src/Pure/thm.ML
author haftmann
Tue Oct 20 16:13:01 2009 +0200 (2009-10-20)
changeset 33037 b22e44496dc2
parent 32810 f3466a5645fa
child 33038 8f9594c31de4
permissions -rw-r--r--
replaced old_style infixes eq_set, subset, union, inter and variants by generic versions
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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 of_class: ctyp * 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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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 capply: cterm -> cterm -> cterm
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  val cabs_name: string * cterm -> cterm -> cterm
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  val cabs: cterm -> cterm -> cterm
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  val adjust_maxidx_cterm: int -> cterm -> cterm
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  val incr_indexes_cterm: int -> cterm -> cterm
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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 fold_terms: (term -> 'a -> 'a) -> thm -> 'a -> 'a
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  val terms_of_tpairs: (term * term) list -> term list
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  val full_prop_of: thm -> term
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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 no_prems: thm -> bool
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  val major_prem_of: thm -> term
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  val join_proofs: thm list -> unit
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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 status_of: thm -> {oracle: bool, unfinished: bool, failed: bool}
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  val future: thm future -> cterm -> thm
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  val get_name: thm -> string
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  val put_name: string -> thm -> thm
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  val axiom: theory -> string -> thm
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  val axioms_of: theory -> (string * thm) list
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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 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 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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  val rename_boundvars: term -> term -> thm -> thm
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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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abstype 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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with
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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 (_, 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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abstype 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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with
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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, ...}) (Cterm {thy_ref = r2, ...}) =
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  Theory.merge_refs (r1, r2);
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(* destructors *)
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fun dest_comb (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 (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 (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 $ _ $ _, 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 (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_name
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  (x, 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_name (x, 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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fun cabs t u = cabs_name ("", t) u;
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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, ...},
wenzelm@20815
   314
     ct2 as Cterm {t = t2, sorts = sorts2, maxidx = maxidx2, ...}) =
berghofe@10416
   315
  let
wenzelm@24143
   316
    val thy = Theory.deref (merge_thys0 ct1 ct2);
wenzelm@24143
   317
    val (Tinsts, tinsts) = match thy (t1, t2) (Vartab.empty, Vartab.empty);
wenzelm@16601
   318
    val sorts = Sorts.union sorts1 sorts2;
wenzelm@20512
   319
    fun mk_cTinst ((a, i), (S, T)) =
wenzelm@24143
   320
      (Ctyp {T = TVar ((a, i), S), thy_ref = Theory.check_thy thy, maxidx = i, sorts = sorts},
wenzelm@24143
   321
       Ctyp {T = T, thy_ref = Theory.check_thy thy, maxidx = maxidx2, sorts = sorts});
wenzelm@20512
   322
    fun mk_ctinst ((x, i), (T, t)) =
wenzelm@32035
   323
      let val T = Envir.subst_type Tinsts T in
wenzelm@24143
   324
        (Cterm {t = Var ((x, i), T), T = T, thy_ref = Theory.check_thy thy,
wenzelm@24143
   325
          maxidx = i, sorts = sorts},
wenzelm@24143
   326
         Cterm {t = t, T = T, thy_ref = Theory.check_thy thy, maxidx = maxidx2, sorts = sorts})
berghofe@10416
   327
      end;
wenzelm@16656
   328
  in (Vartab.fold (cons o mk_cTinst) Tinsts [], Vartab.fold (cons o mk_ctinst) tinsts []) end;
berghofe@10416
   329
wenzelm@22909
   330
in
berghofe@10416
   331
wenzelm@22909
   332
val match = gen_match Pattern.match;
wenzelm@22909
   333
val first_order_match = gen_match Pattern.first_order_match;
wenzelm@22909
   334
wenzelm@22909
   335
end;
berghofe@10416
   336
wenzelm@2509
   337
wenzelm@2509
   338
wenzelm@28321
   339
(*** Derivations and Theorems ***)
lcp@229
   340
wenzelm@32590
   341
abstype thm = Thm of
wenzelm@28378
   342
 deriv *                                        (*derivation*)
wenzelm@28378
   343
 {thy_ref: theory_ref,                          (*dynamic reference to theory*)
wenzelm@28378
   344
  tags: Properties.T,                           (*additional annotations/comments*)
wenzelm@28378
   345
  maxidx: int,                                  (*maximum index of any Var or TVar*)
wenzelm@28378
   346
  shyps: sort OrdList.T,                        (*sort hypotheses*)
wenzelm@28378
   347
  hyps: term OrdList.T,                         (*hypotheses*)
wenzelm@28378
   348
  tpairs: (term * term) list,                   (*flex-flex pairs*)
wenzelm@28378
   349
  prop: term}                                   (*conclusion*)
wenzelm@28624
   350
and deriv = Deriv of
wenzelm@32059
   351
 {promises: (serial * thm future) OrdList.T,
wenzelm@32590
   352
  body: Pt.proof_body}
wenzelm@32590
   353
with
clasohm@0
   354
wenzelm@23601
   355
type conv = cterm -> thm;
wenzelm@23601
   356
wenzelm@22365
   357
(*attributes subsume any kind of rules or context modifiers*)
wenzelm@22365
   358
type attribute = Context.generic * thm -> Context.generic * thm;
wenzelm@22365
   359
wenzelm@16725
   360
(*errors involving theorems*)
wenzelm@16725
   361
exception THM of string * int * thm list;
berghofe@13658
   362
wenzelm@28321
   363
fun rep_thm (Thm (_, args)) = args;
clasohm@0
   364
wenzelm@28321
   365
fun crep_thm (Thm (_, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@26631
   366
  let fun cterm max t = Cterm {thy_ref = thy_ref, t = t, T = propT, maxidx = max, sorts = shyps} in
wenzelm@28321
   367
   {thy_ref = thy_ref, tags = tags, maxidx = maxidx, shyps = shyps,
wenzelm@16425
   368
    hyps = map (cterm ~1) hyps,
wenzelm@16425
   369
    tpairs = map (pairself (cterm maxidx)) tpairs,
wenzelm@16425
   370
    prop = cterm maxidx prop}
clasohm@1517
   371
  end;
clasohm@1517
   372
wenzelm@31947
   373
fun fold_terms f (Thm (_, {tpairs, prop, hyps, ...})) =
wenzelm@31947
   374
  fold (fn (t, u) => f t #> f u) tpairs #> f prop #> fold f hyps;
wenzelm@31947
   375
wenzelm@16725
   376
fun terms_of_tpairs tpairs = fold_rev (fn (t, u) => cons t o cons u) tpairs [];
wenzelm@16725
   377
wenzelm@16725
   378
fun eq_tpairs ((t, u), (t', u')) = t aconv t' andalso u aconv u';
wenzelm@18944
   379
fun union_tpairs ts us = Library.merge eq_tpairs (ts, us);
wenzelm@16884
   380
val maxidx_tpairs = fold (fn (t, u) => Term.maxidx_term t #> Term.maxidx_term u);
wenzelm@16725
   381
wenzelm@16725
   382
fun attach_tpairs tpairs prop =
wenzelm@16725
   383
  Logic.list_implies (map Logic.mk_equals tpairs, prop);
wenzelm@16725
   384
wenzelm@28321
   385
fun full_prop_of (Thm (_, {tpairs, prop, ...})) = attach_tpairs tpairs prop;
wenzelm@16945
   386
wenzelm@29269
   387
val union_hyps = OrdList.union TermOrd.fast_term_ord;
wenzelm@29269
   388
val insert_hyps = OrdList.insert TermOrd.fast_term_ord;
wenzelm@29269
   389
val remove_hyps = OrdList.remove TermOrd.fast_term_ord;
wenzelm@22365
   390
wenzelm@16945
   391
wenzelm@24143
   392
(* merge theories of cterms/thms -- trivial absorption only *)
wenzelm@16945
   393
wenzelm@32784
   394
fun merge_thys1 (Cterm {thy_ref = r1, ...}) (Thm (_, {thy_ref = r2, ...})) =
wenzelm@23601
   395
  Theory.merge_refs (r1, r2);
wenzelm@16945
   396
wenzelm@32784
   397
fun merge_thys2 (Thm (_, {thy_ref = r1, ...})) (Thm (_, {thy_ref = r2, ...})) =
wenzelm@23601
   398
  Theory.merge_refs (r1, r2);
wenzelm@16945
   399
clasohm@0
   400
wenzelm@22365
   401
(* basic components *)
wenzelm@16135
   402
wenzelm@28321
   403
val theory_of_thm = Theory.deref o #thy_ref o rep_thm;
wenzelm@28321
   404
val maxidx_of = #maxidx o rep_thm;
wenzelm@19910
   405
fun maxidx_thm th i = Int.max (maxidx_of th, i);
wenzelm@28321
   406
val hyps_of = #hyps o rep_thm;
wenzelm@28321
   407
val prop_of = #prop o rep_thm;
wenzelm@28321
   408
val tpairs_of = #tpairs o rep_thm;
clasohm@0
   409
wenzelm@16601
   410
val concl_of = Logic.strip_imp_concl o prop_of;
wenzelm@16601
   411
val prems_of = Logic.strip_imp_prems o prop_of;
wenzelm@21576
   412
val nprems_of = Logic.count_prems o prop_of;
wenzelm@19305
   413
fun no_prems th = nprems_of th = 0;
wenzelm@16601
   414
wenzelm@16601
   415
fun major_prem_of th =
wenzelm@16601
   416
  (case prems_of th of
wenzelm@16601
   417
    prem :: _ => Logic.strip_assums_concl prem
wenzelm@16601
   418
  | [] => raise THM ("major_prem_of: rule with no premises", 0, [th]));
wenzelm@16601
   419
wenzelm@16601
   420
(*the statement of any thm is a cterm*)
wenzelm@28321
   421
fun cprop_of (Thm (_, {thy_ref, maxidx, shyps, prop, ...})) =
wenzelm@16601
   422
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, t = prop, sorts = shyps};
wenzelm@16601
   423
wenzelm@28321
   424
fun cprem_of (th as Thm (_, {thy_ref, maxidx, shyps, prop, ...})) i =
wenzelm@18035
   425
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, sorts = shyps,
wenzelm@18145
   426
    t = Logic.nth_prem (i, prop) handle TERM _ => raise THM ("cprem_of", i, [th])};
wenzelm@18035
   427
wenzelm@16656
   428
(*explicit transfer to a super theory*)
wenzelm@16425
   429
fun transfer thy' thm =
wenzelm@3895
   430
  let
wenzelm@28321
   431
    val Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop}) = thm;
wenzelm@16425
   432
    val thy = Theory.deref thy_ref;
wenzelm@26665
   433
    val _ = Theory.subthy (thy, thy') orelse raise THM ("transfer: not a super theory", 0, [thm]);
wenzelm@26665
   434
    val is_eq = Theory.eq_thy (thy, thy');
wenzelm@24143
   435
    val _ = Theory.check_thy thy;
wenzelm@3895
   436
  in
wenzelm@24143
   437
    if is_eq then thm
wenzelm@16945
   438
    else
wenzelm@28321
   439
      Thm (der,
wenzelm@28321
   440
       {thy_ref = Theory.check_thy thy',
wenzelm@21646
   441
        tags = tags,
wenzelm@16945
   442
        maxidx = maxidx,
wenzelm@16945
   443
        shyps = shyps,
wenzelm@16945
   444
        hyps = hyps,
wenzelm@16945
   445
        tpairs = tpairs,
wenzelm@28321
   446
        prop = prop})
wenzelm@3895
   447
  end;
wenzelm@387
   448
wenzelm@16945
   449
(*explicit weakening: maps |- B to A |- B*)
wenzelm@16945
   450
fun weaken raw_ct th =
wenzelm@16945
   451
  let
wenzelm@20261
   452
    val ct as Cterm {t = A, T, sorts, maxidx = maxidxA, ...} = adjust_maxidx_cterm ~1 raw_ct;
wenzelm@28321
   453
    val Thm (der, {tags, maxidx, shyps, hyps, tpairs, prop, ...}) = th;
wenzelm@16945
   454
  in
wenzelm@16945
   455
    if T <> propT then
wenzelm@16945
   456
      raise THM ("weaken: assumptions must have type prop", 0, [])
wenzelm@16945
   457
    else if maxidxA <> ~1 then
wenzelm@16945
   458
      raise THM ("weaken: assumptions may not contain schematic variables", maxidxA, [])
wenzelm@16945
   459
    else
wenzelm@28321
   460
      Thm (der,
wenzelm@28321
   461
       {thy_ref = merge_thys1 ct th,
wenzelm@21646
   462
        tags = tags,
wenzelm@16945
   463
        maxidx = maxidx,
wenzelm@16945
   464
        shyps = Sorts.union sorts shyps,
wenzelm@28354
   465
        hyps = insert_hyps A hyps,
wenzelm@16945
   466
        tpairs = tpairs,
wenzelm@28321
   467
        prop = prop})
wenzelm@16945
   468
  end;
wenzelm@16656
   469
wenzelm@28624
   470
fun weaken_sorts raw_sorts ct =
wenzelm@28624
   471
  let
wenzelm@28624
   472
    val Cterm {thy_ref, t, T, maxidx, sorts} = ct;
wenzelm@28624
   473
    val thy = Theory.deref thy_ref;
wenzelm@28624
   474
    val more_sorts = Sorts.make (map (Sign.certify_sort thy) raw_sorts);
wenzelm@28624
   475
    val sorts' = Sorts.union sorts more_sorts;
wenzelm@28624
   476
  in Cterm {thy_ref = Theory.check_thy thy, t = t, T = T, maxidx = maxidx, sorts = sorts'} end;
wenzelm@28624
   477
wenzelm@16656
   478
clasohm@0
   479
wenzelm@1238
   480
(** sort contexts of theorems **)
wenzelm@1238
   481
wenzelm@31947
   482
(*remove extra sorts that are witnessed by 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@31947
   487
        val present =
wenzelm@31947
   488
          (fold_terms o fold_types o fold_atyps)
wenzelm@31947
   489
            (fn T as TFree (_, S) => insert (eq_snd op =) (T, S)
wenzelm@31947
   490
              | T as TVar (_, S) => insert (eq_snd op =) (T, S)) thm [];
wenzelm@31947
   491
        val extra = fold (Sorts.remove_sort o #2) present shyps;
wenzelm@31947
   492
        val witnessed = Sign.witness_sorts thy present extra;
wenzelm@31947
   493
        val extra' = fold (Sorts.remove_sort o #2) witnessed extra
wenzelm@28624
   494
          |> Sorts.minimal_sorts (Sign.classes_of thy);
wenzelm@31947
   495
        val shyps' = fold (Sorts.insert_sort o #2) present extra';
wenzelm@7642
   496
      in
wenzelm@28321
   497
        Thm (der, {thy_ref = Theory.check_thy thy, tags = tags, maxidx = maxidx,
wenzelm@28321
   498
          shyps = shyps', hyps = hyps, tpairs = tpairs, prop = prop})
wenzelm@7642
   499
      end;
wenzelm@1238
   500
wenzelm@16656
   501
(*dangling sort constraints of a thm*)
wenzelm@31947
   502
fun extra_shyps (th as Thm (_, {shyps, ...})) =
wenzelm@31947
   503
  Sorts.subtract (fold_terms Sorts.insert_term th []) shyps;
wenzelm@28321
   504
wenzelm@28321
   505
wenzelm@28321
   506
wenzelm@32725
   507
(** derivations and promised proofs **)
wenzelm@28321
   508
wenzelm@32059
   509
fun make_deriv promises oracles thms proof =
wenzelm@32059
   510
  Deriv {promises = promises, body = PBody {oracles = oracles, thms = thms, proof = proof}};
wenzelm@28321
   511
wenzelm@32059
   512
val empty_deriv = make_deriv [] [] [] Pt.MinProof;
wenzelm@28321
   513
wenzelm@28330
   514
wenzelm@28354
   515
(* inference rules *)
wenzelm@28321
   516
wenzelm@28378
   517
fun promise_ord ((i, _), (j, _)) = int_ord (j, i);
wenzelm@28330
   518
wenzelm@28321
   519
fun deriv_rule2 f
wenzelm@32059
   520
    (Deriv {promises = ps1, body = PBody {oracles = oras1, thms = thms1, proof = prf1}})
wenzelm@32059
   521
    (Deriv {promises = ps2, body = PBody {oracles = oras2, thms = thms2, proof = prf2}}) =
wenzelm@28321
   522
  let
wenzelm@28330
   523
    val ps = OrdList.union promise_ord ps1 ps2;
wenzelm@28804
   524
    val oras = Pt.merge_oracles oras1 oras2;
wenzelm@28804
   525
    val thms = Pt.merge_thms thms1 thms2;
wenzelm@28321
   526
    val prf =
wenzelm@28321
   527
      (case ! Pt.proofs of
wenzelm@28321
   528
        2 => f prf1 prf2
wenzelm@28804
   529
      | 1 => MinProof
wenzelm@28804
   530
      | 0 => MinProof
wenzelm@28321
   531
      | i => error ("Illegal level of detail for proof objects: " ^ string_of_int i));
wenzelm@32059
   532
  in make_deriv ps oras thms prf end;
wenzelm@28321
   533
wenzelm@28321
   534
fun deriv_rule1 f = deriv_rule2 (K f) empty_deriv;
wenzelm@32059
   535
fun deriv_rule0 prf = deriv_rule1 I (make_deriv [] [] [] prf);
wenzelm@28321
   536
wenzelm@1238
   537
wenzelm@32725
   538
(* fulfilled proofs *)
wenzelm@32725
   539
wenzelm@32725
   540
fun raw_body (Thm (Deriv {body, ...}, _)) = body;
wenzelm@32725
   541
wenzelm@32725
   542
fun fulfill_body (Thm (Deriv {promises, body}, {thy_ref, ...})) =
wenzelm@32810
   543
  Pt.fulfill_proof (Theory.deref thy_ref)
wenzelm@32725
   544
    (map #1 promises ~~ fulfill_bodies (map #2 promises)) body
wenzelm@32725
   545
and fulfill_bodies futures = map fulfill_body (Exn.release_all (Future.join_results futures));
wenzelm@32725
   546
wenzelm@32725
   547
val join_proofs = Pt.join_bodies o map fulfill_body;
wenzelm@32725
   548
wenzelm@32725
   549
fun proof_body_of thm = (Pt.join_bodies [raw_body thm]; fulfill_body thm);
wenzelm@32725
   550
val proof_of = Pt.proof_of o proof_body_of;
wenzelm@32725
   551
wenzelm@32725
   552
wenzelm@32725
   553
(* derivation status *)
wenzelm@32725
   554
wenzelm@32725
   555
fun status_of (Thm (Deriv {promises, body}, _)) =
wenzelm@32725
   556
  let
wenzelm@32725
   557
    val ps = map (Future.peek o snd) promises;
wenzelm@32725
   558
    val bodies = body ::
wenzelm@32725
   559
      map_filter (fn SOME (Exn.Result th) => SOME (raw_body th) | _ => NONE) ps;
wenzelm@32725
   560
    val {oracle, unfinished, failed} = Pt.status_of bodies;
wenzelm@32725
   561
  in
wenzelm@32725
   562
   {oracle = oracle,
wenzelm@32725
   563
    unfinished = unfinished orelse exists is_none ps,
wenzelm@32725
   564
    failed = failed orelse exists (fn SOME (Exn.Exn _) => true | _ => false) ps}
wenzelm@32725
   565
  end;
wenzelm@32725
   566
wenzelm@32725
   567
wenzelm@32725
   568
(* future rule *)
wenzelm@32725
   569
wenzelm@32725
   570
fun future_result i orig_thy orig_shyps orig_prop raw_thm =
wenzelm@32725
   571
  let
wenzelm@32725
   572
    val _ = Theory.check_thy orig_thy;
wenzelm@32725
   573
    val thm = strip_shyps (transfer orig_thy raw_thm);
wenzelm@32725
   574
    val _ = Theory.check_thy orig_thy;
wenzelm@32725
   575
    fun err msg = raise THM ("future_result: " ^ msg, 0, [thm]);
wenzelm@32725
   576
wenzelm@32725
   577
    val Thm (Deriv {promises, ...}, {shyps, hyps, tpairs, prop, ...}) = thm;
wenzelm@32725
   578
    val _ = prop aconv orig_prop orelse err "bad prop";
wenzelm@32725
   579
    val _ = null tpairs orelse err "bad tpairs";
wenzelm@32725
   580
    val _ = null hyps orelse err "bad hyps";
wenzelm@32725
   581
    val _ = Sorts.subset (shyps, orig_shyps) orelse err "bad shyps";
wenzelm@32725
   582
    val _ = forall (fn (j, _) => i <> j) promises orelse err "bad dependencies";
wenzelm@32725
   583
    val _ = fulfill_bodies (map #2 promises);
wenzelm@32725
   584
  in thm end;
wenzelm@32725
   585
wenzelm@32725
   586
fun future future_thm ct =
wenzelm@32725
   587
  let
wenzelm@32725
   588
    val Cterm {thy_ref = thy_ref, t = prop, T, maxidx, sorts} = ct;
wenzelm@32725
   589
    val thy = Context.reject_draft (Theory.deref thy_ref);
wenzelm@32725
   590
    val _ = T <> propT andalso raise CTERM ("future: prop expected", [ct]);
wenzelm@32725
   591
wenzelm@32725
   592
    val i = serial ();
wenzelm@32725
   593
    val future = future_thm |> Future.map (future_result i thy sorts prop);
wenzelm@32725
   594
  in
wenzelm@32725
   595
    Thm (make_deriv [(i, future)] [] [] (Pt.promise_proof thy i prop),
wenzelm@32725
   596
     {thy_ref = thy_ref,
wenzelm@32725
   597
      tags = [],
wenzelm@32725
   598
      maxidx = maxidx,
wenzelm@32725
   599
      shyps = sorts,
wenzelm@32725
   600
      hyps = [],
wenzelm@32725
   601
      tpairs = [],
wenzelm@32725
   602
      prop = prop})
wenzelm@32725
   603
  end;
wenzelm@32725
   604
wenzelm@32725
   605
wenzelm@32725
   606
(* closed derivations with official name *)
wenzelm@32725
   607
wenzelm@32725
   608
fun get_name thm =
wenzelm@32725
   609
  Pt.get_name (hyps_of thm) (prop_of thm) (Pt.proof_of (raw_body thm));
wenzelm@32725
   610
wenzelm@32725
   611
fun put_name name (thm as Thm (der, args)) =
wenzelm@32725
   612
  let
wenzelm@32725
   613
    val Deriv {promises, body} = der;
wenzelm@32725
   614
    val {thy_ref, hyps, prop, tpairs, ...} = args;
wenzelm@32725
   615
    val _ = null tpairs orelse raise THM ("put_name: unsolved flex-flex constraints", 0, [thm]);
wenzelm@32725
   616
wenzelm@32725
   617
    val ps = map (apsnd (Future.map proof_body_of)) promises;
wenzelm@32725
   618
    val thy = Theory.deref thy_ref;
wenzelm@32725
   619
    val (pthm, proof) = Pt.thm_proof thy name hyps prop ps body;
wenzelm@32725
   620
    val der' = make_deriv [] [] [pthm] proof;
wenzelm@32725
   621
    val _ = Theory.check_thy thy;
wenzelm@32725
   622
  in Thm (der', args) end;
wenzelm@32725
   623
wenzelm@32725
   624
wenzelm@1238
   625
paulson@1529
   626
(** Axioms **)
wenzelm@387
   627
wenzelm@28675
   628
fun axiom theory name =
wenzelm@387
   629
  let
wenzelm@16425
   630
    fun get_ax thy =
wenzelm@22685
   631
      Symtab.lookup (Theory.axiom_table thy) name
wenzelm@16601
   632
      |> Option.map (fn prop =>
wenzelm@24143
   633
           let
wenzelm@28321
   634
             val der = deriv_rule0 (Pt.axm_proof name prop);
wenzelm@24143
   635
             val maxidx = maxidx_of_term prop;
wenzelm@26640
   636
             val shyps = Sorts.insert_term prop [];
wenzelm@24143
   637
           in
wenzelm@28321
   638
             Thm (der, {thy_ref = Theory.check_thy thy, tags = [],
wenzelm@28321
   639
               maxidx = maxidx, shyps = shyps, hyps = [], tpairs = [], prop = prop})
wenzelm@24143
   640
           end);
wenzelm@387
   641
  in
wenzelm@16425
   642
    (case get_first get_ax (theory :: Theory.ancestors_of theory) of
skalberg@15531
   643
      SOME thm => thm
skalberg@15531
   644
    | NONE => raise THEORY ("No axiom " ^ quote name, [theory]))
wenzelm@387
   645
  end;
wenzelm@387
   646
wenzelm@776
   647
(*return additional axioms of this theory node*)
wenzelm@776
   648
fun axioms_of thy =
wenzelm@28675
   649
  map (fn s => (s, axiom thy s)) (Symtab.keys (Theory.axiom_table thy));
wenzelm@776
   650
wenzelm@6089
   651
wenzelm@28804
   652
(* tags *)
wenzelm@6089
   653
wenzelm@21646
   654
val get_tags = #tags o rep_thm;
wenzelm@6089
   655
wenzelm@28321
   656
fun map_tags f (Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@28321
   657
  Thm (der, {thy_ref = thy_ref, tags = f tags, maxidx = maxidx,
wenzelm@28321
   658
    shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop});
clasohm@0
   659
clasohm@0
   660
wenzelm@28321
   661
fun norm_proof (Thm (der, args as {thy_ref, ...})) =
wenzelm@24143
   662
  let
wenzelm@24143
   663
    val thy = Theory.deref thy_ref;
wenzelm@28321
   664
    val der' = deriv_rule1 (Pt.rew_proof thy) der;
wenzelm@28321
   665
    val _ = Theory.check_thy thy;
wenzelm@28321
   666
  in Thm (der', args) end;
berghofe@23781
   667
wenzelm@28321
   668
fun adjust_maxidx_thm i (th as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@20261
   669
  if maxidx = i then th
wenzelm@20261
   670
  else if maxidx < i then
wenzelm@28321
   671
    Thm (der, {maxidx = i, thy_ref = thy_ref, tags = tags, shyps = shyps,
wenzelm@28321
   672
      hyps = hyps, tpairs = tpairs, prop = prop})
wenzelm@20261
   673
  else
wenzelm@28321
   674
    Thm (der, {maxidx = Int.max (maxidx_tpairs tpairs (maxidx_of_term prop), i), thy_ref = thy_ref,
wenzelm@28321
   675
      tags = tags, shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop});
wenzelm@564
   676
wenzelm@387
   677
wenzelm@2509
   678
paulson@1529
   679
(*** Meta rules ***)
clasohm@0
   680
wenzelm@16601
   681
(** primitive rules **)
clasohm@0
   682
wenzelm@16656
   683
(*The assumption rule A |- A*)
wenzelm@16601
   684
fun assume raw_ct =
wenzelm@20261
   685
  let val Cterm {thy_ref, t = prop, T, maxidx, sorts} = adjust_maxidx_cterm ~1 raw_ct in
wenzelm@16601
   686
    if T <> propT then
mengj@19230
   687
      raise THM ("assume: prop", 0, [])
wenzelm@16601
   688
    else if maxidx <> ~1 then
mengj@19230
   689
      raise THM ("assume: variables", maxidx, [])
wenzelm@28321
   690
    else Thm (deriv_rule0 (Pt.Hyp prop),
wenzelm@28321
   691
     {thy_ref = thy_ref,
wenzelm@21646
   692
      tags = [],
wenzelm@16601
   693
      maxidx = ~1,
wenzelm@16601
   694
      shyps = sorts,
wenzelm@16601
   695
      hyps = [prop],
wenzelm@16601
   696
      tpairs = [],
wenzelm@28321
   697
      prop = prop})
clasohm@0
   698
  end;
clasohm@0
   699
wenzelm@1220
   700
(*Implication introduction
wenzelm@3529
   701
    [A]
wenzelm@3529
   702
     :
wenzelm@3529
   703
     B
wenzelm@1220
   704
  -------
wenzelm@1220
   705
  A ==> B
wenzelm@1220
   706
*)
wenzelm@16601
   707
fun implies_intr
wenzelm@16679
   708
    (ct as Cterm {t = A, T, maxidx = maxidxA, sorts, ...})
wenzelm@28321
   709
    (th as Thm (der, {maxidx, hyps, shyps, tpairs, prop, ...})) =
wenzelm@16601
   710
  if T <> propT then
wenzelm@16601
   711
    raise THM ("implies_intr: assumptions must have type prop", 0, [th])
wenzelm@16601
   712
  else
wenzelm@28321
   713
    Thm (deriv_rule1 (Pt.implies_intr_proof A) der,
wenzelm@28321
   714
     {thy_ref = merge_thys1 ct th,
wenzelm@21646
   715
      tags = [],
wenzelm@16601
   716
      maxidx = Int.max (maxidxA, maxidx),
wenzelm@16601
   717
      shyps = Sorts.union sorts shyps,
wenzelm@28354
   718
      hyps = remove_hyps A hyps,
wenzelm@16601
   719
      tpairs = tpairs,
wenzelm@28321
   720
      prop = Logic.mk_implies (A, prop)});
clasohm@0
   721
paulson@1529
   722
wenzelm@1220
   723
(*Implication elimination
wenzelm@1220
   724
  A ==> B    A
wenzelm@1220
   725
  ------------
wenzelm@1220
   726
        B
wenzelm@1220
   727
*)
wenzelm@16601
   728
fun implies_elim thAB thA =
wenzelm@16601
   729
  let
wenzelm@28321
   730
    val Thm (derA, {maxidx = maxA, hyps = hypsA, shyps = shypsA, tpairs = tpairsA,
wenzelm@28321
   731
      prop = propA, ...}) = thA
wenzelm@28321
   732
    and Thm (der, {maxidx, hyps, shyps, tpairs, prop, ...}) = thAB;
wenzelm@16601
   733
    fun err () = raise THM ("implies_elim: major premise", 0, [thAB, thA]);
wenzelm@16601
   734
  in
wenzelm@16601
   735
    case prop of
wenzelm@20512
   736
      Const ("==>", _) $ A $ B =>
wenzelm@20512
   737
        if A aconv propA then
wenzelm@28321
   738
          Thm (deriv_rule2 (curry Pt.%%) der derA,
wenzelm@28321
   739
           {thy_ref = merge_thys2 thAB thA,
wenzelm@21646
   740
            tags = [],
wenzelm@16601
   741
            maxidx = Int.max (maxA, maxidx),
wenzelm@16601
   742
            shyps = Sorts.union shypsA shyps,
wenzelm@16601
   743
            hyps = union_hyps hypsA hyps,
wenzelm@16601
   744
            tpairs = union_tpairs tpairsA tpairs,
wenzelm@28321
   745
            prop = B})
wenzelm@16601
   746
        else err ()
wenzelm@16601
   747
    | _ => err ()
wenzelm@16601
   748
  end;
wenzelm@250
   749
wenzelm@1220
   750
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@16656
   751
    [x]
wenzelm@16656
   752
     :
wenzelm@16656
   753
     A
wenzelm@16656
   754
  ------
wenzelm@16656
   755
  !!x. A
wenzelm@1220
   756
*)
wenzelm@16601
   757
fun forall_intr
wenzelm@16601
   758
    (ct as Cterm {t = x, T, sorts, ...})
wenzelm@28321
   759
    (th as Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   760
  let
wenzelm@16601
   761
    fun result a =
wenzelm@28321
   762
      Thm (deriv_rule1 (Pt.forall_intr_proof x a) der,
wenzelm@28321
   763
       {thy_ref = merge_thys1 ct th,
wenzelm@21646
   764
        tags = [],
wenzelm@16601
   765
        maxidx = maxidx,
wenzelm@16601
   766
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   767
        hyps = hyps,
wenzelm@16601
   768
        tpairs = tpairs,
wenzelm@28321
   769
        prop = Term.all T $ Abs (a, T, abstract_over (x, prop))});
wenzelm@21798
   770
    fun check_occs a x ts =
wenzelm@16847
   771
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@21798
   772
        raise THM ("forall_intr: variable " ^ quote a ^ " free in assumptions", 0, [th])
wenzelm@16601
   773
      else ();
wenzelm@16601
   774
  in
wenzelm@16601
   775
    case x of
wenzelm@21798
   776
      Free (a, _) => (check_occs a x hyps; check_occs a x (terms_of_tpairs tpairs); result a)
wenzelm@21798
   777
    | Var ((a, _), _) => (check_occs a x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   778
    | _ => raise THM ("forall_intr: not a variable", 0, [th])
clasohm@0
   779
  end;
clasohm@0
   780
wenzelm@1220
   781
(*Forall elimination
wenzelm@16656
   782
  !!x. A
wenzelm@1220
   783
  ------
wenzelm@1220
   784
  A[t/x]
wenzelm@1220
   785
*)
wenzelm@16601
   786
fun forall_elim
wenzelm@16601
   787
    (ct as Cterm {t, T, maxidx = maxt, sorts, ...})
wenzelm@28321
   788
    (th as Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   789
  (case prop of
wenzelm@16601
   790
    Const ("all", Type ("fun", [Type ("fun", [qary, _]), _])) $ A =>
wenzelm@16601
   791
      if T <> qary then
wenzelm@16601
   792
        raise THM ("forall_elim: type mismatch", 0, [th])
wenzelm@16601
   793
      else
wenzelm@28321
   794
        Thm (deriv_rule1 (Pt.% o rpair (SOME t)) der,
wenzelm@28321
   795
         {thy_ref = merge_thys1 ct th,
wenzelm@21646
   796
          tags = [],
wenzelm@16601
   797
          maxidx = Int.max (maxidx, maxt),
wenzelm@16601
   798
          shyps = Sorts.union sorts shyps,
wenzelm@16601
   799
          hyps = hyps,
wenzelm@16601
   800
          tpairs = tpairs,
wenzelm@28321
   801
          prop = Term.betapply (A, t)})
wenzelm@16601
   802
  | _ => raise THM ("forall_elim: not quantified", 0, [th]));
clasohm@0
   803
clasohm@0
   804
wenzelm@1220
   805
(* Equality *)
clasohm@0
   806
wenzelm@16601
   807
(*Reflexivity
wenzelm@16601
   808
  t == t
wenzelm@16601
   809
*)
wenzelm@32784
   810
fun reflexive (Cterm {thy_ref, t, T = _, maxidx, sorts}) =
wenzelm@28321
   811
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   812
   {thy_ref = thy_ref,
wenzelm@21646
   813
    tags = [],
wenzelm@16601
   814
    maxidx = maxidx,
wenzelm@16601
   815
    shyps = sorts,
wenzelm@16601
   816
    hyps = [],
wenzelm@16601
   817
    tpairs = [],
wenzelm@28321
   818
    prop = Logic.mk_equals (t, t)});
clasohm@0
   819
wenzelm@16601
   820
(*Symmetry
wenzelm@16601
   821
  t == u
wenzelm@16601
   822
  ------
wenzelm@16601
   823
  u == t
wenzelm@1220
   824
*)
wenzelm@28321
   825
fun symmetric (th as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   826
  (case prop of
wenzelm@32784
   827
    (eq as Const ("==", _)) $ t $ u =>
wenzelm@28321
   828
      Thm (deriv_rule1 Pt.symmetric der,
wenzelm@28321
   829
       {thy_ref = thy_ref,
wenzelm@21646
   830
        tags = [],
wenzelm@16601
   831
        maxidx = maxidx,
wenzelm@16601
   832
        shyps = shyps,
wenzelm@16601
   833
        hyps = hyps,
wenzelm@16601
   834
        tpairs = tpairs,
wenzelm@28321
   835
        prop = eq $ u $ t})
wenzelm@16601
   836
    | _ => raise THM ("symmetric", 0, [th]));
clasohm@0
   837
wenzelm@16601
   838
(*Transitivity
wenzelm@16601
   839
  t1 == u    u == t2
wenzelm@16601
   840
  ------------------
wenzelm@16601
   841
       t1 == t2
wenzelm@1220
   842
*)
clasohm@0
   843
fun transitive th1 th2 =
wenzelm@16601
   844
  let
wenzelm@28321
   845
    val Thm (der1, {maxidx = max1, hyps = hyps1, shyps = shyps1, tpairs = tpairs1,
wenzelm@28321
   846
      prop = prop1, ...}) = th1
wenzelm@28321
   847
    and Thm (der2, {maxidx = max2, hyps = hyps2, shyps = shyps2, tpairs = tpairs2,
wenzelm@28321
   848
      prop = prop2, ...}) = th2;
wenzelm@16601
   849
    fun err msg = raise THM ("transitive: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   850
  in
wenzelm@16601
   851
    case (prop1, prop2) of
wenzelm@16601
   852
      ((eq as Const ("==", Type (_, [T, _]))) $ t1 $ u, Const ("==", _) $ u' $ t2) =>
wenzelm@16601
   853
        if not (u aconv u') then err "middle term"
wenzelm@16601
   854
        else
wenzelm@28321
   855
          Thm (deriv_rule2 (Pt.transitive u T) der1 der2,
wenzelm@28321
   856
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   857
            tags = [],
wenzelm@16601
   858
            maxidx = Int.max (max1, max2),
wenzelm@16601
   859
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   860
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   861
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   862
            prop = eq $ t1 $ t2})
wenzelm@16601
   863
     | _ =>  err "premises"
clasohm@0
   864
  end;
clasohm@0
   865
wenzelm@16601
   866
(*Beta-conversion
wenzelm@16656
   867
  (%x. t)(u) == t[u/x]
wenzelm@16601
   868
  fully beta-reduces the term if full = true
berghofe@10416
   869
*)
wenzelm@32784
   870
fun beta_conversion full (Cterm {thy_ref, t, T = _, maxidx, sorts}) =
wenzelm@16601
   871
  let val t' =
wenzelm@16601
   872
    if full then Envir.beta_norm t
wenzelm@16601
   873
    else
wenzelm@16601
   874
      (case t of Abs (_, _, bodt) $ u => subst_bound (u, bodt)
wenzelm@16601
   875
      | _ => raise THM ("beta_conversion: not a redex", 0, []));
wenzelm@16601
   876
  in
wenzelm@28321
   877
    Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   878
     {thy_ref = thy_ref,
wenzelm@21646
   879
      tags = [],
wenzelm@16601
   880
      maxidx = maxidx,
wenzelm@16601
   881
      shyps = sorts,
wenzelm@16601
   882
      hyps = [],
wenzelm@16601
   883
      tpairs = [],
wenzelm@28321
   884
      prop = Logic.mk_equals (t, t')})
berghofe@10416
   885
  end;
berghofe@10416
   886
wenzelm@32784
   887
fun eta_conversion (Cterm {thy_ref, t, T = _, maxidx, sorts}) =
wenzelm@28321
   888
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   889
   {thy_ref = thy_ref,
wenzelm@21646
   890
    tags = [],
wenzelm@16601
   891
    maxidx = maxidx,
wenzelm@16601
   892
    shyps = sorts,
wenzelm@16601
   893
    hyps = [],
wenzelm@16601
   894
    tpairs = [],
wenzelm@28321
   895
    prop = Logic.mk_equals (t, Envir.eta_contract t)});
clasohm@0
   896
wenzelm@32784
   897
fun eta_long_conversion (Cterm {thy_ref, t, T = _, maxidx, sorts}) =
wenzelm@28321
   898
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   899
   {thy_ref = thy_ref,
wenzelm@23493
   900
    tags = [],
wenzelm@23493
   901
    maxidx = maxidx,
wenzelm@23493
   902
    shyps = sorts,
wenzelm@23493
   903
    hyps = [],
wenzelm@23493
   904
    tpairs = [],
wenzelm@28321
   905
    prop = Logic.mk_equals (t, Pattern.eta_long [] t)});
wenzelm@23493
   906
clasohm@0
   907
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   908
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@16601
   909
      t == u
wenzelm@16601
   910
  --------------
wenzelm@16601
   911
  %x. t == %x. u
wenzelm@1220
   912
*)
wenzelm@16601
   913
fun abstract_rule a
wenzelm@16601
   914
    (Cterm {t = x, T, sorts, ...})
wenzelm@28321
   915
    (th as Thm (der, {thy_ref, maxidx, hyps, shyps, tpairs, prop, ...})) =
wenzelm@16601
   916
  let
wenzelm@16601
   917
    val (t, u) = Logic.dest_equals prop
wenzelm@16601
   918
      handle TERM _ => raise THM ("abstract_rule: premise not an equality", 0, [th]);
wenzelm@16601
   919
    val result =
wenzelm@28321
   920
      Thm (deriv_rule1 (Pt.abstract_rule x a) der,
wenzelm@28321
   921
       {thy_ref = thy_ref,
wenzelm@21646
   922
        tags = [],
wenzelm@16601
   923
        maxidx = maxidx,
wenzelm@16601
   924
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   925
        hyps = hyps,
wenzelm@16601
   926
        tpairs = tpairs,
wenzelm@16601
   927
        prop = Logic.mk_equals
wenzelm@28321
   928
          (Abs (a, T, abstract_over (x, t)), Abs (a, T, abstract_over (x, u)))});
wenzelm@21798
   929
    fun check_occs a x ts =
wenzelm@16847
   930
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@21798
   931
        raise THM ("abstract_rule: variable " ^ quote a ^ " free in assumptions", 0, [th])
wenzelm@16601
   932
      else ();
wenzelm@16601
   933
  in
wenzelm@16601
   934
    case x of
wenzelm@21798
   935
      Free (a, _) => (check_occs a x hyps; check_occs a x (terms_of_tpairs tpairs); result)
wenzelm@21798
   936
    | Var ((a, _), _) => (check_occs a x (terms_of_tpairs tpairs); result)
wenzelm@21798
   937
    | _ => raise THM ("abstract_rule: not a variable", 0, [th])
clasohm@0
   938
  end;
clasohm@0
   939
clasohm@0
   940
(*The combination rule
wenzelm@3529
   941
  f == g  t == u
wenzelm@3529
   942
  --------------
wenzelm@16601
   943
    f t == g u
wenzelm@1220
   944
*)
clasohm@0
   945
fun combination th1 th2 =
wenzelm@16601
   946
  let
wenzelm@28321
   947
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@28321
   948
      prop = prop1, ...}) = th1
wenzelm@28321
   949
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@28321
   950
      prop = prop2, ...}) = th2;
wenzelm@16601
   951
    fun chktypes fT tT =
wenzelm@16601
   952
      (case fT of
wenzelm@32784
   953
        Type ("fun", [T1, _]) =>
wenzelm@16601
   954
          if T1 <> tT then
wenzelm@16601
   955
            raise THM ("combination: types", 0, [th1, th2])
wenzelm@16601
   956
          else ()
wenzelm@16601
   957
      | _ => raise THM ("combination: not function type", 0, [th1, th2]));
wenzelm@16601
   958
  in
wenzelm@16601
   959
    case (prop1, prop2) of
wenzelm@16601
   960
      (Const ("==", Type ("fun", [fT, _])) $ f $ g,
wenzelm@16601
   961
       Const ("==", Type ("fun", [tT, _])) $ t $ u) =>
wenzelm@16601
   962
        (chktypes fT tT;
wenzelm@28321
   963
          Thm (deriv_rule2 (Pt.combination f g t u fT) der1 der2,
wenzelm@28321
   964
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   965
            tags = [],
wenzelm@16601
   966
            maxidx = Int.max (max1, max2),
wenzelm@16601
   967
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   968
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   969
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   970
            prop = Logic.mk_equals (f $ t, g $ u)}))
wenzelm@16601
   971
     | _ => raise THM ("combination: premises", 0, [th1, th2])
clasohm@0
   972
  end;
clasohm@0
   973
wenzelm@16601
   974
(*Equality introduction
wenzelm@3529
   975
  A ==> B  B ==> A
wenzelm@3529
   976
  ----------------
wenzelm@3529
   977
       A == B
wenzelm@1220
   978
*)
clasohm@0
   979
fun equal_intr th1 th2 =
wenzelm@16601
   980
  let
wenzelm@28321
   981
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@28321
   982
      prop = prop1, ...}) = th1
wenzelm@28321
   983
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@28321
   984
      prop = prop2, ...}) = th2;
wenzelm@16601
   985
    fun err msg = raise THM ("equal_intr: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   986
  in
wenzelm@16601
   987
    case (prop1, prop2) of
wenzelm@16601
   988
      (Const("==>", _) $ A $ B, Const("==>", _) $ B' $ A') =>
wenzelm@16601
   989
        if A aconv A' andalso B aconv B' then
wenzelm@28321
   990
          Thm (deriv_rule2 (Pt.equal_intr A B) der1 der2,
wenzelm@28321
   991
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   992
            tags = [],
wenzelm@16601
   993
            maxidx = Int.max (max1, max2),
wenzelm@16601
   994
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   995
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   996
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   997
            prop = Logic.mk_equals (A, B)})
wenzelm@16601
   998
        else err "not equal"
wenzelm@16601
   999
    | _ =>  err "premises"
paulson@1529
  1000
  end;
paulson@1529
  1001
paulson@1529
  1002
(*The equal propositions rule
wenzelm@3529
  1003
  A == B  A
paulson@1529
  1004
  ---------
paulson@1529
  1005
      B
paulson@1529
  1006
*)
paulson@1529
  1007
fun equal_elim th1 th2 =
wenzelm@16601
  1008
  let
wenzelm@28321
  1009
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1,
wenzelm@28321
  1010
      tpairs = tpairs1, prop = prop1, ...}) = th1
wenzelm@28321
  1011
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2,
wenzelm@28321
  1012
      tpairs = tpairs2, prop = prop2, ...}) = th2;
wenzelm@16601
  1013
    fun err msg = raise THM ("equal_elim: " ^ msg, 0, [th1, th2]);
wenzelm@16601
  1014
  in
wenzelm@16601
  1015
    case prop1 of
wenzelm@16601
  1016
      Const ("==", _) $ A $ B =>
wenzelm@16601
  1017
        if prop2 aconv A then
wenzelm@28321
  1018
          Thm (deriv_rule2 (Pt.equal_elim A B) der1 der2,
wenzelm@28321
  1019
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
  1020
            tags = [],
wenzelm@16601
  1021
            maxidx = Int.max (max1, max2),
wenzelm@16601
  1022
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
  1023
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
  1024
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
  1025
            prop = B})
wenzelm@16601
  1026
        else err "not equal"
paulson@1529
  1027
     | _ =>  err"major premise"
paulson@1529
  1028
  end;
clasohm@0
  1029
wenzelm@1220
  1030
wenzelm@1220
  1031
clasohm@0
  1032
(**** Derived rules ****)
clasohm@0
  1033
wenzelm@16601
  1034
(*Smash unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@24143
  1035
  Instantiates the theorem and deletes trivial tpairs.  Resulting
wenzelm@24143
  1036
  sequence may contain multiple elements if the tpairs are not all
wenzelm@24143
  1037
  flex-flex.*)
wenzelm@28321
  1038
fun flexflex_rule (th as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@24143
  1039
  let val thy = Theory.deref thy_ref in
wenzelm@24143
  1040
    Unify.smash_unifiers thy tpairs (Envir.empty maxidx)
wenzelm@24143
  1041
    |> Seq.map (fn env =>
wenzelm@24143
  1042
        if Envir.is_empty env then th
wenzelm@24143
  1043
        else
wenzelm@24143
  1044
          let
wenzelm@24143
  1045
            val tpairs' = tpairs |> map (pairself (Envir.norm_term env))
wenzelm@24143
  1046
              (*remove trivial tpairs, of the form t==t*)
wenzelm@24143
  1047
              |> filter_out (op aconv);
wenzelm@28321
  1048
            val der' = deriv_rule1 (Pt.norm_proof' env) der;
wenzelm@24143
  1049
            val prop' = Envir.norm_term env prop;
wenzelm@24143
  1050
            val maxidx = maxidx_tpairs tpairs' (maxidx_of_term prop');
wenzelm@26640
  1051
            val shyps = Envir.insert_sorts env shyps;
wenzelm@24143
  1052
          in
wenzelm@28321
  1053
            Thm (der', {thy_ref = Theory.check_thy thy, tags = [], maxidx = maxidx,
wenzelm@28321
  1054
              shyps = shyps, hyps = hyps, tpairs = tpairs', prop = prop'})
wenzelm@24143
  1055
          end)
wenzelm@24143
  1056
  end;
wenzelm@16601
  1057
clasohm@0
  1058
wenzelm@19910
  1059
(*Generalization of fixed variables
wenzelm@19910
  1060
           A
wenzelm@19910
  1061
  --------------------
wenzelm@19910
  1062
  A[?'a/'a, ?x/x, ...]
wenzelm@19910
  1063
*)
wenzelm@19910
  1064
wenzelm@19910
  1065
fun generalize ([], []) _ th = th
wenzelm@19910
  1066
  | generalize (tfrees, frees) idx th =
wenzelm@19910
  1067
      let
wenzelm@28321
  1068
        val Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...}) = th;
wenzelm@19910
  1069
        val _ = idx <= maxidx andalso raise THM ("generalize: bad index", idx, [th]);
wenzelm@19910
  1070
wenzelm@19910
  1071
        val bad_type = if null tfrees then K false else
wenzelm@19910
  1072
          Term.exists_subtype (fn TFree (a, _) => member (op =) tfrees a | _ => false);
wenzelm@19910
  1073
        fun bad_term (Free (x, T)) = bad_type T orelse member (op =) frees x
wenzelm@19910
  1074
          | bad_term (Var (_, T)) = bad_type T
wenzelm@19910
  1075
          | bad_term (Const (_, T)) = bad_type T
wenzelm@19910
  1076
          | bad_term (Abs (_, T, t)) = bad_type T orelse bad_term t
wenzelm@19910
  1077
          | bad_term (t $ u) = bad_term t orelse bad_term u
wenzelm@19910
  1078
          | bad_term (Bound _) = false;
wenzelm@19910
  1079
        val _ = exists bad_term hyps andalso
wenzelm@19910
  1080
          raise THM ("generalize: variable free in assumptions", 0, [th]);
wenzelm@19910
  1081
wenzelm@31977
  1082
        val gen = Term_Subst.generalize (tfrees, frees) idx;
wenzelm@19910
  1083
        val prop' = gen prop;
wenzelm@19910
  1084
        val tpairs' = map (pairself gen) tpairs;
wenzelm@19910
  1085
        val maxidx' = maxidx_tpairs tpairs' (maxidx_of_term prop');
wenzelm@19910
  1086
      in
wenzelm@28321
  1087
        Thm (deriv_rule1 (Pt.generalize (tfrees, frees) idx) der,
wenzelm@28321
  1088
         {thy_ref = thy_ref,
wenzelm@21646
  1089
          tags = [],
wenzelm@19910
  1090
          maxidx = maxidx',
wenzelm@19910
  1091
          shyps = shyps,
wenzelm@19910
  1092
          hyps = hyps,
wenzelm@19910
  1093
          tpairs = tpairs',
wenzelm@28321
  1094
          prop = prop'})
wenzelm@19910
  1095
      end;
wenzelm@19910
  1096
wenzelm@19910
  1097
wenzelm@22584
  1098
(*Instantiation of schematic variables
wenzelm@16656
  1099
           A
wenzelm@16656
  1100
  --------------------
wenzelm@16656
  1101
  A[t1/v1, ..., tn/vn]
wenzelm@1220
  1102
*)
clasohm@0
  1103
wenzelm@6928
  1104
local
wenzelm@6928
  1105
wenzelm@26939
  1106
fun pretty_typing thy t T = Pretty.block
wenzelm@26939
  1107
  [Syntax.pretty_term_global thy t, Pretty.str " ::", Pretty.brk 1, Syntax.pretty_typ_global thy T];
berghofe@15797
  1108
wenzelm@16884
  1109
fun add_inst (ct, cu) (thy_ref, sorts) =
wenzelm@6928
  1110
  let
wenzelm@26939
  1111
    val Cterm {t = t, T = T, ...} = ct;
wenzelm@26939
  1112
    val Cterm {t = u, T = U, sorts = sorts_u, maxidx = maxidx_u, ...} = cu;
wenzelm@16884
  1113
    val thy_ref' = Theory.merge_refs (thy_ref, merge_thys0 ct cu);
wenzelm@16884
  1114
    val sorts' = Sorts.union sorts_u sorts;
wenzelm@3967
  1115
  in
wenzelm@16884
  1116
    (case t of Var v =>
wenzelm@20512
  1117
      if T = U then ((v, (u, maxidx_u)), (thy_ref', sorts'))
wenzelm@16884
  1118
      else raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
  1119
       [Pretty.str "instantiate: type conflict",
wenzelm@16884
  1120
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') t T,
wenzelm@16884
  1121
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') u U]), [T, U], [t, u])
wenzelm@16884
  1122
    | _ => raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
  1123
       [Pretty.str "instantiate: not a variable",
wenzelm@26939
  1124
        Pretty.fbrk, Syntax.pretty_term_global (Theory.deref thy_ref') t]), [], [t]))
clasohm@0
  1125
  end;
clasohm@0
  1126
wenzelm@16884
  1127
fun add_instT (cT, cU) (thy_ref, sorts) =
wenzelm@16656
  1128
  let
wenzelm@16884
  1129
    val Ctyp {T, thy_ref = thy_ref1, ...} = cT
wenzelm@20512
  1130
    and Ctyp {T = U, thy_ref = thy_ref2, sorts = sorts_U, maxidx = maxidx_U, ...} = cU;
wenzelm@24143
  1131
    val thy' = Theory.deref (Theory.merge_refs (thy_ref, Theory.merge_refs (thy_ref1, thy_ref2)));
wenzelm@16884
  1132
    val sorts' = Sorts.union sorts_U sorts;
wenzelm@16656
  1133
  in
wenzelm@16884
  1134
    (case T of TVar (v as (_, S)) =>
wenzelm@24143
  1135
      if Sign.of_sort thy' (U, S) then ((v, (U, maxidx_U)), (Theory.check_thy thy', sorts'))
wenzelm@26939
  1136
      else raise TYPE ("Type not of sort " ^ Syntax.string_of_sort_global thy' S, [U], [])
wenzelm@16656
  1137
    | _ => raise TYPE (Pretty.string_of (Pretty.block
berghofe@15797
  1138
        [Pretty.str "instantiate: not a type variable",
wenzelm@26939
  1139
         Pretty.fbrk, Syntax.pretty_typ_global thy' T]), [T], []))
wenzelm@16656
  1140
  end;
clasohm@0
  1141
wenzelm@6928
  1142
in
wenzelm@6928
  1143
wenzelm@16601
  1144
(*Left-to-right replacements: ctpairs = [..., (vi, ti), ...].
clasohm@0
  1145
  Instantiates distinct Vars by terms of same type.
wenzelm@16601
  1146
  Does NOT normalize the resulting theorem!*)
paulson@1529
  1147
fun instantiate ([], []) th = th
wenzelm@16884
  1148
  | instantiate (instT, inst) th =
wenzelm@16656
  1149
      let
wenzelm@28321
  1150
        val Thm (der, {thy_ref, hyps, shyps, tpairs, prop, ...}) = th;
wenzelm@16884
  1151
        val (inst', (instT', (thy_ref', shyps'))) =
wenzelm@16884
  1152
          (thy_ref, shyps) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@31977
  1153
        val subst = Term_Subst.instantiate_maxidx (instT', inst');
wenzelm@20512
  1154
        val (prop', maxidx1) = subst prop ~1;
wenzelm@20512
  1155
        val (tpairs', maxidx') =
wenzelm@20512
  1156
          fold_map (fn (t, u) => fn i => subst t i ||>> subst u) tpairs maxidx1;
wenzelm@16656
  1157
      in
wenzelm@28321
  1158
        Thm (deriv_rule1 (fn d => Pt.instantiate (map (apsnd #1) instT', map (apsnd #1) inst') d) der,
wenzelm@28321
  1159
         {thy_ref = thy_ref',
wenzelm@21646
  1160
          tags = [],
wenzelm@20545
  1161
          maxidx = maxidx',
wenzelm@20545
  1162
          shyps = shyps',
wenzelm@20545
  1163
          hyps = hyps,
wenzelm@20545
  1164
          tpairs = tpairs',
wenzelm@28321
  1165
          prop = prop'})
wenzelm@16656
  1166
      end
wenzelm@16656
  1167
      handle TYPE (msg, _, _) => raise THM (msg, 0, [th]);
wenzelm@6928
  1168
wenzelm@22584
  1169
fun instantiate_cterm ([], []) ct = ct
wenzelm@22584
  1170
  | instantiate_cterm (instT, inst) ct =
wenzelm@22584
  1171
      let
wenzelm@22584
  1172
        val Cterm {thy_ref, t, T, sorts, ...} = ct;
wenzelm@22584
  1173
        val (inst', (instT', (thy_ref', sorts'))) =
wenzelm@22584
  1174
          (thy_ref, sorts) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@31977
  1175
        val subst = Term_Subst.instantiate_maxidx (instT', inst');
wenzelm@31977
  1176
        val substT = Term_Subst.instantiateT_maxidx instT';
wenzelm@22584
  1177
        val (t', maxidx1) = subst t ~1;
wenzelm@22584
  1178
        val (T', maxidx') = substT T maxidx1;
wenzelm@22584
  1179
      in Cterm {thy_ref = thy_ref', t = t', T = T', sorts = sorts', maxidx = maxidx'} end
wenzelm@22584
  1180
      handle TYPE (msg, _, _) => raise CTERM (msg, [ct]);
wenzelm@22584
  1181
wenzelm@6928
  1182
end;
wenzelm@6928
  1183
clasohm@0
  1184
wenzelm@16601
  1185
(*The trivial implication A ==> A, justified by assume and forall rules.
wenzelm@16601
  1186
  A can contain Vars, not so for assume!*)
wenzelm@16601
  1187
fun trivial (Cterm {thy_ref, t =A, T, maxidx, sorts}) =
wenzelm@16601
  1188
  if T <> propT then
wenzelm@16601
  1189
    raise THM ("trivial: the term must have type prop", 0, [])
wenzelm@16601
  1190
  else
wenzelm@28321
  1191
    Thm (deriv_rule0 (Pt.AbsP ("H", NONE, Pt.PBound 0)),
wenzelm@28321
  1192
     {thy_ref = thy_ref,
wenzelm@21646
  1193
      tags = [],
wenzelm@16601
  1194
      maxidx = maxidx,
wenzelm@16601
  1195
      shyps = sorts,
wenzelm@16601
  1196
      hyps = [],
wenzelm@16601
  1197
      tpairs = [],
wenzelm@28321
  1198
      prop = Logic.mk_implies (A, A)});
clasohm@0
  1199
wenzelm@31944
  1200
(*Axiom-scheme reflecting signature contents
wenzelm@31944
  1201
        T :: c
wenzelm@31944
  1202
  -------------------
wenzelm@31944
  1203
  OFCLASS(T, c_class)
wenzelm@31944
  1204
*)
wenzelm@31944
  1205
fun of_class (cT, raw_c) =
wenzelm@24143
  1206
  let
wenzelm@31944
  1207
    val Ctyp {thy_ref, T, ...} = cT;
wenzelm@31944
  1208
    val thy = Theory.deref thy_ref;
wenzelm@31903
  1209
    val c = Sign.certify_class thy raw_c;
wenzelm@31944
  1210
    val Cterm {t = prop, maxidx, sorts, ...} = cterm_of thy (Logic.mk_of_class (T, c));
wenzelm@399
  1211
  in
wenzelm@31944
  1212
    if Sign.of_sort thy (T, [c]) then
wenzelm@31944
  1213
      Thm (deriv_rule0 (Pt.OfClass (T, c)),
wenzelm@31944
  1214
       {thy_ref = Theory.check_thy thy,
wenzelm@31944
  1215
        tags = [],
wenzelm@31944
  1216
        maxidx = maxidx,
wenzelm@31944
  1217
        shyps = sorts,
wenzelm@31944
  1218
        hyps = [],
wenzelm@31944
  1219
        tpairs = [],
wenzelm@31944
  1220
        prop = prop})
wenzelm@31944
  1221
    else raise THM ("of_class: type not of class " ^ Syntax.string_of_sort_global thy [c], 0, [])
wenzelm@399
  1222
  end;
wenzelm@399
  1223
wenzelm@19505
  1224
(*Internalize sort constraints of type variable*)
wenzelm@19505
  1225
fun unconstrainT
wenzelm@19505
  1226
    (Ctyp {thy_ref = thy_ref1, T, ...})
wenzelm@28321
  1227
    (th as Thm (_, {thy_ref = thy_ref2, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@19505
  1228
  let
wenzelm@19505
  1229
    val ((x, i), S) = Term.dest_TVar T handle TYPE _ =>
wenzelm@19505
  1230
      raise THM ("unconstrainT: not a type variable", 0, [th]);
wenzelm@19505
  1231
    val T' = TVar ((x, i), []);
wenzelm@20548
  1232
    val unconstrain = Term.map_types (Term.map_atyps (fn U => if U = T then T' else U));
wenzelm@31943
  1233
    val constraints = map (curry Logic.mk_of_class T') S;
wenzelm@19505
  1234
  in
wenzelm@28321
  1235
    Thm (deriv_rule0 (Pt.PAxm ("Pure.unconstrainT", prop, SOME [])),
wenzelm@28321
  1236
     {thy_ref = Theory.merge_refs (thy_ref1, thy_ref2),
wenzelm@21646
  1237
      tags = [],
wenzelm@19505
  1238
      maxidx = Int.max (maxidx, i),
wenzelm@19505
  1239
      shyps = Sorts.remove_sort S shyps,
wenzelm@19505
  1240
      hyps = hyps,
wenzelm@19505
  1241
      tpairs = map (pairself unconstrain) tpairs,
wenzelm@28321
  1242
      prop = Logic.list_implies (constraints, unconstrain prop)})
wenzelm@19505
  1243
  end;
wenzelm@399
  1244
wenzelm@6786
  1245
(* Replace all TFrees not fixed or in the hyps by new TVars *)
wenzelm@28321
  1246
fun varifyT' fixed (Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@12500
  1247
  let
wenzelm@29272
  1248
    val tfrees = fold Term.add_tfrees hyps fixed;
berghofe@13658
  1249
    val prop1 = attach_tpairs tpairs prop;
haftmann@21116
  1250
    val (al, prop2) = Type.varify tfrees prop1;
wenzelm@16601
  1251
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1252
  in
wenzelm@28321
  1253
    (al, Thm (deriv_rule1 (Pt.varify_proof prop tfrees) der,
wenzelm@28321
  1254
     {thy_ref = thy_ref,
wenzelm@21646
  1255
      tags = [],
wenzelm@16601
  1256
      maxidx = Int.max (0, maxidx),
wenzelm@16601
  1257
      shyps = shyps,
wenzelm@16601
  1258
      hyps = hyps,
wenzelm@16601
  1259
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@28321
  1260
      prop = prop3}))
wenzelm@28321
  1261
  end;
wenzelm@28321
  1262
wenzelm@28321
  1263
val varifyT = #2 o varifyT' [];
wenzelm@28321
  1264
wenzelm@28321
  1265
(* Replace all TVars by new TFrees *)
wenzelm@32784
  1266
fun freezeT (Thm (der, {thy_ref, shyps, hyps, tpairs, prop, ...})) =
wenzelm@28321
  1267
  let
wenzelm@28321
  1268
    val prop1 = attach_tpairs tpairs prop;
wenzelm@28321
  1269
    val prop2 = Type.freeze prop1;
wenzelm@28321
  1270
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@28321
  1271
  in
wenzelm@28321
  1272
    Thm (deriv_rule1 (Pt.freezeT prop1) der,
wenzelm@28321
  1273
     {thy_ref = thy_ref,
wenzelm@28321
  1274
      tags = [],
wenzelm@28321
  1275
      maxidx = maxidx_of_term prop2,
wenzelm@28321
  1276
      shyps = shyps,
wenzelm@28321
  1277
      hyps = hyps,
wenzelm@28321
  1278
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@18127
  1279
      prop = prop3})
clasohm@0
  1280
  end;
clasohm@0
  1281
clasohm@0
  1282
clasohm@0
  1283
(*** Inference rules for tactics ***)
clasohm@0
  1284
clasohm@0
  1285
(*Destruct proof state into constraints, other goals, goal(i), rest *)
wenzelm@28321
  1286
fun dest_state (state as Thm (_, {prop,tpairs,...}), i) =
berghofe@13658
  1287
  (case  Logic.strip_prems(i, [], prop) of
berghofe@13658
  1288
      (B::rBs, C) => (tpairs, rev rBs, B, C)
berghofe@13658
  1289
    | _ => raise THM("dest_state", i, [state]))
clasohm@0
  1290
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1291
lcp@309
  1292
(*Increment variables and parameters of orule as required for
wenzelm@18035
  1293
  resolution with a goal.*)
wenzelm@18035
  1294
fun lift_rule goal orule =
wenzelm@16601
  1295
  let
wenzelm@18035
  1296
    val Cterm {t = gprop, T, maxidx = gmax, sorts, ...} = goal;
wenzelm@18035
  1297
    val inc = gmax + 1;
wenzelm@18035
  1298
    val lift_abs = Logic.lift_abs inc gprop;
wenzelm@18035
  1299
    val lift_all = Logic.lift_all inc gprop;
wenzelm@28321
  1300
    val Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...}) = orule;
wenzelm@16601
  1301
    val (As, B) = Logic.strip_horn prop;
wenzelm@16601
  1302
  in
wenzelm@18035
  1303
    if T <> propT then raise THM ("lift_rule: the term must have type prop", 0, [])
wenzelm@18035
  1304
    else
wenzelm@28321
  1305
      Thm (deriv_rule1 (Pt.lift_proof gprop inc prop) der,
wenzelm@28321
  1306
       {thy_ref = merge_thys1 goal orule,
wenzelm@21646
  1307
        tags = [],
wenzelm@18035
  1308
        maxidx = maxidx + inc,
wenzelm@18035
  1309
        shyps = Sorts.union shyps sorts,  (*sic!*)
wenzelm@18035
  1310
        hyps = hyps,
wenzelm@18035
  1311
        tpairs = map (pairself lift_abs) tpairs,
wenzelm@28321
  1312
        prop = Logic.list_implies (map lift_all As, lift_all B)})
clasohm@0
  1313
  end;
clasohm@0
  1314
wenzelm@28321
  1315
fun incr_indexes i (thm as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
  1316
  if i < 0 then raise THM ("negative increment", 0, [thm])
wenzelm@16601
  1317
  else if i = 0 then thm
wenzelm@16601
  1318
  else
wenzelm@32027
  1319
    Thm (deriv_rule1 (Pt.incr_indexes i) der,
wenzelm@28321
  1320
     {thy_ref = thy_ref,
wenzelm@21646
  1321
      tags = [],
wenzelm@16601
  1322
      maxidx = maxidx + i,
wenzelm@16601
  1323
      shyps = shyps,
wenzelm@16601
  1324
      hyps = hyps,
wenzelm@16601
  1325
      tpairs = map (pairself (Logic.incr_indexes ([], i))) tpairs,
wenzelm@28321
  1326
      prop = Logic.incr_indexes ([], i) prop});
berghofe@10416
  1327
clasohm@0
  1328
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1329
fun assumption i state =
wenzelm@16601
  1330
  let
wenzelm@32784
  1331
    val Thm (der, {thy_ref, maxidx, shyps, hyps, ...}) = state;
wenzelm@16656
  1332
    val thy = Theory.deref thy_ref;
wenzelm@16601
  1333
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@32032
  1334
    fun newth n (env, tpairs) =
wenzelm@28321
  1335
      Thm (deriv_rule1
wenzelm@16601
  1336
          ((if Envir.is_empty env then I else (Pt.norm_proof' env)) o
wenzelm@16601
  1337
            Pt.assumption_proof Bs Bi n) der,
wenzelm@28321
  1338
       {tags = [],
wenzelm@32032
  1339
        maxidx = Envir.maxidx_of env,
wenzelm@26640
  1340
        shyps = Envir.insert_sorts env shyps,
wenzelm@16601
  1341
        hyps = hyps,
wenzelm@16601
  1342
        tpairs =
wenzelm@16601
  1343
          if Envir.is_empty env then tpairs
wenzelm@16601
  1344
          else map (pairself (Envir.norm_term env)) tpairs,
wenzelm@16601
  1345
        prop =
wenzelm@16601
  1346
          if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@16601
  1347
            Logic.list_implies (Bs, C)
wenzelm@16601
  1348
          else (*normalize the new rule fully*)
wenzelm@24143
  1349
            Envir.norm_term env (Logic.list_implies (Bs, C)),
wenzelm@28321
  1350
        thy_ref = Theory.check_thy thy});
wenzelm@30554
  1351
wenzelm@30556
  1352
    val (close, asms, concl) = Logic.assum_problems (~1, Bi);
wenzelm@30556
  1353
    val concl' = close concl;
wenzelm@16601
  1354
    fun addprfs [] _ = Seq.empty
wenzelm@30556
  1355
      | addprfs (asm :: rest) n = Seq.make (fn () => Seq.pull
wenzelm@16601
  1356
          (Seq.mapp (newth n)
wenzelm@30556
  1357
            (if Term.could_unify (asm, concl) then
wenzelm@30556
  1358
              (Unify.unifiers (thy, Envir.empty maxidx, (close asm, concl') :: tpairs))
wenzelm@30554
  1359
             else Seq.empty)
wenzelm@30554
  1360
            (addprfs rest (n + 1))))
wenzelm@30556
  1361
  in addprfs asms 1 end;
clasohm@0
  1362
wenzelm@250
  1363
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1364
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1365
fun eq_assumption i state =
wenzelm@16601
  1366
  let
wenzelm@32784
  1367
    val Thm (der, {thy_ref, maxidx, shyps, hyps, ...}) = state;
wenzelm@16601
  1368
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@30556
  1369
    val (_, asms, concl) = Logic.assum_problems (~1, Bi);
wenzelm@16601
  1370
  in
wenzelm@30556
  1371
    (case find_index (fn asm => Pattern.aeconv (asm, concl)) asms of
wenzelm@16601
  1372
      ~1 => raise THM ("eq_assumption", 0, [state])
wenzelm@16601
  1373
    | n =>
wenzelm@28321
  1374
        Thm (deriv_rule1 (Pt.assumption_proof Bs Bi (n + 1)) der,
wenzelm@28321
  1375
         {thy_ref = thy_ref,
wenzelm@21646
  1376
          tags = [],
wenzelm@16601
  1377
          maxidx = maxidx,
wenzelm@16601
  1378
          shyps = shyps,
wenzelm@16601
  1379
          hyps = hyps,
wenzelm@16601
  1380
          tpairs = tpairs,
wenzelm@28321
  1381
          prop = Logic.list_implies (Bs, C)}))
clasohm@0
  1382
  end;
clasohm@0
  1383
clasohm@0
  1384
paulson@2671
  1385
(*For rotate_tac: fast rotation of assumptions of subgoal i*)
paulson@2671
  1386
fun rotate_rule k i state =
wenzelm@16601
  1387
  let
wenzelm@32784
  1388
    val Thm (der, {thy_ref, maxidx, shyps, hyps, ...}) = state;
wenzelm@16601
  1389
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1390
    val params = Term.strip_all_vars Bi
wenzelm@16601
  1391
    and rest   = Term.strip_all_body Bi;
wenzelm@16601
  1392
    val asms   = Logic.strip_imp_prems rest
wenzelm@16601
  1393
    and concl  = Logic.strip_imp_concl rest;
wenzelm@16601
  1394
    val n = length asms;
wenzelm@16601
  1395
    val m = if k < 0 then n + k else k;
wenzelm@16601
  1396
    val Bi' =
wenzelm@16601
  1397
      if 0 = m orelse m = n then Bi
wenzelm@16601
  1398
      else if 0 < m andalso m < n then
wenzelm@19012
  1399
        let val (ps, qs) = chop m asms
wenzelm@16601
  1400
        in list_all (params, Logic.list_implies (qs @ ps, concl)) end
wenzelm@16601
  1401
      else raise THM ("rotate_rule", k, [state]);
wenzelm@16601
  1402
  in
wenzelm@28321
  1403
    Thm (deriv_rule1 (Pt.rotate_proof Bs Bi m) der,
wenzelm@28321
  1404
     {thy_ref = thy_ref,
wenzelm@21646
  1405
      tags = [],
wenzelm@16601
  1406
      maxidx = maxidx,
wenzelm@16601
  1407
      shyps = shyps,
wenzelm@16601
  1408
      hyps = hyps,
wenzelm@16601
  1409
      tpairs = tpairs,
wenzelm@28321
  1410
      prop = Logic.list_implies (Bs @ [Bi'], C)})
paulson@2671
  1411
  end;
paulson@2671
  1412
paulson@2671
  1413
paulson@7248
  1414
(*Rotates a rule's premises to the left by k, leaving the first j premises
paulson@7248
  1415
  unchanged.  Does nothing if k=0 or if k equals n-j, where n is the
wenzelm@16656
  1416
  number of premises.  Useful with etac and underlies defer_tac*)
paulson@7248
  1417
fun permute_prems j k rl =
wenzelm@16601
  1418
  let
wenzelm@28321
  1419
    val Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...}) = rl;
wenzelm@16601
  1420
    val prems = Logic.strip_imp_prems prop
wenzelm@16601
  1421
    and concl = Logic.strip_imp_concl prop;
wenzelm@16601
  1422
    val moved_prems = List.drop (prems, j)
wenzelm@16601
  1423
    and fixed_prems = List.take (prems, j)
wenzelm@16601
  1424
      handle Subscript => raise THM ("permute_prems: j", j, [rl]);
wenzelm@16601
  1425
    val n_j = length moved_prems;
wenzelm@16601
  1426
    val m = if k < 0 then n_j + k else k;
wenzelm@16601
  1427
    val prop' =
wenzelm@16601
  1428
      if 0 = m orelse m = n_j then prop
wenzelm@16601
  1429
      else if 0 < m andalso m < n_j then
wenzelm@19012
  1430
        let val (ps, qs) = chop m moved_prems
wenzelm@16601
  1431
        in Logic.list_implies (fixed_prems @ qs @ ps, concl) end
wenzelm@16725
  1432
      else raise THM ("permute_prems: k", k, [rl]);
wenzelm@16601
  1433
  in
wenzelm@28321
  1434
    Thm (deriv_rule1 (Pt.permute_prems_prf prems j m) der,
wenzelm@28321
  1435
     {thy_ref = thy_ref,
wenzelm@21646
  1436
      tags = [],
wenzelm@16601
  1437
      maxidx = maxidx,
wenzelm@16601
  1438
      shyps = shyps,
wenzelm@16601
  1439
      hyps = hyps,
wenzelm@16601
  1440
      tpairs = tpairs,
wenzelm@28321
  1441
      prop = prop'})
paulson@7248
  1442
  end;
paulson@7248
  1443
paulson@7248
  1444
clasohm@0
  1445
(** User renaming of parameters in a subgoal **)
clasohm@0
  1446
clasohm@0
  1447
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1448
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1449
  The names in cs, if distinct, are used for the innermost parameters;
wenzelm@17868
  1450
  preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1451
fun rename_params_rule (cs, i) state =
wenzelm@16601
  1452
  let
wenzelm@28321
  1453
    val Thm (der, {thy_ref, tags, maxidx, shyps, hyps, ...}) = state;
wenzelm@16601
  1454
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1455
    val iparams = map #1 (Logic.strip_params Bi);
wenzelm@16601
  1456
    val short = length iparams - length cs;
wenzelm@16601
  1457
    val newnames =
wenzelm@16601
  1458
      if short < 0 then error "More names than abstractions!"
wenzelm@20071
  1459
      else Name.variant_list cs (Library.take (short, iparams)) @ cs;
wenzelm@20330
  1460
    val freenames = Term.fold_aterms (fn Free (x, _) => insert (op =) x | _ => I) Bi [];
wenzelm@16601
  1461
    val newBi = Logic.list_rename_params (newnames, Bi);
wenzelm@250
  1462
  in
wenzelm@21182
  1463
    (case duplicates (op =) cs of
wenzelm@21182
  1464
      a :: _ => (warning ("Can't rename.  Bound variables not distinct: " ^ a); state)
wenzelm@21182
  1465
    | [] =>
haftmann@33037
  1466
      (case gen_inter (op =) (cs, freenames) of
wenzelm@16601
  1467
        a :: _ => (warning ("Can't rename.  Bound/Free variable clash: " ^ a); state)
wenzelm@16601
  1468
      | [] =>
wenzelm@28321
  1469
        Thm (der,
wenzelm@28321
  1470
         {thy_ref = thy_ref,
wenzelm@21646
  1471
          tags = tags,
wenzelm@16601
  1472
          maxidx = maxidx,
wenzelm@16601
  1473
          shyps = shyps,
wenzelm@16601
  1474
          hyps = hyps,
wenzelm@16601
  1475
          tpairs = tpairs,
wenzelm@28321
  1476
          prop = Logic.list_implies (Bs @ [newBi], C)})))
clasohm@0
  1477
  end;
clasohm@0
  1478
wenzelm@12982
  1479
clasohm@0
  1480
(*** Preservation of bound variable names ***)
clasohm@0
  1481
wenzelm@28321
  1482
fun rename_boundvars pat obj (thm as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@12982
  1483
  (case Term.rename_abs pat obj prop of
skalberg@15531
  1484
    NONE => thm
wenzelm@28321
  1485
  | SOME prop' => Thm (der,
wenzelm@16425
  1486
      {thy_ref = thy_ref,
wenzelm@21646
  1487
       tags = tags,
wenzelm@12982
  1488
       maxidx = maxidx,
wenzelm@12982
  1489
       hyps = hyps,
wenzelm@12982
  1490
       shyps = shyps,
berghofe@13658
  1491
       tpairs = tpairs,
wenzelm@28321
  1492
       prop = prop'}));
berghofe@10416
  1493
clasohm@0
  1494
wenzelm@16656
  1495
(* strip_apply f (A, B) strips off all assumptions/parameters from A
clasohm@0
  1496
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
  1497
fun strip_apply f =
clasohm@0
  1498
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@27336
  1499
                Const("==>",_)$ _  $ B2) = Logic.mk_implies (A1, strip(B1,B2))
wenzelm@250
  1500
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
  1501
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
  1502
        | strip(A,_) = f A
clasohm@0
  1503
  in strip end;
clasohm@0
  1504
clasohm@0
  1505
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1506
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1507
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1508
fun rename_bvs([],_,_,_) = I
clasohm@0
  1509
  | rename_bvs(al,dpairs,tpairs,B) =
wenzelm@20330
  1510
      let
wenzelm@20330
  1511
        val add_var = fold_aterms (fn Var ((x, _), _) => insert (op =) x | _ => I);
wenzelm@20330
  1512
        val vids = []
wenzelm@20330
  1513
          |> fold (add_var o fst) dpairs
wenzelm@20330
  1514
          |> fold (add_var o fst) tpairs
wenzelm@20330
  1515
          |> fold (add_var o snd) tpairs;
wenzelm@250
  1516
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1517
        fun rename(t as Var((x,i),T)) =
wenzelm@20330
  1518
              (case AList.lookup (op =) al x of
wenzelm@20330
  1519
                SOME y =>
wenzelm@20330
  1520
                  if member (op =) vids x orelse member (op =) vids y then t
wenzelm@20330
  1521
                  else Var((y,i),T)
wenzelm@20330
  1522
              | NONE=> t)
clasohm@0
  1523
          | rename(Abs(x,T,t)) =
wenzelm@18944
  1524
              Abs (the_default x (AList.lookup (op =) al x), T, rename t)
clasohm@0
  1525
          | rename(f$t) = rename f $ rename t
clasohm@0
  1526
          | rename(t) = t;
wenzelm@250
  1527
        fun strip_ren Ai = strip_apply rename (Ai,B)
wenzelm@20330
  1528
      in strip_ren end;
clasohm@0
  1529
clasohm@0
  1530
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
  1531
fun rename_bvars(dpairs, tpairs, B) =
wenzelm@23178
  1532
        rename_bvs(List.foldr Term.match_bvars [] dpairs, dpairs, tpairs, B);
clasohm@0
  1533
clasohm@0
  1534
clasohm@0
  1535
(*** RESOLUTION ***)
clasohm@0
  1536
lcp@721
  1537
(** Lifting optimizations **)
lcp@721
  1538
clasohm@0
  1539
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
  1540
  identical because of lifting*)
wenzelm@250
  1541
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
  1542
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
  1543
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
  1544
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
  1545
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
  1546
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
  1547
  | strip_assums2 BB = BB;
clasohm@0
  1548
clasohm@0
  1549
lcp@721
  1550
(*Faster normalization: skip assumptions that were lifted over*)
lcp@721
  1551
fun norm_term_skip env 0 t = Envir.norm_term env t
wenzelm@32032
  1552
  | norm_term_skip env n (Const ("all", _) $ Abs (a, T, t)) =
wenzelm@32032
  1553
      let
wenzelm@32035
  1554
        val T' = Envir.subst_type (Envir.type_env env) T
wenzelm@32032
  1555
        (*Must instantiate types of parameters because they are flattened;
wenzelm@32032
  1556
          this could be a NEW parameter*)
wenzelm@32032
  1557
      in Term.all T' $ Abs (a, T', norm_term_skip env n t) end
wenzelm@32032
  1558
  | norm_term_skip env n (Const ("==>", _) $ A $ B) =
wenzelm@32032
  1559
      Logic.mk_implies (A, norm_term_skip env (n - 1) B)
wenzelm@32784
  1560
  | norm_term_skip _ _ _ = error "norm_term_skip: too few assumptions??";
lcp@721
  1561
lcp@721
  1562
clasohm@0
  1563
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
  1564
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
  1565
  If match then forbid instantiations in proof state
clasohm@0
  1566
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
  1567
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
  1568
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
  1569
  Curried so that resolution calls dest_state only once.
clasohm@0
  1570
*)
wenzelm@4270
  1571
local exception COMPOSE
clasohm@0
  1572
in
wenzelm@18486
  1573
fun bicompose_aux flatten match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
  1574
                        (eres_flg, orule, nsubgoal) =
wenzelm@28321
  1575
 let val Thm (sder, {maxidx=smax, shyps=sshyps, hyps=shyps, ...}) = state
wenzelm@28321
  1576
     and Thm (rder, {maxidx=rmax, shyps=rshyps, hyps=rhyps,
wenzelm@28321
  1577
             tpairs=rtpairs, prop=rprop,...}) = orule
paulson@1529
  1578
         (*How many hyps to skip over during normalization*)
wenzelm@21576
  1579
     and nlift = Logic.count_prems (strip_all_body Bi) + (if eres_flg then ~1 else 0)
wenzelm@24143
  1580
     val thy = Theory.deref (merge_thys2 state orule);
clasohm@0
  1581
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
wenzelm@32032
  1582
     fun addth A (As, oldAs, rder', n) ((env, tpairs), thq) =
wenzelm@250
  1583
       let val normt = Envir.norm_term env;
wenzelm@250
  1584
           (*perform minimal copying here by examining env*)
berghofe@13658
  1585
           val (ntpairs, normp) =
berghofe@13658
  1586
             if Envir.is_empty env then (tpairs, (Bs @ As, C))
wenzelm@250
  1587
             else
wenzelm@250
  1588
             let val ntps = map (pairself normt) tpairs
wenzelm@19861
  1589
             in if Envir.above env smax then
wenzelm@1238
  1590
                  (*no assignments in state; normalize the rule only*)
wenzelm@1238
  1591
                  if lifted
berghofe@13658
  1592
                  then (ntps, (Bs @ map (norm_term_skip env nlift) As, C))
berghofe@13658
  1593
                  else (ntps, (Bs @ map normt As, C))
paulson@1529
  1594
                else if match then raise COMPOSE
wenzelm@250
  1595
                else (*normalize the new rule fully*)
berghofe@13658
  1596
                  (ntps, (map normt (Bs @ As), normt C))
wenzelm@250
  1597
             end
wenzelm@16601
  1598
           val th =
wenzelm@28321
  1599
             Thm (deriv_rule2
berghofe@11518
  1600
                   ((if Envir.is_empty env then I
wenzelm@19861
  1601
                     else if Envir.above env smax then
berghofe@11518
  1602
                       (fn f => fn der => f (Pt.norm_proof' env der))
berghofe@11518
  1603
                     else
berghofe@11518
  1604
                       curry op oo (Pt.norm_proof' env))
berghofe@23296
  1605
                    (Pt.bicompose_proof flatten Bs oldAs As A n (nlift+1))) rder' sder,
wenzelm@28321
  1606
                {tags = [],
wenzelm@32032
  1607
                 maxidx = Envir.maxidx_of env,
wenzelm@26640
  1608
                 shyps = Envir.insert_sorts env (Sorts.union rshyps sshyps),
wenzelm@16601
  1609
                 hyps = union_hyps rhyps shyps,
berghofe@13658
  1610
                 tpairs = ntpairs,
wenzelm@24143
  1611
                 prop = Logic.list_implies normp,
wenzelm@28321
  1612
                 thy_ref = Theory.check_thy thy})
wenzelm@19475
  1613
        in  Seq.cons th thq  end  handle COMPOSE => thq;
berghofe@13658
  1614
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rprop)
clasohm@0
  1615
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
  1616
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
  1617
     fun newAs(As0, n, dpairs, tpairs) =
berghofe@11518
  1618
       let val (As1, rder') =
berghofe@25939
  1619
         if not lifted then (As0, rder)
berghofe@11518
  1620
         else (map (rename_bvars(dpairs,tpairs,B)) As0,
wenzelm@28321
  1621
           deriv_rule1 (Pt.map_proof_terms
berghofe@11518
  1622
             (rename_bvars (dpairs, tpairs, Bound 0)) I) rder);
wenzelm@18486
  1623
       in (map (if flatten then (Logic.flatten_params n) else I) As1, As1, rder', n)
wenzelm@250
  1624
          handle TERM _ =>
wenzelm@250
  1625
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
  1626
       end;
paulson@2147
  1627
     val env = Envir.empty(Int.max(rmax,smax));
clasohm@0
  1628
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
  1629
     val dpairs = BBi :: (rtpairs@stpairs);
wenzelm@30554
  1630
wenzelm@30554
  1631
     (*elim-resolution: try each assumption in turn*)
wenzelm@30554
  1632
     fun eres [] = raise THM ("bicompose: no premises", 0, [orule, state])
wenzelm@30554
  1633
       | eres (A1 :: As) =
wenzelm@30554
  1634
           let
wenzelm@30554
  1635
             val A = SOME A1;
wenzelm@30556
  1636
             val (close, asms, concl) = Logic.assum_problems (nlift + 1, A1);
wenzelm@30556
  1637
             val concl' = close concl;
wenzelm@30554
  1638
             fun tryasms [] _ = Seq.empty
wenzelm@30556
  1639
               | tryasms (asm :: rest) n =
wenzelm@30556
  1640
                   if Term.could_unify (asm, concl) then
wenzelm@30556
  1641
                     let val asm' = close asm in
wenzelm@30556
  1642
                       (case Seq.pull (Unify.unifiers (thy, env, (asm', concl') :: dpairs)) of
wenzelm@30554
  1643
                         NONE => tryasms rest (n + 1)
wenzelm@30554
  1644
                       | cell as SOME ((_, tpairs), _) =>
wenzelm@30556
  1645
                           Seq.it_right (addth A (newAs (As, n, [BBi, (concl', asm')], tpairs)))
wenzelm@30554
  1646
                             (Seq.make (fn () => cell),
wenzelm@30554
  1647
                              Seq.make (fn () => Seq.pull (tryasms rest (n + 1)))))
wenzelm@30554
  1648
                     end
wenzelm@30554
  1649
                   else tryasms rest (n + 1);
wenzelm@30556
  1650
           in tryasms asms 1 end;
wenzelm@30554
  1651
clasohm@0
  1652
     (*ordinary resolution*)
wenzelm@30554
  1653
     fun res () =
wenzelm@30554
  1654
       (case Seq.pull (Unify.unifiers (thy, env, dpairs)) of
wenzelm@30554
  1655
         NONE => Seq.empty
wenzelm@30554
  1656
       | cell as SOME ((_, tpairs), _) =>
wenzelm@30554
  1657
           Seq.it_right (addth NONE (newAs (rev rAs, 0, [BBi], tpairs)))
wenzelm@30554
  1658
             (Seq.make (fn () => cell), Seq.empty));
wenzelm@30554
  1659
 in
wenzelm@30554
  1660
   if eres_flg then eres (rev rAs) else res ()
clasohm@0
  1661
 end;
wenzelm@7528
  1662
end;
clasohm@0
  1663
wenzelm@18501
  1664
fun compose_no_flatten match (orule, nsubgoal) i state =
wenzelm@18501
  1665
  bicompose_aux false match (state, dest_state (state, i), false) (false, orule, nsubgoal);
clasohm@0
  1666
wenzelm@18501
  1667
fun bicompose match arg i state =
wenzelm@18501
  1668
  bicompose_aux true match (state, dest_state (state,i), false) arg;
clasohm@0
  1669
clasohm@0
  1670
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1671
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1672
fun could_bires (Hs, B, eres_flg, rule) =
wenzelm@29269
  1673
    let fun could_reshyp (A1::_) = exists (fn H => Term.could_unify (A1, H)) Hs
wenzelm@250
  1674
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@29269
  1675
    in  Term.could_unify(concl_of rule, B) andalso
wenzelm@250
  1676
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1677
    end;
clasohm@0
  1678
clasohm@0
  1679
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1680
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1681
fun biresolution match brules i state =
wenzelm@18035
  1682
    let val (stpairs, Bs, Bi, C) = dest_state(state,i);
wenzelm@18145
  1683
        val lift = lift_rule (cprem_of state i);
wenzelm@250
  1684
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1685
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@22573
  1686
        val compose = bicompose_aux true match (state, (stpairs, Bs, Bi, C), true);
wenzelm@4270
  1687
        fun res [] = Seq.empty
wenzelm@250
  1688
          | res ((eres_flg, rule)::brules) =
nipkow@13642
  1689
              if !Pattern.trace_unify_fail orelse
nipkow@13642
  1690
                 could_bires (Hs, B, eres_flg, rule)
wenzelm@4270
  1691
              then Seq.make (*delay processing remainder till needed*)
wenzelm@22573
  1692
                  (fn()=> SOME(compose (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1693
                               res brules))
wenzelm@250
  1694
              else res brules
wenzelm@4270
  1695
    in  Seq.flat (res brules)  end;
clasohm@0
  1696
clasohm@0
  1697
wenzelm@28321
  1698
wenzelm@2509
  1699
(*** Oracles ***)
wenzelm@2509
  1700
wenzelm@28290
  1701
(* oracle rule *)
wenzelm@28290
  1702
wenzelm@28290
  1703
fun invoke_oracle thy_ref1 name oracle arg =
wenzelm@28624
  1704
  let val Cterm {thy_ref = thy_ref2, t = prop, T, maxidx, sorts} = oracle arg in
wenzelm@28290
  1705
    if T <> propT then
wenzelm@28290
  1706
      raise THM ("Oracle's result must have type prop: " ^ name, 0, [])
wenzelm@28290
  1707
    else
wenzelm@30717
  1708
      let val (ora, prf) = Pt.oracle_proof name prop in
wenzelm@32059
  1709
        Thm (make_deriv [] [ora] [] prf,
wenzelm@28804
  1710
         {thy_ref = Theory.merge_refs (thy_ref1, thy_ref2),
wenzelm@28804
  1711
          tags = [],
wenzelm@28804
  1712
          maxidx = maxidx,
wenzelm@28804
  1713
          shyps = sorts,
wenzelm@28804
  1714
          hyps = [],
wenzelm@28804
  1715
          tpairs = [],
wenzelm@28804
  1716
          prop = prop})
wenzelm@28804
  1717
      end
wenzelm@3812
  1718
  end;
wenzelm@3812
  1719
wenzelm@32590
  1720
end;
wenzelm@32590
  1721
end;
wenzelm@32590
  1722
end;
wenzelm@32590
  1723
wenzelm@28290
  1724
wenzelm@28290
  1725
(* authentic derivation names *)
wenzelm@28290
  1726
wenzelm@28290
  1727
fun err_dup_ora dup = error ("Duplicate oracle: " ^ quote dup);
wenzelm@28290
  1728
wenzelm@28290
  1729
structure Oracles = TheoryDataFun
wenzelm@28290
  1730
(
wenzelm@30288
  1731
  type T = serial NameSpace.table;
wenzelm@28290
  1732
  val empty = NameSpace.empty_table;
wenzelm@28290
  1733
  val copy = I;
wenzelm@28290
  1734
  val extend = I;
wenzelm@29288
  1735
  fun merge _ oracles : T = NameSpace.merge_tables (op =) oracles
wenzelm@28290
  1736
    handle Symtab.DUP dup => err_dup_ora dup;
wenzelm@28290
  1737
);
wenzelm@28290
  1738
wenzelm@28290
  1739
val extern_oracles = map #1 o NameSpace.extern_table o Oracles.get;
wenzelm@28290
  1740
wenzelm@30288
  1741
fun add_oracle (b, oracle) thy =
wenzelm@28290
  1742
  let
wenzelm@28290
  1743
    val naming = Sign.naming_of thy;
wenzelm@30466
  1744
    val (name, tab') = NameSpace.define naming (b, serial ()) (Oracles.get thy)
wenzelm@30288
  1745
      handle Symtab.DUP _ => err_dup_ora (Binding.str_of b);
wenzelm@30288
  1746
    val thy' = Oracles.put tab' thy;
wenzelm@28290
  1747
  in ((name, invoke_oracle (Theory.check_thy thy') name oracle), thy') end;
wenzelm@28290
  1748
clasohm@0
  1749
end;
paulson@1503
  1750
wenzelm@32104
  1751
structure Basic_Thm: BASIC_THM = Thm;
wenzelm@32104
  1752
open Basic_Thm;