1000
          | bad_term (Bound _) = false;
wenzelm@19910
  1001
        val _ = exists bad_term hyps andalso
wenzelm@19910
  1002
          raise THM ("generalize: variable free in assumptions", 0, [th]);
wenzelm@19910
  1003
wenzelm@20512
  1004
        val gen = TermSubst.generalize (tfrees, frees) idx;
wenzelm@19910
  1005
        val prop' = gen prop;
wenzelm@19910
  1006
        val tpairs' = map (pairself gen) tpairs;
wenzelm@19910
  1007
        val maxidx' = maxidx_tpairs tpairs' (maxidx_of_term prop');
wenzelm@19910
  1008
      in
wenzelm@28321
  1009
        Thm (deriv_rule1 (Pt.generalize (tfrees, frees) idx) der,
wenzelm@28321
  1010
         {thy_ref = thy_ref,
wenzelm@21646
  1011
          tags = [],
wenzelm@19910
  1012
          maxidx = maxidx',
wenzelm@19910
  1013
          shyps = shyps,
wenzelm@19910
  1014
          hyps = hyps,
wenzelm@19910
  1015
          tpairs = tpairs',
wenzelm@28321
  1016
          prop = prop'})
wenzelm@19910
  1017
      end;
wenzelm@19910
  1018
wenzelm@19910
  1019
wenzelm@22584
  1020
(*Instantiation of schematic variables
wenzelm@16656
  1021
           A
wenzelm@16656
  1022
  --------------------
wenzelm@16656
  1023
  A[t1/v1, ..., tn/vn]
wenzelm@1220
  1024
*)
clasohm@0
  1025
wenzelm@6928
  1026
local
wenzelm@6928
  1027
wenzelm@26939
  1028
fun pretty_typing thy t T = Pretty.block
wenzelm@26939
  1029
  [Syntax.pretty_term_global thy t, Pretty.str " ::", Pretty.brk 1, Syntax.pretty_typ_global thy T];
berghofe@15797
  1030
wenzelm@16884
  1031
fun add_inst (ct, cu) (thy_ref, sorts) =
wenzelm@6928
  1032
  let
wenzelm@26939
  1033
    val Cterm {t = t, T = T, ...} = ct;
wenzelm@26939
  1034
    val Cterm {t = u, T = U, sorts = sorts_u, maxidx = maxidx_u, ...} = cu;
wenzelm@16884
  1035
    val thy_ref' = Theory.merge_refs (thy_ref, merge_thys0 ct cu);
wenzelm@16884
  1036
    val sorts' = Sorts.union sorts_u sorts;
wenzelm@3967
  1037
  in
wenzelm@16884
  1038
    (case t of Var v =>
wenzelm@20512
  1039
      if T = U then ((v, (u, maxidx_u)), (thy_ref', sorts'))
wenzelm@16884
  1040
      else raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
  1041
       [Pretty.str "instantiate: type conflict",
wenzelm@16884
  1042
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') t T,
wenzelm@16884
  1043
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') u U]), [T, U], [t, u])
wenzelm@16884
  1044
    | _ => raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
  1045
       [Pretty.str "instantiate: not a variable",
wenzelm@26939
  1046
        Pretty.fbrk, Syntax.pretty_term_global (Theory.deref thy_ref') t]), [], [t]))
clasohm@0
  1047
  end;
clasohm@0
  1048
wenzelm@16884
  1049
fun add_instT (cT, cU) (thy_ref, sorts) =
wenzelm@16656
  1050
  let
wenzelm@16884
  1051
    val Ctyp {T, thy_ref = thy_ref1, ...} = cT
wenzelm@20512
  1052
    and Ctyp {T = U, thy_ref = thy_ref2, sorts = sorts_U, maxidx = maxidx_U, ...} = cU;
wenzelm@24143
  1053
    val thy' = Theory.deref (Theory.merge_refs (thy_ref, Theory.merge_refs (thy_ref1, thy_ref2)));
wenzelm@16884
  1054
    val sorts' = Sorts.union sorts_U sorts;
wenzelm@16656
  1055
  in
wenzelm@16884
  1056
    (case T of TVar (v as (_, S)) =>
wenzelm@24143
  1057
      if Sign.of_sort thy' (U, S) then ((v, (U, maxidx_U)), (Theory.check_thy thy', sorts'))
wenzelm@26939
  1058
      else raise TYPE ("Type not of sort " ^ Syntax.string_of_sort_global thy' S, [U], [])
wenzelm@16656
  1059
    | _ => raise TYPE (Pretty.string_of (Pretty.block
berghofe@15797
  1060
        [Pretty.str "instantiate: not a type variable",
wenzelm@26939
  1061
         Pretty.fbrk, Syntax.pretty_typ_global thy' T]), [T], []))
wenzelm@16656
  1062
  end;
clasohm@0
  1063
wenzelm@6928
  1064
in
wenzelm@6928
  1065
wenzelm@16601
  1066
(*Left-to-right replacements: ctpairs = [..., (vi, ti), ...].
clasohm@0
  1067
  Instantiates distinct Vars by terms of same type.
wenzelm@16601
  1068
  Does NOT normalize the resulting theorem!*)
paulson@1529
  1069
fun instantiate ([], []) th = th
wenzelm@16884
  1070
  | instantiate (instT, inst) th =
wenzelm@16656
  1071
      let
wenzelm@28321
  1072
        val Thm (der, {thy_ref, hyps, shyps, tpairs, prop, ...}) = th;
wenzelm@16884
  1073
        val (inst', (instT', (thy_ref', shyps'))) =
wenzelm@16884
  1074
          (thy_ref, shyps) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@20512
  1075
        val subst = TermSubst.instantiate_maxidx (instT', inst');
wenzelm@20512
  1076
        val (prop', maxidx1) = subst prop ~1;
wenzelm@20512
  1077
        val (tpairs', maxidx') =
wenzelm@20512
  1078
          fold_map (fn (t, u) => fn i => subst t i ||>> subst u) tpairs maxidx1;
wenzelm@16656
  1079
      in
wenzelm@28321
  1080
        Thm (deriv_rule1 (fn d => Pt.instantiate (map (apsnd #1) instT', map (apsnd #1) inst') d) der,
wenzelm@28321
  1081
         {thy_ref = thy_ref',
wenzelm@21646
  1082
          tags = [],
wenzelm@20545
  1083
          maxidx = maxidx',
wenzelm@20545
  1084
          shyps = shyps',
wenzelm@20545
  1085
          hyps = hyps,
wenzelm@20545
  1086
          tpairs = tpairs',
wenzelm@28321
  1087
          prop = prop'})
wenzelm@16656
  1088
      end
wenzelm@16656
  1089
      handle TYPE (msg, _, _) => raise THM (msg, 0, [th]);
wenzelm@6928
  1090
wenzelm@22584
  1091
fun instantiate_cterm ([], []) ct = ct
wenzelm@22584
  1092
  | instantiate_cterm (instT, inst) ct =
wenzelm@22584
  1093
      let
wenzelm@22584
  1094
        val Cterm {thy_ref, t, T, sorts, ...} = ct;
wenzelm@22584
  1095
        val (inst', (instT', (thy_ref', sorts'))) =
wenzelm@22584
  1096
          (thy_ref, sorts) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@22584
  1097
        val subst = TermSubst.instantiate_maxidx (instT', inst');
wenzelm@22584
  1098
        val substT = TermSubst.instantiateT_maxidx instT';
wenzelm@22584
  1099
        val (t', maxidx1) = subst t ~1;
wenzelm@22584
  1100
        val (T', maxidx') = substT T maxidx1;
wenzelm@22584
  1101
      in Cterm {thy_ref = thy_ref', t = t', T = T', sorts = sorts', maxidx = maxidx'} end
wenzelm@22584
  1102
      handle TYPE (msg, _, _) => raise CTERM (msg, [ct]);
wenzelm@22584
  1103
wenzelm@6928
  1104
end;
wenzelm@6928
  1105
clasohm@0
  1106
wenzelm@16601
  1107
(*The trivial implication A ==> A, justified by assume and forall rules.
wenzelm@16601
  1108
  A can contain Vars, not so for assume!*)
wenzelm@16601
  1109
fun trivial (Cterm {thy_ref, t =A, T, maxidx, sorts}) =
wenzelm@16601
  1110
  if T <> propT then
wenzelm@16601
  1111
    raise THM ("trivial: the term must have type prop", 0, [])
wenzelm@16601
  1112
  else
wenzelm@28321
  1113
    Thm (deriv_rule0 (Pt.AbsP ("H", NONE, Pt.PBound 0)),
wenzelm@28321
  1114
     {thy_ref = thy_ref,
wenzelm@21646
  1115
      tags = [],
wenzelm@16601
  1116
      maxidx = maxidx,
wenzelm@16601
  1117
      shyps = sorts,
wenzelm@16601
  1118
      hyps = [],
wenzelm@16601
  1119
      tpairs = [],
wenzelm@28321
  1120
      prop = Logic.mk_implies (A, A)});
clasohm@0
  1121
paulson@1503
  1122
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)" *)
wenzelm@16425
  1123
fun class_triv thy c =
wenzelm@24143
  1124
  let
wenzelm@24143
  1125
    val Cterm {t, maxidx, sorts, ...} =
wenzelm@24848
  1126
      cterm_of thy (Logic.mk_inclass (TVar ((Name.aT, 0), [c]), Sign.certify_class thy c))
wenzelm@24143
  1127
        handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@28321
  1128
    val der = deriv_rule0 (Pt.PAxm ("Pure.class_triv:" ^ c, t, SOME []));
wenzelm@399
  1129
  in
wenzelm@28321
  1130
    Thm (der, {thy_ref = Theory.check_thy thy, tags = [], maxidx = maxidx,
wenzelm@28321
  1131
      shyps = sorts, hyps = [], tpairs = [], prop = t})
wenzelm@399
  1132
  end;
wenzelm@399
  1133
wenzelm@19505
  1134
(*Internalize sort constraints of type variable*)
wenzelm@19505
  1135
fun unconstrainT
wenzelm@19505
  1136
    (Ctyp {thy_ref = thy_ref1, T, ...})
wenzelm@28321
  1137
    (th as Thm (_, {thy_ref = thy_ref2, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@19505
  1138
  let
wenzelm@19505
  1139
    val ((x, i), S) = Term.dest_TVar T handle TYPE _ =>
wenzelm@19505
  1140
      raise THM ("unconstrainT: not a type variable", 0, [th]);
wenzelm@19505
  1141
    val T' = TVar ((x, i), []);
wenzelm@20548
  1142
    val unconstrain = Term.map_types (Term.map_atyps (fn U => if U = T then T' else U));
wenzelm@19505
  1143
    val constraints = map (curry Logic.mk_inclass T') S;
wenzelm@19505
  1144
  in
wenzelm@28321
  1145
    Thm (deriv_rule0 (Pt.PAxm ("Pure.unconstrainT", prop, SOME [])),
wenzelm@28321
  1146
     {thy_ref = Theory.merge_refs (thy_ref1, thy_ref2),
wenzelm@21646
  1147
      tags = [],
wenzelm@19505
  1148
      maxidx = Int.max (maxidx, i),
wenzelm@19505
  1149
      shyps = Sorts.remove_sort S shyps,
wenzelm@19505
  1150
      hyps = hyps,
wenzelm@19505
  1151
      tpairs = map (pairself unconstrain) tpairs,
wenzelm@28321
  1152
      prop = Logic.list_implies (constraints, unconstrain prop)})
wenzelm@19505
  1153
  end;
wenzelm@399
  1154
wenzelm@6786
  1155
(* Replace all TFrees not fixed or in the hyps by new TVars *)
wenzelm@28321
  1156
fun varifyT' fixed (Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@12500
  1157
  let
wenzelm@29272
  1158
    val tfrees = fold Term.add_tfrees hyps fixed;
berghofe@13658
  1159
    val prop1 = attach_tpairs tpairs prop;
haftmann@21116
  1160
    val (al, prop2) = Type.varify tfrees prop1;
wenzelm@16601
  1161
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1162
  in
wenzelm@28321
  1163
    (al, Thm (deriv_rule1 (Pt.varify_proof prop tfrees) der,
wenzelm@28321
  1164
     {thy_ref = thy_ref,
wenzelm@21646
  1165
      tags = [],
wenzelm@16601
  1166
      maxidx = Int.max (0, maxidx),
wenzelm@16601
  1167
      shyps = shyps,
wenzelm@16601
  1168
      hyps = hyps,
wenzelm@16601
  1169
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@28321
  1170
      prop = prop3}))
wenzelm@28321
  1171
  end;
wenzelm@28321
  1172
wenzelm@28321
  1173
val varifyT = #2 o varifyT' [];
wenzelm@28321
  1174
wenzelm@28321
  1175
(* Replace all TVars by new TFrees *)
wenzelm@28321
  1176
fun freezeT (Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@28321
  1177
  let
wenzelm@28321
  1178
    val prop1 = attach_tpairs tpairs prop;
wenzelm@28321
  1179
    val prop2 = Type.freeze prop1;
wenzelm@28321
  1180
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@28321
  1181
  in
wenzelm@28321
  1182
    Thm (deriv_rule1 (Pt.freezeT prop1) der,
wenzelm@28321
  1183
     {thy_ref = thy_ref,
wenzelm@28321
  1184
      tags = [],
wenzelm@28321
  1185
      maxidx = maxidx_of_term prop2,
wenzelm@28321
  1186
      shyps = shyps,
wenzelm@28321
  1187
      hyps = hyps,
wenzelm@28321
  1188
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@18127
  1189
      prop = prop3})
clasohm@0
  1190
  end;
clasohm@0
  1191
clasohm@0
  1192
clasohm@0
  1193
(*** Inference rules for tactics ***)
clasohm@0
  1194
clasohm@0
  1195
(*Destruct proof state into constraints, other goals, goal(i), rest *)
wenzelm@28321
  1196
fun dest_state (state as Thm (_, {prop,tpairs,...}), i) =
berghofe@13658
  1197
  (case  Logic.strip_prems(i, [], prop) of
berghofe@13658
  1198
      (B::rBs, C) => (tpairs, rev rBs, B, C)
berghofe@13658
  1199
    | _ => raise THM("dest_state", i, [state]))
clasohm@0
  1200
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1201
lcp@309
  1202
(*Increment variables and parameters of orule as required for
wenzelm@18035
  1203
  resolution with a goal.*)
wenzelm@18035
  1204
fun lift_rule goal orule =
wenzelm@16601
  1205
  let
wenzelm@18035
  1206
    val Cterm {t = gprop, T, maxidx = gmax, sorts, ...} = goal;
wenzelm@18035
  1207
    val inc = gmax + 1;
wenzelm@18035
  1208
    val lift_abs = Logic.lift_abs inc gprop;
wenzelm@18035
  1209
    val lift_all = Logic.lift_all inc gprop;
wenzelm@28321
  1210
    val Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...}) = orule;
wenzelm@16601
  1211
    val (As, B) = Logic.strip_horn prop;
wenzelm@16601
  1212
  in
wenzelm@18035
  1213
    if T <> propT then raise THM ("lift_rule: the term must have type prop", 0, [])
wenzelm@18035
  1214
    else
wenzelm@28321
  1215
      Thm (deriv_rule1 (Pt.lift_proof gprop inc prop) der,
wenzelm@28321
  1216
       {thy_ref = merge_thys1 goal orule,
wenzelm@21646
  1217
        tags = [],
wenzelm@18035
  1218
        maxidx = maxidx + inc,
wenzelm@18035
  1219
        shyps = Sorts.union shyps sorts,  (*sic!*)
wenzelm@18035
  1220
        hyps = hyps,
wenzelm@18035
  1221
        tpairs = map (pairself lift_abs) tpairs,
wenzelm@28321
  1222
        prop = Logic.list_implies (map lift_all As, lift_all B)})
clasohm@0
  1223
  end;
clasohm@0
  1224
wenzelm@28321
  1225
fun incr_indexes i (thm as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
  1226
  if i < 0 then raise THM ("negative increment", 0, [thm])
wenzelm@16601
  1227
  else if i = 0 then thm
wenzelm@16601
  1228
  else
wenzelm@28321
  1229
    Thm (deriv_rule1 (Pt.map_proof_terms (Logic.incr_indexes ([], i)) (Logic.incr_tvar i)) der,
wenzelm@28321
  1230
     {thy_ref = thy_ref,
wenzelm@21646
  1231
      tags = [],
wenzelm@16601
  1232
      maxidx = maxidx + i,
wenzelm@16601
  1233
      shyps = shyps,
wenzelm@16601
  1234
      hyps = hyps,
wenzelm@16601
  1235
      tpairs = map (pairself (Logic.incr_indexes ([], i))) tpairs,
wenzelm@28321
  1236
      prop = Logic.incr_indexes ([], i) prop});
berghofe@10416
  1237
clasohm@0
  1238
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1239
fun assumption i state =
wenzelm@16601
  1240
  let
wenzelm@28321
  1241
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16656
  1242
    val thy = Theory.deref thy_ref;
wenzelm@16601
  1243
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1244
    fun newth n (env as Envir.Envir {maxidx, ...}, tpairs) =
wenzelm@28321
  1245
      Thm (deriv_rule1
wenzelm@16601
  1246
          ((if Envir.is_empty env then I else (Pt.norm_proof' env)) o
wenzelm@16601
  1247
            Pt.assumption_proof Bs Bi n) der,
wenzelm@28321
  1248
       {tags = [],
wenzelm@16601
  1249
        maxidx = maxidx,
wenzelm@26640
  1250
        shyps = Envir.insert_sorts env shyps,
wenzelm@16601
  1251
        hyps = hyps,
wenzelm@16601
  1252
        tpairs =
wenzelm@16601
  1253
          if Envir.is_empty env then tpairs
wenzelm@16601
  1254
          else map (pairself (Envir.norm_term env)) tpairs,
wenzelm@16601
  1255
        prop =
wenzelm@16601
  1256
          if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@16601
  1257
            Logic.list_implies (Bs, C)
wenzelm@16601
  1258
          else (*normalize the new rule fully*)
wenzelm@24143
  1259
            Envir.norm_term env (Logic.list_implies (Bs, C)),
wenzelm@28321
  1260
        thy_ref = Theory.check_thy thy});
wenzelm@16601
  1261
    fun addprfs [] _ = Seq.empty
wenzelm@16601
  1262
      | addprfs ((t, u) :: apairs) n = Seq.make (fn () => Seq.pull
wenzelm@16601
  1263
          (Seq.mapp (newth n)
wenzelm@16656
  1264
            (Unify.unifiers (thy, Envir.empty maxidx, (t, u) :: tpairs))
wenzelm@16601
  1265
            (addprfs apairs (n + 1))))
wenzelm@16601
  1266
  in addprfs (Logic.assum_pairs (~1, Bi)) 1 end;
clasohm@0
  1267
wenzelm@250
  1268
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1269
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1270
fun eq_assumption i state =
wenzelm@16601
  1271
  let
wenzelm@28321
  1272
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16601
  1273
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1274
  in
berghofe@26832
  1275
    (case find_index Pattern.aeconv (Logic.assum_pairs (~1, Bi)) of
wenzelm@16601
  1276
      ~1 => raise THM ("eq_assumption", 0, [state])
wenzelm@16601
  1277
    | n =>
wenzelm@28321
  1278
        Thm (deriv_rule1 (Pt.assumption_proof Bs Bi (n + 1)) der,
wenzelm@28321
  1279
         {thy_ref = thy_ref,
wenzelm@21646
  1280
          tags = [],
wenzelm@16601
  1281
          maxidx = maxidx,
wenzelm@16601
  1282
          shyps = shyps,
wenzelm@16601
  1283
          hyps = hyps,
wenzelm@16601
  1284
          tpairs = tpairs,
wenzelm@28321
  1285
          prop = Logic.list_implies (Bs, C)}))
clasohm@0
  1286
  end;
clasohm@0
  1287
clasohm@0
  1288
paulson@2671
  1289
(*For rotate_tac: fast rotation of assumptions of subgoal i*)
paulson@2671
  1290
fun rotate_rule k i state =
wenzelm@16601
  1291
  let
wenzelm@28321
  1292
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16601
  1293
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1294
    val params = Term.strip_all_vars Bi
wenzelm@16601
  1295
    and rest   = Term.strip_all_body Bi;
wenzelm@16601
  1296
    val asms   = Logic.strip_imp_prems rest
wenzelm@16601
  1297
    and concl  = Logic.strip_imp_concl rest;
wenzelm@16601
  1298
    val n = length asms;
wenzelm@16601
  1299
    val m = if k < 0 then n + k else k;
wenzelm@16601
  1300
    val Bi' =
wenzelm@16601
  1301
      if 0 = m orelse m = n then Bi
wenzelm@16601
  1302
      else if 0 < m andalso m < n then
wenzelm@19012
  1303
        let val (ps, qs) = chop m asms
wenzelm@16601
  1304
        in list_all (params, Logic.list_implies (qs @ ps, concl)) end
wenzelm@16601
  1305
      else raise THM ("rotate_rule", k, [state]);
wenzelm@16601
  1306
  in
wenzelm@28321
  1307
    Thm (deriv_rule1 (Pt.rotate_proof Bs Bi m) der,
wenzelm@28321
  1308
     {thy_ref = thy_ref,
wenzelm@21646
  1309
      tags = [],
wenzelm@16601
  1310
      maxidx = maxidx,
wenzelm@16601
  1311
      shyps = shyps,
wenzelm@16601
  1312
      hyps = hyps,
wenzelm@16601
  1313
      tpairs = tpairs,
wenzelm@28321
  1314
      prop = Logic.list_implies (Bs @ [Bi'], C)})
paulson@2671
  1315
  end;
paulson@2671
  1316
paulson@2671
  1317
paulson@7248
  1318
(*Rotates a rule's premises to the left by k, leaving the first j premises
paulson@7248
  1319
  unchanged.  Does nothing if k=0 or if k equals n-j, where n is the
wenzelm@16656
  1320
  number of premises.  Useful with etac and underlies defer_tac*)
paulson@7248
  1321
fun permute_prems j k rl =
wenzelm@16601
  1322
  let
wenzelm@28321
  1323
    val Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...}) = rl;
wenzelm@16601
  1324
    val prems = Logic.strip_imp_prems prop
wenzelm@16601
  1325
    and concl = Logic.strip_imp_concl prop;
wenzelm@16601
  1326
    val moved_prems = List.drop (prems, j)
wenzelm@16601
  1327
    and fixed_prems = List.take (prems, j)
wenzelm@16601
  1328
      handle Subscript => raise THM ("permute_prems: j", j, [rl]);
wenzelm@16601
  1329
    val n_j = length moved_prems;
wenzelm@16601
  1330
    val m = if k < 0 then n_j + k else k;
wenzelm@16601
  1331
    val prop' =
wenzelm@16601
  1332
      if 0 = m orelse m = n_j then prop
wenzelm@16601
  1333
      else if 0 < m andalso m < n_j then
wenzelm@19012
  1334
        let val (ps, qs) = chop m moved_prems
wenzelm@16601
  1335
        in Logic.list_implies (fixed_prems @ qs @ ps, concl) end
wenzelm@16725
  1336
      else raise THM ("permute_prems: k", k, [rl]);
wenzelm@16601
  1337
  in
wenzelm@28321
  1338
    Thm (deriv_rule1 (Pt.permute_prems_prf prems j m) der,
wenzelm@28321
  1339
     {thy_ref = thy_ref,
wenzelm@21646
  1340
      tags = [],
wenzelm@16601
  1341
      maxidx = maxidx,
wenzelm@16601
  1342
      shyps = shyps,
wenzelm@16601
  1343
      hyps = hyps,
wenzelm@16601
  1344
      tpairs = tpairs,
wenzelm@28321
  1345
      prop = prop'})
paulson@7248
  1346
  end;
paulson@7248
  1347
paulson@7248
  1348
clasohm@0
  1349
(** User renaming of parameters in a subgoal **)
clasohm@0
  1350
clasohm@0
  1351
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1352
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1353
  The names in cs, if distinct, are used for the innermost parameters;
wenzelm@17868
  1354
  preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1355
fun rename_params_rule (cs, i) state =
wenzelm@16601
  1356
  let
wenzelm@28321
  1357
    val Thm (der, {thy_ref, tags, maxidx, shyps, hyps, ...}) = state;
wenzelm@16601
  1358
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1359
    val iparams = map #1 (Logic.strip_params Bi);
wenzelm@16601
  1360
    val short = length iparams - length cs;
wenzelm@16601
  1361
    val newnames =
wenzelm@16601
  1362
      if short < 0 then error "More names than abstractions!"
wenzelm@20071
  1363
      else Name.variant_list cs (Library.take (short, iparams)) @ cs;
wenzelm@20330
  1364
    val freenames = Term.fold_aterms (fn Free (x, _) => insert (op =) x | _ => I) Bi [];
wenzelm@16601
  1365
    val newBi = Logic.list_rename_params (newnames, Bi);
wenzelm@250
  1366
  in
wenzelm@21182
  1367
    (case duplicates (op =) cs of
wenzelm@21182
  1368
      a :: _ => (warning ("Can't rename.  Bound variables not distinct: " ^ a); state)
wenzelm@21182
  1369
    | [] =>
wenzelm@16601
  1370
      (case cs inter_string freenames of
wenzelm@16601
  1371
        a :: _ => (warning ("Can't rename.  Bound/Free variable clash: " ^ a); state)
wenzelm@16601
  1372
      | [] =>
wenzelm@28321
  1373
        Thm (der,
wenzelm@28321
  1374
         {thy_ref = thy_ref,
wenzelm@21646
  1375
          tags = tags,
wenzelm@16601
  1376
          maxidx = maxidx,
wenzelm@16601
  1377
          shyps = shyps,
wenzelm@16601
  1378
          hyps = hyps,
wenzelm@16601
  1379
          tpairs = tpairs,
wenzelm@28321
  1380
          prop = Logic.list_implies (Bs @ [newBi], C)})))
clasohm@0
  1381
  end;
clasohm@0
  1382
wenzelm@12982
  1383
clasohm@0
  1384
(*** Preservation of bound variable names ***)
clasohm@0
  1385
wenzelm@28321
  1386
fun rename_boundvars pat obj (thm as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@12982
  1387
  (case Term.rename_abs pat obj prop of
skalberg@15531
  1388
    NONE => thm
wenzelm@28321
  1389
  | SOME prop' => Thm (der,
wenzelm@16425
  1390
      {thy_ref = thy_ref,
wenzelm@21646
  1391
       tags = tags,
wenzelm@12982
  1392
       maxidx = maxidx,
wenzelm@12982
  1393
       hyps = hyps,
wenzelm@12982
  1394
       shyps = shyps,
berghofe@13658
  1395
       tpairs = tpairs,
wenzelm@28321
  1396
       prop = prop'}));
berghofe@10416
  1397
clasohm@0
  1398
wenzelm@16656
  1399
(* strip_apply f (A, B) strips off all assumptions/parameters from A
clasohm@0
  1400
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
  1401
fun strip_apply f =
clasohm@0
  1402
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@27336
  1403
                Const("==>",_)$ _  $ B2) = Logic.mk_implies (A1, strip(B1,B2))
wenzelm@250
  1404
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
  1405
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
  1406
        | strip(A,_) = f A
clasohm@0
  1407
  in strip end;
clasohm@0
  1408
clasohm@0
  1409
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1410
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1411
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1412
fun rename_bvs([],_,_,_) = I
clasohm@0
  1413
  | rename_bvs(al,dpairs,tpairs,B) =
wenzelm@20330
  1414
      let
wenzelm@20330
  1415
        val add_var = fold_aterms (fn Var ((x, _), _) => insert (op =) x | _ => I);
wenzelm@20330
  1416
        val vids = []
wenzelm@20330
  1417
          |> fold (add_var o fst) dpairs
wenzelm@20330
  1418
          |> fold (add_var o fst) tpairs
wenzelm@20330
  1419
          |> fold (add_var o snd) tpairs;
wenzelm@250
  1420
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1421
        fun rename(t as Var((x,i),T)) =
wenzelm@20330
  1422
              (case AList.lookup (op =) al x of
wenzelm@20330
  1423
                SOME y =>
wenzelm@20330
  1424
                  if member (op =) vids x orelse member (op =) vids y then t
wenzelm@20330
  1425
                  else Var((y,i),T)
wenzelm@20330
  1426
              | NONE=> t)
clasohm@0
  1427
          | rename(Abs(x,T,t)) =
wenzelm@18944
  1428
              Abs (the_default x (AList.lookup (op =) al x), T, rename t)
clasohm@0
  1429
          | rename(f$t) = rename f $ rename t
clasohm@0
  1430
          | rename(t) = t;
wenzelm@250
  1431
        fun strip_ren Ai = strip_apply rename (Ai,B)
wenzelm@20330
  1432
      in strip_ren end;
clasohm@0
  1433
clasohm@0
  1434
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
  1435
fun rename_bvars(dpairs, tpairs, B) =
wenzelm@23178
  1436
        rename_bvs(List.foldr Term.match_bvars [] dpairs, dpairs, tpairs, B);
clasohm@0
  1437
clasohm@0
  1438
clasohm@0
  1439
(*** RESOLUTION ***)
clasohm@0
  1440
lcp@721
  1441
(** Lifting optimizations **)
lcp@721
  1442
clasohm@0
  1443
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
  1444
  identical because of lifting*)
wenzelm@250
  1445
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
  1446
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
  1447
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
  1448
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
  1449
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
  1450
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
  1451
  | strip_assums2 BB = BB;
clasohm@0
  1452
clasohm@0
  1453
lcp@721
  1454
(*Faster normalization: skip assumptions that were lifted over*)
lcp@721
  1455
fun norm_term_skip env 0 t = Envir.norm_term env t
lcp@721
  1456
  | norm_term_skip env n (Const("all",_)$Abs(a,T,t)) =
lcp@721
  1457
        let val Envir.Envir{iTs, ...} = env
berghofe@15797
  1458
            val T' = Envir.typ_subst_TVars iTs T
wenzelm@1238
  1459
            (*Must instantiate types of parameters because they are flattened;
lcp@721
  1460
              this could be a NEW parameter*)
wenzelm@27336
  1461
        in Term.all T' $ Abs(a, T', norm_term_skip env n t)  end
lcp@721
  1462
  | norm_term_skip env n (Const("==>", _) $ A $ B) =
wenzelm@27336
  1463
        Logic.mk_implies (A, norm_term_skip env (n-1) B)
lcp@721
  1464
  | norm_term_skip env n t = error"norm_term_skip: too few assumptions??";
lcp@721
  1465
lcp@721
  1466
clasohm@0
  1467
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
  1468
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
  1469
  If match then forbid instantiations in proof state
clasohm@0
  1470
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
  1471
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
  1472
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
  1473
  Curried so that resolution calls dest_state only once.
clasohm@0
  1474
*)
wenzelm@4270
  1475
local exception COMPOSE
clasohm@0
  1476
in
wenzelm@18486
  1477
fun bicompose_aux flatten match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
  1478
                        (eres_flg, orule, nsubgoal) =
wenzelm@28321
  1479
 let val Thm (sder, {maxidx=smax, shyps=sshyps, hyps=shyps, ...}) = state
wenzelm@28321
  1480
     and Thm (rder, {maxidx=rmax, shyps=rshyps, hyps=rhyps,
wenzelm@28321
  1481
             tpairs=rtpairs, prop=rprop,...}) = orule
paulson@1529
  1482
         (*How many hyps to skip over during normalization*)
wenzelm@21576
  1483
     and nlift = Logic.count_prems (strip_all_body Bi) + (if eres_flg then ~1 else 0)
wenzelm@24143
  1484
     val thy = Theory.deref (merge_thys2 state orule);
clasohm@0
  1485
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
berghofe@11518
  1486
     fun addth A (As, oldAs, rder', n) ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
  1487
       let val normt = Envir.norm_term env;
wenzelm@250
  1488
           (*perform minimal copying here by examining env*)
berghofe@13658
  1489
           val (ntpairs, normp) =
berghofe@13658
  1490
             if Envir.is_empty env then (tpairs, (Bs @ As, C))
wenzelm@250
  1491
             else
wenzelm@250
  1492
             let val ntps = map (pairself normt) tpairs
wenzelm@19861
  1493
             in if Envir.above env smax then
wenzelm@1238
  1494
                  (*no assignments in state; normalize the rule only*)
wenzelm@1238
  1495
                  if lifted
berghofe@13658
  1496
                  then (ntps, (Bs @ map (norm_term_skip env nlift) As, C))
berghofe@13658
  1497
                  else (ntps, (Bs @ map normt As, C))
paulson@1529
  1498
                else if match then raise COMPOSE
wenzelm@250
  1499
                else (*normalize the new rule fully*)
berghofe@13658
  1500
                  (ntps, (map normt (Bs @ As), normt C))
wenzelm@250
  1501
             end
wenzelm@16601
  1502
           val th =
wenzelm@28321
  1503
             Thm (deriv_rule2
berghofe@11518
  1504
                   ((if Envir.is_empty env then I
wenzelm@19861
  1505
                     else if Envir.above env smax then
berghofe@11518
  1506
                       (fn f => fn der => f (Pt.norm_proof' env der))
berghofe@11518
  1507
                     else
berghofe@11518
  1508
                       curry op oo (Pt.norm_proof' env))
berghofe@23296
  1509
                    (Pt.bicompose_proof flatten Bs oldAs As A n (nlift+1))) rder' sder,
wenzelm@28321
  1510
                {tags = [],
wenzelm@2386
  1511
                 maxidx = maxidx,
wenzelm@26640
  1512
                 shyps = Envir.insert_sorts env (Sorts.union rshyps sshyps),
wenzelm@16601
  1513
                 hyps = union_hyps rhyps shyps,
berghofe@13658
  1514
                 tpairs = ntpairs,
wenzelm@24143
  1515
                 prop = Logic.list_implies normp,
wenzelm@28321
  1516
                 thy_ref = Theory.check_thy thy})
wenzelm@19475
  1517
        in  Seq.cons th thq  end  handle COMPOSE => thq;
berghofe@13658
  1518
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rprop)
clasohm@0
  1519
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
  1520
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
  1521
     fun newAs(As0, n, dpairs, tpairs) =
berghofe@11518
  1522
       let val (As1, rder') =
berghofe@25939
  1523
         if not lifted then (As0, rder)
berghofe@11518
  1524
         else (map (rename_bvars(dpairs,tpairs,B)) As0,
wenzelm@28321
  1525
           deriv_rule1 (Pt.map_proof_terms
berghofe@11518
  1526
             (rename_bvars (dpairs, tpairs, Bound 0)) I) rder);
wenzelm@18486
  1527
       in (map (if flatten then (Logic.flatten_params n) else I) As1, As1, rder', n)
wenzelm@250
  1528
          handle TERM _ =>
wenzelm@250
  1529
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
  1530
       end;
paulson@2147
  1531
     val env = Envir.empty(Int.max(rmax,smax));
clasohm@0
  1532
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
  1533
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
  1534
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
berghofe@11518
  1535
     fun tryasms (_, _, _, []) = Seq.empty
berghofe@11518
  1536
       | tryasms (A, As, n, (t,u)::apairs) =
wenzelm@16425
  1537
          (case Seq.pull(Unify.unifiers(thy, env, (t,u)::dpairs))  of
wenzelm@16425
  1538
              NONE                   => tryasms (A, As, n+1, apairs)
wenzelm@16425
  1539
            | cell as SOME((_,tpairs),_) =>
wenzelm@16425
  1540
                Seq.it_right (addth A (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@16425
  1541
                    (Seq.make(fn()=> cell),
wenzelm@16425
  1542
                     Seq.make(fn()=> Seq.pull (tryasms(A, As, n+1, apairs)))))
clasohm@0
  1543
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
skalberg@15531
  1544
       | eres (A1::As) = tryasms(SOME A1, As, 1, Logic.assum_pairs(nlift+1,A1))
clasohm@0
  1545
     (*ordinary resolution*)
skalberg@15531
  1546
     fun res(NONE) = Seq.empty
skalberg@15531
  1547
       | res(cell as SOME((_,tpairs),_)) =
skalberg@15531
  1548
             Seq.it_right (addth NONE (newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@4270
  1549
                       (Seq.make (fn()=> cell), Seq.empty)
clasohm@0
  1550
 in  if eres_flg then eres(rev rAs)
wenzelm@16425
  1551
     else res(Seq.pull(Unify.unifiers(thy, env, dpairs)))
clasohm@0
  1552
 end;
wenzelm@7528
  1553
end;
clasohm@0
  1554
wenzelm@18501
  1555
fun compose_no_flatten match (orule, nsubgoal) i state =
wenzelm@18501
  1556
  bicompose_aux false match (state, dest_state (state, i), false) (false, orule, nsubgoal);
clasohm@0
  1557
wenzelm@18501
  1558
fun bicompose match arg i state =
wenzelm@18501
  1559
  bicompose_aux true match (state, dest_state (state,i), false) arg;
clasohm@0
  1560
clasohm@0
  1561
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1562
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1563
fun could_bires (Hs, B, eres_flg, rule) =
wenzelm@29269
  1564
    let fun could_reshyp (A1::_) = exists (fn H => Term.could_unify (A1, H)) Hs
wenzelm@250
  1565
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@29269
  1566
    in  Term.could_unify(concl_of rule, B) andalso
wenzelm@250
  1567
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1568
    end;
clasohm@0
  1569
clasohm@0
  1570
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1571
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1572
fun biresolution match brules i state =
wenzelm@18035
  1573
    let val (stpairs, Bs, Bi, C) = dest_state(state,i);
wenzelm@18145
  1574
        val lift = lift_rule (cprem_of state i);
wenzelm@250
  1575
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1576
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@22573
  1577
        val compose = bicompose_aux true match (state, (stpairs, Bs, Bi, C), true);
wenzelm@4270
  1578
        fun res [] = Seq.empty
wenzelm@250
  1579
          | res ((eres_flg, rule)::brules) =
nipkow@13642
  1580
              if !Pattern.trace_unify_fail orelse
nipkow@13642
  1581
                 could_bires (Hs, B, eres_flg, rule)
wenzelm@4270
  1582
              then Seq.make (*delay processing remainder till needed*)
wenzelm@22573
  1583
                  (fn()=> SOME(compose (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1584
                               res brules))
wenzelm@250
  1585
              else res brules
wenzelm@4270
  1586
    in  Seq.flat (res brules)  end;
clasohm@0
  1587
clasohm@0
  1588
wenzelm@28321
  1589
wenzelm@28978
  1590
(*** Future theorems -- proofs with promises ***)
wenzelm@28356
  1591
wenzelm@28446
  1592
(* future rule *)
wenzelm@28330
  1593
wenzelm@28446
  1594
fun future_result i orig_thy orig_shyps orig_prop raw_thm =
wenzelm@28378
  1595
  let
wenzelm@28378
  1596
    val _ = Theory.check_thy orig_thy;
wenzelm@28378
  1597
    val thm = strip_shyps (transfer orig_thy raw_thm);
wenzelm@28378
  1598
    val _ = Theory.check_thy orig_thy;
wenzelm@28446
  1599
    fun err msg = raise THM ("future_result: " ^ msg, 0, [thm]);
wenzelm@28378
  1600
wenzelm@28996
  1601
    val Thm (Deriv {max_promise, ...}, {shyps, hyps, tpairs, prop, ...}) = thm;
wenzelm@28378
  1602
    val _ = prop aconv orig_prop orelse err "bad prop";
wenzelm@28378
  1603
    val _ = null tpairs orelse err "bad tpairs";
wenzelm@28378
  1604
    val _ = null hyps orelse err "bad hyps";
wenzelm@28378
  1605
    val _ = Sorts.subset (shyps, orig_shyps) orelse err "bad shyps";
wenzelm@28996
  1606
    val _ = max_promise < i orelse err "bad dependencies";
wenzelm@28378
  1607
  in thm end;
wenzelm@28378
  1608
wenzelm@28978
  1609
fun future future_thm ct =
wenzelm@28321
  1610
  let
wenzelm@28624
  1611
    val Cterm {thy_ref = thy_ref, t = prop, T, maxidx, sorts} = ct;
wenzelm@28321
  1612
    val thy = Context.reject_draft (Theory.deref thy_ref);
wenzelm@28446
  1613
    val _ = T <> propT andalso raise CTERM ("future: prop expected", [ct]);
wenzelm@28378
  1614
wenzelm@28389
  1615
    val i = serial ();
wenzelm@29436
  1616
    val future = future_thm |> Future.map (future_result i thy sorts prop);
wenzelm@28829
  1617
    val promise = (i, future);
wenzelm@28321
  1618
  in
wenzelm@28996
  1619
    Thm (make_deriv i [promise] [promise] [] [] (Pt.promise_proof thy i prop),
wenzelm@28321
  1620
     {thy_ref = thy_ref,
wenzelm@28321
  1621
      tags = [],
wenzelm@28321
  1622
      maxidx = maxidx,
wenzelm@28321
  1623
      shyps = sorts,
wenzelm@28321
  1624
      hyps = [],
wenzelm@28321
  1625
      tpairs = [],
wenzelm@28321
  1626
      prop = prop})
wenzelm@28321
  1627
  end;
wenzelm@28321
  1628
wenzelm@28330
  1629
wenzelm@29432
  1630
(* pending task groups *)
wenzelm@29432
  1631
wenzelm@29432
  1632
fun pending_groups (Thm (Deriv {open_promises, ...}, _)) =
wenzelm@29432
  1633
  fold (insert Task_Queue.eq_group o Future.group_of o #2) open_promises;
wenzelm@29432
  1634
wenzelm@29432
  1635
wenzelm@29432
  1636
(* fulfilled proofs *)
wenzelm@28330
  1637
wenzelm@28816
  1638
fun raw_proof_of (Thm (Deriv {body, ...}, _)) = Proofterm.proof_of body;
wenzelm@28814
  1639
wenzelm@28996
  1640
fun proof_body_of (Thm (Deriv {open_promises, promises, body, ...}, {thy_ref, ...})) =
wenzelm@28330
  1641
  let
wenzelm@28996
  1642
    val _ = Exn.release_all (map (Future.join_result o #2) (rev open_promises));
wenzelm@28847
  1643
    val ps = map (apsnd (raw_proof_of o Future.join)) promises;
wenzelm@28829
  1644
  in Pt.fulfill_proof (Theory.deref thy_ref) ps body end;
wenzelm@28804
  1645
wenzelm@28814
  1646
val proof_of = Proofterm.proof_of o proof_body_of;
wenzelm@29003
  1647
val join_proof = ignore o proof_body_of;
wenzelm@28814
  1648
wenzelm@28804
  1649
wenzelm@28804
  1650
(* closed derivations with official name *)
wenzelm@28804
  1651
wenzelm@28804
  1652
fun get_name thm =
wenzelm@28814
  1653
  Pt.get_name (hyps_of thm) (prop_of thm) (raw_proof_of thm);
wenzelm@28330
  1654
wenzelm@28804
  1655
fun put_name name (thm as Thm (der, args)) =
wenzelm@28804
  1656
  let
wenzelm@28996
  1657
    val Deriv {max_promise, open_promises, promises, body, ...} = der;
wenzelm@28804
  1658
    val {thy_ref, hyps, prop, tpairs, ...} = args;
wenzelm@28996
  1659
    val _ = null tpairs orelse raise THM ("put_name: unsolved flex-flex constraints", 0, [thm]);
wenzelm@28804
  1660
wenzelm@29636
  1661
    val ps = map (apsnd (Future.map proof_of)) promises;
wenzelm@28804
  1662
    val thy = Theory.deref thy_ref;
wenzelm@28804
  1663
    val (pthm, proof) = Pt.thm_proof thy name hyps prop ps body;
wenzelm@28996
  1664
wenzelm@28996
  1665
    val open_promises' = open_promises |> filter (fn (_, p) =>
wenzelm@28996
  1666
      (case Future.peek p of SOME (Exn.Result _) => false | _ => true));
wenzelm@28996
  1667
    val der' = make_deriv max_promise open_promises' [] [] [pthm] proof;
wenzelm@28804
  1668
    val _ = Theory.check_thy thy;
wenzelm@28804
  1669
  in Thm (der', args) end;
wenzelm@28330
  1670
wenzelm@28321
  1671
wenzelm@28321
  1672
wenzelm@2509
  1673
(*** Oracles ***)
wenzelm@2509
  1674
wenzelm@28290
  1675
(* oracle rule *)
wenzelm@28290
  1676
wenzelm@28290
  1677
fun invoke_oracle thy_ref1 name oracle arg =
wenzelm@28624
  1678
  let val Cterm {thy_ref = thy_ref2, t = prop, T, maxidx, sorts} = oracle arg in
wenzelm@28290
  1679
    if T <> propT then
wenzelm@28290
  1680
      raise THM ("Oracle's result must have type prop: " ^ name, 0, [])
wenzelm@28290
  1681
    else
wenzelm@28804
  1682
      let val prf = Pt.oracle_proof name prop in
wenzelm@28996
  1683
        Thm (make_deriv ~1 [] [] (Pt.make_oracles prf) [] prf,
wenzelm@28804
  1684
         {thy_ref = Theory.merge_refs (thy_ref1, thy_ref2),
wenzelm@28804
  1685
          tags = [],
wenzelm@28804
  1686
          maxidx = maxidx,
wenzelm@28804
  1687
          shyps = sorts,
wenzelm@28804
  1688
          hyps = [],
wenzelm@28804
  1689
          tpairs = [],
wenzelm@28804
  1690
          prop = prop})
wenzelm@28804
  1691
      end
wenzelm@3812
  1692
  end;
wenzelm@3812
  1693
wenzelm@28290
  1694
wenzelm@28290
  1695
(* authentic derivation names *)
wenzelm@28290
  1696
wenzelm@28290
  1697
fun err_dup_ora dup = error ("Duplicate oracle: " ^ quote dup);
wenzelm@28290
  1698
wenzelm@28290
  1699
structure Oracles = TheoryDataFun
wenzelm@28290
  1700
(
wenzelm@30288
  1701
  type T = serial NameSpace.table;
wenzelm@28290
  1702
  val empty = NameSpace.empty_table;
wenzelm@28290
  1703
  val copy = I;
wenzelm@28290
  1704
  val extend = I;
wenzelm@29288
  1705
  fun merge _ oracles : T = NameSpace.merge_tables (op =) oracles
wenzelm@28290
  1706
    handle Symtab.DUP dup => err_dup_ora dup;
wenzelm@28290
  1707
);
wenzelm@28290
  1708
wenzelm@28290
  1709
val extern_oracles = map #1 o NameSpace.extern_table o Oracles.get;
wenzelm@28290
  1710
wenzelm@30288
  1711
fun add_oracle (b, oracle) thy =
wenzelm@28290
  1712
  let
wenzelm@28290
  1713
    val naming = Sign.naming_of thy;
wenzelm@30288
  1714
    val (name, tab') = NameSpace.bind naming (b, serial ()) (Oracles.get thy)
wenzelm@30288
  1715
      handle Symtab.DUP _ => err_dup_ora (Binding.str_of b);
wenzelm@30288
  1716
    val thy' = Oracles.put tab' thy;
wenzelm@28290
  1717
  in ((name, invoke_oracle (Theory.check_thy thy') name oracle), thy') end;
wenzelm@28290
  1718
clasohm@0
  1719
end;
paulson@1503
  1720
wenzelm@6089
  1721
structure BasicThm: BASIC_THM = Thm;
wenzelm@6089
  1722
open BasicThm;