src/Pure/thm.ML
author wenzelm
Tue Sep 23 15:48:52 2008 +0200 (2008-09-23)
changeset 28330 7e803c392342
parent 28321 9f4499bf9384
child 28354 c5fe7372ae4e
permissions -rw-r--r--
added dest_deriv, removed external type deriv;
misc tuning of internal deriv;
more substantial promise/fulfill;
promise_ord: reverse order on serial numbers;
removed unused is_named;
get_name: unfinished proof term;
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(*  Title:      Pure/thm.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1994  University of Cambridge
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The 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 list}
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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 list}
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  val crep_cterm: cterm -> {thy_ref: theory_ref, t: term, T: ctyp, maxidx: int, sorts: sort list}
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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 list,
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    hyps: term list,
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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 list,
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    hyps: cterm list,
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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 extra_shyps: thm -> sort list
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  val strip_shyps: thm -> thm
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  val get_axiom_i: theory -> string -> thm
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  val get_axiom: theory -> xstring -> thm
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  val def_name: string -> string
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  val def_name_optional: string -> string -> string
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  val get_def: theory -> xstring -> thm
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  val axioms_of: theory -> (string * thm) list
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  (*meta rules*)
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  val assume: cterm -> thm
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  val implies_intr: cterm -> thm -> thm
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  val implies_elim: thm -> thm -> thm
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  val forall_intr: cterm -> thm -> thm
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  val forall_elim: cterm -> thm -> thm
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  val reflexive: cterm -> thm
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  val symmetric: thm -> thm
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  val transitive: thm -> thm -> thm
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  val beta_conversion: bool -> conv
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  val eta_conversion: conv
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  val eta_long_conversion: conv
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  val abstract_rule: string -> cterm -> thm -> thm
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  val combination: thm -> thm -> thm
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  val equal_intr: thm -> thm -> thm
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  val equal_elim: thm -> thm -> thm
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  val flexflex_rule: thm -> thm Seq.seq
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  val generalize: string list * string list -> int -> thm -> thm
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  val instantiate: (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm
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  val instantiate_cterm: (ctyp * ctyp) list * (cterm * cterm) list -> cterm -> cterm
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  val trivial: cterm -> thm
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  val class_triv: theory -> class -> thm
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  val unconstrainT: ctyp -> thm -> thm
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  val dest_state: thm * int -> (term * term) list * term list * term * term
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  val lift_rule: cterm -> thm -> thm
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  val incr_indexes: int -> thm -> thm
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  val assumption: int -> thm -> thm Seq.seq
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  val eq_assumption: int -> thm -> thm
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  val rotate_rule: int -> int -> thm -> thm
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  val permute_prems: int -> int -> thm -> thm
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  val rename_params_rule: string list * int -> thm -> thm
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  val compose_no_flatten: bool -> thm * int -> int -> thm -> thm Seq.seq
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  val bicompose: bool -> bool * thm * int -> int -> thm -> thm Seq.seq
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  val biresolution: bool -> (bool * thm) list -> int -> thm -> thm Seq.seq
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end;
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signature THM =
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sig
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  include BASIC_THM
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  val dest_ctyp: ctyp -> ctyp list
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  val dest_comb: cterm -> cterm * cterm
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  val dest_fun: cterm -> cterm
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  val dest_arg: cterm -> cterm
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  val dest_fun2: cterm -> cterm
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  val dest_arg1: cterm -> cterm
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  val dest_abs: string option -> cterm -> cterm * cterm
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  val adjust_maxidx_cterm: int -> cterm -> cterm
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  val capply: cterm -> cterm -> cterm
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  val cabs: cterm -> cterm -> cterm
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  val dest_deriv: thm ->
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   {oracle: bool,
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    proof: Proofterm.proof,
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    promises: (serial * (thm Future.T * theory * sort list * term)) list}
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  val oracle_of: thm -> bool
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  val major_prem_of: thm -> term
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  val no_prems: thm -> bool
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  val terms_of_tpairs: (term * term) list -> term list
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  val maxidx_of: thm -> int
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  val maxidx_thm: thm -> int -> int
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  val hyps_of: thm -> term list
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  val full_prop_of: thm -> term
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  val get_name: thm -> string
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  val put_name: string -> thm -> thm
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  val get_tags: thm -> Properties.T
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  val map_tags: (Properties.T -> Properties.T) -> thm -> thm
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  val norm_proof: thm -> thm
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  val adjust_maxidx_thm: int -> thm -> thm
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  val rename_boundvars: term -> term -> thm -> thm
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  val match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
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  val first_order_match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
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  val incr_indexes_cterm: int -> cterm -> cterm
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  val varifyT: thm -> thm
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  val varifyT': (string * sort) list -> thm -> ((string * sort) * indexname) list * thm
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  val freezeT: thm -> thm
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  val promise: thm Future.T -> cterm -> thm
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  val fulfill: thm -> thm
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  val proof_of: thm -> Proofterm.proof
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  val extern_oracles: theory -> xstring list
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  val add_oracle: bstring * ('a -> cterm) -> theory -> (string * ('a -> thm)) * theory
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end;
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structure Thm: THM =
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struct
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structure Pt = Proofterm;
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(*** Certified terms and types ***)
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(** certified types **)
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abstype ctyp = Ctyp of
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 {thy_ref: theory_ref,
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  T: typ,
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  maxidx: int,
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  sorts: sort list}
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with
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fun rep_ctyp (Ctyp args) = args;
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fun theory_of_ctyp (Ctyp {thy_ref, ...}) = Theory.deref thy_ref;
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fun typ_of (Ctyp {T, ...}) = T;
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fun ctyp_of thy raw_T =
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  let
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    val T = Sign.certify_typ thy raw_T;
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    val maxidx = Term.maxidx_of_typ T;
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    val sorts = Sorts.insert_typ T [];
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  in Ctyp {thy_ref = Theory.check_thy thy, T = T, maxidx = maxidx, sorts = sorts} end;
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fun dest_ctyp (Ctyp {thy_ref, T = Type (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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abstype cterm = Cterm of
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 {thy_ref: theory_ref,
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  t: term,
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  T: typ,
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  maxidx: int,
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  sorts: sort list}
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with
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exception CTERM of string * cterm list;
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fun rep_cterm (Cterm args) = args;
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fun crep_cterm (Cterm {thy_ref, t, T, maxidx, sorts}) =
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  {thy_ref = thy_ref, t = t, maxidx = maxidx, sorts = sorts,
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    T = Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts}};
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fun theory_of_cterm (Cterm {thy_ref, ...}) = Theory.deref thy_ref;
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fun term_of (Cterm {t, ...}) = t;
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fun ctyp_of_term (Cterm {thy_ref, T, maxidx, sorts, ...}) =
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  Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts};
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fun cterm_of thy tm =
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  let
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    val (t, T, maxidx) = Sign.certify_term thy tm;
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    val sorts = Sorts.insert_term t [];
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  in Cterm {thy_ref = Theory.check_thy thy, t = t, T = T, maxidx = maxidx, sorts = sorts} end;
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fun merge_thys0 (Cterm {thy_ref = r1, 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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wenzelm@22909
   313
local
wenzelm@22909
   314
wenzelm@22909
   315
fun gen_match match
wenzelm@20512
   316
    (ct1 as Cterm {t = t1, sorts = sorts1, ...},
wenzelm@20815
   317
     ct2 as Cterm {t = t2, sorts = sorts2, maxidx = maxidx2, ...}) =
berghofe@10416
   318
  let
wenzelm@24143
   319
    val thy = Theory.deref (merge_thys0 ct1 ct2);
wenzelm@24143
   320
    val (Tinsts, tinsts) = match thy (t1, t2) (Vartab.empty, Vartab.empty);
wenzelm@16601
   321
    val sorts = Sorts.union sorts1 sorts2;
wenzelm@20512
   322
    fun mk_cTinst ((a, i), (S, T)) =
wenzelm@24143
   323
      (Ctyp {T = TVar ((a, i), S), thy_ref = Theory.check_thy thy, maxidx = i, sorts = sorts},
wenzelm@24143
   324
       Ctyp {T = T, thy_ref = Theory.check_thy thy, maxidx = maxidx2, sorts = sorts});
wenzelm@20512
   325
    fun mk_ctinst ((x, i), (T, t)) =
wenzelm@16601
   326
      let val T = Envir.typ_subst_TVars Tinsts T in
wenzelm@24143
   327
        (Cterm {t = Var ((x, i), T), T = T, thy_ref = Theory.check_thy thy,
wenzelm@24143
   328
          maxidx = i, sorts = sorts},
wenzelm@24143
   329
         Cterm {t = t, T = T, thy_ref = Theory.check_thy thy, maxidx = maxidx2, sorts = sorts})
berghofe@10416
   330
      end;
wenzelm@16656
   331
  in (Vartab.fold (cons o mk_cTinst) Tinsts [], Vartab.fold (cons o mk_ctinst) tinsts []) end;
berghofe@10416
   332
wenzelm@22909
   333
in
berghofe@10416
   334
wenzelm@22909
   335
val match = gen_match Pattern.match;
wenzelm@22909
   336
val first_order_match = gen_match Pattern.first_order_match;
wenzelm@22909
   337
wenzelm@22909
   338
end;
berghofe@10416
   339
wenzelm@2509
   340
wenzelm@2509
   341
wenzelm@28321
   342
(*** Derivations and Theorems ***)
lcp@229
   343
wenzelm@28330
   344
abstype thm = Thm of
wenzelm@28330
   345
 deriv *                               (*derivation*)
wenzelm@28330
   346
 {thy_ref: theory_ref,                 (*dynamic reference to theory*)
wenzelm@28330
   347
  tags: Properties.T,                  (*additional annotations/comments*)
wenzelm@28330
   348
  maxidx: int,                         (*maximum index of any Var or TVar*)
wenzelm@28330
   349
  shyps: sort list,                    (*sort hypotheses as ordered list*)
wenzelm@28330
   350
  hyps: term list,                     (*hypotheses as ordered list*)
wenzelm@28330
   351
  tpairs: (term * term) list,          (*flex-flex pairs*)
wenzelm@28330
   352
  prop: term}                          (*conclusion*)
wenzelm@28330
   353
and deriv = Deriv of
wenzelm@28330
   354
 {oracle: bool,                        (*oracle occurrence flag*)
wenzelm@28330
   355
  proof: Pt.proof,                     (*proof term*)
wenzelm@28330
   356
  promises: (serial * promise) list}   (*promised derivations*)
wenzelm@28330
   357
and promise = Promise of
wenzelm@28330
   358
  thm Future.T * theory * sort list * term
wenzelm@22237
   359
with
clasohm@0
   360
wenzelm@23601
   361
type conv = cterm -> thm;
wenzelm@23601
   362
wenzelm@22365
   363
(*attributes subsume any kind of rules or context modifiers*)
wenzelm@22365
   364
type attribute = Context.generic * thm -> Context.generic * thm;
wenzelm@22365
   365
wenzelm@16725
   366
(*errors involving theorems*)
wenzelm@16725
   367
exception THM of string * int * thm list;
berghofe@13658
   368
wenzelm@28321
   369
fun rep_thm (Thm (_, args)) = args;
clasohm@0
   370
wenzelm@28321
   371
fun crep_thm (Thm (_, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@26631
   372
  let fun cterm max t = Cterm {thy_ref = thy_ref, t = t, T = propT, maxidx = max, sorts = shyps} in
wenzelm@28321
   373
   {thy_ref = thy_ref, tags = tags, maxidx = maxidx, shyps = shyps,
wenzelm@16425
   374
    hyps = map (cterm ~1) hyps,
wenzelm@16425
   375
    tpairs = map (pairself (cterm maxidx)) tpairs,
wenzelm@16425
   376
    prop = cterm maxidx prop}
clasohm@1517
   377
  end;
clasohm@1517
   378
wenzelm@16725
   379
fun terms_of_tpairs tpairs = fold_rev (fn (t, u) => cons t o cons u) tpairs [];
wenzelm@16725
   380
wenzelm@16725
   381
fun eq_tpairs ((t, u), (t', u')) = t aconv t' andalso u aconv u';
wenzelm@18944
   382
fun union_tpairs ts us = Library.merge eq_tpairs (ts, us);
wenzelm@16884
   383
val maxidx_tpairs = fold (fn (t, u) => Term.maxidx_term t #> Term.maxidx_term u);
wenzelm@16725
   384
wenzelm@16725
   385
fun attach_tpairs tpairs prop =
wenzelm@16725
   386
  Logic.list_implies (map Logic.mk_equals tpairs, prop);
wenzelm@16725
   387
wenzelm@28321
   388
fun full_prop_of (Thm (_, {tpairs, prop, ...})) = attach_tpairs tpairs prop;
wenzelm@16945
   389
wenzelm@22365
   390
val union_hyps = OrdList.union Term.fast_term_ord;
wenzelm@22365
   391
wenzelm@16945
   392
wenzelm@24143
   393
(* merge theories of cterms/thms -- trivial absorption only *)
wenzelm@16945
   394
wenzelm@28321
   395
fun merge_thys1 (Cterm {thy_ref = r1, ...}) (th as Thm (_, {thy_ref = r2, ...})) =
wenzelm@23601
   396
  Theory.merge_refs (r1, r2);
wenzelm@16945
   397
wenzelm@28321
   398
fun merge_thys2 (th1 as Thm (_, {thy_ref = r1, ...})) (th2 as Thm (_, {thy_ref = r2, ...})) =
wenzelm@23601
   399
  Theory.merge_refs (r1, r2);
wenzelm@16945
   400
clasohm@0
   401
wenzelm@22365
   402
(* basic components *)
wenzelm@16135
   403
wenzelm@28330
   404
fun dest_deriv (Thm (Deriv {oracle, proof, promises}, _)) =
wenzelm@28330
   405
  {oracle = oracle, proof = proof, promises = map (fn (i, Promise args) => (i, args)) promises};
wenzelm@28330
   406
wenzelm@28330
   407
fun oracle_of (Thm (Deriv {oracle, ...}, _)) = oracle;
wenzelm@28330
   408
wenzelm@28321
   409
val theory_of_thm = Theory.deref o #thy_ref o rep_thm;
wenzelm@28321
   410
val maxidx_of = #maxidx o rep_thm;
wenzelm@19910
   411
fun maxidx_thm th i = Int.max (maxidx_of th, i);
wenzelm@28321
   412
val hyps_of = #hyps o rep_thm;
wenzelm@28321
   413
val prop_of = #prop o rep_thm;
wenzelm@28321
   414
val tpairs_of = #tpairs o rep_thm;
clasohm@0
   415
wenzelm@16601
   416
val concl_of = Logic.strip_imp_concl o prop_of;
wenzelm@16601
   417
val prems_of = Logic.strip_imp_prems o prop_of;
wenzelm@21576
   418
val nprems_of = Logic.count_prems o prop_of;
wenzelm@19305
   419
fun no_prems th = nprems_of th = 0;
wenzelm@16601
   420
wenzelm@16601
   421
fun major_prem_of th =
wenzelm@16601
   422
  (case prems_of th of
wenzelm@16601
   423
    prem :: _ => Logic.strip_assums_concl prem
wenzelm@16601
   424
  | [] => raise THM ("major_prem_of: rule with no premises", 0, [th]));
wenzelm@16601
   425
wenzelm@16601
   426
(*the statement of any thm is a cterm*)
wenzelm@28321
   427
fun cprop_of (Thm (_, {thy_ref, maxidx, shyps, prop, ...})) =
wenzelm@16601
   428
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, t = prop, sorts = shyps};
wenzelm@16601
   429
wenzelm@28321
   430
fun cprem_of (th as Thm (_, {thy_ref, maxidx, shyps, prop, ...})) i =
wenzelm@18035
   431
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, sorts = shyps,
wenzelm@18145
   432
    t = Logic.nth_prem (i, prop) handle TERM _ => raise THM ("cprem_of", i, [th])};
wenzelm@18035
   433
wenzelm@16656
   434
(*explicit transfer to a super theory*)
wenzelm@16425
   435
fun transfer thy' thm =
wenzelm@3895
   436
  let
wenzelm@28321
   437
    val Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop}) = thm;
wenzelm@16425
   438
    val thy = Theory.deref thy_ref;
wenzelm@26665
   439
    val _ = Theory.subthy (thy, thy') orelse raise THM ("transfer: not a super theory", 0, [thm]);
wenzelm@26665
   440
    val is_eq = Theory.eq_thy (thy, thy');
wenzelm@24143
   441
    val _ = Theory.check_thy thy;
wenzelm@3895
   442
  in
wenzelm@24143
   443
    if is_eq then thm
wenzelm@16945
   444
    else
wenzelm@28321
   445
      Thm (der,
wenzelm@28321
   446
       {thy_ref = Theory.check_thy thy',
wenzelm@21646
   447
        tags = tags,
wenzelm@16945
   448
        maxidx = maxidx,
wenzelm@16945
   449
        shyps = shyps,
wenzelm@16945
   450
        hyps = hyps,
wenzelm@16945
   451
        tpairs = tpairs,
wenzelm@28321
   452
        prop = prop})
wenzelm@3895
   453
  end;
wenzelm@387
   454
wenzelm@16945
   455
(*explicit weakening: maps |- B to A |- B*)
wenzelm@16945
   456
fun weaken raw_ct th =
wenzelm@16945
   457
  let
wenzelm@20261
   458
    val ct as Cterm {t = A, T, sorts, maxidx = maxidxA, ...} = adjust_maxidx_cterm ~1 raw_ct;
wenzelm@28321
   459
    val Thm (der, {tags, maxidx, shyps, hyps, tpairs, prop, ...}) = th;
wenzelm@16945
   460
  in
wenzelm@16945
   461
    if T <> propT then
wenzelm@16945
   462
      raise THM ("weaken: assumptions must have type prop", 0, [])
wenzelm@16945
   463
    else if maxidxA <> ~1 then
wenzelm@16945
   464
      raise THM ("weaken: assumptions may not contain schematic variables", maxidxA, [])
wenzelm@16945
   465
    else
wenzelm@28321
   466
      Thm (der,
wenzelm@28321
   467
       {thy_ref = merge_thys1 ct th,
wenzelm@21646
   468
        tags = tags,
wenzelm@16945
   469
        maxidx = maxidx,
wenzelm@16945
   470
        shyps = Sorts.union sorts shyps,
wenzelm@22365
   471
        hyps = OrdList.insert Term.fast_term_ord A hyps,
wenzelm@16945
   472
        tpairs = tpairs,
wenzelm@28321
   473
        prop = prop})
wenzelm@16945
   474
  end;
wenzelm@16656
   475
wenzelm@16656
   476
clasohm@0
   477
wenzelm@1238
   478
(** sort contexts of theorems **)
wenzelm@1238
   479
wenzelm@28321
   480
fun present_sorts (Thm (_, {hyps, tpairs, prop, ...})) =
wenzelm@16656
   481
  fold (fn (t, u) => Sorts.insert_term t o Sorts.insert_term u) tpairs
wenzelm@16656
   482
    (Sorts.insert_terms hyps (Sorts.insert_term prop []));
wenzelm@1238
   483
wenzelm@7642
   484
(*remove extra sorts that are non-empty by virtue of type signature information*)
wenzelm@28321
   485
fun strip_shyps (thm as Thm (_, {shyps = [], ...})) = thm
wenzelm@28321
   486
  | strip_shyps (thm as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@7642
   487
      let
wenzelm@16425
   488
        val thy = Theory.deref thy_ref;
wenzelm@26640
   489
        val present = present_sorts thm;
wenzelm@26640
   490
        val extra = Sorts.subtract present shyps;
wenzelm@26640
   491
        val shyps' = Sorts.subtract (map #2 (Sign.witness_sorts thy present extra)) shyps;
wenzelm@7642
   492
      in
wenzelm@28321
   493
        Thm (der, {thy_ref = Theory.check_thy thy, tags = tags, maxidx = maxidx,
wenzelm@28321
   494
          shyps = shyps', hyps = hyps, tpairs = tpairs, prop = prop})
wenzelm@7642
   495
      end;
wenzelm@1238
   496
wenzelm@16656
   497
(*dangling sort constraints of a thm*)
wenzelm@28321
   498
fun extra_shyps (th as Thm (_, {shyps, ...})) = Sorts.subtract (present_sorts th) shyps;
wenzelm@28321
   499
wenzelm@28321
   500
wenzelm@28321
   501
wenzelm@28321
   502
(** derivations **)
wenzelm@28321
   503
wenzelm@28330
   504
(* type deriv *)
wenzelm@28321
   505
wenzelm@28321
   506
fun make_deriv oracle promises proof =
wenzelm@28321
   507
  Deriv {oracle = oracle, promises = promises, proof = proof};
wenzelm@28321
   508
wenzelm@28321
   509
val empty_deriv = make_deriv false [] Pt.min_proof;
wenzelm@28321
   510
wenzelm@28330
   511
wenzelm@28330
   512
(* type promise *)
wenzelm@28321
   513
wenzelm@28330
   514
fun promise_ord ((i, Promise _), (j, Promise _)) = int_ord (j, i);
wenzelm@28330
   515
wenzelm@28330
   516
wenzelm@28330
   517
(* inference rules *)
wenzelm@28321
   518
wenzelm@28321
   519
fun deriv_rule2 f
wenzelm@28321
   520
    (Deriv {oracle = ora1, promises = ps1, proof = prf1})
wenzelm@28321
   521
    (Deriv {oracle = ora2, promises = ps2, proof = prf2}) =
wenzelm@28321
   522
  let
wenzelm@28321
   523
    val ora = ora1 orelse ora2;
wenzelm@28330
   524
    val ps = OrdList.union promise_ord ps1 ps2;
wenzelm@28321
   525
    val prf =
wenzelm@28321
   526
      (case ! Pt.proofs of
wenzelm@28321
   527
        2 => f prf1 prf2
wenzelm@28321
   528
      | 1 => MinProof (([], [], []) |> Pt.mk_min_proof prf1 |> Pt.mk_min_proof prf2)
wenzelm@28321
   529
      | 0 =>
wenzelm@28330
   530
          if ora then MinProof ([], [], [] |> Pt.add_oracles ora1 prf1 |> Pt.add_oracles ora2 prf2)
wenzelm@28321
   531
          else Pt.min_proof
wenzelm@28321
   532
      | i => error ("Illegal level of detail for proof objects: " ^ string_of_int i));
wenzelm@28321
   533
  in make_deriv ora ps prf end;
wenzelm@28321
   534
wenzelm@28321
   535
fun deriv_rule1 f = deriv_rule2 (K f) empty_deriv;
wenzelm@28321
   536
fun deriv_rule0 prf = deriv_rule1 I (make_deriv false [] prf);
wenzelm@28321
   537
wenzelm@1238
   538
wenzelm@1238
   539
paulson@1529
   540
(** Axioms **)
wenzelm@387
   541
wenzelm@16425
   542
(*look up the named axiom in the theory or its ancestors*)
wenzelm@15672
   543
fun get_axiom_i theory name =
wenzelm@387
   544
  let
wenzelm@16425
   545
    fun get_ax thy =
wenzelm@22685
   546
      Symtab.lookup (Theory.axiom_table thy) name
wenzelm@16601
   547
      |> Option.map (fn prop =>
wenzelm@24143
   548
           let
wenzelm@28321
   549
             val der = deriv_rule0 (Pt.axm_proof name prop);
wenzelm@24143
   550
             val maxidx = maxidx_of_term prop;
wenzelm@26640
   551
             val shyps = Sorts.insert_term prop [];
wenzelm@24143
   552
           in
wenzelm@28321
   553
             Thm (der, {thy_ref = Theory.check_thy thy, tags = [],
wenzelm@28321
   554
               maxidx = maxidx, shyps = shyps, hyps = [], tpairs = [], prop = prop})
wenzelm@24143
   555
           end);
wenzelm@387
   556
  in
wenzelm@16425
   557
    (case get_first get_ax (theory :: Theory.ancestors_of theory) of
skalberg@15531
   558
      SOME thm => thm
skalberg@15531
   559
    | NONE => raise THEORY ("No axiom " ^ quote name, [theory]))
wenzelm@387
   560
  end;
wenzelm@387
   561
wenzelm@16352
   562
fun get_axiom thy =
wenzelm@16425
   563
  get_axiom_i thy o NameSpace.intern (Theory.axiom_space thy);
wenzelm@15672
   564
wenzelm@20884
   565
fun def_name c = c ^ "_def";
wenzelm@20884
   566
wenzelm@20884
   567
fun def_name_optional c "" = def_name c
wenzelm@20884
   568
  | def_name_optional _ name = name;
wenzelm@20884
   569
wenzelm@6368
   570
fun get_def thy = get_axiom thy o def_name;
wenzelm@4847
   571
paulson@1529
   572
wenzelm@776
   573
(*return additional axioms of this theory node*)
wenzelm@776
   574
fun axioms_of thy =
wenzelm@22685
   575
  map (fn s => (s, get_axiom_i thy s)) (Symtab.keys (Theory.axiom_table thy));
wenzelm@776
   576
wenzelm@6089
   577
wenzelm@21646
   578
(* official name and additional tags *)
wenzelm@6089
   579
wenzelm@28330
   580
fun get_name (Thm (Deriv {proof, ...}, {hyps, prop, ...})) = Pt.get_name hyps prop proof;
wenzelm@4018
   581
wenzelm@28330
   582
fun put_name name thm =
wenzelm@28330
   583
  let
wenzelm@28330
   584
    val Thm (Deriv {oracle, promises, proof}, args as {thy_ref, hyps, prop, tpairs, ...}) = thm;
wenzelm@28330
   585
    val _ = null tpairs orelse raise THM ("name_thm: unsolved flex-flex constraints", 0, [thm]);
wenzelm@28330
   586
    val thy = Theory.deref thy_ref;
wenzelm@28330
   587
    val der' = make_deriv oracle promises (Pt.thm_proof thy name hyps prop proof);
wenzelm@28330
   588
    val _ = Theory.check_thy thy;
wenzelm@28330
   589
  in Thm (der', args) end;
wenzelm@28321
   590
wenzelm@6089
   591
wenzelm@21646
   592
val get_tags = #tags o rep_thm;
wenzelm@6089
   593
wenzelm@28321
   594
fun map_tags f (Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@28321
   595
  Thm (der, {thy_ref = thy_ref, tags = f tags, maxidx = maxidx,
wenzelm@28321
   596
    shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop});
clasohm@0
   597
clasohm@0
   598
wenzelm@28321
   599
fun norm_proof (Thm (der, args as {thy_ref, ...})) =
wenzelm@24143
   600
  let
wenzelm@24143
   601
    val thy = Theory.deref thy_ref;
wenzelm@28321
   602
    val der' = deriv_rule1 (Pt.rew_proof thy) der;
wenzelm@28321
   603
    val _ = Theory.check_thy thy;
wenzelm@28321
   604
  in Thm (der', args) end;
berghofe@23781
   605
wenzelm@28321
   606
fun adjust_maxidx_thm i (th as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@20261
   607
  if maxidx = i then th
wenzelm@20261
   608
  else if maxidx < i then
wenzelm@28321
   609
    Thm (der, {maxidx = i, thy_ref = thy_ref, tags = tags, shyps = shyps,
wenzelm@28321
   610
      hyps = hyps, tpairs = tpairs, prop = prop})
wenzelm@20261
   611
  else
wenzelm@28321
   612
    Thm (der, {maxidx = Int.max (maxidx_tpairs tpairs (maxidx_of_term prop), i), thy_ref = thy_ref,
wenzelm@28321
   613
      tags = tags, shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop});
wenzelm@564
   614
wenzelm@387
   615
wenzelm@2509
   616
paulson@1529
   617
(*** Meta rules ***)
clasohm@0
   618
wenzelm@16601
   619
(** primitive rules **)
clasohm@0
   620
wenzelm@16656
   621
(*The assumption rule A |- A*)
wenzelm@16601
   622
fun assume raw_ct =
wenzelm@20261
   623
  let val Cterm {thy_ref, t = prop, T, maxidx, sorts} = adjust_maxidx_cterm ~1 raw_ct in
wenzelm@16601
   624
    if T <> propT then
mengj@19230
   625
      raise THM ("assume: prop", 0, [])
wenzelm@16601
   626
    else if maxidx <> ~1 then
mengj@19230
   627
      raise THM ("assume: variables", maxidx, [])
wenzelm@28321
   628
    else Thm (deriv_rule0 (Pt.Hyp prop),
wenzelm@28321
   629
     {thy_ref = thy_ref,
wenzelm@21646
   630
      tags = [],
wenzelm@16601
   631
      maxidx = ~1,
wenzelm@16601
   632
      shyps = sorts,
wenzelm@16601
   633
      hyps = [prop],
wenzelm@16601
   634
      tpairs = [],
wenzelm@28321
   635
      prop = prop})
clasohm@0
   636
  end;
clasohm@0
   637
wenzelm@1220
   638
(*Implication introduction
wenzelm@3529
   639
    [A]
wenzelm@3529
   640
     :
wenzelm@3529
   641
     B
wenzelm@1220
   642
  -------
wenzelm@1220
   643
  A ==> B
wenzelm@1220
   644
*)
wenzelm@16601
   645
fun implies_intr
wenzelm@16679
   646
    (ct as Cterm {t = A, T, maxidx = maxidxA, sorts, ...})
wenzelm@28321
   647
    (th as Thm (der, {maxidx, hyps, shyps, tpairs, prop, ...})) =
wenzelm@16601
   648
  if T <> propT then
wenzelm@16601
   649
    raise THM ("implies_intr: assumptions must have type prop", 0, [th])
wenzelm@16601
   650
  else
wenzelm@28321
   651
    Thm (deriv_rule1 (Pt.implies_intr_proof A) der,
wenzelm@28321
   652
     {thy_ref = merge_thys1 ct th,
wenzelm@21646
   653
      tags = [],
wenzelm@16601
   654
      maxidx = Int.max (maxidxA, maxidx),
wenzelm@16601
   655
      shyps = Sorts.union sorts shyps,
wenzelm@22365
   656
      hyps = OrdList.remove Term.fast_term_ord A hyps,
wenzelm@16601
   657
      tpairs = tpairs,
wenzelm@28321
   658
      prop = Logic.mk_implies (A, prop)});
clasohm@0
   659
paulson@1529
   660
wenzelm@1220
   661
(*Implication elimination
wenzelm@1220
   662
  A ==> B    A
wenzelm@1220
   663
  ------------
wenzelm@1220
   664
        B
wenzelm@1220
   665
*)
wenzelm@16601
   666
fun implies_elim thAB thA =
wenzelm@16601
   667
  let
wenzelm@28321
   668
    val Thm (derA, {maxidx = maxA, hyps = hypsA, shyps = shypsA, tpairs = tpairsA,
wenzelm@28321
   669
      prop = propA, ...}) = thA
wenzelm@28321
   670
    and Thm (der, {maxidx, hyps, shyps, tpairs, prop, ...}) = thAB;
wenzelm@16601
   671
    fun err () = raise THM ("implies_elim: major premise", 0, [thAB, thA]);
wenzelm@16601
   672
  in
wenzelm@16601
   673
    case prop of
wenzelm@20512
   674
      Const ("==>", _) $ A $ B =>
wenzelm@20512
   675
        if A aconv propA then
wenzelm@28321
   676
          Thm (deriv_rule2 (curry Pt.%%) der derA,
wenzelm@28321
   677
           {thy_ref = merge_thys2 thAB thA,
wenzelm@21646
   678
            tags = [],
wenzelm@16601
   679
            maxidx = Int.max (maxA, maxidx),
wenzelm@16601
   680
            shyps = Sorts.union shypsA shyps,
wenzelm@16601
   681
            hyps = union_hyps hypsA hyps,
wenzelm@16601
   682
            tpairs = union_tpairs tpairsA tpairs,
wenzelm@28321
   683
            prop = B})
wenzelm@16601
   684
        else err ()
wenzelm@16601
   685
    | _ => err ()
wenzelm@16601
   686
  end;
wenzelm@250
   687
wenzelm@1220
   688
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@16656
   689
    [x]
wenzelm@16656
   690
     :
wenzelm@16656
   691
     A
wenzelm@16656
   692
  ------
wenzelm@16656
   693
  !!x. A
wenzelm@1220
   694
*)
wenzelm@16601
   695
fun forall_intr
wenzelm@16601
   696
    (ct as Cterm {t = x, T, sorts, ...})
wenzelm@28321
   697
    (th as Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   698
  let
wenzelm@16601
   699
    fun result a =
wenzelm@28321
   700
      Thm (deriv_rule1 (Pt.forall_intr_proof x a) der,
wenzelm@28321
   701
       {thy_ref = merge_thys1 ct th,
wenzelm@21646
   702
        tags = [],
wenzelm@16601
   703
        maxidx = maxidx,
wenzelm@16601
   704
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   705
        hyps = hyps,
wenzelm@16601
   706
        tpairs = tpairs,
wenzelm@28321
   707
        prop = Term.all T $ Abs (a, T, abstract_over (x, prop))});
wenzelm@21798
   708
    fun check_occs a x ts =
wenzelm@16847
   709
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@21798
   710
        raise THM ("forall_intr: variable " ^ quote a ^ " free in assumptions", 0, [th])
wenzelm@16601
   711
      else ();
wenzelm@16601
   712
  in
wenzelm@16601
   713
    case x of
wenzelm@21798
   714
      Free (a, _) => (check_occs a x hyps; check_occs a x (terms_of_tpairs tpairs); result a)
wenzelm@21798
   715
    | Var ((a, _), _) => (check_occs a x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   716
    | _ => raise THM ("forall_intr: not a variable", 0, [th])
clasohm@0
   717
  end;
clasohm@0
   718
wenzelm@1220
   719
(*Forall elimination
wenzelm@16656
   720
  !!x. A
wenzelm@1220
   721
  ------
wenzelm@1220
   722
  A[t/x]
wenzelm@1220
   723
*)
wenzelm@16601
   724
fun forall_elim
wenzelm@16601
   725
    (ct as Cterm {t, T, maxidx = maxt, sorts, ...})
wenzelm@28321
   726
    (th as Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   727
  (case prop of
wenzelm@16601
   728
    Const ("all", Type ("fun", [Type ("fun", [qary, _]), _])) $ A =>
wenzelm@16601
   729
      if T <> qary then
wenzelm@16601
   730
        raise THM ("forall_elim: type mismatch", 0, [th])
wenzelm@16601
   731
      else
wenzelm@28321
   732
        Thm (deriv_rule1 (Pt.% o rpair (SOME t)) der,
wenzelm@28321
   733
         {thy_ref = merge_thys1 ct th,
wenzelm@21646
   734
          tags = [],
wenzelm@16601
   735
          maxidx = Int.max (maxidx, maxt),
wenzelm@16601
   736
          shyps = Sorts.union sorts shyps,
wenzelm@16601
   737
          hyps = hyps,
wenzelm@16601
   738
          tpairs = tpairs,
wenzelm@28321
   739
          prop = Term.betapply (A, t)})
wenzelm@16601
   740
  | _ => raise THM ("forall_elim: not quantified", 0, [th]));
clasohm@0
   741
clasohm@0
   742
wenzelm@1220
   743
(* Equality *)
clasohm@0
   744
wenzelm@16601
   745
(*Reflexivity
wenzelm@16601
   746
  t == t
wenzelm@16601
   747
*)
wenzelm@16601
   748
fun reflexive (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   749
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   750
   {thy_ref = thy_ref,
wenzelm@21646
   751
    tags = [],
wenzelm@16601
   752
    maxidx = maxidx,
wenzelm@16601
   753
    shyps = sorts,
wenzelm@16601
   754
    hyps = [],
wenzelm@16601
   755
    tpairs = [],
wenzelm@28321
   756
    prop = Logic.mk_equals (t, t)});
clasohm@0
   757
wenzelm@16601
   758
(*Symmetry
wenzelm@16601
   759
  t == u
wenzelm@16601
   760
  ------
wenzelm@16601
   761
  u == t
wenzelm@1220
   762
*)
wenzelm@28321
   763
fun symmetric (th as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   764
  (case prop of
wenzelm@16601
   765
    (eq as Const ("==", Type (_, [T, _]))) $ t $ u =>
wenzelm@28321
   766
      Thm (deriv_rule1 Pt.symmetric der,
wenzelm@28321
   767
       {thy_ref = thy_ref,
wenzelm@21646
   768
        tags = [],
wenzelm@16601
   769
        maxidx = maxidx,
wenzelm@16601
   770
        shyps = shyps,
wenzelm@16601
   771
        hyps = hyps,
wenzelm@16601
   772
        tpairs = tpairs,
wenzelm@28321
   773
        prop = eq $ u $ t})
wenzelm@16601
   774
    | _ => raise THM ("symmetric", 0, [th]));
clasohm@0
   775
wenzelm@16601
   776
(*Transitivity
wenzelm@16601
   777
  t1 == u    u == t2
wenzelm@16601
   778
  ------------------
wenzelm@16601
   779
       t1 == t2
wenzelm@1220
   780
*)
clasohm@0
   781
fun transitive th1 th2 =
wenzelm@16601
   782
  let
wenzelm@28321
   783
    val Thm (der1, {maxidx = max1, hyps = hyps1, shyps = shyps1, tpairs = tpairs1,
wenzelm@28321
   784
      prop = prop1, ...}) = th1
wenzelm@28321
   785
    and Thm (der2, {maxidx = max2, hyps = hyps2, shyps = shyps2, tpairs = tpairs2,
wenzelm@28321
   786
      prop = prop2, ...}) = th2;
wenzelm@16601
   787
    fun err msg = raise THM ("transitive: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   788
  in
wenzelm@16601
   789
    case (prop1, prop2) of
wenzelm@16601
   790
      ((eq as Const ("==", Type (_, [T, _]))) $ t1 $ u, Const ("==", _) $ u' $ t2) =>
wenzelm@16601
   791
        if not (u aconv u') then err "middle term"
wenzelm@16601
   792
        else
wenzelm@28321
   793
          Thm (deriv_rule2 (Pt.transitive u T) der1 der2,
wenzelm@28321
   794
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   795
            tags = [],
wenzelm@16601
   796
            maxidx = Int.max (max1, max2),
wenzelm@16601
   797
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   798
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   799
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   800
            prop = eq $ t1 $ t2})
wenzelm@16601
   801
     | _ =>  err "premises"
clasohm@0
   802
  end;
clasohm@0
   803
wenzelm@16601
   804
(*Beta-conversion
wenzelm@16656
   805
  (%x. t)(u) == t[u/x]
wenzelm@16601
   806
  fully beta-reduces the term if full = true
berghofe@10416
   807
*)
wenzelm@16601
   808
fun beta_conversion full (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   809
  let val t' =
wenzelm@16601
   810
    if full then Envir.beta_norm t
wenzelm@16601
   811
    else
wenzelm@16601
   812
      (case t of Abs (_, _, bodt) $ u => subst_bound (u, bodt)
wenzelm@16601
   813
      | _ => raise THM ("beta_conversion: not a redex", 0, []));
wenzelm@16601
   814
  in
wenzelm@28321
   815
    Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   816
     {thy_ref = thy_ref,
wenzelm@21646
   817
      tags = [],
wenzelm@16601
   818
      maxidx = maxidx,
wenzelm@16601
   819
      shyps = sorts,
wenzelm@16601
   820
      hyps = [],
wenzelm@16601
   821
      tpairs = [],
wenzelm@28321
   822
      prop = Logic.mk_equals (t, t')})
berghofe@10416
   823
  end;
berghofe@10416
   824
wenzelm@16601
   825
fun eta_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   826
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   827
   {thy_ref = thy_ref,
wenzelm@21646
   828
    tags = [],
wenzelm@16601
   829
    maxidx = maxidx,
wenzelm@16601
   830
    shyps = sorts,
wenzelm@16601
   831
    hyps = [],
wenzelm@16601
   832
    tpairs = [],
wenzelm@28321
   833
    prop = Logic.mk_equals (t, Envir.eta_contract t)});
clasohm@0
   834
wenzelm@23493
   835
fun eta_long_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   836
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   837
   {thy_ref = thy_ref,
wenzelm@23493
   838
    tags = [],
wenzelm@23493
   839
    maxidx = maxidx,
wenzelm@23493
   840
    shyps = sorts,
wenzelm@23493
   841
    hyps = [],
wenzelm@23493
   842
    tpairs = [],
wenzelm@28321
   843
    prop = Logic.mk_equals (t, Pattern.eta_long [] t)});
wenzelm@23493
   844
clasohm@0
   845
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   846
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@16601
   847
      t == u
wenzelm@16601
   848
  --------------
wenzelm@16601
   849
  %x. t == %x. u
wenzelm@1220
   850
*)
wenzelm@16601
   851
fun abstract_rule a
wenzelm@16601
   852
    (Cterm {t = x, T, sorts, ...})
wenzelm@28321
   853
    (th as Thm (der, {thy_ref, maxidx, hyps, shyps, tpairs, prop, ...})) =
wenzelm@16601
   854
  let
wenzelm@16601
   855
    val (t, u) = Logic.dest_equals prop
wenzelm@16601
   856
      handle TERM _ => raise THM ("abstract_rule: premise not an equality", 0, [th]);
wenzelm@16601
   857
    val result =
wenzelm@28321
   858
      Thm (deriv_rule1 (Pt.abstract_rule x a) der,
wenzelm@28321
   859
       {thy_ref = thy_ref,
wenzelm@21646
   860
        tags = [],
wenzelm@16601
   861
        maxidx = maxidx,
wenzelm@16601
   862
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   863
        hyps = hyps,
wenzelm@16601
   864
        tpairs = tpairs,
wenzelm@16601
   865
        prop = Logic.mk_equals
wenzelm@28321
   866
          (Abs (a, T, abstract_over (x, t)), Abs (a, T, abstract_over (x, u)))});
wenzelm@21798
   867
    fun check_occs a x ts =
wenzelm@16847
   868
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@21798
   869
        raise THM ("abstract_rule: variable " ^ quote a ^ " free in assumptions", 0, [th])
wenzelm@16601
   870
      else ();
wenzelm@16601
   871
  in
wenzelm@16601
   872
    case x of
wenzelm@21798
   873
      Free (a, _) => (check_occs a x hyps; check_occs a x (terms_of_tpairs tpairs); result)
wenzelm@21798
   874
    | Var ((a, _), _) => (check_occs a x (terms_of_tpairs tpairs); result)
wenzelm@21798
   875
    | _ => raise THM ("abstract_rule: not a variable", 0, [th])
clasohm@0
   876
  end;
clasohm@0
   877
clasohm@0
   878
(*The combination rule
wenzelm@3529
   879
  f == g  t == u
wenzelm@3529
   880
  --------------
wenzelm@16601
   881
    f t == g u
wenzelm@1220
   882
*)
clasohm@0
   883
fun combination th1 th2 =
wenzelm@16601
   884
  let
wenzelm@28321
   885
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@28321
   886
      prop = prop1, ...}) = th1
wenzelm@28321
   887
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@28321
   888
      prop = prop2, ...}) = th2;
wenzelm@16601
   889
    fun chktypes fT tT =
wenzelm@16601
   890
      (case fT of
wenzelm@16601
   891
        Type ("fun", [T1, T2]) =>
wenzelm@16601
   892
          if T1 <> tT then
wenzelm@16601
   893
            raise THM ("combination: types", 0, [th1, th2])
wenzelm@16601
   894
          else ()
wenzelm@16601
   895
      | _ => raise THM ("combination: not function type", 0, [th1, th2]));
wenzelm@16601
   896
  in
wenzelm@16601
   897
    case (prop1, prop2) of
wenzelm@16601
   898
      (Const ("==", Type ("fun", [fT, _])) $ f $ g,
wenzelm@16601
   899
       Const ("==", Type ("fun", [tT, _])) $ t $ u) =>
wenzelm@16601
   900
        (chktypes fT tT;
wenzelm@28321
   901
          Thm (deriv_rule2 (Pt.combination f g t u fT) der1 der2,
wenzelm@28321
   902
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   903
            tags = [],
wenzelm@16601
   904
            maxidx = Int.max (max1, max2),
wenzelm@16601
   905
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   906
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   907
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   908
            prop = Logic.mk_equals (f $ t, g $ u)}))
wenzelm@16601
   909
     | _ => raise THM ("combination: premises", 0, [th1, th2])
clasohm@0
   910
  end;
clasohm@0
   911
wenzelm@16601
   912
(*Equality introduction
wenzelm@3529
   913
  A ==> B  B ==> A
wenzelm@3529
   914
  ----------------
wenzelm@3529
   915
       A == B
wenzelm@1220
   916
*)
clasohm@0
   917
fun equal_intr th1 th2 =
wenzelm@16601
   918
  let
wenzelm@28321
   919
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@28321
   920
      prop = prop1, ...}) = th1
wenzelm@28321
   921
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@28321
   922
      prop = prop2, ...}) = th2;
wenzelm@16601
   923
    fun err msg = raise THM ("equal_intr: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   924
  in
wenzelm@16601
   925
    case (prop1, prop2) of
wenzelm@16601
   926
      (Const("==>", _) $ A $ B, Const("==>", _) $ B' $ A') =>
wenzelm@16601
   927
        if A aconv A' andalso B aconv B' then
wenzelm@28321
   928
          Thm (deriv_rule2 (Pt.equal_intr A B) der1 der2,
wenzelm@28321
   929
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   930
            tags = [],
wenzelm@16601
   931
            maxidx = Int.max (max1, max2),
wenzelm@16601
   932
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   933
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   934
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   935
            prop = Logic.mk_equals (A, B)})
wenzelm@16601
   936
        else err "not equal"
wenzelm@16601
   937
    | _ =>  err "premises"
paulson@1529
   938
  end;
paulson@1529
   939
paulson@1529
   940
(*The equal propositions rule
wenzelm@3529
   941
  A == B  A
paulson@1529
   942
  ---------
paulson@1529
   943
      B
paulson@1529
   944
*)
paulson@1529
   945
fun equal_elim th1 th2 =
wenzelm@16601
   946
  let
wenzelm@28321
   947
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1,
wenzelm@28321
   948
      tpairs = tpairs1, prop = prop1, ...}) = th1
wenzelm@28321
   949
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2,
wenzelm@28321
   950
      tpairs = tpairs2, prop = prop2, ...}) = th2;
wenzelm@16601
   951
    fun err msg = raise THM ("equal_elim: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   952
  in
wenzelm@16601
   953
    case prop1 of
wenzelm@16601
   954
      Const ("==", _) $ A $ B =>
wenzelm@16601
   955
        if prop2 aconv A then
wenzelm@28321
   956
          Thm (deriv_rule2 (Pt.equal_elim A B) der1 der2,
wenzelm@28321
   957
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   958
            tags = [],
wenzelm@16601
   959
            maxidx = Int.max (max1, max2),
wenzelm@16601
   960
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   961
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   962
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   963
            prop = B})
wenzelm@16601
   964
        else err "not equal"
paulson@1529
   965
     | _ =>  err"major premise"
paulson@1529
   966
  end;
clasohm@0
   967
wenzelm@1220
   968
wenzelm@1220
   969
clasohm@0
   970
(**** Derived rules ****)
clasohm@0
   971
wenzelm@16601
   972
(*Smash unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@24143
   973
  Instantiates the theorem and deletes trivial tpairs.  Resulting
wenzelm@24143
   974
  sequence may contain multiple elements if the tpairs are not all
wenzelm@24143
   975
  flex-flex.*)
wenzelm@28321
   976
fun flexflex_rule (th as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@24143
   977
  let val thy = Theory.deref thy_ref in
wenzelm@24143
   978
    Unify.smash_unifiers thy tpairs (Envir.empty maxidx)
wenzelm@24143
   979
    |> Seq.map (fn env =>
wenzelm@24143
   980
        if Envir.is_empty env then th
wenzelm@24143
   981
        else
wenzelm@24143
   982
          let
wenzelm@24143
   983
            val tpairs' = tpairs |> map (pairself (Envir.norm_term env))
wenzelm@24143
   984
              (*remove trivial tpairs, of the form t==t*)
wenzelm@24143
   985
              |> filter_out (op aconv);
wenzelm@28321
   986
            val der' = deriv_rule1 (Pt.norm_proof' env) der;
wenzelm@24143
   987
            val prop' = Envir.norm_term env prop;
wenzelm@24143
   988
            val maxidx = maxidx_tpairs tpairs' (maxidx_of_term prop');
wenzelm@26640
   989
            val shyps = Envir.insert_sorts env shyps;
wenzelm@24143
   990
          in
wenzelm@28321
   991
            Thm (der', {thy_ref = Theory.check_thy thy, tags = [], maxidx = maxidx,
wenzelm@28321
   992
              shyps = shyps, hyps = hyps, tpairs = tpairs', prop = prop'})
wenzelm@24143
   993
          end)
wenzelm@24143
   994
  end;
wenzelm@16601
   995
clasohm@0
   996
wenzelm@19910
   997
(*Generalization of fixed variables
wenzelm@19910
   998
           A
wenzelm@19910
   999
  --------------------
wenzelm@19910
  1000
  A[?'a/'a, ?x/x, ...]
wenzelm@19910
  1001
*)
wenzelm@19910
  1002
wenzelm@19910
  1003
fun generalize ([], []) _ th = th
wenzelm@19910
  1004
  | generalize (tfrees, frees) idx th =
wenzelm@19910
  1005
      let
wenzelm@28321
  1006
        val Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...}) = th;
wenzelm@19910
  1007
        val _ = idx <= maxidx andalso raise THM ("generalize: bad index", idx, [th]);
wenzelm@19910
  1008
wenzelm@19910
  1009
        val bad_type = if null tfrees then K false else
wenzelm@19910
  1010
          Term.exists_subtype (fn TFree (a, _) => member (op =) tfrees a | _ => false);
wenzelm@19910
  1011
        fun bad_term (Free (x, T)) = bad_type T orelse member (op =) frees x
wenzelm@19910
  1012
          | bad_term (Var (_, T)) = bad_type T
wenzelm@19910
  1013
          | bad_term (Const (_, T)) = bad_type T
wenzelm@19910
  1014
          | bad_term (Abs (_, T, t)) = bad_type T orelse bad_term t
wenzelm@19910
  1015
          | bad_term (t $ u) = bad_term t orelse bad_term u
wenzelm@19910
  1016
          | bad_term (Bound _) = false;
wenzelm@19910
  1017
        val _ = exists bad_term hyps andalso
wenzelm@19910
  1018
          raise THM ("generalize: variable free in assumptions", 0, [th]);
wenzelm@19910
  1019
wenzelm@20512
  1020
        val gen = TermSubst.generalize (tfrees, frees) idx;
wenzelm@19910
  1021
        val prop' = gen prop;
wenzelm@19910
  1022
        val tpairs' = map (pairself gen) tpairs;
wenzelm@19910
  1023
        val maxidx' = maxidx_tpairs tpairs' (maxidx_of_term prop');
wenzelm@19910
  1024
      in
wenzelm@28321
  1025
        Thm (deriv_rule1 (Pt.generalize (tfrees, frees) idx) der,
wenzelm@28321
  1026
         {thy_ref = thy_ref,
wenzelm@21646
  1027
          tags = [],
wenzelm@19910
  1028
          maxidx = maxidx',
wenzelm@19910
  1029
          shyps = shyps,
wenzelm@19910
  1030
          hyps = hyps,
wenzelm@19910
  1031
          tpairs = tpairs',
wenzelm@28321
  1032
          prop = prop'})
wenzelm@19910
  1033
      end;
wenzelm@19910
  1034
wenzelm@19910
  1035
wenzelm@22584
  1036
(*Instantiation of schematic variables
wenzelm@16656
  1037
           A
wenzelm@16656
  1038
  --------------------
wenzelm@16656
  1039
  A[t1/v1, ..., tn/vn]
wenzelm@1220
  1040
*)
clasohm@0
  1041
wenzelm@6928
  1042
local
wenzelm@6928
  1043
wenzelm@26939
  1044
fun pretty_typing thy t T = Pretty.block
wenzelm@26939
  1045
  [Syntax.pretty_term_global thy t, Pretty.str " ::", Pretty.brk 1, Syntax.pretty_typ_global thy T];
berghofe@15797
  1046
wenzelm@16884
  1047
fun add_inst (ct, cu) (thy_ref, sorts) =
wenzelm@6928
  1048
  let
wenzelm@26939
  1049
    val Cterm {t = t, T = T, ...} = ct;
wenzelm@26939
  1050
    val Cterm {t = u, T = U, sorts = sorts_u, maxidx = maxidx_u, ...} = cu;
wenzelm@16884
  1051
    val thy_ref' = Theory.merge_refs (thy_ref, merge_thys0 ct cu);
wenzelm@16884
  1052
    val sorts' = Sorts.union sorts_u sorts;
wenzelm@3967
  1053
  in
wenzelm@16884
  1054
    (case t of Var v =>
wenzelm@20512
  1055
      if T = U then ((v, (u, maxidx_u)), (thy_ref', sorts'))
wenzelm@16884
  1056
      else raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
  1057
       [Pretty.str "instantiate: type conflict",
wenzelm@16884
  1058
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') t T,
wenzelm@16884
  1059
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') u U]), [T, U], [t, u])
wenzelm@16884
  1060
    | _ => raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
  1061
       [Pretty.str "instantiate: not a variable",
wenzelm@26939
  1062
        Pretty.fbrk, Syntax.pretty_term_global (Theory.deref thy_ref') t]), [], [t]))
clasohm@0
  1063
  end;
clasohm@0
  1064
wenzelm@16884
  1065
fun add_instT (cT, cU) (thy_ref, sorts) =
wenzelm@16656
  1066
  let
wenzelm@16884
  1067
    val Ctyp {T, thy_ref = thy_ref1, ...} = cT
wenzelm@20512
  1068
    and Ctyp {T = U, thy_ref = thy_ref2, sorts = sorts_U, maxidx = maxidx_U, ...} = cU;
wenzelm@24143
  1069
    val thy' = Theory.deref (Theory.merge_refs (thy_ref, Theory.merge_refs (thy_ref1, thy_ref2)));
wenzelm@16884
  1070
    val sorts' = Sorts.union sorts_U sorts;
wenzelm@16656
  1071
  in
wenzelm@16884
  1072
    (case T of TVar (v as (_, S)) =>
wenzelm@24143
  1073
      if Sign.of_sort thy' (U, S) then ((v, (U, maxidx_U)), (Theory.check_thy thy', sorts'))
wenzelm@26939
  1074
      else raise TYPE ("Type not of sort " ^ Syntax.string_of_sort_global thy' S, [U], [])
wenzelm@16656
  1075
    | _ => raise TYPE (Pretty.string_of (Pretty.block
berghofe@15797
  1076
        [Pretty.str "instantiate: not a type variable",
wenzelm@26939
  1077
         Pretty.fbrk, Syntax.pretty_typ_global thy' T]), [T], []))
wenzelm@16656
  1078
  end;
clasohm@0
  1079
wenzelm@6928
  1080
in
wenzelm@6928
  1081
wenzelm@16601
  1082
(*Left-to-right replacements: ctpairs = [..., (vi, ti), ...].
clasohm@0
  1083
  Instantiates distinct Vars by terms of same type.
wenzelm@16601
  1084
  Does NOT normalize the resulting theorem!*)
paulson@1529
  1085
fun instantiate ([], []) th = th
wenzelm@16884
  1086
  | instantiate (instT, inst) th =
wenzelm@16656
  1087
      let
wenzelm@28321
  1088
        val Thm (der, {thy_ref, hyps, shyps, tpairs, prop, ...}) = th;
wenzelm@16884
  1089
        val (inst', (instT', (thy_ref', shyps'))) =
wenzelm@16884
  1090
          (thy_ref, shyps) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@20512
  1091
        val subst = TermSubst.instantiate_maxidx (instT', inst');
wenzelm@20512
  1092
        val (prop', maxidx1) = subst prop ~1;
wenzelm@20512
  1093
        val (tpairs', maxidx') =
wenzelm@20512
  1094
          fold_map (fn (t, u) => fn i => subst t i ||>> subst u) tpairs maxidx1;
wenzelm@16656
  1095
      in
wenzelm@28321
  1096
        Thm (deriv_rule1 (fn d => Pt.instantiate (map (apsnd #1) instT', map (apsnd #1) inst') d) der,
wenzelm@28321
  1097
         {thy_ref = thy_ref',
wenzelm@21646
  1098
          tags = [],
wenzelm@20545
  1099
          maxidx = maxidx',
wenzelm@20545
  1100
          shyps = shyps',
wenzelm@20545
  1101
          hyps = hyps,
wenzelm@20545
  1102
          tpairs = tpairs',
wenzelm@28321
  1103
          prop = prop'})
wenzelm@16656
  1104
      end
wenzelm@16656
  1105
      handle TYPE (msg, _, _) => raise THM (msg, 0, [th]);
wenzelm@6928
  1106
wenzelm@22584
  1107
fun instantiate_cterm ([], []) ct = ct
wenzelm@22584
  1108
  | instantiate_cterm (instT, inst) ct =
wenzelm@22584
  1109
      let
wenzelm@22584
  1110
        val Cterm {thy_ref, t, T, sorts, ...} = ct;
wenzelm@22584
  1111
        val (inst', (instT', (thy_ref', sorts'))) =
wenzelm@22584
  1112
          (thy_ref, sorts) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@22584
  1113
        val subst = TermSubst.instantiate_maxidx (instT', inst');
wenzelm@22584
  1114
        val substT = TermSubst.instantiateT_maxidx instT';
wenzelm@22584
  1115
        val (t', maxidx1) = subst t ~1;
wenzelm@22584
  1116
        val (T', maxidx') = substT T maxidx1;
wenzelm@22584
  1117
      in Cterm {thy_ref = thy_ref', t = t', T = T', sorts = sorts', maxidx = maxidx'} end
wenzelm@22584
  1118
      handle TYPE (msg, _, _) => raise CTERM (msg, [ct]);
wenzelm@22584
  1119
wenzelm@6928
  1120
end;
wenzelm@6928
  1121
clasohm@0
  1122
wenzelm@16601
  1123
(*The trivial implication A ==> A, justified by assume and forall rules.
wenzelm@16601
  1124
  A can contain Vars, not so for assume!*)
wenzelm@16601
  1125
fun trivial (Cterm {thy_ref, t =A, T, maxidx, sorts}) =
wenzelm@16601
  1126
  if T <> propT then
wenzelm@16601
  1127
    raise THM ("trivial: the term must have type prop", 0, [])
wenzelm@16601
  1128
  else
wenzelm@28321
  1129
    Thm (deriv_rule0 (Pt.AbsP ("H", NONE, Pt.PBound 0)),
wenzelm@28321
  1130
     {thy_ref = thy_ref,
wenzelm@21646
  1131
      tags = [],
wenzelm@16601
  1132
      maxidx = maxidx,
wenzelm@16601
  1133
      shyps = sorts,
wenzelm@16601
  1134
      hyps = [],
wenzelm@16601
  1135
      tpairs = [],
wenzelm@28321
  1136
      prop = Logic.mk_implies (A, A)});
clasohm@0
  1137
paulson@1503
  1138
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)" *)
wenzelm@16425
  1139
fun class_triv thy c =
wenzelm@24143
  1140
  let
wenzelm@24143
  1141
    val Cterm {t, maxidx, sorts, ...} =
wenzelm@24848
  1142
      cterm_of thy (Logic.mk_inclass (TVar ((Name.aT, 0), [c]), Sign.certify_class thy c))
wenzelm@24143
  1143
        handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@28321
  1144
    val der = deriv_rule0 (Pt.PAxm ("Pure.class_triv:" ^ c, t, SOME []));
wenzelm@399
  1145
  in
wenzelm@28321
  1146
    Thm (der, {thy_ref = Theory.check_thy thy, tags = [], maxidx = maxidx,
wenzelm@28321
  1147
      shyps = sorts, hyps = [], tpairs = [], prop = t})
wenzelm@399
  1148
  end;
wenzelm@399
  1149
wenzelm@19505
  1150
(*Internalize sort constraints of type variable*)
wenzelm@19505
  1151
fun unconstrainT
wenzelm@19505
  1152
    (Ctyp {thy_ref = thy_ref1, T, ...})
wenzelm@28321
  1153
    (th as Thm (_, {thy_ref = thy_ref2, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@19505
  1154
  let
wenzelm@19505
  1155
    val ((x, i), S) = Term.dest_TVar T handle TYPE _ =>
wenzelm@19505
  1156
      raise THM ("unconstrainT: not a type variable", 0, [th]);
wenzelm@19505
  1157
    val T' = TVar ((x, i), []);
wenzelm@20548
  1158
    val unconstrain = Term.map_types (Term.map_atyps (fn U => if U = T then T' else U));
wenzelm@19505
  1159
    val constraints = map (curry Logic.mk_inclass T') S;
wenzelm@19505
  1160
  in
wenzelm@28321
  1161
    Thm (deriv_rule0 (Pt.PAxm ("Pure.unconstrainT", prop, SOME [])),
wenzelm@28321
  1162
     {thy_ref = Theory.merge_refs (thy_ref1, thy_ref2),
wenzelm@21646
  1163
      tags = [],
wenzelm@19505
  1164
      maxidx = Int.max (maxidx, i),
wenzelm@19505
  1165
      shyps = Sorts.remove_sort S shyps,
wenzelm@19505
  1166
      hyps = hyps,
wenzelm@19505
  1167
      tpairs = map (pairself unconstrain) tpairs,
wenzelm@28321
  1168
      prop = Logic.list_implies (constraints, unconstrain prop)})
wenzelm@19505
  1169
  end;
wenzelm@399
  1170
wenzelm@6786
  1171
(* Replace all TFrees not fixed or in the hyps by new TVars *)
wenzelm@28321
  1172
fun varifyT' fixed (Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@12500
  1173
  let
wenzelm@23178
  1174
    val tfrees = List.foldr add_term_tfrees fixed hyps;
berghofe@13658
  1175
    val prop1 = attach_tpairs tpairs prop;
haftmann@21116
  1176
    val (al, prop2) = Type.varify tfrees prop1;
wenzelm@16601
  1177
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1178
  in
wenzelm@28321
  1179
    (al, Thm (deriv_rule1 (Pt.varify_proof prop tfrees) der,
wenzelm@28321
  1180
     {thy_ref = thy_ref,
wenzelm@21646
  1181
      tags = [],
wenzelm@16601
  1182
      maxidx = Int.max (0, maxidx),
wenzelm@16601
  1183
      shyps = shyps,
wenzelm@16601
  1184
      hyps = hyps,
wenzelm@16601
  1185
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@28321
  1186
      prop = prop3}))
wenzelm@28321
  1187
  end;
wenzelm@28321
  1188
wenzelm@28321
  1189
val varifyT = #2 o varifyT' [];
wenzelm@28321
  1190
wenzelm@28321
  1191
(* Replace all TVars by new TFrees *)
wenzelm@28321
  1192
fun freezeT (Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@28321
  1193
  let
wenzelm@28321
  1194
    val prop1 = attach_tpairs tpairs prop;
wenzelm@28321
  1195
    val prop2 = Type.freeze prop1;
wenzelm@28321
  1196
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@28321
  1197
  in
wenzelm@28321
  1198
    Thm (deriv_rule1 (Pt.freezeT prop1) der,
wenzelm@28321
  1199
     {thy_ref = thy_ref,
wenzelm@28321
  1200
      tags = [],
wenzelm@28321
  1201
      maxidx = maxidx_of_term prop2,
wenzelm@28321
  1202
      shyps = shyps,
wenzelm@28321
  1203
      hyps = hyps,
wenzelm@28321
  1204
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@18127
  1205
      prop = prop3})
clasohm@0
  1206
  end;
clasohm@0
  1207
clasohm@0
  1208
clasohm@0
  1209
(*** Inference rules for tactics ***)
clasohm@0
  1210
clasohm@0
  1211
(*Destruct proof state into constraints, other goals, goal(i), rest *)
wenzelm@28321
  1212
fun dest_state (state as Thm (_, {prop,tpairs,...}), i) =
berghofe@13658
  1213
  (case  Logic.strip_prems(i, [], prop) of
berghofe@13658
  1214
      (B::rBs, C) => (tpairs, rev rBs, B, C)
berghofe@13658
  1215
    | _ => raise THM("dest_state", i, [state]))
clasohm@0
  1216
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1217
lcp@309
  1218
(*Increment variables and parameters of orule as required for
wenzelm@18035
  1219
  resolution with a goal.*)
wenzelm@18035
  1220
fun lift_rule goal orule =
wenzelm@16601
  1221
  let
wenzelm@18035
  1222
    val Cterm {t = gprop, T, maxidx = gmax, sorts, ...} = goal;
wenzelm@18035
  1223
    val inc = gmax + 1;
wenzelm@18035
  1224
    val lift_abs = Logic.lift_abs inc gprop;
wenzelm@18035
  1225
    val lift_all = Logic.lift_all inc gprop;
wenzelm@28321
  1226
    val Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...}) = orule;
wenzelm@16601
  1227
    val (As, B) = Logic.strip_horn prop;
wenzelm@16601
  1228
  in
wenzelm@18035
  1229
    if T <> propT then raise THM ("lift_rule: the term must have type prop", 0, [])
wenzelm@18035
  1230
    else
wenzelm@28321
  1231
      Thm (deriv_rule1 (Pt.lift_proof gprop inc prop) der,
wenzelm@28321
  1232
       {thy_ref = merge_thys1 goal orule,
wenzelm@21646
  1233
        tags = [],
wenzelm@18035
  1234
        maxidx = maxidx + inc,
wenzelm@18035
  1235
        shyps = Sorts.union shyps sorts,  (*sic!*)
wenzelm@18035
  1236
        hyps = hyps,
wenzelm@18035
  1237
        tpairs = map (pairself lift_abs) tpairs,
wenzelm@28321
  1238
        prop = Logic.list_implies (map lift_all As, lift_all B)})
clasohm@0
  1239
  end;
clasohm@0
  1240
wenzelm@28321
  1241
fun incr_indexes i (thm as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
  1242
  if i < 0 then raise THM ("negative increment", 0, [thm])
wenzelm@16601
  1243
  else if i = 0 then thm
wenzelm@16601
  1244
  else
wenzelm@28321
  1245
    Thm (deriv_rule1 (Pt.map_proof_terms (Logic.incr_indexes ([], i)) (Logic.incr_tvar i)) der,
wenzelm@28321
  1246
     {thy_ref = thy_ref,
wenzelm@21646
  1247
      tags = [],
wenzelm@16601
  1248
      maxidx = maxidx + i,
wenzelm@16601
  1249
      shyps = shyps,
wenzelm@16601
  1250
      hyps = hyps,
wenzelm@16601
  1251
      tpairs = map (pairself (Logic.incr_indexes ([], i))) tpairs,
wenzelm@28321
  1252
      prop = Logic.incr_indexes ([], i) prop});
berghofe@10416
  1253
clasohm@0
  1254
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1255
fun assumption i state =
wenzelm@16601
  1256
  let
wenzelm@28321
  1257
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16656
  1258
    val thy = Theory.deref thy_ref;
wenzelm@16601
  1259
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1260
    fun newth n (env as Envir.Envir {maxidx, ...}, tpairs) =
wenzelm@28321
  1261
      Thm (deriv_rule1
wenzelm@16601
  1262
          ((if Envir.is_empty env then I else (Pt.norm_proof' env)) o
wenzelm@16601
  1263
            Pt.assumption_proof Bs Bi n) der,
wenzelm@28321
  1264
       {tags = [],
wenzelm@16601
  1265
        maxidx = maxidx,
wenzelm@26640
  1266
        shyps = Envir.insert_sorts env shyps,
wenzelm@16601
  1267
        hyps = hyps,
wenzelm@16601
  1268
        tpairs =
wenzelm@16601
  1269
          if Envir.is_empty env then tpairs
wenzelm@16601
  1270
          else map (pairself (Envir.norm_term env)) tpairs,
wenzelm@16601
  1271
        prop =
wenzelm@16601
  1272
          if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@16601
  1273
            Logic.list_implies (Bs, C)
wenzelm@16601
  1274
          else (*normalize the new rule fully*)
wenzelm@24143
  1275
            Envir.norm_term env (Logic.list_implies (Bs, C)),
wenzelm@28321
  1276
        thy_ref = Theory.check_thy thy});
wenzelm@16601
  1277
    fun addprfs [] _ = Seq.empty
wenzelm@16601
  1278
      | addprfs ((t, u) :: apairs) n = Seq.make (fn () => Seq.pull
wenzelm@16601
  1279
          (Seq.mapp (newth n)
wenzelm@16656
  1280
            (Unify.unifiers (thy, Envir.empty maxidx, (t, u) :: tpairs))
wenzelm@16601
  1281
            (addprfs apairs (n + 1))))
wenzelm@16601
  1282
  in addprfs (Logic.assum_pairs (~1, Bi)) 1 end;
clasohm@0
  1283
wenzelm@250
  1284
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1285
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1286
fun eq_assumption i state =
wenzelm@16601
  1287
  let
wenzelm@28321
  1288
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16601
  1289
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1290
  in
berghofe@26832
  1291
    (case find_index Pattern.aeconv (Logic.assum_pairs (~1, Bi)) of
wenzelm@16601
  1292
      ~1 => raise THM ("eq_assumption", 0, [state])
wenzelm@16601
  1293
    | n =>
wenzelm@28321
  1294
        Thm (deriv_rule1 (Pt.assumption_proof Bs Bi (n + 1)) der,
wenzelm@28321
  1295
         {thy_ref = thy_ref,
wenzelm@21646
  1296
          tags = [],
wenzelm@16601
  1297
          maxidx = maxidx,
wenzelm@16601
  1298
          shyps = shyps,
wenzelm@16601
  1299
          hyps = hyps,
wenzelm@16601
  1300
          tpairs = tpairs,
wenzelm@28321
  1301
          prop = Logic.list_implies (Bs, C)}))
clasohm@0
  1302
  end;
clasohm@0
  1303
clasohm@0
  1304
paulson@2671
  1305
(*For rotate_tac: fast rotation of assumptions of subgoal i*)
paulson@2671
  1306
fun rotate_rule k i state =
wenzelm@16601
  1307
  let
wenzelm@28321
  1308
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16601
  1309
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1310
    val params = Term.strip_all_vars Bi
wenzelm@16601
  1311
    and rest   = Term.strip_all_body Bi;
wenzelm@16601
  1312
    val asms   = Logic.strip_imp_prems rest
wenzelm@16601
  1313
    and concl  = Logic.strip_imp_concl rest;
wenzelm@16601
  1314
    val n = length asms;
wenzelm@16601
  1315
    val m = if k < 0 then n + k else k;
wenzelm@16601
  1316
    val Bi' =
wenzelm@16601
  1317
      if 0 = m orelse m = n then Bi
wenzelm@16601
  1318
      else if 0 < m andalso m < n then
wenzelm@19012
  1319
        let val (ps, qs) = chop m asms
wenzelm@16601
  1320
        in list_all (params, Logic.list_implies (qs @ ps, concl)) end
wenzelm@16601
  1321
      else raise THM ("rotate_rule", k, [state]);
wenzelm@16601
  1322
  in
wenzelm@28321
  1323
    Thm (deriv_rule1 (Pt.rotate_proof Bs Bi m) der,
wenzelm@28321
  1324
     {thy_ref = thy_ref,
wenzelm@21646
  1325
      tags = [],
wenzelm@16601
  1326
      maxidx = maxidx,
wenzelm@16601
  1327
      shyps = shyps,
wenzelm@16601
  1328
      hyps = hyps,
wenzelm@16601
  1329
      tpairs = tpairs,
wenzelm@28321
  1330
      prop = Logic.list_implies (Bs @ [Bi'], C)})
paulson@2671
  1331
  end;
paulson@2671
  1332
paulson@2671
  1333
paulson@7248
  1334
(*Rotates a rule's premises to the left by k, leaving the first j premises
paulson@7248
  1335
  unchanged.  Does nothing if k=0 or if k equals n-j, where n is the
wenzelm@16656
  1336
  number of premises.  Useful with etac and underlies defer_tac*)
paulson@7248
  1337
fun permute_prems j k rl =
wenzelm@16601
  1338
  let
wenzelm@28321
  1339
    val Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...}) = rl;
wenzelm@16601
  1340
    val prems = Logic.strip_imp_prems prop
wenzelm@16601
  1341
    and concl = Logic.strip_imp_concl prop;
wenzelm@16601
  1342
    val moved_prems = List.drop (prems, j)
wenzelm@16601
  1343
    and fixed_prems = List.take (prems, j)
wenzelm@16601
  1344
      handle Subscript => raise THM ("permute_prems: j", j, [rl]);
wenzelm@16601
  1345
    val n_j = length moved_prems;
wenzelm@16601
  1346
    val m = if k < 0 then n_j + k else k;
wenzelm@16601
  1347
    val prop' =
wenzelm@16601
  1348
      if 0 = m orelse m = n_j then prop
wenzelm@16601
  1349
      else if 0 < m andalso m < n_j then
wenzelm@19012
  1350
        let val (ps, qs) = chop m moved_prems
wenzelm@16601
  1351
        in Logic.list_implies (fixed_prems @ qs @ ps, concl) end
wenzelm@16725
  1352
      else raise THM ("permute_prems: k", k, [rl]);
wenzelm@16601
  1353
  in
wenzelm@28321
  1354
    Thm (deriv_rule1 (Pt.permute_prems_prf prems j m) der,
wenzelm@28321
  1355
     {thy_ref = thy_ref,
wenzelm@21646
  1356
      tags = [],
wenzelm@16601
  1357
      maxidx = maxidx,
wenzelm@16601
  1358
      shyps = shyps,
wenzelm@16601
  1359
      hyps = hyps,
wenzelm@16601
  1360
      tpairs = tpairs,
wenzelm@28321
  1361
      prop = prop'})
paulson@7248
  1362
  end;
paulson@7248
  1363
paulson@7248
  1364
clasohm@0
  1365
(** User renaming of parameters in a subgoal **)
clasohm@0
  1366
clasohm@0
  1367
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1368
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1369
  The names in cs, if distinct, are used for the innermost parameters;
wenzelm@17868
  1370
  preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1371
fun rename_params_rule (cs, i) state =
wenzelm@16601
  1372
  let
wenzelm@28321
  1373
    val Thm (der, {thy_ref, tags, maxidx, shyps, hyps, ...}) = state;
wenzelm@16601
  1374
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1375
    val iparams = map #1 (Logic.strip_params Bi);
wenzelm@16601
  1376
    val short = length iparams - length cs;
wenzelm@16601
  1377
    val newnames =
wenzelm@16601
  1378
      if short < 0 then error "More names than abstractions!"
wenzelm@20071
  1379
      else Name.variant_list cs (Library.take (short, iparams)) @ cs;
wenzelm@20330
  1380
    val freenames = Term.fold_aterms (fn Free (x, _) => insert (op =) x | _ => I) Bi [];
wenzelm@16601
  1381
    val newBi = Logic.list_rename_params (newnames, Bi);
wenzelm@250
  1382
  in
wenzelm@21182
  1383
    (case duplicates (op =) cs of
wenzelm@21182
  1384
      a :: _ => (warning ("Can't rename.  Bound variables not distinct: " ^ a); state)
wenzelm@21182
  1385
    | [] =>
wenzelm@16601
  1386
      (case cs inter_string freenames of
wenzelm@16601
  1387
        a :: _ => (warning ("Can't rename.  Bound/Free variable clash: " ^ a); state)
wenzelm@16601
  1388
      | [] =>
wenzelm@28321
  1389
        Thm (der,
wenzelm@28321
  1390
         {thy_ref = thy_ref,
wenzelm@21646
  1391
          tags = tags,
wenzelm@16601
  1392
          maxidx = maxidx,
wenzelm@16601
  1393
          shyps = shyps,
wenzelm@16601
  1394
          hyps = hyps,
wenzelm@16601
  1395
          tpairs = tpairs,
wenzelm@28321
  1396
          prop = Logic.list_implies (Bs @ [newBi], C)})))
clasohm@0
  1397
  end;
clasohm@0
  1398
wenzelm@12982
  1399
clasohm@0
  1400
(*** Preservation of bound variable names ***)
clasohm@0
  1401
wenzelm@28321
  1402
fun rename_boundvars pat obj (thm as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@12982
  1403
  (case Term.rename_abs pat obj prop of
skalberg@15531
  1404
    NONE => thm
wenzelm@28321
  1405
  | SOME prop' => Thm (der,
wenzelm@16425
  1406
      {thy_ref = thy_ref,
wenzelm@21646
  1407
       tags = tags,
wenzelm@12982
  1408
       maxidx = maxidx,
wenzelm@12982
  1409
       hyps = hyps,
wenzelm@12982
  1410
       shyps = shyps,
berghofe@13658
  1411
       tpairs = tpairs,
wenzelm@28321
  1412
       prop = prop'}));
berghofe@10416
  1413
clasohm@0
  1414
wenzelm@16656
  1415
(* strip_apply f (A, B) strips off all assumptions/parameters from A
clasohm@0
  1416
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
  1417
fun strip_apply f =
clasohm@0
  1418
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@27336
  1419
                Const("==>",_)$ _  $ B2) = Logic.mk_implies (A1, strip(B1,B2))
wenzelm@250
  1420
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
  1421
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
  1422
        | strip(A,_) = f A
clasohm@0
  1423
  in strip end;
clasohm@0
  1424
clasohm@0
  1425
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1426
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1427
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1428
fun rename_bvs([],_,_,_) = I
clasohm@0
  1429
  | rename_bvs(al,dpairs,tpairs,B) =
wenzelm@20330
  1430
      let
wenzelm@20330
  1431
        val add_var = fold_aterms (fn Var ((x, _), _) => insert (op =) x | _ => I);
wenzelm@20330
  1432
        val vids = []
wenzelm@20330
  1433
          |> fold (add_var o fst) dpairs
wenzelm@20330
  1434
          |> fold (add_var o fst) tpairs
wenzelm@20330
  1435
          |> fold (add_var o snd) tpairs;
wenzelm@250
  1436
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1437
        fun rename(t as Var((x,i),T)) =
wenzelm@20330
  1438
              (case AList.lookup (op =) al x of
wenzelm@20330
  1439
                SOME y =>
wenzelm@20330
  1440
                  if member (op =) vids x orelse member (op =) vids y then t
wenzelm@20330
  1441
                  else Var((y,i),T)
wenzelm@20330
  1442
              | NONE=> t)
clasohm@0
  1443
          | rename(Abs(x,T,t)) =
wenzelm@18944
  1444
              Abs (the_default x (AList.lookup (op =) al x), T, rename t)
clasohm@0
  1445
          | rename(f$t) = rename f $ rename t
clasohm@0
  1446
          | rename(t) = t;
wenzelm@250
  1447
        fun strip_ren Ai = strip_apply rename (Ai,B)
wenzelm@20330
  1448
      in strip_ren end;
clasohm@0
  1449
clasohm@0
  1450
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
  1451
fun rename_bvars(dpairs, tpairs, B) =
wenzelm@23178
  1452
        rename_bvs(List.foldr Term.match_bvars [] dpairs, dpairs, tpairs, B);
clasohm@0
  1453
clasohm@0
  1454
clasohm@0
  1455
(*** RESOLUTION ***)
clasohm@0
  1456
lcp@721
  1457
(** Lifting optimizations **)
lcp@721
  1458
clasohm@0
  1459
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
  1460
  identical because of lifting*)
wenzelm@250
  1461
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
  1462
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
  1463
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
  1464
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
  1465
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
  1466
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
  1467
  | strip_assums2 BB = BB;
clasohm@0
  1468
clasohm@0
  1469
lcp@721
  1470
(*Faster normalization: skip assumptions that were lifted over*)
lcp@721
  1471
fun norm_term_skip env 0 t = Envir.norm_term env t
lcp@721
  1472
  | norm_term_skip env n (Const("all",_)$Abs(a,T,t)) =
lcp@721
  1473
        let val Envir.Envir{iTs, ...} = env
berghofe@15797
  1474
            val T' = Envir.typ_subst_TVars iTs T
wenzelm@1238
  1475
            (*Must instantiate types of parameters because they are flattened;
lcp@721
  1476
              this could be a NEW parameter*)
wenzelm@27336
  1477
        in Term.all T' $ Abs(a, T', norm_term_skip env n t)  end
lcp@721
  1478
  | norm_term_skip env n (Const("==>", _) $ A $ B) =
wenzelm@27336
  1479
        Logic.mk_implies (A, norm_term_skip env (n-1) B)
lcp@721
  1480
  | norm_term_skip env n t = error"norm_term_skip: too few assumptions??";
lcp@721
  1481
lcp@721
  1482
clasohm@0
  1483
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
  1484
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
  1485
  If match then forbid instantiations in proof state
clasohm@0
  1486
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
  1487
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
  1488
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
  1489
  Curried so that resolution calls dest_state only once.
clasohm@0
  1490
*)
wenzelm@4270
  1491
local exception COMPOSE
clasohm@0
  1492
in
wenzelm@18486
  1493
fun bicompose_aux flatten match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
  1494
                        (eres_flg, orule, nsubgoal) =
wenzelm@28321
  1495
 let val Thm (sder, {maxidx=smax, shyps=sshyps, hyps=shyps, ...}) = state
wenzelm@28321
  1496
     and Thm (rder, {maxidx=rmax, shyps=rshyps, hyps=rhyps,
wenzelm@28321
  1497
             tpairs=rtpairs, prop=rprop,...}) = orule
paulson@1529
  1498
         (*How many hyps to skip over during normalization*)
wenzelm@21576
  1499
     and nlift = Logic.count_prems (strip_all_body Bi) + (if eres_flg then ~1 else 0)
wenzelm@24143
  1500
     val thy = Theory.deref (merge_thys2 state orule);
clasohm@0
  1501
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
berghofe@11518
  1502
     fun addth A (As, oldAs, rder', n) ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
  1503
       let val normt = Envir.norm_term env;
wenzelm@250
  1504
           (*perform minimal copying here by examining env*)
berghofe@13658
  1505
           val (ntpairs, normp) =
berghofe@13658
  1506
             if Envir.is_empty env then (tpairs, (Bs @ As, C))
wenzelm@250
  1507
             else
wenzelm@250
  1508
             let val ntps = map (pairself normt) tpairs
wenzelm@19861
  1509
             in if Envir.above env smax then
wenzelm@1238
  1510
                  (*no assignments in state; normalize the rule only*)
wenzelm@1238
  1511
                  if lifted
berghofe@13658
  1512
                  then (ntps, (Bs @ map (norm_term_skip env nlift) As, C))
berghofe@13658
  1513
                  else (ntps, (Bs @ map normt As, C))
paulson@1529
  1514
                else if match then raise COMPOSE
wenzelm@250
  1515
                else (*normalize the new rule fully*)
berghofe@13658
  1516
                  (ntps, (map normt (Bs @ As), normt C))
wenzelm@250
  1517
             end
wenzelm@16601
  1518
           val th =
wenzelm@28321
  1519
             Thm (deriv_rule2
berghofe@11518
  1520
                   ((if Envir.is_empty env then I
wenzelm@19861
  1521
                     else if Envir.above env smax then
berghofe@11518
  1522
                       (fn f => fn der => f (Pt.norm_proof' env der))
berghofe@11518
  1523
                     else
berghofe@11518
  1524
                       curry op oo (Pt.norm_proof' env))
berghofe@23296
  1525
                    (Pt.bicompose_proof flatten Bs oldAs As A n (nlift+1))) rder' sder,
wenzelm@28321
  1526
                {tags = [],
wenzelm@2386
  1527
                 maxidx = maxidx,
wenzelm@26640
  1528
                 shyps = Envir.insert_sorts env (Sorts.union rshyps sshyps),
wenzelm@16601
  1529
                 hyps = union_hyps rhyps shyps,
berghofe@13658
  1530
                 tpairs = ntpairs,
wenzelm@24143
  1531
                 prop = Logic.list_implies normp,
wenzelm@28321
  1532
                 thy_ref = Theory.check_thy thy})
wenzelm@19475
  1533
        in  Seq.cons th thq  end  handle COMPOSE => thq;
berghofe@13658
  1534
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rprop)
clasohm@0
  1535
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
  1536
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
  1537
     fun newAs(As0, n, dpairs, tpairs) =
berghofe@11518
  1538
       let val (As1, rder') =
berghofe@25939
  1539
         if not lifted then (As0, rder)
berghofe@11518
  1540
         else (map (rename_bvars(dpairs,tpairs,B)) As0,
wenzelm@28321
  1541
           deriv_rule1 (Pt.map_proof_terms
berghofe@11518
  1542
             (rename_bvars (dpairs, tpairs, Bound 0)) I) rder);
wenzelm@18486
  1543
       in (map (if flatten then (Logic.flatten_params n) else I) As1, As1, rder', n)
wenzelm@250
  1544
          handle TERM _ =>
wenzelm@250
  1545
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
  1546
       end;
paulson@2147
  1547
     val env = Envir.empty(Int.max(rmax,smax));
clasohm@0
  1548
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
  1549
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
  1550
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
berghofe@11518
  1551
     fun tryasms (_, _, _, []) = Seq.empty
berghofe@11518
  1552
       | tryasms (A, As, n, (t,u)::apairs) =
wenzelm@16425
  1553
          (case Seq.pull(Unify.unifiers(thy, env, (t,u)::dpairs))  of
wenzelm@16425
  1554
              NONE                   => tryasms (A, As, n+1, apairs)
wenzelm@16425
  1555
            | cell as SOME((_,tpairs),_) =>
wenzelm@16425
  1556
                Seq.it_right (addth A (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@16425
  1557
                    (Seq.make(fn()=> cell),
wenzelm@16425
  1558
                     Seq.make(fn()=> Seq.pull (tryasms(A, As, n+1, apairs)))))
clasohm@0
  1559
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
skalberg@15531
  1560
       | eres (A1::As) = tryasms(SOME A1, As, 1, Logic.assum_pairs(nlift+1,A1))
clasohm@0
  1561
     (*ordinary resolution*)
skalberg@15531
  1562
     fun res(NONE) = Seq.empty
skalberg@15531
  1563
       | res(cell as SOME((_,tpairs),_)) =
skalberg@15531
  1564
             Seq.it_right (addth NONE (newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@4270
  1565
                       (Seq.make (fn()=> cell), Seq.empty)
clasohm@0
  1566
 in  if eres_flg then eres(rev rAs)
wenzelm@16425
  1567
     else res(Seq.pull(Unify.unifiers(thy, env, dpairs)))
clasohm@0
  1568
 end;
wenzelm@7528
  1569
end;
clasohm@0
  1570
wenzelm@18501
  1571
fun compose_no_flatten match (orule, nsubgoal) i state =
wenzelm@18501
  1572
  bicompose_aux false match (state, dest_state (state, i), false) (false, orule, nsubgoal);
clasohm@0
  1573
wenzelm@18501
  1574
fun bicompose match arg i state =
wenzelm@18501
  1575
  bicompose_aux true match (state, dest_state (state,i), false) arg;
clasohm@0
  1576
clasohm@0
  1577
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1578
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1579
fun could_bires (Hs, B, eres_flg, rule) =
wenzelm@16847
  1580
    let fun could_reshyp (A1::_) = exists (fn H => could_unify (A1, H)) Hs
wenzelm@250
  1581
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@250
  1582
    in  could_unify(concl_of rule, B) andalso
wenzelm@250
  1583
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1584
    end;
clasohm@0
  1585
clasohm@0
  1586
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1587
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1588
fun biresolution match brules i state =
wenzelm@18035
  1589
    let val (stpairs, Bs, Bi, C) = dest_state(state,i);
wenzelm@18145
  1590
        val lift = lift_rule (cprem_of state i);
wenzelm@250
  1591
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1592
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@22573
  1593
        val compose = bicompose_aux true match (state, (stpairs, Bs, Bi, C), true);
wenzelm@4270
  1594
        fun res [] = Seq.empty
wenzelm@250
  1595
          | res ((eres_flg, rule)::brules) =
nipkow@13642
  1596
              if !Pattern.trace_unify_fail orelse
nipkow@13642
  1597
                 could_bires (Hs, B, eres_flg, rule)
wenzelm@4270
  1598
              then Seq.make (*delay processing remainder till needed*)
wenzelm@22573
  1599
                  (fn()=> SOME(compose (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1600
                               res brules))
wenzelm@250
  1601
              else res brules
wenzelm@4270
  1602
    in  Seq.flat (res brules)  end;
clasohm@0
  1603
clasohm@0
  1604
wenzelm@28321
  1605
wenzelm@28321
  1606
(*** Promises ***)
wenzelm@28321
  1607
wenzelm@28330
  1608
(* promise *)
wenzelm@28330
  1609
wenzelm@28321
  1610
fun promise future ct =
wenzelm@28321
  1611
  let
wenzelm@28321
  1612
    val {thy_ref = thy_ref, t = prop, T, maxidx, sorts} = rep_cterm ct;
wenzelm@28321
  1613
    val thy = Context.reject_draft (Theory.deref thy_ref);
wenzelm@28321
  1614
    val _ = T <> propT andalso raise CTERM ("promise: prop expected", [ct]);
wenzelm@28321
  1615
    val i = serial ();
wenzelm@28321
  1616
  in
wenzelm@28330
  1617
    Thm (make_deriv false [(i, Promise (future, thy, sorts, prop))] (Pt.promise_proof i prop),
wenzelm@28321
  1618
     {thy_ref = thy_ref,
wenzelm@28321
  1619
      tags = [],
wenzelm@28321
  1620
      maxidx = maxidx,
wenzelm@28321
  1621
      shyps = sorts,
wenzelm@28321
  1622
      hyps = [],
wenzelm@28321
  1623
      tpairs = [],
wenzelm@28321
  1624
      prop = prop})
wenzelm@28321
  1625
  end;
wenzelm@28321
  1626
wenzelm@28330
  1627
fun check_promise (i, Promise (future, thy1, shyps1, prop1)) =
wenzelm@28330
  1628
  let
wenzelm@28330
  1629
    val thm = transfer thy1 (Future.join future);
wenzelm@28330
  1630
    val _ = Theory.check_thy thy1;
wenzelm@28330
  1631
    fun err msg = raise THM ("check_promise: " ^ msg, 0, [thm]);
wenzelm@28330
  1632
wenzelm@28330
  1633
    val Thm (Deriv {oracle, proof, promises}, {shyps, hyps, tpairs, prop, ...}) = thm;
wenzelm@28330
  1634
    val _ = null promises orelse err "illegal nested promises";
wenzelm@28330
  1635
    val _ = shyps = shyps1 orelse err "bad shyps";
wenzelm@28330
  1636
    val _ = null hyps orelse err "bad hyps";
wenzelm@28330
  1637
    val _ = null tpairs orelse err "bad tpairs";
wenzelm@28330
  1638
    val _ = prop aconv prop1 orelse err "bad prop";
wenzelm@28330
  1639
  in (oracle, (i, proof)) end;
wenzelm@28330
  1640
wenzelm@28330
  1641
wenzelm@28330
  1642
(* fulfill *)
wenzelm@28330
  1643
wenzelm@28330
  1644
fun fulfill (thm as Thm (Deriv {oracle, proof, promises}, args)) =
wenzelm@28330
  1645
  let
wenzelm@28330
  1646
    val _ = Future.join_results (map (fn (_, Promise (future, _, _, _)) => future) promises);
wenzelm@28330
  1647
    val results = map check_promise promises;
wenzelm@28330
  1648
wenzelm@28330
  1649
    val ora = oracle orelse exists #1 results;
wenzelm@28330
  1650
    val prf = Pt.fulfill (fold (Inttab.update o #2) results Inttab.empty) proof;
wenzelm@28330
  1651
  in Thm (make_deriv ora [] prf, args) end;
wenzelm@28330
  1652
wenzelm@28330
  1653
val proof_of = fulfill #> (fn Thm (Deriv {proof, ...}, _) => proof);
wenzelm@28330
  1654
wenzelm@28321
  1655
wenzelm@28321
  1656
wenzelm@2509
  1657
(*** Oracles ***)
wenzelm@2509
  1658
wenzelm@28290
  1659
(* oracle rule *)
wenzelm@28290
  1660
wenzelm@28290
  1661
fun invoke_oracle thy_ref1 name oracle arg =
wenzelm@28290
  1662
  let val {thy_ref = thy_ref2, t = prop, T, maxidx, sorts} = rep_cterm (oracle arg) in
wenzelm@28290
  1663
    if T <> propT then
wenzelm@28290
  1664
      raise THM ("Oracle's result must have type prop: " ^ name, 0, [])
wenzelm@28290
  1665
    else
wenzelm@28330
  1666
      Thm (make_deriv true [] (Pt.oracle_proof name prop),
wenzelm@28321
  1667
       {thy_ref = Theory.merge_refs (thy_ref1, thy_ref2),
wenzelm@28290
  1668
        tags = [],
wenzelm@28290
  1669
        maxidx = maxidx,
wenzelm@28290
  1670
        shyps = sorts,
wenzelm@28290
  1671
        hyps = [],
wenzelm@28290
  1672
        tpairs = [],
wenzelm@28321
  1673
        prop = prop})
wenzelm@3812
  1674
  end;
wenzelm@3812
  1675
wenzelm@22237
  1676
end;
wenzelm@22237
  1677
end;
wenzelm@22237
  1678
end;
wenzelm@28290
  1679
wenzelm@28290
  1680
wenzelm@28290
  1681
(* authentic derivation names *)
wenzelm@28290
  1682
wenzelm@28290
  1683
fun err_dup_ora dup = error ("Duplicate oracle: " ^ quote dup);
wenzelm@28290
  1684
wenzelm@28290
  1685
structure Oracles = TheoryDataFun
wenzelm@28290
  1686
(
wenzelm@28290
  1687
  type T = stamp NameSpace.table;
wenzelm@28290
  1688
  val empty = NameSpace.empty_table;
wenzelm@28290
  1689
  val copy = I;
wenzelm@28290
  1690
  val extend = I;
wenzelm@28290
  1691
  fun merge _ oracles = NameSpace.merge_tables (op =) oracles
wenzelm@28290
  1692
    handle Symtab.DUP dup => err_dup_ora dup;
wenzelm@28290
  1693
);
wenzelm@28290
  1694
wenzelm@28290
  1695
val extern_oracles = map #1 o NameSpace.extern_table o Oracles.get;
wenzelm@28290
  1696
wenzelm@28290
  1697
fun add_oracle (bname, oracle) thy =
wenzelm@28290
  1698
  let
wenzelm@28290
  1699
    val naming = Sign.naming_of thy;
wenzelm@28290
  1700
    val name = NameSpace.full naming bname;
wenzelm@28290
  1701
    val thy' = thy |> Oracles.map (fn (space, tab) =>
wenzelm@28290
  1702
      (NameSpace.declare naming name space,
wenzelm@28290
  1703
        Symtab.update_new (name, stamp ()) tab handle Symtab.DUP dup => err_dup_ora dup));
wenzelm@28290
  1704
  in ((name, invoke_oracle (Theory.check_thy thy') name oracle), thy') end;
wenzelm@28290
  1705
clasohm@0
  1706
end;
paulson@1503
  1707
wenzelm@6089
  1708
structure BasicThm: BASIC_THM = Thm;
wenzelm@6089
  1709
open BasicThm;