src/Pure/thm.ML
author wenzelm
Fri Jul 17 23:11:40 2009 +0200 (2009-07-17)
changeset 32035 8e77b6a250d5
parent 32032 a6a6e8031c14
child 32059 7991cdf10a54
permissions -rw-r--r--
tuned/modernized Envir.subst_XXX;
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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: 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 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 future: thm future -> cterm -> thm
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  val pending_groups: thm -> Task_Queue.group list -> Task_Queue.group list
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  val status_of: thm -> {oracle: bool, unfinished: bool, failed: bool}
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  val proof_body_of: thm -> proof_body
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  val proof_of: thm -> proof
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  val join_proof: thm -> unit
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  val get_name: thm -> string
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  val put_name: string -> 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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datatype ctyp = Ctyp of
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 {thy_ref: theory_ref,
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  T: typ,
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  maxidx: int,
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  sorts: sort OrdList.T};
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fun rep_ctyp (Ctyp args) = args;
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fun theory_of_ctyp (Ctyp {thy_ref, ...}) = Theory.deref thy_ref;
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fun typ_of (Ctyp {T, ...}) = T;
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fun ctyp_of thy raw_T =
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  let
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    val T = Sign.certify_typ thy raw_T;
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    val maxidx = Term.maxidx_of_typ T;
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    val sorts = Sorts.insert_typ T [];
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  in Ctyp {thy_ref = Theory.check_thy thy, T = T, maxidx = maxidx, sorts = sorts} end;
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fun dest_ctyp (Ctyp {thy_ref, T = Type (s, Ts), maxidx, sorts}) =
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      map (fn T => Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts}) Ts
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  | dest_ctyp cT = raise TYPE ("dest_ctyp", [typ_of cT], []);
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(** certified terms **)
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(*certified terms with checked typ, maxidx, and sorts*)
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datatype cterm = Cterm of
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 {thy_ref: theory_ref,
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  t: term,
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  T: typ,
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  maxidx: int,
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  sorts: sort OrdList.T};
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exception CTERM of string * cterm list;
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fun rep_cterm (Cterm args) = args;
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fun crep_cterm (Cterm {thy_ref, t, T, maxidx, sorts}) =
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  {thy_ref = thy_ref, t = t, maxidx = maxidx, sorts = sorts,
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    T = Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts}};
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fun theory_of_cterm (Cterm {thy_ref, ...}) = Theory.deref thy_ref;
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fun term_of (Cterm {t, ...}) = t;
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fun ctyp_of_term (Cterm {thy_ref, T, maxidx, sorts, ...}) =
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  Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts};
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fun cterm_of thy tm =
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  let
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    val (t, T, maxidx) = Sign.certify_term thy tm;
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    val sorts = Sorts.insert_term t [];
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  in Cterm {thy_ref = Theory.check_thy thy, t = t, T = T, maxidx = maxidx, sorts = sorts} end;
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fun merge_thys0 (Cterm {thy_ref = r1, t = t1, ...}) (Cterm {thy_ref = r2, t = t2, ...}) =
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  Theory.merge_refs (r1, r2);
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(* destructors *)
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fun dest_comb (ct as Cterm {t = c $ a, T, thy_ref, maxidx, sorts}) =
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      let val A = Term.argument_type_of c 0 in
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        (Cterm {t = c, T = A --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
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         Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
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      end
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  | dest_comb ct = raise CTERM ("dest_comb", [ct]);
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fun dest_fun (ct as Cterm {t = c $ _, T, thy_ref, maxidx, sorts}) =
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      let val A = Term.argument_type_of c 0
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      in Cterm {t = c, T = A --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
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  | dest_fun ct = raise CTERM ("dest_fun", [ct]);
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fun dest_arg (ct as Cterm {t = c $ a, T = _, thy_ref, maxidx, sorts}) =
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      let val A = Term.argument_type_of c 0
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      in Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
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  | dest_arg ct = raise CTERM ("dest_arg", [ct]);
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fun dest_fun2 (Cterm {t = c $ a $ b, T, thy_ref, maxidx, sorts}) =
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      let
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        val A = Term.argument_type_of c 0;
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        val B = Term.argument_type_of c 1;
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      in Cterm {t = c, T = A --> B --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
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  | dest_fun2 ct = raise CTERM ("dest_fun2", [ct]);
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fun dest_arg1 (Cterm {t = c $ a $ _, T = _, thy_ref, maxidx, sorts}) =
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      let val A = Term.argument_type_of c 0
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      in Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
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  | dest_arg1 ct = raise CTERM ("dest_arg1", [ct]);
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fun dest_abs a (ct as
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        Cterm {t = Abs (x, T, t), T = Type ("fun", [_, U]), thy_ref, maxidx, sorts}) =
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      let val (y', t') = Term.dest_abs (the_default x a, T, t) in
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        (Cterm {t = Free (y', T), T = T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
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          Cterm {t = t', T = U, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
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      end
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  | dest_abs _ ct = raise CTERM ("dest_abs", [ct]);
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(* constructors *)
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fun capply
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  (cf as Cterm {t = f, T = Type ("fun", [dty, rty]), maxidx = maxidx1, sorts = sorts1, ...})
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  (cx as Cterm {t = x, T, maxidx = maxidx2, sorts = sorts2, ...}) =
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    if T = dty then
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      Cterm {thy_ref = merge_thys0 cf cx,
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        t = f $ x,
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        T = rty,
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        maxidx = Int.max (maxidx1, maxidx2),
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        sorts = Sorts.union sorts1 sorts2}
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      else raise CTERM ("capply: types don't agree", [cf, cx])
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  | capply cf cx = raise CTERM ("capply: first arg is not a function", [cf, cx]);
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fun cabs
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  (ct1 as Cterm {t = t1, T = T1, maxidx = maxidx1, sorts = sorts1, ...})
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  (ct2 as Cterm {t = t2, T = T2, maxidx = maxidx2, sorts = sorts2, ...}) =
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    let val t = Term.lambda t1 t2 in
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      Cterm {thy_ref = merge_thys0 ct1 ct2,
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        t = t, T = T1 --> T2,
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        maxidx = Int.max (maxidx1, maxidx2),
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        sorts = Sorts.union sorts1 sorts2}
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    end;
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(* indexes *)
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fun adjust_maxidx_cterm i (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
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  if maxidx = i then ct
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  else if maxidx < i then
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    Cterm {maxidx = i, thy_ref = thy_ref, t = t, T = T, sorts = sorts}
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  else
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    Cterm {maxidx = Int.max (maxidx_of_term t, i), thy_ref = thy_ref, t = t, T = T, sorts = sorts};
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fun incr_indexes_cterm i (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
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  if i < 0 then raise CTERM ("negative increment", [ct])
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  else if i = 0 then ct
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  else Cterm {thy_ref = thy_ref, t = Logic.incr_indexes ([], i) t,
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    T = Logic.incr_tvar i T, maxidx = maxidx + i, sorts = sorts};
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(* matching *)
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local
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fun gen_match match
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    (ct1 as Cterm {t = t1, sorts = sorts1, ...},
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     ct2 as Cterm {t = t2, sorts = sorts2, maxidx = maxidx2, ...}) =
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   312
  let
wenzelm@24143
   313
    val thy = Theory.deref (merge_thys0 ct1 ct2);
wenzelm@24143
   314
    val (Tinsts, tinsts) = match thy (t1, t2) (Vartab.empty, Vartab.empty);
wenzelm@16601
   315
    val sorts = Sorts.union sorts1 sorts2;
wenzelm@20512
   316
    fun mk_cTinst ((a, i), (S, T)) =
wenzelm@24143
   317
      (Ctyp {T = TVar ((a, i), S), thy_ref = Theory.check_thy thy, maxidx = i, sorts = sorts},
wenzelm@24143
   318
       Ctyp {T = T, thy_ref = Theory.check_thy thy, maxidx = maxidx2, sorts = sorts});
wenzelm@20512
   319
    fun mk_ctinst ((x, i), (T, t)) =
wenzelm@32035
   320
      let val T = Envir.subst_type Tinsts T in
wenzelm@24143
   321
        (Cterm {t = Var ((x, i), T), T = T, thy_ref = Theory.check_thy thy,
wenzelm@24143
   322
          maxidx = i, sorts = sorts},
wenzelm@24143
   323
         Cterm {t = t, T = T, thy_ref = Theory.check_thy thy, maxidx = maxidx2, sorts = sorts})
berghofe@10416
   324
      end;
wenzelm@16656
   325
  in (Vartab.fold (cons o mk_cTinst) Tinsts [], Vartab.fold (cons o mk_ctinst) tinsts []) end;
berghofe@10416
   326
wenzelm@22909
   327
in
berghofe@10416
   328
wenzelm@22909
   329
val match = gen_match Pattern.match;
wenzelm@22909
   330
val first_order_match = gen_match Pattern.first_order_match;
wenzelm@22909
   331
wenzelm@22909
   332
end;
berghofe@10416
   333
wenzelm@2509
   334
wenzelm@2509
   335
wenzelm@28321
   336
(*** Derivations and Theorems ***)
lcp@229
   337
wenzelm@28356
   338
datatype thm = Thm of
wenzelm@28378
   339
 deriv *                                        (*derivation*)
wenzelm@28378
   340
 {thy_ref: theory_ref,                          (*dynamic reference to theory*)
wenzelm@28378
   341
  tags: Properties.T,                           (*additional annotations/comments*)
wenzelm@28378
   342
  maxidx: int,                                  (*maximum index of any Var or TVar*)
wenzelm@28378
   343
  shyps: sort OrdList.T,                        (*sort hypotheses*)
wenzelm@28378
   344
  hyps: term OrdList.T,                         (*hypotheses*)
wenzelm@28378
   345
  tpairs: (term * term) list,                   (*flex-flex pairs*)
wenzelm@28378
   346
  prop: term}                                   (*conclusion*)
wenzelm@28624
   347
and deriv = Deriv of
wenzelm@28996
   348
 {max_promise: serial,
wenzelm@28996
   349
  open_promises: (serial * thm future) OrdList.T,
wenzelm@28978
   350
  promises: (serial * thm future) OrdList.T,
wenzelm@28804
   351
  body: Pt.proof_body};
clasohm@0
   352
wenzelm@23601
   353
type conv = cterm -> thm;
wenzelm@23601
   354
wenzelm@22365
   355
(*attributes subsume any kind of rules or context modifiers*)
wenzelm@22365
   356
type attribute = Context.generic * thm -> Context.generic * thm;
wenzelm@22365
   357
wenzelm@16725
   358
(*errors involving theorems*)
wenzelm@16725
   359
exception THM of string * int * thm list;
berghofe@13658
   360
wenzelm@28321
   361
fun rep_thm (Thm (_, args)) = args;
clasohm@0
   362
wenzelm@28321
   363
fun crep_thm (Thm (_, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@26631
   364
  let fun cterm max t = Cterm {thy_ref = thy_ref, t = t, T = propT, maxidx = max, sorts = shyps} in
wenzelm@28321
   365
   {thy_ref = thy_ref, tags = tags, maxidx = maxidx, shyps = shyps,
wenzelm@16425
   366
    hyps = map (cterm ~1) hyps,
wenzelm@16425
   367
    tpairs = map (pairself (cterm maxidx)) tpairs,
wenzelm@16425
   368
    prop = cterm maxidx prop}
clasohm@1517
   369
  end;
clasohm@1517
   370
wenzelm@31947
   371
fun fold_terms f (Thm (_, {tpairs, prop, hyps, ...})) =
wenzelm@31947
   372
  fold (fn (t, u) => f t #> f u) tpairs #> f prop #> fold f hyps;
wenzelm@31947
   373
wenzelm@16725
   374
fun terms_of_tpairs tpairs = fold_rev (fn (t, u) => cons t o cons u) tpairs [];
wenzelm@16725
   375
wenzelm@16725
   376
fun eq_tpairs ((t, u), (t', u')) = t aconv t' andalso u aconv u';
wenzelm@18944
   377
fun union_tpairs ts us = Library.merge eq_tpairs (ts, us);
wenzelm@16884
   378
val maxidx_tpairs = fold (fn (t, u) => Term.maxidx_term t #> Term.maxidx_term u);
wenzelm@16725
   379
wenzelm@16725
   380
fun attach_tpairs tpairs prop =
wenzelm@16725
   381
  Logic.list_implies (map Logic.mk_equals tpairs, prop);
wenzelm@16725
   382
wenzelm@28321
   383
fun full_prop_of (Thm (_, {tpairs, prop, ...})) = attach_tpairs tpairs prop;
wenzelm@16945
   384
wenzelm@29269
   385
val union_hyps = OrdList.union TermOrd.fast_term_ord;
wenzelm@29269
   386
val insert_hyps = OrdList.insert TermOrd.fast_term_ord;
wenzelm@29269
   387
val remove_hyps = OrdList.remove TermOrd.fast_term_ord;
wenzelm@22365
   388
wenzelm@16945
   389
wenzelm@24143
   390
(* merge theories of cterms/thms -- trivial absorption only *)
wenzelm@16945
   391
wenzelm@28321
   392
fun merge_thys1 (Cterm {thy_ref = r1, ...}) (th as Thm (_, {thy_ref = r2, ...})) =
wenzelm@23601
   393
  Theory.merge_refs (r1, r2);
wenzelm@16945
   394
wenzelm@28321
   395
fun merge_thys2 (th1 as Thm (_, {thy_ref = r1, ...})) (th2 as Thm (_, {thy_ref = r2, ...})) =
wenzelm@23601
   396
  Theory.merge_refs (r1, r2);
wenzelm@16945
   397
clasohm@0
   398
wenzelm@22365
   399
(* basic components *)
wenzelm@16135
   400
wenzelm@28321
   401
val theory_of_thm = Theory.deref o #thy_ref o rep_thm;
wenzelm@28321
   402
val maxidx_of = #maxidx o rep_thm;
wenzelm@19910
   403
fun maxidx_thm th i = Int.max (maxidx_of th, i);
wenzelm@28321
   404
val hyps_of = #hyps o rep_thm;
wenzelm@28321
   405
val prop_of = #prop o rep_thm;
wenzelm@28321
   406
val tpairs_of = #tpairs o rep_thm;
clasohm@0
   407
wenzelm@16601
   408
val concl_of = Logic.strip_imp_concl o prop_of;
wenzelm@16601
   409
val prems_of = Logic.strip_imp_prems o prop_of;
wenzelm@21576
   410
val nprems_of = Logic.count_prems o prop_of;
wenzelm@19305
   411
fun no_prems th = nprems_of th = 0;
wenzelm@16601
   412
wenzelm@16601
   413
fun major_prem_of th =
wenzelm@16601
   414
  (case prems_of th of
wenzelm@16601
   415
    prem :: _ => Logic.strip_assums_concl prem
wenzelm@16601
   416
  | [] => raise THM ("major_prem_of: rule with no premises", 0, [th]));
wenzelm@16601
   417
wenzelm@16601
   418
(*the statement of any thm is a cterm*)
wenzelm@28321
   419
fun cprop_of (Thm (_, {thy_ref, maxidx, shyps, prop, ...})) =
wenzelm@16601
   420
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, t = prop, sorts = shyps};
wenzelm@16601
   421
wenzelm@28321
   422
fun cprem_of (th as Thm (_, {thy_ref, maxidx, shyps, prop, ...})) i =
wenzelm@18035
   423
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, sorts = shyps,
wenzelm@18145
   424
    t = Logic.nth_prem (i, prop) handle TERM _ => raise THM ("cprem_of", i, [th])};
wenzelm@18035
   425
wenzelm@16656
   426
(*explicit transfer to a super theory*)
wenzelm@16425
   427
fun transfer thy' thm =
wenzelm@3895
   428
  let
wenzelm@28321
   429
    val Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop}) = thm;
wenzelm@16425
   430
    val thy = Theory.deref thy_ref;
wenzelm@26665
   431
    val _ = Theory.subthy (thy, thy') orelse raise THM ("transfer: not a super theory", 0, [thm]);
wenzelm@26665
   432
    val is_eq = Theory.eq_thy (thy, thy');
wenzelm@24143
   433
    val _ = Theory.check_thy thy;
wenzelm@3895
   434
  in
wenzelm@24143
   435
    if is_eq then thm
wenzelm@16945
   436
    else
wenzelm@28321
   437
      Thm (der,
wenzelm@28321
   438
       {thy_ref = Theory.check_thy thy',
wenzelm@21646
   439
        tags = tags,
wenzelm@16945
   440
        maxidx = maxidx,
wenzelm@16945
   441
        shyps = shyps,
wenzelm@16945
   442
        hyps = hyps,
wenzelm@16945
   443
        tpairs = tpairs,
wenzelm@28321
   444
        prop = prop})
wenzelm@3895
   445
  end;
wenzelm@387
   446
wenzelm@16945
   447
(*explicit weakening: maps |- B to A |- B*)
wenzelm@16945
   448
fun weaken raw_ct th =
wenzelm@16945
   449
  let
wenzelm@20261
   450
    val ct as Cterm {t = A, T, sorts, maxidx = maxidxA, ...} = adjust_maxidx_cterm ~1 raw_ct;
wenzelm@28321
   451
    val Thm (der, {tags, maxidx, shyps, hyps, tpairs, prop, ...}) = th;
wenzelm@16945
   452
  in
wenzelm@16945
   453
    if T <> propT then
wenzelm@16945
   454
      raise THM ("weaken: assumptions must have type prop", 0, [])
wenzelm@16945
   455
    else if maxidxA <> ~1 then
wenzelm@16945
   456
      raise THM ("weaken: assumptions may not contain schematic variables", maxidxA, [])
wenzelm@16945
   457
    else
wenzelm@28321
   458
      Thm (der,
wenzelm@28321
   459
       {thy_ref = merge_thys1 ct th,
wenzelm@21646
   460
        tags = tags,
wenzelm@16945
   461
        maxidx = maxidx,
wenzelm@16945
   462
        shyps = Sorts.union sorts shyps,
wenzelm@28354
   463
        hyps = insert_hyps A hyps,
wenzelm@16945
   464
        tpairs = tpairs,
wenzelm@28321
   465
        prop = prop})
wenzelm@16945
   466
  end;
wenzelm@16656
   467
wenzelm@28624
   468
fun weaken_sorts raw_sorts ct =
wenzelm@28624
   469
  let
wenzelm@28624
   470
    val Cterm {thy_ref, t, T, maxidx, sorts} = ct;
wenzelm@28624
   471
    val thy = Theory.deref thy_ref;
wenzelm@28624
   472
    val more_sorts = Sorts.make (map (Sign.certify_sort thy) raw_sorts);
wenzelm@28624
   473
    val sorts' = Sorts.union sorts more_sorts;
wenzelm@28624
   474
  in Cterm {thy_ref = Theory.check_thy thy, t = t, T = T, maxidx = maxidx, sorts = sorts'} end;
wenzelm@28624
   475
wenzelm@16656
   476
clasohm@0
   477
wenzelm@1238
   478
(** sort contexts of theorems **)
wenzelm@1238
   479
wenzelm@31947
   480
(*remove extra sorts that are witnessed by type signature information*)
wenzelm@28321
   481
fun strip_shyps (thm as Thm (_, {shyps = [], ...})) = thm
wenzelm@28321
   482
  | strip_shyps (thm as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@7642
   483
      let
wenzelm@16425
   484
        val thy = Theory.deref thy_ref;
wenzelm@31947
   485
        val present =
wenzelm@31947
   486
          (fold_terms o fold_types o fold_atyps)
wenzelm@31947
   487
            (fn T as TFree (_, S) => insert (eq_snd op =) (T, S)
wenzelm@31947
   488
              | T as TVar (_, S) => insert (eq_snd op =) (T, S)) thm [];
wenzelm@31947
   489
        val extra = fold (Sorts.remove_sort o #2) present shyps;
wenzelm@31947
   490
        val witnessed = Sign.witness_sorts thy present extra;
wenzelm@31947
   491
        val extra' = fold (Sorts.remove_sort o #2) witnessed extra
wenzelm@28624
   492
          |> Sorts.minimal_sorts (Sign.classes_of thy);
wenzelm@31947
   493
        val shyps' = fold (Sorts.insert_sort o #2) present extra';
wenzelm@7642
   494
      in
wenzelm@28321
   495
        Thm (der, {thy_ref = Theory.check_thy thy, tags = tags, maxidx = maxidx,
wenzelm@28321
   496
          shyps = shyps', hyps = hyps, tpairs = tpairs, prop = prop})
wenzelm@7642
   497
      end;
wenzelm@1238
   498
wenzelm@16656
   499
(*dangling sort constraints of a thm*)
wenzelm@31947
   500
fun extra_shyps (th as Thm (_, {shyps, ...})) =
wenzelm@31947
   501
  Sorts.subtract (fold_terms Sorts.insert_term th []) shyps;
wenzelm@28321
   502
wenzelm@28321
   503
wenzelm@28321
   504
wenzelm@28321
   505
(** derivations **)
wenzelm@28321
   506
wenzelm@28996
   507
fun make_deriv max_promise open_promises promises oracles thms proof =
wenzelm@28996
   508
  Deriv {max_promise = max_promise, open_promises = open_promises, promises = promises,
wenzelm@28804
   509
    body = PBody {oracles = oracles, thms = thms, proof = proof}};
wenzelm@28321
   510
wenzelm@28996
   511
val empty_deriv = make_deriv ~1 [] [] [] [] Pt.MinProof;
wenzelm@28321
   512
wenzelm@28330
   513
wenzelm@28354
   514
(* inference rules *)
wenzelm@28321
   515
wenzelm@28378
   516
fun promise_ord ((i, _), (j, _)) = int_ord (j, i);
wenzelm@28330
   517
wenzelm@28321
   518
fun deriv_rule2 f
wenzelm@28996
   519
    (Deriv {max_promise = max1, open_promises = open_ps1, promises = ps1,
wenzelm@28804
   520
      body = PBody {oracles = oras1, thms = thms1, proof = prf1}})
wenzelm@28996
   521
    (Deriv {max_promise = max2, open_promises = open_ps2, promises = ps2,
wenzelm@28804
   522
      body = PBody {oracles = oras2, thms = thms2, proof = prf2}}) =
wenzelm@28321
   523
  let
wenzelm@28996
   524
    val max = Int.max (max1, max2);
wenzelm@28996
   525
    val open_ps = OrdList.union promise_ord open_ps1 open_ps2;
wenzelm@28330
   526
    val ps = OrdList.union promise_ord ps1 ps2;
wenzelm@28804
   527
    val oras = Pt.merge_oracles oras1 oras2;
wenzelm@28804
   528
    val thms = Pt.merge_thms thms1 thms2;
wenzelm@28321
   529
    val prf =
wenzelm@28321
   530
      (case ! Pt.proofs of
wenzelm@28321
   531
        2 => f prf1 prf2
wenzelm@28804
   532
      | 1 => MinProof
wenzelm@28804
   533
      | 0 => MinProof
wenzelm@28321
   534
      | i => error ("Illegal level of detail for proof objects: " ^ string_of_int i));
wenzelm@28996
   535
  in make_deriv max open_ps ps oras thms prf end;
wenzelm@28321
   536
wenzelm@28321
   537
fun deriv_rule1 f = deriv_rule2 (K f) empty_deriv;
wenzelm@28996
   538
fun deriv_rule0 prf = deriv_rule1 I (make_deriv ~1 [] [] [] [] prf);
wenzelm@28321
   539
wenzelm@1238
   540
wenzelm@1238
   541
paulson@1529
   542
(** Axioms **)
wenzelm@387
   543
wenzelm@28675
   544
fun axiom theory name =
wenzelm@387
   545
  let
wenzelm@16425
   546
    fun get_ax thy =
wenzelm@22685
   547
      Symtab.lookup (Theory.axiom_table thy) name
wenzelm@16601
   548
      |> Option.map (fn prop =>
wenzelm@24143
   549
           let
wenzelm@28321
   550
             val der = deriv_rule0 (Pt.axm_proof name prop);
wenzelm@24143
   551
             val maxidx = maxidx_of_term prop;
wenzelm@26640
   552
             val shyps = Sorts.insert_term prop [];
wenzelm@24143
   553
           in
wenzelm@28321
   554
             Thm (der, {thy_ref = Theory.check_thy thy, tags = [],
wenzelm@28321
   555
               maxidx = maxidx, shyps = shyps, hyps = [], tpairs = [], prop = prop})
wenzelm@24143
   556
           end);
wenzelm@387
   557
  in
wenzelm@16425
   558
    (case get_first get_ax (theory :: Theory.ancestors_of theory) of
skalberg@15531
   559
      SOME thm => thm
skalberg@15531
   560
    | NONE => raise THEORY ("No axiom " ^ quote name, [theory]))
wenzelm@387
   561
  end;
wenzelm@387
   562
wenzelm@776
   563
(*return additional axioms of this theory node*)
wenzelm@776
   564
fun axioms_of thy =
wenzelm@28675
   565
  map (fn s => (s, axiom thy s)) (Symtab.keys (Theory.axiom_table thy));
wenzelm@776
   566
wenzelm@6089
   567
wenzelm@28804
   568
(* tags *)
wenzelm@6089
   569
wenzelm@21646
   570
val get_tags = #tags o rep_thm;
wenzelm@6089
   571
wenzelm@28321
   572
fun map_tags f (Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@28321
   573
  Thm (der, {thy_ref = thy_ref, tags = f tags, maxidx = maxidx,
wenzelm@28321
   574
    shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop});
clasohm@0
   575
clasohm@0
   576
wenzelm@28321
   577
fun norm_proof (Thm (der, args as {thy_ref, ...})) =
wenzelm@24143
   578
  let
wenzelm@24143
   579
    val thy = Theory.deref thy_ref;
wenzelm@28321
   580
    val der' = deriv_rule1 (Pt.rew_proof thy) der;
wenzelm@28321
   581
    val _ = Theory.check_thy thy;
wenzelm@28321
   582
  in Thm (der', args) end;
berghofe@23781
   583
wenzelm@28321
   584
fun adjust_maxidx_thm i (th as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@20261
   585
  if maxidx = i then th
wenzelm@20261
   586
  else if maxidx < i then
wenzelm@28321
   587
    Thm (der, {maxidx = i, thy_ref = thy_ref, tags = tags, shyps = shyps,
wenzelm@28321
   588
      hyps = hyps, tpairs = tpairs, prop = prop})
wenzelm@20261
   589
  else
wenzelm@28321
   590
    Thm (der, {maxidx = Int.max (maxidx_tpairs tpairs (maxidx_of_term prop), i), thy_ref = thy_ref,
wenzelm@28321
   591
      tags = tags, shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop});
wenzelm@564
   592
wenzelm@387
   593
wenzelm@2509
   594
paulson@1529
   595
(*** Meta rules ***)
clasohm@0
   596
wenzelm@16601
   597
(** primitive rules **)
clasohm@0
   598
wenzelm@16656
   599
(*The assumption rule A |- A*)
wenzelm@16601
   600
fun assume raw_ct =
wenzelm@20261
   601
  let val Cterm {thy_ref, t = prop, T, maxidx, sorts} = adjust_maxidx_cterm ~1 raw_ct in
wenzelm@16601
   602
    if T <> propT then
mengj@19230
   603
      raise THM ("assume: prop", 0, [])
wenzelm@16601
   604
    else if maxidx <> ~1 then
mengj@19230
   605
      raise THM ("assume: variables", maxidx, [])
wenzelm@28321
   606
    else Thm (deriv_rule0 (Pt.Hyp prop),
wenzelm@28321
   607
     {thy_ref = thy_ref,
wenzelm@21646
   608
      tags = [],
wenzelm@16601
   609
      maxidx = ~1,
wenzelm@16601
   610
      shyps = sorts,
wenzelm@16601
   611
      hyps = [prop],
wenzelm@16601
   612
      tpairs = [],
wenzelm@28321
   613
      prop = prop})
clasohm@0
   614
  end;
clasohm@0
   615
wenzelm@1220
   616
(*Implication introduction
wenzelm@3529
   617
    [A]
wenzelm@3529
   618
     :
wenzelm@3529
   619
     B
wenzelm@1220
   620
  -------
wenzelm@1220
   621
  A ==> B
wenzelm@1220
   622
*)
wenzelm@16601
   623
fun implies_intr
wenzelm@16679
   624
    (ct as Cterm {t = A, T, maxidx = maxidxA, sorts, ...})
wenzelm@28321
   625
    (th as Thm (der, {maxidx, hyps, shyps, tpairs, prop, ...})) =
wenzelm@16601
   626
  if T <> propT then
wenzelm@16601
   627
    raise THM ("implies_intr: assumptions must have type prop", 0, [th])
wenzelm@16601
   628
  else
wenzelm@28321
   629
    Thm (deriv_rule1 (Pt.implies_intr_proof A) der,
wenzelm@28321
   630
     {thy_ref = merge_thys1 ct th,
wenzelm@21646
   631
      tags = [],
wenzelm@16601
   632
      maxidx = Int.max (maxidxA, maxidx),
wenzelm@16601
   633
      shyps = Sorts.union sorts shyps,
wenzelm@28354
   634
      hyps = remove_hyps A hyps,
wenzelm@16601
   635
      tpairs = tpairs,
wenzelm@28321
   636
      prop = Logic.mk_implies (A, prop)});
clasohm@0
   637
paulson@1529
   638
wenzelm@1220
   639
(*Implication elimination
wenzelm@1220
   640
  A ==> B    A
wenzelm@1220
   641
  ------------
wenzelm@1220
   642
        B
wenzelm@1220
   643
*)
wenzelm@16601
   644
fun implies_elim thAB thA =
wenzelm@16601
   645
  let
wenzelm@28321
   646
    val Thm (derA, {maxidx = maxA, hyps = hypsA, shyps = shypsA, tpairs = tpairsA,
wenzelm@28321
   647
      prop = propA, ...}) = thA
wenzelm@28321
   648
    and Thm (der, {maxidx, hyps, shyps, tpairs, prop, ...}) = thAB;
wenzelm@16601
   649
    fun err () = raise THM ("implies_elim: major premise", 0, [thAB, thA]);
wenzelm@16601
   650
  in
wenzelm@16601
   651
    case prop of
wenzelm@20512
   652
      Const ("==>", _) $ A $ B =>
wenzelm@20512
   653
        if A aconv propA then
wenzelm@28321
   654
          Thm (deriv_rule2 (curry Pt.%%) der derA,
wenzelm@28321
   655
           {thy_ref = merge_thys2 thAB thA,
wenzelm@21646
   656
            tags = [],
wenzelm@16601
   657
            maxidx = Int.max (maxA, maxidx),
wenzelm@16601
   658
            shyps = Sorts.union shypsA shyps,
wenzelm@16601
   659
            hyps = union_hyps hypsA hyps,
wenzelm@16601
   660
            tpairs = union_tpairs tpairsA tpairs,
wenzelm@28321
   661
            prop = B})
wenzelm@16601
   662
        else err ()
wenzelm@16601
   663
    | _ => err ()
wenzelm@16601
   664
  end;
wenzelm@250
   665
wenzelm@1220
   666
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@16656
   667
    [x]
wenzelm@16656
   668
     :
wenzelm@16656
   669
     A
wenzelm@16656
   670
  ------
wenzelm@16656
   671
  !!x. A
wenzelm@1220
   672
*)
wenzelm@16601
   673
fun forall_intr
wenzelm@16601
   674
    (ct as Cterm {t = x, T, sorts, ...})
wenzelm@28321
   675
    (th as Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   676
  let
wenzelm@16601
   677
    fun result a =
wenzelm@28321
   678
      Thm (deriv_rule1 (Pt.forall_intr_proof x a) der,
wenzelm@28321
   679
       {thy_ref = merge_thys1 ct th,
wenzelm@21646
   680
        tags = [],
wenzelm@16601
   681
        maxidx = maxidx,
wenzelm@16601
   682
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   683
        hyps = hyps,
wenzelm@16601
   684
        tpairs = tpairs,
wenzelm@28321
   685
        prop = Term.all T $ Abs (a, T, abstract_over (x, prop))});
wenzelm@21798
   686
    fun check_occs a x ts =
wenzelm@16847
   687
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@21798
   688
        raise THM ("forall_intr: variable " ^ quote a ^ " free in assumptions", 0, [th])
wenzelm@16601
   689
      else ();
wenzelm@16601
   690
  in
wenzelm@16601
   691
    case x of
wenzelm@21798
   692
      Free (a, _) => (check_occs a x hyps; check_occs a x (terms_of_tpairs tpairs); result a)
wenzelm@21798
   693
    | Var ((a, _), _) => (check_occs a x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   694
    | _ => raise THM ("forall_intr: not a variable", 0, [th])
clasohm@0
   695
  end;
clasohm@0
   696
wenzelm@1220
   697
(*Forall elimination
wenzelm@16656
   698
  !!x. A
wenzelm@1220
   699
  ------
wenzelm@1220
   700
  A[t/x]
wenzelm@1220
   701
*)
wenzelm@16601
   702
fun forall_elim
wenzelm@16601
   703
    (ct as Cterm {t, T, maxidx = maxt, sorts, ...})
wenzelm@28321
   704
    (th as Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   705
  (case prop of
wenzelm@16601
   706
    Const ("all", Type ("fun", [Type ("fun", [qary, _]), _])) $ A =>
wenzelm@16601
   707
      if T <> qary then
wenzelm@16601
   708
        raise THM ("forall_elim: type mismatch", 0, [th])
wenzelm@16601
   709
      else
wenzelm@28321
   710
        Thm (deriv_rule1 (Pt.% o rpair (SOME t)) der,
wenzelm@28321
   711
         {thy_ref = merge_thys1 ct th,
wenzelm@21646
   712
          tags = [],
wenzelm@16601
   713
          maxidx = Int.max (maxidx, maxt),
wenzelm@16601
   714
          shyps = Sorts.union sorts shyps,
wenzelm@16601
   715
          hyps = hyps,
wenzelm@16601
   716
          tpairs = tpairs,
wenzelm@28321
   717
          prop = Term.betapply (A, t)})
wenzelm@16601
   718
  | _ => raise THM ("forall_elim: not quantified", 0, [th]));
clasohm@0
   719
clasohm@0
   720
wenzelm@1220
   721
(* Equality *)
clasohm@0
   722
wenzelm@16601
   723
(*Reflexivity
wenzelm@16601
   724
  t == t
wenzelm@16601
   725
*)
wenzelm@16601
   726
fun reflexive (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   727
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   728
   {thy_ref = thy_ref,
wenzelm@21646
   729
    tags = [],
wenzelm@16601
   730
    maxidx = maxidx,
wenzelm@16601
   731
    shyps = sorts,
wenzelm@16601
   732
    hyps = [],
wenzelm@16601
   733
    tpairs = [],
wenzelm@28321
   734
    prop = Logic.mk_equals (t, t)});
clasohm@0
   735
wenzelm@16601
   736
(*Symmetry
wenzelm@16601
   737
  t == u
wenzelm@16601
   738
  ------
wenzelm@16601
   739
  u == t
wenzelm@1220
   740
*)
wenzelm@28321
   741
fun symmetric (th as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   742
  (case prop of
wenzelm@16601
   743
    (eq as Const ("==", Type (_, [T, _]))) $ t $ u =>
wenzelm@28321
   744
      Thm (deriv_rule1 Pt.symmetric der,
wenzelm@28321
   745
       {thy_ref = thy_ref,
wenzelm@21646
   746
        tags = [],
wenzelm@16601
   747
        maxidx = maxidx,
wenzelm@16601
   748
        shyps = shyps,
wenzelm@16601
   749
        hyps = hyps,
wenzelm@16601
   750
        tpairs = tpairs,
wenzelm@28321
   751
        prop = eq $ u $ t})
wenzelm@16601
   752
    | _ => raise THM ("symmetric", 0, [th]));
clasohm@0
   753
wenzelm@16601
   754
(*Transitivity
wenzelm@16601
   755
  t1 == u    u == t2
wenzelm@16601
   756
  ------------------
wenzelm@16601
   757
       t1 == t2
wenzelm@1220
   758
*)
clasohm@0
   759
fun transitive th1 th2 =
wenzelm@16601
   760
  let
wenzelm@28321
   761
    val Thm (der1, {maxidx = max1, hyps = hyps1, shyps = shyps1, tpairs = tpairs1,
wenzelm@28321
   762
      prop = prop1, ...}) = th1
wenzelm@28321
   763
    and Thm (der2, {maxidx = max2, hyps = hyps2, shyps = shyps2, tpairs = tpairs2,
wenzelm@28321
   764
      prop = prop2, ...}) = th2;
wenzelm@16601
   765
    fun err msg = raise THM ("transitive: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   766
  in
wenzelm@16601
   767
    case (prop1, prop2) of
wenzelm@16601
   768
      ((eq as Const ("==", Type (_, [T, _]))) $ t1 $ u, Const ("==", _) $ u' $ t2) =>
wenzelm@16601
   769
        if not (u aconv u') then err "middle term"
wenzelm@16601
   770
        else
wenzelm@28321
   771
          Thm (deriv_rule2 (Pt.transitive u T) der1 der2,
wenzelm@28321
   772
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   773
            tags = [],
wenzelm@16601
   774
            maxidx = Int.max (max1, max2),
wenzelm@16601
   775
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   776
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   777
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   778
            prop = eq $ t1 $ t2})
wenzelm@16601
   779
     | _ =>  err "premises"
clasohm@0
   780
  end;
clasohm@0
   781
wenzelm@16601
   782
(*Beta-conversion
wenzelm@16656
   783
  (%x. t)(u) == t[u/x]
wenzelm@16601
   784
  fully beta-reduces the term if full = true
berghofe@10416
   785
*)
wenzelm@16601
   786
fun beta_conversion full (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   787
  let val t' =
wenzelm@16601
   788
    if full then Envir.beta_norm t
wenzelm@16601
   789
    else
wenzelm@16601
   790
      (case t of Abs (_, _, bodt) $ u => subst_bound (u, bodt)
wenzelm@16601
   791
      | _ => raise THM ("beta_conversion: not a redex", 0, []));
wenzelm@16601
   792
  in
wenzelm@28321
   793
    Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   794
     {thy_ref = thy_ref,
wenzelm@21646
   795
      tags = [],
wenzelm@16601
   796
      maxidx = maxidx,
wenzelm@16601
   797
      shyps = sorts,
wenzelm@16601
   798
      hyps = [],
wenzelm@16601
   799
      tpairs = [],
wenzelm@28321
   800
      prop = Logic.mk_equals (t, t')})
berghofe@10416
   801
  end;
berghofe@10416
   802
wenzelm@16601
   803
fun eta_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   804
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   805
   {thy_ref = thy_ref,
wenzelm@21646
   806
    tags = [],
wenzelm@16601
   807
    maxidx = maxidx,
wenzelm@16601
   808
    shyps = sorts,
wenzelm@16601
   809
    hyps = [],
wenzelm@16601
   810
    tpairs = [],
wenzelm@28321
   811
    prop = Logic.mk_equals (t, Envir.eta_contract t)});
clasohm@0
   812
wenzelm@23493
   813
fun eta_long_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   814
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   815
   {thy_ref = thy_ref,
wenzelm@23493
   816
    tags = [],
wenzelm@23493
   817
    maxidx = maxidx,
wenzelm@23493
   818
    shyps = sorts,
wenzelm@23493
   819
    hyps = [],
wenzelm@23493
   820
    tpairs = [],
wenzelm@28321
   821
    prop = Logic.mk_equals (t, Pattern.eta_long [] t)});
wenzelm@23493
   822
clasohm@0
   823
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   824
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@16601
   825
      t == u
wenzelm@16601
   826
  --------------
wenzelm@16601
   827
  %x. t == %x. u
wenzelm@1220
   828
*)
wenzelm@16601
   829
fun abstract_rule a
wenzelm@16601
   830
    (Cterm {t = x, T, sorts, ...})
wenzelm@28321
   831
    (th as Thm (der, {thy_ref, maxidx, hyps, shyps, tpairs, prop, ...})) =
wenzelm@16601
   832
  let
wenzelm@16601
   833
    val (t, u) = Logic.dest_equals prop
wenzelm@16601
   834
      handle TERM _ => raise THM ("abstract_rule: premise not an equality", 0, [th]);
wenzelm@16601
   835
    val result =
wenzelm@28321
   836
      Thm (deriv_rule1 (Pt.abstract_rule x a) der,
wenzelm@28321
   837
       {thy_ref = thy_ref,
wenzelm@21646
   838
        tags = [],
wenzelm@16601
   839
        maxidx = maxidx,
wenzelm@16601
   840
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   841
        hyps = hyps,
wenzelm@16601
   842
        tpairs = tpairs,
wenzelm@16601
   843
        prop = Logic.mk_equals
wenzelm@28321
   844
          (Abs (a, T, abstract_over (x, t)), Abs (a, T, abstract_over (x, u)))});
wenzelm@21798
   845
    fun check_occs a x ts =
wenzelm@16847
   846
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@21798
   847
        raise THM ("abstract_rule: variable " ^ quote a ^ " free in assumptions", 0, [th])
wenzelm@16601
   848
      else ();
wenzelm@16601
   849
  in
wenzelm@16601
   850
    case x of
wenzelm@21798
   851
      Free (a, _) => (check_occs a x hyps; check_occs a x (terms_of_tpairs tpairs); result)
wenzelm@21798
   852
    | Var ((a, _), _) => (check_occs a x (terms_of_tpairs tpairs); result)
wenzelm@21798
   853
    | _ => raise THM ("abstract_rule: not a variable", 0, [th])
clasohm@0
   854
  end;
clasohm@0
   855
clasohm@0
   856
(*The combination rule
wenzelm@3529
   857
  f == g  t == u
wenzelm@3529
   858
  --------------
wenzelm@16601
   859
    f t == g u
wenzelm@1220
   860
*)
clasohm@0
   861
fun combination th1 th2 =
wenzelm@16601
   862
  let
wenzelm@28321
   863
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@28321
   864
      prop = prop1, ...}) = th1
wenzelm@28321
   865
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@28321
   866
      prop = prop2, ...}) = th2;
wenzelm@16601
   867
    fun chktypes fT tT =
wenzelm@16601
   868
      (case fT of
wenzelm@16601
   869
        Type ("fun", [T1, T2]) =>
wenzelm@16601
   870
          if T1 <> tT then
wenzelm@16601
   871
            raise THM ("combination: types", 0, [th1, th2])
wenzelm@16601
   872
          else ()
wenzelm@16601
   873
      | _ => raise THM ("combination: not function type", 0, [th1, th2]));
wenzelm@16601
   874
  in
wenzelm@16601
   875
    case (prop1, prop2) of
wenzelm@16601
   876
      (Const ("==", Type ("fun", [fT, _])) $ f $ g,
wenzelm@16601
   877
       Const ("==", Type ("fun", [tT, _])) $ t $ u) =>
wenzelm@16601
   878
        (chktypes fT tT;
wenzelm@28321
   879
          Thm (deriv_rule2 (Pt.combination f g t u fT) der1 der2,
wenzelm@28321
   880
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   881
            tags = [],
wenzelm@16601
   882
            maxidx = Int.max (max1, max2),
wenzelm@16601
   883
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   884
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   885
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   886
            prop = Logic.mk_equals (f $ t, g $ u)}))
wenzelm@16601
   887
     | _ => raise THM ("combination: premises", 0, [th1, th2])
clasohm@0
   888
  end;
clasohm@0
   889
wenzelm@16601
   890
(*Equality introduction
wenzelm@3529
   891
  A ==> B  B ==> A
wenzelm@3529
   892
  ----------------
wenzelm@3529
   893
       A == B
wenzelm@1220
   894
*)
clasohm@0
   895
fun equal_intr th1 th2 =
wenzelm@16601
   896
  let
wenzelm@28321
   897
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@28321
   898
      prop = prop1, ...}) = th1
wenzelm@28321
   899
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@28321
   900
      prop = prop2, ...}) = th2;
wenzelm@16601
   901
    fun err msg = raise THM ("equal_intr: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   902
  in
wenzelm@16601
   903
    case (prop1, prop2) of
wenzelm@16601
   904
      (Const("==>", _) $ A $ B, Const("==>", _) $ B' $ A') =>
wenzelm@16601
   905
        if A aconv A' andalso B aconv B' then
wenzelm@28321
   906
          Thm (deriv_rule2 (Pt.equal_intr A B) der1 der2,
wenzelm@28321
   907
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   908
            tags = [],
wenzelm@16601
   909
            maxidx = Int.max (max1, max2),
wenzelm@16601
   910
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   911
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   912
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   913
            prop = Logic.mk_equals (A, B)})
wenzelm@16601
   914
        else err "not equal"
wenzelm@16601
   915
    | _ =>  err "premises"
paulson@1529
   916
  end;
paulson@1529
   917
paulson@1529
   918
(*The equal propositions rule
wenzelm@3529
   919
  A == B  A
paulson@1529
   920
  ---------
paulson@1529
   921
      B
paulson@1529
   922
*)
paulson@1529
   923
fun equal_elim th1 th2 =
wenzelm@16601
   924
  let
wenzelm@28321
   925
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1,
wenzelm@28321
   926
      tpairs = tpairs1, prop = prop1, ...}) = th1
wenzelm@28321
   927
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2,
wenzelm@28321
   928
      tpairs = tpairs2, prop = prop2, ...}) = th2;
wenzelm@16601
   929
    fun err msg = raise THM ("equal_elim: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   930
  in
wenzelm@16601
   931
    case prop1 of
wenzelm@16601
   932
      Const ("==", _) $ A $ B =>
wenzelm@16601
   933
        if prop2 aconv A then
wenzelm@28321
   934
          Thm (deriv_rule2 (Pt.equal_elim A B) der1 der2,
wenzelm@28321
   935
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   936
            tags = [],
wenzelm@16601
   937
            maxidx = Int.max (max1, max2),
wenzelm@16601
   938
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   939
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   940
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   941
            prop = B})
wenzelm@16601
   942
        else err "not equal"
paulson@1529
   943
     | _ =>  err"major premise"
paulson@1529
   944
  end;
clasohm@0
   945
wenzelm@1220
   946
wenzelm@1220
   947
clasohm@0
   948
(**** Derived rules ****)
clasohm@0
   949
wenzelm@16601
   950
(*Smash unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@24143
   951
  Instantiates the theorem and deletes trivial tpairs.  Resulting
wenzelm@24143
   952
  sequence may contain multiple elements if the tpairs are not all
wenzelm@24143
   953
  flex-flex.*)
wenzelm@28321
   954
fun flexflex_rule (th as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@24143
   955
  let val thy = Theory.deref thy_ref in
wenzelm@24143
   956
    Unify.smash_unifiers thy tpairs (Envir.empty maxidx)
wenzelm@24143
   957
    |> Seq.map (fn env =>
wenzelm@24143
   958
        if Envir.is_empty env then th
wenzelm@24143
   959
        else
wenzelm@24143
   960
          let
wenzelm@24143
   961
            val tpairs' = tpairs |> map (pairself (Envir.norm_term env))
wenzelm@24143
   962
              (*remove trivial tpairs, of the form t==t*)
wenzelm@24143
   963
              |> filter_out (op aconv);
wenzelm@28321
   964
            val der' = deriv_rule1 (Pt.norm_proof' env) der;
wenzelm@24143
   965
            val prop' = Envir.norm_term env prop;
wenzelm@24143
   966
            val maxidx = maxidx_tpairs tpairs' (maxidx_of_term prop');
wenzelm@26640
   967
            val shyps = Envir.insert_sorts env shyps;
wenzelm@24143
   968
          in
wenzelm@28321
   969
            Thm (der', {thy_ref = Theory.check_thy thy, tags = [], maxidx = maxidx,
wenzelm@28321
   970
              shyps = shyps, hyps = hyps, tpairs = tpairs', prop = prop'})
wenzelm@24143
   971
          end)
wenzelm@24143
   972
  end;
wenzelm@16601
   973
clasohm@0
   974
wenzelm@19910
   975
(*Generalization of fixed variables
wenzelm@19910
   976
           A
wenzelm@19910
   977
  --------------------
wenzelm@19910
   978
  A[?'a/'a, ?x/x, ...]
wenzelm@19910
   979
*)
wenzelm@19910
   980
wenzelm@19910
   981
fun generalize ([], []) _ th = th
wenzelm@19910
   982
  | generalize (tfrees, frees) idx th =
wenzelm@19910
   983
      let
wenzelm@28321
   984
        val Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...}) = th;
wenzelm@19910
   985
        val _ = idx <= maxidx andalso raise THM ("generalize: bad index", idx, [th]);
wenzelm@19910
   986
wenzelm@19910
   987
        val bad_type = if null tfrees then K false else
wenzelm@19910
   988
          Term.exists_subtype (fn TFree (a, _) => member (op =) tfrees a | _ => false);
wenzelm@19910
   989
        fun bad_term (Free (x, T)) = bad_type T orelse member (op =) frees x
wenzelm@19910
   990
          | bad_term (Var (_, T)) = bad_type T
wenzelm@19910
   991
          | bad_term (Const (_, T)) = bad_type T
wenzelm@19910
   992
          | bad_term (Abs (_, T, t)) = bad_type T orelse bad_term t
wenzelm@19910
   993
          | bad_term (t $ u) = bad_term t orelse bad_term u
wenzelm@19910
   994
          | bad_term (Bound _) = false;
wenzelm@19910
   995
        val _ = exists bad_term hyps andalso
wenzelm@19910
   996
          raise THM ("generalize: variable free in assumptions", 0, [th]);
wenzelm@19910
   997
wenzelm@31977
   998
        val gen = Term_Subst.generalize (tfrees, frees) idx;
wenzelm@19910
   999
        val prop' = gen prop;
wenzelm@19910
  1000
        val tpairs' = map (pairself gen) tpairs;
wenzelm@19910
  1001
        val maxidx' = maxidx_tpairs tpairs' (maxidx_of_term prop');
wenzelm@19910
  1002
      in
wenzelm@28321
  1003
        Thm (deriv_rule1 (Pt.generalize (tfrees, frees) idx) der,
wenzelm@28321
  1004
         {thy_ref = thy_ref,
wenzelm@21646
  1005
          tags = [],
wenzelm@19910
  1006
          maxidx = maxidx',
wenzelm@19910
  1007
          shyps = shyps,
wenzelm@19910
  1008
          hyps = hyps,
wenzelm@19910
  1009
          tpairs = tpairs',
wenzelm@28321
  1010
          prop = prop'})
wenzelm@19910
  1011
      end;
wenzelm@19910
  1012
wenzelm@19910
  1013
wenzelm@22584
  1014
(*Instantiation of schematic variables
wenzelm@16656
  1015
           A
wenzelm@16656
  1016
  --------------------
wenzelm@16656
  1017
  A[t1/v1, ..., tn/vn]
wenzelm@1220
  1018
*)
clasohm@0
  1019
wenzelm@6928
  1020
local
wenzelm@6928
  1021
wenzelm@26939
  1022
fun pretty_typing thy t T = Pretty.block
wenzelm@26939
  1023
  [Syntax.pretty_term_global thy t, Pretty.str " ::", Pretty.brk 1, Syntax.pretty_typ_global thy T];
berghofe@15797
  1024
wenzelm@16884
  1025
fun add_inst (ct, cu) (thy_ref, sorts) =
wenzelm@6928
  1026
  let
wenzelm@26939
  1027
    val Cterm {t = t, T = T, ...} = ct;
wenzelm@26939
  1028
    val Cterm {t = u, T = U, sorts = sorts_u, maxidx = maxidx_u, ...} = cu;
wenzelm@16884
  1029
    val thy_ref' = Theory.merge_refs (thy_ref, merge_thys0 ct cu);
wenzelm@16884
  1030
    val sorts' = Sorts.union sorts_u sorts;
wenzelm@3967
  1031
  in
wenzelm@16884
  1032
    (case t of Var v =>
wenzelm@20512
  1033
      if T = U then ((v, (u, maxidx_u)), (thy_ref', sorts'))
wenzelm@16884
  1034
      else raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
  1035
       [Pretty.str "instantiate: type conflict",
wenzelm@16884
  1036
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') t T,
wenzelm@16884
  1037
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') u U]), [T, U], [t, u])
wenzelm@16884
  1038
    | _ => raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
  1039
       [Pretty.str "instantiate: not a variable",
wenzelm@26939
  1040
        Pretty.fbrk, Syntax.pretty_term_global (Theory.deref thy_ref') t]), [], [t]))
clasohm@0
  1041
  end;
clasohm@0
  1042
wenzelm@16884
  1043
fun add_instT (cT, cU) (thy_ref, sorts) =
wenzelm@16656
  1044
  let
wenzelm@16884
  1045
    val Ctyp {T, thy_ref = thy_ref1, ...} = cT
wenzelm@20512
  1046
    and Ctyp {T = U, thy_ref = thy_ref2, sorts = sorts_U, maxidx = maxidx_U, ...} = cU;
wenzelm@24143
  1047
    val thy' = Theory.deref (Theory.merge_refs (thy_ref, Theory.merge_refs (thy_ref1, thy_ref2)));
wenzelm@16884
  1048
    val sorts' = Sorts.union sorts_U sorts;
wenzelm@16656
  1049
  in
wenzelm@16884
  1050
    (case T of TVar (v as (_, S)) =>
wenzelm@24143
  1051
      if Sign.of_sort thy' (U, S) then ((v, (U, maxidx_U)), (Theory.check_thy thy', sorts'))
wenzelm@26939
  1052
      else raise TYPE ("Type not of sort " ^ Syntax.string_of_sort_global thy' S, [U], [])
wenzelm@16656
  1053
    | _ => raise TYPE (Pretty.string_of (Pretty.block
berghofe@15797
  1054
        [Pretty.str "instantiate: not a type variable",
wenzelm@26939
  1055
         Pretty.fbrk, Syntax.pretty_typ_global thy' T]), [T], []))
wenzelm@16656
  1056
  end;
clasohm@0
  1057
wenzelm@6928
  1058
in
wenzelm@6928
  1059
wenzelm@16601
  1060
(*Left-to-right replacements: ctpairs = [..., (vi, ti), ...].
clasohm@0
  1061
  Instantiates distinct Vars by terms of same type.
wenzelm@16601
  1062
  Does NOT normalize the resulting theorem!*)
paulson@1529
  1063
fun instantiate ([], []) th = th
wenzelm@16884
  1064
  | instantiate (instT, inst) th =
wenzelm@16656
  1065
      let
wenzelm@28321
  1066
        val Thm (der, {thy_ref, hyps, shyps, tpairs, prop, ...}) = th;
wenzelm@16884
  1067
        val (inst', (instT', (thy_ref', shyps'))) =
wenzelm@16884
  1068
          (thy_ref, shyps) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@31977
  1069
        val subst = Term_Subst.instantiate_maxidx (instT', inst');
wenzelm@20512
  1070
        val (prop', maxidx1) = subst prop ~1;
wenzelm@20512
  1071
        val (tpairs', maxidx') =
wenzelm@20512
  1072
          fold_map (fn (t, u) => fn i => subst t i ||>> subst u) tpairs maxidx1;
wenzelm@16656
  1073
      in
wenzelm@28321
  1074
        Thm (deriv_rule1 (fn d => Pt.instantiate (map (apsnd #1) instT', map (apsnd #1) inst') d) der,
wenzelm@28321
  1075
         {thy_ref = thy_ref',
wenzelm@21646
  1076
          tags = [],
wenzelm@20545
  1077
          maxidx = maxidx',
wenzelm@20545
  1078
          shyps = shyps',
wenzelm@20545
  1079
          hyps = hyps,
wenzelm@20545
  1080
          tpairs = tpairs',
wenzelm@28321
  1081
          prop = prop'})
wenzelm@16656
  1082
      end
wenzelm@16656
  1083
      handle TYPE (msg, _, _) => raise THM (msg, 0, [th]);
wenzelm@6928
  1084
wenzelm@22584
  1085
fun instantiate_cterm ([], []) ct = ct
wenzelm@22584
  1086
  | instantiate_cterm (instT, inst) ct =
wenzelm@22584
  1087
      let
wenzelm@22584
  1088
        val Cterm {thy_ref, t, T, sorts, ...} = ct;
wenzelm@22584
  1089
        val (inst', (instT', (thy_ref', sorts'))) =
wenzelm@22584
  1090
          (thy_ref, sorts) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@31977
  1091
        val subst = Term_Subst.instantiate_maxidx (instT', inst');
wenzelm@31977
  1092
        val substT = Term_Subst.instantiateT_maxidx instT';
wenzelm@22584
  1093
        val (t', maxidx1) = subst t ~1;
wenzelm@22584
  1094
        val (T', maxidx') = substT T maxidx1;
wenzelm@22584
  1095
      in Cterm {thy_ref = thy_ref', t = t', T = T', sorts = sorts', maxidx = maxidx'} end
wenzelm@22584
  1096
      handle TYPE (msg, _, _) => raise CTERM (msg, [ct]);
wenzelm@22584
  1097
wenzelm@6928
  1098
end;
wenzelm@6928
  1099
clasohm@0
  1100
wenzelm@16601
  1101
(*The trivial implication A ==> A, justified by assume and forall rules.
wenzelm@16601
  1102
  A can contain Vars, not so for assume!*)
wenzelm@16601
  1103
fun trivial (Cterm {thy_ref, t =A, T, maxidx, sorts}) =
wenzelm@16601
  1104
  if T <> propT then
wenzelm@16601
  1105
    raise THM ("trivial: the term must have type prop", 0, [])
wenzelm@16601
  1106
  else
wenzelm@28321
  1107
    Thm (deriv_rule0 (Pt.AbsP ("H", NONE, Pt.PBound 0)),
wenzelm@28321
  1108
     {thy_ref = thy_ref,
wenzelm@21646
  1109
      tags = [],
wenzelm@16601
  1110
      maxidx = maxidx,
wenzelm@16601
  1111
      shyps = sorts,
wenzelm@16601
  1112
      hyps = [],
wenzelm@16601
  1113
      tpairs = [],
wenzelm@28321
  1114
      prop = Logic.mk_implies (A, A)});
clasohm@0
  1115
wenzelm@31944
  1116
(*Axiom-scheme reflecting signature contents
wenzelm@31944
  1117
        T :: c
wenzelm@31944
  1118
  -------------------
wenzelm@31944
  1119
  OFCLASS(T, c_class)
wenzelm@31944
  1120
*)
wenzelm@31944
  1121
fun of_class (cT, raw_c) =
wenzelm@24143
  1122
  let
wenzelm@31944
  1123
    val Ctyp {thy_ref, T, ...} = cT;
wenzelm@31944
  1124
    val thy = Theory.deref thy_ref;
wenzelm@31903
  1125
    val c = Sign.certify_class thy raw_c;
wenzelm@31944
  1126
    val Cterm {t = prop, maxidx, sorts, ...} = cterm_of thy (Logic.mk_of_class (T, c));
wenzelm@399
  1127
  in
wenzelm@31944
  1128
    if Sign.of_sort thy (T, [c]) then
wenzelm@31944
  1129
      Thm (deriv_rule0 (Pt.OfClass (T, c)),
wenzelm@31944
  1130
       {thy_ref = Theory.check_thy thy,
wenzelm@31944
  1131
        tags = [],
wenzelm@31944
  1132
        maxidx = maxidx,
wenzelm@31944
  1133
        shyps = sorts,
wenzelm@31944
  1134
        hyps = [],
wenzelm@31944
  1135
        tpairs = [],
wenzelm@31944
  1136
        prop = prop})
wenzelm@31944
  1137
    else raise THM ("of_class: type not of class " ^ Syntax.string_of_sort_global thy [c], 0, [])
wenzelm@399
  1138
  end;
wenzelm@399
  1139
wenzelm@19505
  1140
(*Internalize sort constraints of type variable*)
wenzelm@19505
  1141
fun unconstrainT
wenzelm@19505
  1142
    (Ctyp {thy_ref = thy_ref1, T, ...})
wenzelm@28321
  1143
    (th as Thm (_, {thy_ref = thy_ref2, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@19505
  1144
  let
wenzelm@19505
  1145
    val ((x, i), S) = Term.dest_TVar T handle TYPE _ =>
wenzelm@19505
  1146
      raise THM ("unconstrainT: not a type variable", 0, [th]);
wenzelm@19505
  1147
    val T' = TVar ((x, i), []);
wenzelm@20548
  1148
    val unconstrain = Term.map_types (Term.map_atyps (fn U => if U = T then T' else U));
wenzelm@31943
  1149
    val constraints = map (curry Logic.mk_of_class T') S;
wenzelm@19505
  1150
  in
wenzelm@28321
  1151
    Thm (deriv_rule0 (Pt.PAxm ("Pure.unconstrainT", prop, SOME [])),
wenzelm@28321
  1152
     {thy_ref = Theory.merge_refs (thy_ref1, thy_ref2),
wenzelm@21646
  1153
      tags = [],
wenzelm@19505
  1154
      maxidx = Int.max (maxidx, i),
wenzelm@19505
  1155
      shyps = Sorts.remove_sort S shyps,
wenzelm@19505
  1156
      hyps = hyps,
wenzelm@19505
  1157
      tpairs = map (pairself unconstrain) tpairs,
wenzelm@28321
  1158
      prop = Logic.list_implies (constraints, unconstrain prop)})
wenzelm@19505
  1159
  end;
wenzelm@399
  1160
wenzelm@6786
  1161
(* Replace all TFrees not fixed or in the hyps by new TVars *)
wenzelm@28321
  1162
fun varifyT' fixed (Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@12500
  1163
  let
wenzelm@29272
  1164
    val tfrees = fold Term.add_tfrees hyps fixed;
berghofe@13658
  1165
    val prop1 = attach_tpairs tpairs prop;
haftmann@21116
  1166
    val (al, prop2) = Type.varify tfrees prop1;
wenzelm@16601
  1167
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1168
  in
wenzelm@28321
  1169
    (al, Thm (deriv_rule1 (Pt.varify_proof prop tfrees) der,
wenzelm@28321
  1170
     {thy_ref = thy_ref,
wenzelm@21646
  1171
      tags = [],
wenzelm@16601
  1172
      maxidx = Int.max (0, maxidx),
wenzelm@16601
  1173
      shyps = shyps,
wenzelm@16601
  1174
      hyps = hyps,
wenzelm@16601
  1175
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@28321
  1176
      prop = prop3}))
wenzelm@28321
  1177
  end;
wenzelm@28321
  1178
wenzelm@28321
  1179
val varifyT = #2 o varifyT' [];
wenzelm@28321
  1180
wenzelm@28321
  1181
(* Replace all TVars by new TFrees *)
wenzelm@28321
  1182
fun freezeT (Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@28321
  1183
  let
wenzelm@28321
  1184
    val prop1 = attach_tpairs tpairs prop;
wenzelm@28321
  1185
    val prop2 = Type.freeze prop1;
wenzelm@28321
  1186
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@28321
  1187
  in
wenzelm@28321
  1188
    Thm (deriv_rule1 (Pt.freezeT prop1) der,
wenzelm@28321
  1189
     {thy_ref = thy_ref,
wenzelm@28321
  1190
      tags = [],
wenzelm@28321
  1191
      maxidx = maxidx_of_term prop2,
wenzelm@28321
  1192
      shyps = shyps,
wenzelm@28321
  1193
      hyps = hyps,
wenzelm@28321
  1194
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@18127
  1195
      prop = prop3})
clasohm@0
  1196
  end;
clasohm@0
  1197
clasohm@0
  1198
clasohm@0
  1199
(*** Inference rules for tactics ***)
clasohm@0
  1200
clasohm@0
  1201
(*Destruct proof state into constraints, other goals, goal(i), rest *)
wenzelm@28321
  1202
fun dest_state (state as Thm (_, {prop,tpairs,...}), i) =
berghofe@13658
  1203
  (case  Logic.strip_prems(i, [], prop) of
berghofe@13658
  1204
      (B::rBs, C) => (tpairs, rev rBs, B, C)
berghofe@13658
  1205
    | _ => raise THM("dest_state", i, [state]))
clasohm@0
  1206
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1207
lcp@309
  1208
(*Increment variables and parameters of orule as required for
wenzelm@18035
  1209
  resolution with a goal.*)
wenzelm@18035
  1210
fun lift_rule goal orule =
wenzelm@16601
  1211
  let
wenzelm@18035
  1212
    val Cterm {t = gprop, T, maxidx = gmax, sorts, ...} = goal;
wenzelm@18035
  1213
    val inc = gmax + 1;
wenzelm@18035
  1214
    val lift_abs = Logic.lift_abs inc gprop;
wenzelm@18035
  1215
    val lift_all = Logic.lift_all inc gprop;
wenzelm@28321
  1216
    val Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...}) = orule;
wenzelm@16601
  1217
    val (As, B) = Logic.strip_horn prop;
wenzelm@16601
  1218
  in
wenzelm@18035
  1219
    if T <> propT then raise THM ("lift_rule: the term must have type prop", 0, [])
wenzelm@18035
  1220
    else
wenzelm@28321
  1221
      Thm (deriv_rule1 (Pt.lift_proof gprop inc prop) der,
wenzelm@28321
  1222
       {thy_ref = merge_thys1 goal orule,
wenzelm@21646
  1223
        tags = [],
wenzelm@18035
  1224
        maxidx = maxidx + inc,
wenzelm@18035
  1225
        shyps = Sorts.union shyps sorts,  (*sic!*)
wenzelm@18035
  1226
        hyps = hyps,
wenzelm@18035
  1227
        tpairs = map (pairself lift_abs) tpairs,
wenzelm@28321
  1228
        prop = Logic.list_implies (map lift_all As, lift_all B)})
clasohm@0
  1229
  end;
clasohm@0
  1230
wenzelm@28321
  1231
fun incr_indexes i (thm as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
  1232
  if i < 0 then raise THM ("negative increment", 0, [thm])
wenzelm@16601
  1233
  else if i = 0 then thm
wenzelm@16601
  1234
  else
wenzelm@32027
  1235
    Thm (deriv_rule1 (Pt.incr_indexes i) der,
wenzelm@28321
  1236
     {thy_ref = thy_ref,
wenzelm@21646
  1237
      tags = [],
wenzelm@16601
  1238
      maxidx = maxidx + i,
wenzelm@16601
  1239
      shyps = shyps,
wenzelm@16601
  1240
      hyps = hyps,
wenzelm@16601
  1241
      tpairs = map (pairself (Logic.incr_indexes ([], i))) tpairs,
wenzelm@28321
  1242
      prop = Logic.incr_indexes ([], i) prop});
berghofe@10416
  1243
clasohm@0
  1244
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1245
fun assumption i state =
wenzelm@16601
  1246
  let
wenzelm@28321
  1247
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16656
  1248
    val thy = Theory.deref thy_ref;
wenzelm@16601
  1249
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@32032
  1250
    fun newth n (env, tpairs) =
wenzelm@28321
  1251
      Thm (deriv_rule1
wenzelm@16601
  1252
          ((if Envir.is_empty env then I else (Pt.norm_proof' env)) o
wenzelm@16601
  1253
            Pt.assumption_proof Bs Bi n) der,
wenzelm@28321
  1254
       {tags = [],
wenzelm@32032
  1255
        maxidx = Envir.maxidx_of env,
wenzelm@26640
  1256
        shyps = Envir.insert_sorts env shyps,
wenzelm@16601
  1257
        hyps = hyps,
wenzelm@16601
  1258
        tpairs =
wenzelm@16601
  1259
          if Envir.is_empty env then tpairs
wenzelm@16601
  1260
          else map (pairself (Envir.norm_term env)) tpairs,
wenzelm@16601
  1261
        prop =
wenzelm@16601
  1262
          if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@16601
  1263
            Logic.list_implies (Bs, C)
wenzelm@16601
  1264
          else (*normalize the new rule fully*)
wenzelm@24143
  1265
            Envir.norm_term env (Logic.list_implies (Bs, C)),
wenzelm@28321
  1266
        thy_ref = Theory.check_thy thy});
wenzelm@30554
  1267
wenzelm@30556
  1268
    val (close, asms, concl) = Logic.assum_problems (~1, Bi);
wenzelm@30556
  1269
    val concl' = close concl;
wenzelm@16601
  1270
    fun addprfs [] _ = Seq.empty
wenzelm@30556
  1271
      | addprfs (asm :: rest) n = Seq.make (fn () => Seq.pull
wenzelm@16601
  1272
          (Seq.mapp (newth n)
wenzelm@30556
  1273
            (if Term.could_unify (asm, concl) then
wenzelm@30556
  1274
              (Unify.unifiers (thy, Envir.empty maxidx, (close asm, concl') :: tpairs))
wenzelm@30554
  1275
             else Seq.empty)
wenzelm@30554
  1276
            (addprfs rest (n + 1))))
wenzelm@30556
  1277
  in addprfs asms 1 end;
clasohm@0
  1278
wenzelm@250
  1279
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1280
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1281
fun eq_assumption i state =
wenzelm@16601
  1282
  let
wenzelm@28321
  1283
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16601
  1284
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@30556
  1285
    val (_, asms, concl) = Logic.assum_problems (~1, Bi);
wenzelm@16601
  1286
  in
wenzelm@30556
  1287
    (case find_index (fn asm => Pattern.aeconv (asm, concl)) asms of
wenzelm@16601
  1288
      ~1 => raise THM ("eq_assumption", 0, [state])
wenzelm@16601
  1289
    | n =>
wenzelm@28321
  1290
        Thm (deriv_rule1 (Pt.assumption_proof Bs Bi (n + 1)) der,
wenzelm@28321
  1291
         {thy_ref = thy_ref,
wenzelm@21646
  1292
          tags = [],
wenzelm@16601
  1293
          maxidx = maxidx,
wenzelm@16601
  1294
          shyps = shyps,
wenzelm@16601
  1295
          hyps = hyps,
wenzelm@16601
  1296
          tpairs = tpairs,
wenzelm@28321
  1297
          prop = Logic.list_implies (Bs, C)}))
clasohm@0
  1298
  end;
clasohm@0
  1299
clasohm@0
  1300
paulson@2671
  1301
(*For rotate_tac: fast rotation of assumptions of subgoal i*)
paulson@2671
  1302
fun rotate_rule k i state =
wenzelm@16601
  1303
  let
wenzelm@28321
  1304
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16601
  1305
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1306
    val params = Term.strip_all_vars Bi
wenzelm@16601
  1307
    and rest   = Term.strip_all_body Bi;
wenzelm@16601
  1308
    val asms   = Logic.strip_imp_prems rest
wenzelm@16601
  1309
    and concl  = Logic.strip_imp_concl rest;
wenzelm@16601
  1310
    val n = length asms;
wenzelm@16601
  1311
    val m = if k < 0 then n + k else k;
wenzelm@16601
  1312
    val Bi' =
wenzelm@16601
  1313
      if 0 = m orelse m = n then Bi
wenzelm@16601
  1314
      else if 0 < m andalso m < n then
wenzelm@19012
  1315
        let val (ps, qs) = chop m asms
wenzelm@16601
  1316
        in list_all (params, Logic.list_implies (qs @ ps, concl)) end
wenzelm@16601
  1317
      else raise THM ("rotate_rule", k, [state]);
wenzelm@16601
  1318
  in
wenzelm@28321
  1319
    Thm (deriv_rule1 (Pt.rotate_proof Bs Bi m) der,
wenzelm@28321
  1320
     {thy_ref = thy_ref,
wenzelm@21646
  1321
      tags = [],
wenzelm@16601
  1322
      maxidx = maxidx,
wenzelm@16601
  1323
      shyps = shyps,
wenzelm@16601
  1324
      hyps = hyps,
wenzelm@16601
  1325
      tpairs = tpairs,
wenzelm@28321
  1326
      prop = Logic.list_implies (Bs @ [Bi'], C)})
paulson@2671
  1327
  end;
paulson@2671
  1328
paulson@2671
  1329
paulson@7248
  1330
(*Rotates a rule's premises to the left by k, leaving the first j premises
paulson@7248
  1331
  unchanged.  Does nothing if k=0 or if k equals n-j, where n is the
wenzelm@16656
  1332
  number of premises.  Useful with etac and underlies defer_tac*)
paulson@7248
  1333
fun permute_prems j k rl =
wenzelm@16601
  1334
  let
wenzelm@28321
  1335
    val Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...}) = rl;
wenzelm@16601
  1336
    val prems = Logic.strip_imp_prems prop
wenzelm@16601
  1337
    and concl = Logic.strip_imp_concl prop;
wenzelm@16601
  1338
    val moved_prems = List.drop (prems, j)
wenzelm@16601
  1339
    and fixed_prems = List.take (prems, j)
wenzelm@16601
  1340
      handle Subscript => raise THM ("permute_prems: j", j, [rl]);
wenzelm@16601
  1341
    val n_j = length moved_prems;
wenzelm@16601
  1342
    val m = if k < 0 then n_j + k else k;
wenzelm@16601
  1343
    val prop' =
wenzelm@16601
  1344
      if 0 = m orelse m = n_j then prop
wenzelm@16601
  1345
      else if 0 < m andalso m < n_j then
wenzelm@19012
  1346
        let val (ps, qs) = chop m moved_prems
wenzelm@16601
  1347
        in Logic.list_implies (fixed_prems @ qs @ ps, concl) end
wenzelm@16725
  1348
      else raise THM ("permute_prems: k", k, [rl]);
wenzelm@16601
  1349
  in
wenzelm@28321
  1350
    Thm (deriv_rule1 (Pt.permute_prems_prf prems j m) der,
wenzelm@28321
  1351
     {thy_ref = thy_ref,
wenzelm@21646
  1352
      tags = [],
wenzelm@16601
  1353
      maxidx = maxidx,
wenzelm@16601
  1354
      shyps = shyps,
wenzelm@16601
  1355
      hyps = hyps,
wenzelm@16601
  1356
      tpairs = tpairs,
wenzelm@28321
  1357
      prop = prop'})
paulson@7248
  1358
  end;
paulson@7248
  1359
paulson@7248
  1360
clasohm@0
  1361
(** User renaming of parameters in a subgoal **)
clasohm@0
  1362
clasohm@0
  1363
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1364
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1365
  The names in cs, if distinct, are used for the innermost parameters;
wenzelm@17868
  1366
  preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1367
fun rename_params_rule (cs, i) state =
wenzelm@16601
  1368
  let
wenzelm@28321
  1369
    val Thm (der, {thy_ref, tags, maxidx, shyps, hyps, ...}) = state;
wenzelm@16601
  1370
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1371
    val iparams = map #1 (Logic.strip_params Bi);
wenzelm@16601
  1372
    val short = length iparams - length cs;
wenzelm@16601
  1373
    val newnames =
wenzelm@16601
  1374
      if short < 0 then error "More names than abstractions!"
wenzelm@20071
  1375
      else Name.variant_list cs (Library.take (short, iparams)) @ cs;
wenzelm@20330
  1376
    val freenames = Term.fold_aterms (fn Free (x, _) => insert (op =) x | _ => I) Bi [];
wenzelm@16601
  1377
    val newBi = Logic.list_rename_params (newnames, Bi);
wenzelm@250
  1378
  in
wenzelm@21182
  1379
    (case duplicates (op =) cs of
wenzelm@21182
  1380
      a :: _ => (warning ("Can't rename.  Bound variables not distinct: " ^ a); state)
wenzelm@21182
  1381
    | [] =>
wenzelm@16601
  1382
      (case cs inter_string freenames of
wenzelm@16601
  1383
        a :: _ => (warning ("Can't rename.  Bound/Free variable clash: " ^ a); state)
wenzelm@16601
  1384
      | [] =>
wenzelm@28321
  1385
        Thm (der,
wenzelm@28321
  1386
         {thy_ref = thy_ref,
wenzelm@21646
  1387
          tags = tags,
wenzelm@16601
  1388
          maxidx = maxidx,
wenzelm@16601
  1389
          shyps = shyps,
wenzelm@16601
  1390
          hyps = hyps,
wenzelm@16601
  1391
          tpairs = tpairs,
wenzelm@28321
  1392
          prop = Logic.list_implies (Bs @ [newBi], C)})))
clasohm@0
  1393
  end;
clasohm@0
  1394
wenzelm@12982
  1395
clasohm@0
  1396
(*** Preservation of bound variable names ***)
clasohm@0
  1397
wenzelm@28321
  1398
fun rename_boundvars pat obj (thm as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@12982
  1399
  (case Term.rename_abs pat obj prop of
skalberg@15531
  1400
    NONE => thm
wenzelm@28321
  1401
  | SOME prop' => Thm (der,
wenzelm@16425
  1402
      {thy_ref = thy_ref,
wenzelm@21646
  1403
       tags = tags,
wenzelm@12982
  1404
       maxidx = maxidx,
wenzelm@12982
  1405
       hyps = hyps,
wenzelm@12982
  1406
       shyps = shyps,
berghofe@13658
  1407
       tpairs = tpairs,
wenzelm@28321
  1408
       prop = prop'}));
berghofe@10416
  1409
clasohm@0
  1410
wenzelm@16656
  1411
(* strip_apply f (A, B) strips off all assumptions/parameters from A
clasohm@0
  1412
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
  1413
fun strip_apply f =
clasohm@0
  1414
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@27336
  1415
                Const("==>",_)$ _  $ B2) = Logic.mk_implies (A1, strip(B1,B2))
wenzelm@250
  1416
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
  1417
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
  1418
        | strip(A,_) = f A
clasohm@0
  1419
  in strip end;
clasohm@0
  1420
clasohm@0
  1421
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1422
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1423
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1424
fun rename_bvs([],_,_,_) = I
clasohm@0
  1425
  | rename_bvs(al,dpairs,tpairs,B) =
wenzelm@20330
  1426
      let
wenzelm@20330
  1427
        val add_var = fold_aterms (fn Var ((x, _), _) => insert (op =) x | _ => I);
wenzelm@20330
  1428
        val vids = []
wenzelm@20330
  1429
          |> fold (add_var o fst) dpairs
wenzelm@20330
  1430
          |> fold (add_var o fst) tpairs
wenzelm@20330
  1431
          |> fold (add_var o snd) tpairs;
wenzelm@250
  1432
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1433
        fun rename(t as Var((x,i),T)) =
wenzelm@20330
  1434
              (case AList.lookup (op =) al x of
wenzelm@20330
  1435
                SOME y =>
wenzelm@20330
  1436
                  if member (op =) vids x orelse member (op =) vids y then t
wenzelm@20330
  1437
                  else Var((y,i),T)
wenzelm@20330
  1438
              | NONE=> t)
clasohm@0
  1439
          | rename(Abs(x,T,t)) =
wenzelm@18944
  1440
              Abs (the_default x (AList.lookup (op =) al x), T, rename t)
clasohm@0
  1441
          | rename(f$t) = rename f $ rename t
clasohm@0
  1442
          | rename(t) = t;
wenzelm@250
  1443
        fun strip_ren Ai = strip_apply rename (Ai,B)
wenzelm@20330
  1444
      in strip_ren end;
clasohm@0
  1445
clasohm@0
  1446
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
  1447
fun rename_bvars(dpairs, tpairs, B) =
wenzelm@23178
  1448
        rename_bvs(List.foldr Term.match_bvars [] dpairs, dpairs, tpairs, B);
clasohm@0
  1449
clasohm@0
  1450
clasohm@0
  1451
(*** RESOLUTION ***)
clasohm@0
  1452
lcp@721
  1453
(** Lifting optimizations **)
lcp@721
  1454
clasohm@0
  1455
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
  1456
  identical because of lifting*)
wenzelm@250
  1457
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
  1458
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
  1459
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
  1460
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
  1461
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
  1462
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
  1463
  | strip_assums2 BB = BB;
clasohm@0
  1464
clasohm@0
  1465
lcp@721
  1466
(*Faster normalization: skip assumptions that were lifted over*)
lcp@721
  1467
fun norm_term_skip env 0 t = Envir.norm_term env t
wenzelm@32032
  1468
  | norm_term_skip env n (Const ("all", _) $ Abs (a, T, t)) =
wenzelm@32032
  1469
      let
wenzelm@32035
  1470
        val T' = Envir.subst_type (Envir.type_env env) T
wenzelm@32032
  1471
        (*Must instantiate types of parameters because they are flattened;
wenzelm@32032
  1472
          this could be a NEW parameter*)
wenzelm@32032
  1473
      in Term.all T' $ Abs (a, T', norm_term_skip env n t) end
wenzelm@32032
  1474
  | norm_term_skip env n (Const ("==>", _) $ A $ B) =
wenzelm@32032
  1475
      Logic.mk_implies (A, norm_term_skip env (n - 1) B)
wenzelm@32032
  1476
  | norm_term_skip env n t = error "norm_term_skip: too few assumptions??";
lcp@721
  1477
lcp@721
  1478
clasohm@0
  1479
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
  1480
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
  1481
  If match then forbid instantiations in proof state
clasohm@0
  1482
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
  1483
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
  1484
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
  1485
  Curried so that resolution calls dest_state only once.
clasohm@0
  1486
*)
wenzelm@4270
  1487
local exception COMPOSE
clasohm@0
  1488
in
wenzelm@18486
  1489
fun bicompose_aux flatten match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
  1490
                        (eres_flg, orule, nsubgoal) =
wenzelm@28321
  1491
 let val Thm (sder, {maxidx=smax, shyps=sshyps, hyps=shyps, ...}) = state
wenzelm@28321
  1492
     and Thm (rder, {maxidx=rmax, shyps=rshyps, hyps=rhyps,
wenzelm@28321
  1493
             tpairs=rtpairs, prop=rprop,...}) = orule
paulson@1529
  1494
         (*How many hyps to skip over during normalization*)
wenzelm@21576
  1495
     and nlift = Logic.count_prems (strip_all_body Bi) + (if eres_flg then ~1 else 0)
wenzelm@24143
  1496
     val thy = Theory.deref (merge_thys2 state orule);
clasohm@0
  1497
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
wenzelm@32032
  1498
     fun addth A (As, oldAs, rder', n) ((env, tpairs), thq) =
wenzelm@250
  1499
       let val normt = Envir.norm_term env;
wenzelm@250
  1500
           (*perform minimal copying here by examining env*)
berghofe@13658
  1501
           val (ntpairs, normp) =
berghofe@13658
  1502
             if Envir.is_empty env then (tpairs, (Bs @ As, C))
wenzelm@250
  1503
             else
wenzelm@250
  1504
             let val ntps = map (pairself normt) tpairs
wenzelm@19861
  1505
             in if Envir.above env smax then
wenzelm@1238
  1506
                  (*no assignments in state; normalize the rule only*)
wenzelm@1238
  1507
                  if lifted
berghofe@13658
  1508
                  then (ntps, (Bs @ map (norm_term_skip env nlift) As, C))
berghofe@13658
  1509
                  else (ntps, (Bs @ map normt As, C))
paulson@1529
  1510
                else if match then raise COMPOSE
wenzelm@250
  1511
                else (*normalize the new rule fully*)
berghofe@13658
  1512
                  (ntps, (map normt (Bs @ As), normt C))
wenzelm@250
  1513
             end
wenzelm@16601
  1514
           val th =
wenzelm@28321
  1515
             Thm (deriv_rule2
berghofe@11518
  1516
                   ((if Envir.is_empty env then I
wenzelm@19861
  1517
                     else if Envir.above env smax then
berghofe@11518
  1518
                       (fn f => fn der => f (Pt.norm_proof' env der))
berghofe@11518
  1519
                     else
berghofe@11518
  1520
                       curry op oo (Pt.norm_proof' env))
berghofe@23296
  1521
                    (Pt.bicompose_proof flatten Bs oldAs As A n (nlift+1))) rder' sder,
wenzelm@28321
  1522
                {tags = [],
wenzelm@32032
  1523
                 maxidx = Envir.maxidx_of env,
wenzelm@26640
  1524
                 shyps = Envir.insert_sorts env (Sorts.union rshyps sshyps),
wenzelm@16601
  1525
                 hyps = union_hyps rhyps shyps,
berghofe@13658
  1526
                 tpairs = ntpairs,
wenzelm@24143
  1527
                 prop = Logic.list_implies normp,
wenzelm@28321
  1528
                 thy_ref = Theory.check_thy thy})
wenzelm@19475
  1529
        in  Seq.cons th thq  end  handle COMPOSE => thq;
berghofe@13658
  1530
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rprop)
clasohm@0
  1531
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
  1532
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
  1533
     fun newAs(As0, n, dpairs, tpairs) =
berghofe@11518
  1534
       let val (As1, rder') =
berghofe@25939
  1535
         if not lifted then (As0, rder)
berghofe@11518
  1536
         else (map (rename_bvars(dpairs,tpairs,B)) As0,
wenzelm@28321
  1537
           deriv_rule1 (Pt.map_proof_terms
berghofe@11518
  1538
             (rename_bvars (dpairs, tpairs, Bound 0)) I) rder);
wenzelm@18486
  1539
       in (map (if flatten then (Logic.flatten_params n) else I) As1, As1, rder', n)
wenzelm@250
  1540
          handle TERM _ =>
wenzelm@250
  1541
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
  1542
       end;
paulson@2147
  1543
     val env = Envir.empty(Int.max(rmax,smax));
clasohm@0
  1544
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
  1545
     val dpairs = BBi :: (rtpairs@stpairs);
wenzelm@30554
  1546
wenzelm@30554
  1547
     (*elim-resolution: try each assumption in turn*)
wenzelm@30554
  1548
     fun eres [] = raise THM ("bicompose: no premises", 0, [orule, state])
wenzelm@30554
  1549
       | eres (A1 :: As) =
wenzelm@30554
  1550
           let
wenzelm@30554
  1551
             val A = SOME A1;
wenzelm@30556
  1552
             val (close, asms, concl) = Logic.assum_problems (nlift + 1, A1);
wenzelm@30556
  1553
             val concl' = close concl;
wenzelm@30554
  1554
             fun tryasms [] _ = Seq.empty
wenzelm@30556
  1555
               | tryasms (asm :: rest) n =
wenzelm@30556
  1556
                   if Term.could_unify (asm, concl) then
wenzelm@30556
  1557
                     let val asm' = close asm in
wenzelm@30556
  1558
                       (case Seq.pull (Unify.unifiers (thy, env, (asm', concl') :: dpairs)) of
wenzelm@30554
  1559
                         NONE => tryasms rest (n + 1)
wenzelm@30554
  1560
                       | cell as SOME ((_, tpairs), _) =>
wenzelm@30556
  1561
                           Seq.it_right (addth A (newAs (As, n, [BBi, (concl', asm')], tpairs)))
wenzelm@30554
  1562
                             (Seq.make (fn () => cell),
wenzelm@30554
  1563
                              Seq.make (fn () => Seq.pull (tryasms rest (n + 1)))))
wenzelm@30554
  1564
                     end
wenzelm@30554
  1565
                   else tryasms rest (n + 1);
wenzelm@30556
  1566
           in tryasms asms 1 end;
wenzelm@30554
  1567
clasohm@0
  1568
     (*ordinary resolution*)
wenzelm@30554
  1569
     fun res () =
wenzelm@30554
  1570
       (case Seq.pull (Unify.unifiers (thy, env, dpairs)) of
wenzelm@30554
  1571
         NONE => Seq.empty
wenzelm@30554
  1572
       | cell as SOME ((_, tpairs), _) =>
wenzelm@30554
  1573
           Seq.it_right (addth NONE (newAs (rev rAs, 0, [BBi], tpairs)))
wenzelm@30554
  1574
             (Seq.make (fn () => cell), Seq.empty));
wenzelm@30554
  1575
 in
wenzelm@30554
  1576
   if eres_flg then eres (rev rAs) else res ()
clasohm@0
  1577
 end;
wenzelm@7528
  1578
end;
clasohm@0
  1579
wenzelm@18501
  1580
fun compose_no_flatten match (orule, nsubgoal) i state =
wenzelm@18501
  1581
  bicompose_aux false match (state, dest_state (state, i), false) (false, orule, nsubgoal);
clasohm@0
  1582
wenzelm@18501
  1583
fun bicompose match arg i state =
wenzelm@18501
  1584
  bicompose_aux true match (state, dest_state (state,i), false) arg;
clasohm@0
  1585
clasohm@0
  1586
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1587
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1588
fun could_bires (Hs, B, eres_flg, rule) =
wenzelm@29269
  1589
    let fun could_reshyp (A1::_) = exists (fn H => Term.could_unify (A1, H)) Hs
wenzelm@250
  1590
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@29269
  1591
    in  Term.could_unify(concl_of rule, B) andalso
wenzelm@250
  1592
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1593
    end;
clasohm@0
  1594
clasohm@0
  1595
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1596
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1597
fun biresolution match brules i state =
wenzelm@18035
  1598
    let val (stpairs, Bs, Bi, C) = dest_state(state,i);
wenzelm@18145
  1599
        val lift = lift_rule (cprem_of state i);
wenzelm@250
  1600
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1601
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@22573
  1602
        val compose = bicompose_aux true match (state, (stpairs, Bs, Bi, C), true);
wenzelm@4270
  1603
        fun res [] = Seq.empty
wenzelm@250
  1604
          | res ((eres_flg, rule)::brules) =
nipkow@13642
  1605
              if !Pattern.trace_unify_fail orelse
nipkow@13642
  1606
                 could_bires (Hs, B, eres_flg, rule)
wenzelm@4270
  1607
              then Seq.make (*delay processing remainder till needed*)
wenzelm@22573
  1608
                  (fn()=> SOME(compose (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1609
                               res brules))
wenzelm@250
  1610
              else res brules
wenzelm@4270
  1611
    in  Seq.flat (res brules)  end;
clasohm@0
  1612
clasohm@0
  1613
wenzelm@28321
  1614
wenzelm@28978
  1615
(*** Future theorems -- proofs with promises ***)
wenzelm@28356
  1616
wenzelm@28446
  1617
(* future rule *)
wenzelm@28330
  1618
wenzelm@28446
  1619
fun future_result i orig_thy orig_shyps orig_prop raw_thm =
wenzelm@28378
  1620
  let
wenzelm@28378
  1621
    val _ = Theory.check_thy orig_thy;
wenzelm@28378
  1622
    val thm = strip_shyps (transfer orig_thy raw_thm);
wenzelm@28378
  1623
    val _ = Theory.check_thy orig_thy;
wenzelm@28446
  1624
    fun err msg = raise THM ("future_result: " ^ msg, 0, [thm]);
wenzelm@28378
  1625
wenzelm@28996
  1626
    val Thm (Deriv {max_promise, ...}, {shyps, hyps, tpairs, prop, ...}) = thm;
wenzelm@28378
  1627
    val _ = prop aconv orig_prop orelse err "bad prop";
wenzelm@28378
  1628
    val _ = null tpairs orelse err "bad tpairs";
wenzelm@28378
  1629
    val _ = null hyps orelse err "bad hyps";
wenzelm@28378
  1630
    val _ = Sorts.subset (shyps, orig_shyps) orelse err "bad shyps";
wenzelm@28996
  1631
    val _ = max_promise < i orelse err "bad dependencies";
wenzelm@28378
  1632
  in thm end;
wenzelm@28378
  1633
wenzelm@28978
  1634
fun future future_thm ct =
wenzelm@28321
  1635
  let
wenzelm@28624
  1636
    val Cterm {thy_ref = thy_ref, t = prop, T, maxidx, sorts} = ct;
wenzelm@28321
  1637
    val thy = Context.reject_draft (Theory.deref thy_ref);
wenzelm@28446
  1638
    val _ = T <> propT andalso raise CTERM ("future: prop expected", [ct]);
wenzelm@28378
  1639
wenzelm@28389
  1640
    val i = serial ();
wenzelm@29436
  1641
    val future = future_thm |> Future.map (future_result i thy sorts prop);
wenzelm@28829
  1642
    val promise = (i, future);
wenzelm@28321
  1643
  in
wenzelm@28996
  1644
    Thm (make_deriv i [promise] [promise] [] [] (Pt.promise_proof thy i prop),
wenzelm@28321
  1645
     {thy_ref = thy_ref,
wenzelm@28321
  1646
      tags = [],
wenzelm@28321
  1647
      maxidx = maxidx,
wenzelm@28321
  1648
      shyps = sorts,
wenzelm@28321
  1649
      hyps = [],
wenzelm@28321
  1650
      tpairs = [],
wenzelm@28321
  1651
      prop = prop})
wenzelm@28321
  1652
  end;
wenzelm@28321
  1653
wenzelm@28330
  1654
wenzelm@30713
  1655
(* derivation status *)
wenzelm@30713
  1656
wenzelm@30713
  1657
fun raw_proof_body_of (Thm (Deriv {body, ...}, _)) = body;
wenzelm@30713
  1658
val raw_proof_of = Proofterm.proof_of o raw_proof_body_of;
wenzelm@29432
  1659
wenzelm@29432
  1660
fun pending_groups (Thm (Deriv {open_promises, ...}, _)) =
wenzelm@29432
  1661
  fold (insert Task_Queue.eq_group o Future.group_of o #2) open_promises;
wenzelm@29432
  1662
wenzelm@30713
  1663
fun status_of (Thm (Deriv {promises, body, ...}, _)) =
wenzelm@30713
  1664
  let
wenzelm@30713
  1665
    val ps = map (Future.peek o snd) promises;
wenzelm@30713
  1666
    val bodies = body ::
wenzelm@30713
  1667
      map_filter (fn SOME (Exn.Result th) => SOME (raw_proof_body_of th) | _ => NONE) ps;
wenzelm@30713
  1668
    val {oracle, unfinished, failed} = Pt.status_of bodies;
wenzelm@30713
  1669
  in
wenzelm@30713
  1670
   {oracle = oracle,
wenzelm@30713
  1671
    unfinished = unfinished orelse exists is_none ps,
wenzelm@30713
  1672
    failed = failed orelse exists (fn SOME (Exn.Exn _) => true | _ => false) ps}
wenzelm@30713
  1673
  end;
wenzelm@30713
  1674
wenzelm@29432
  1675
wenzelm@29432
  1676
(* fulfilled proofs *)
wenzelm@28330
  1677
wenzelm@28996
  1678
fun proof_body_of (Thm (Deriv {open_promises, promises, body, ...}, {thy_ref, ...})) =
wenzelm@28330
  1679
  let
wenzelm@28996
  1680
    val _ = Exn.release_all (map (Future.join_result o #2) (rev open_promises));
wenzelm@30717
  1681
    val ps = map (apsnd (raw_proof_body_of o Future.join)) promises;
wenzelm@28829
  1682
  in Pt.fulfill_proof (Theory.deref thy_ref) ps body end;
wenzelm@28804
  1683
wenzelm@28814
  1684
val proof_of = Proofterm.proof_of o proof_body_of;
wenzelm@29003
  1685
val join_proof = ignore o proof_body_of;
wenzelm@28814
  1686
wenzelm@28804
  1687
wenzelm@28804
  1688
(* closed derivations with official name *)
wenzelm@28804
  1689
wenzelm@28804
  1690
fun get_name thm =
wenzelm@28814
  1691
  Pt.get_name (hyps_of thm) (prop_of thm) (raw_proof_of thm);
wenzelm@28330
  1692
wenzelm@28804
  1693
fun put_name name (thm as Thm (der, args)) =
wenzelm@28804
  1694
  let
wenzelm@28996
  1695
    val Deriv {max_promise, open_promises, promises, body, ...} = der;
wenzelm@28804
  1696
    val {thy_ref, hyps, prop, tpairs, ...} = args;
wenzelm@28996
  1697
    val _ = null tpairs orelse raise THM ("put_name: unsolved flex-flex constraints", 0, [thm]);
wenzelm@28804
  1698
wenzelm@30717
  1699
    val ps = map (apsnd (Future.map proof_body_of)) promises;
wenzelm@28804
  1700
    val thy = Theory.deref thy_ref;
wenzelm@28804
  1701
    val (pthm, proof) = Pt.thm_proof thy name hyps prop ps body;
wenzelm@28996
  1702
wenzelm@28996
  1703
    val open_promises' = open_promises |> filter (fn (_, p) =>
wenzelm@28996
  1704
      (case Future.peek p of SOME (Exn.Result _) => false | _ => true));
wenzelm@28996
  1705
    val der' = make_deriv max_promise open_promises' [] [] [pthm] proof;
wenzelm@28804
  1706
    val _ = Theory.check_thy thy;
wenzelm@28804
  1707
  in Thm (der', args) end;
wenzelm@28330
  1708
wenzelm@28321
  1709
wenzelm@28321
  1710
wenzelm@2509
  1711
(*** Oracles ***)
wenzelm@2509
  1712
wenzelm@28290
  1713
(* oracle rule *)
wenzelm@28290
  1714
wenzelm@28290
  1715
fun invoke_oracle thy_ref1 name oracle arg =
wenzelm@28624
  1716
  let val Cterm {thy_ref = thy_ref2, t = prop, T, maxidx, sorts} = oracle arg in
wenzelm@28290
  1717
    if T <> propT then
wenzelm@28290
  1718
      raise THM ("Oracle's result must have type prop: " ^ name, 0, [])
wenzelm@28290
  1719
    else
wenzelm@30717
  1720
      let val (ora, prf) = Pt.oracle_proof name prop in
wenzelm@30717
  1721
        Thm (make_deriv ~1 [] [] [ora] [] prf,
wenzelm@28804
  1722
         {thy_ref = Theory.merge_refs (thy_ref1, thy_ref2),
wenzelm@28804
  1723
          tags = [],
wenzelm@28804
  1724
          maxidx = maxidx,
wenzelm@28804
  1725
          shyps = sorts,
wenzelm@28804
  1726
          hyps = [],
wenzelm@28804
  1727
          tpairs = [],
wenzelm@28804
  1728
          prop = prop})
wenzelm@28804
  1729
      end
wenzelm@3812
  1730
  end;
wenzelm@3812
  1731
wenzelm@28290
  1732
wenzelm@28290
  1733
(* authentic derivation names *)
wenzelm@28290
  1734
wenzelm@28290
  1735
fun err_dup_ora dup = error ("Duplicate oracle: " ^ quote dup);
wenzelm@28290
  1736
wenzelm@28290
  1737
structure Oracles = TheoryDataFun
wenzelm@28290
  1738
(
wenzelm@30288
  1739
  type T = serial NameSpace.table;
wenzelm@28290
  1740
  val empty = NameSpace.empty_table;
wenzelm@28290
  1741
  val copy = I;
wenzelm@28290
  1742
  val extend = I;
wenzelm@29288
  1743
  fun merge _ oracles : T = NameSpace.merge_tables (op =) oracles
wenzelm@28290
  1744
    handle Symtab.DUP dup => err_dup_ora dup;
wenzelm@28290
  1745
);
wenzelm@28290
  1746
wenzelm@28290
  1747
val extern_oracles = map #1 o NameSpace.extern_table o Oracles.get;
wenzelm@28290
  1748
wenzelm@30288
  1749
fun add_oracle (b, oracle) thy =
wenzelm@28290
  1750
  let
wenzelm@28290
  1751
    val naming = Sign.naming_of thy;
wenzelm@30466
  1752
    val (name, tab') = NameSpace.define naming (b, serial ()) (Oracles.get thy)
wenzelm@30288
  1753
      handle Symtab.DUP _ => err_dup_ora (Binding.str_of b);
wenzelm@30288
  1754
    val thy' = Oracles.put tab' thy;
wenzelm@28290
  1755
  in ((name, invoke_oracle (Theory.check_thy thy') name oracle), thy') end;
wenzelm@28290
  1756
clasohm@0
  1757
end;
paulson@1503
  1758
wenzelm@6089
  1759
structure BasicThm: BASIC_THM = Thm;
wenzelm@6089
  1760
open BasicThm;