src/Pure/thm.ML
author wenzelm
Fri Jun 17 18:33:08 2005 +0200 (2005-06-17)
changeset 16425 2427be27cc60
parent 16352 d7f9978e5752
child 16601 ee8eefade568
permissions -rw-r--r--
accomodate identification of type Sign.sg and theory;
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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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meta theorems, meta rules (including lifting and resolution).
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*)
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signature BASIC_THM =
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  sig
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  (*certified types*)
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  type ctyp
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  val rep_ctyp: ctyp -> {thy: theory, sign: theory, T: typ}
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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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  val read_ctyp: theory -> string -> ctyp
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  (*certified terms*)
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  type cterm
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  exception CTERM of string
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  val rep_cterm: cterm -> {thy: theory, sign: theory, t: term, T: typ, maxidx: int}
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  val crep_cterm: cterm -> {thy: theory, sign: theory, t: term, T: ctyp, maxidx: int}
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  val theory_of_cterm: cterm -> theory
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  val sign_of_cterm: cterm -> theory    (*obsolete*)
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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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  val read_cterm: theory -> string * typ -> cterm
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  val adjust_maxidx: cterm -> cterm
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  val read_def_cterm:
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    theory * (indexname -> typ option) * (indexname -> sort option) ->
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    string list -> bool -> string * typ -> cterm * (indexname * typ) list
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  val read_def_cterms:
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    theory * (indexname -> typ option) * (indexname -> sort option) ->
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    string list -> bool -> (string * typ)list
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    -> cterm list * (indexname * typ)list
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  type tag              (* = string * string list *)
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  (*meta theorems*)
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  type thm
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  val rep_thm: thm ->
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   {thy: theory, sign: theory,
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    der: bool * Proofterm.proof,
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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: theory, sign: theory,
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    der: bool * Proofterm.proof,
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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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  type 'a attribute     (* = 'a * thm -> 'a * thm *)
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  val eq_thm: thm * thm -> bool
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  val eq_thms: thm list * thm list -> bool
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  val theory_of_thm: thm -> theory
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  val sign_of_thm: thm -> theory    (*obsolete*)
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  val prop_of: thm -> term
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  val proof_of: thm -> Proofterm.proof
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  val transfer: theory -> thm -> thm
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  val tpairs_of: thm -> (term * term) list
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  val prems_of: thm -> term list
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  val nprems_of: thm -> int
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  val concl_of: thm -> term
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  val cprop_of: thm -> cterm
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  val extra_shyps: thm -> sort list
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  val strip_shyps: thm -> thm
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  val get_axiom_i: theory -> string -> thm
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  val get_axiom: theory -> xstring -> thm
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  val def_name: string -> string
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  val get_def: theory -> xstring -> thm
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  val axioms_of: theory -> (string * thm) list
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  (*meta rules*)
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  val assume: cterm -> thm
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  val compress: thm -> thm
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  val implies_intr: cterm -> thm -> thm
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  val implies_elim: thm -> thm -> thm
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  val forall_intr: cterm -> thm -> thm
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  val forall_elim: cterm -> thm -> thm
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  val reflexive: cterm -> thm
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  val symmetric: thm -> thm
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  val transitive: thm -> thm -> thm
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  val beta_conversion: bool -> cterm -> thm
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  val eta_conversion: cterm -> thm
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  val abstract_rule: string -> cterm -> thm -> thm
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  val combination: thm -> thm -> thm
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  val equal_intr: thm -> thm -> thm
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  val equal_elim: thm -> thm -> thm
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  val implies_intr_hyps: thm -> thm
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  val flexflex_rule: thm -> thm Seq.seq
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  val instantiate: (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm
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  val trivial: cterm -> thm
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  val class_triv: theory -> class -> thm
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  val varifyT: thm -> thm
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  val varifyT': (string * sort) list -> thm -> thm * ((string * sort) * indexname) list
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  val freezeT: thm -> thm
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  val dest_state: thm * int -> (term * term) list * term list * term * term
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  val lift_rule: (thm * int) -> thm -> thm
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  val incr_indexes: int -> thm -> thm
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  val assumption: int -> thm -> thm Seq.seq
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  val eq_assumption: int -> thm -> thm
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  val rotate_rule: int -> int -> thm -> thm
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  val permute_prems: int -> int -> thm -> thm
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  val rename_params_rule: string list * int -> thm -> thm
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  val bicompose: bool -> bool * thm * int -> int -> thm -> thm Seq.seq
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  val biresolution: bool -> (bool * thm) list -> int -> thm -> thm Seq.seq
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  val invoke_oracle: theory -> xstring -> theory * Object.T -> thm
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  val invoke_oracle_i: theory -> string -> theory * Object.T -> thm
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end;
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signature THM =
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sig
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  include BASIC_THM
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  val dest_ctyp: ctyp -> ctyp list
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  val dest_comb: cterm -> cterm * cterm
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  val dest_abs: string option -> cterm -> cterm * cterm
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  val capply: cterm -> cterm -> cterm
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  val cabs: cterm -> cterm -> cterm
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  val major_prem_of: thm -> term
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  val no_prems: thm -> bool
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  val no_attributes: 'a -> 'a * 'b attribute list
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  val apply_attributes: ('a * thm) * 'a attribute list -> ('a * thm)
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  val applys_attributes: ('a * thm list) * 'a attribute list -> ('a * thm list)
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  val get_name_tags: thm -> string * tag list
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  val put_name_tags: string * tag list -> thm -> thm
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  val name_of_thm: thm -> string
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  val tags_of_thm: thm -> tag list
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  val name_thm: string * thm -> thm
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  val rename_boundvars: term -> term -> thm -> thm
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  val cterm_match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
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  val cterm_first_order_match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
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  val cterm_incr_indexes: int -> cterm -> cterm
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  val terms_of_tpairs: (term * term) list -> term list
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end;
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structure Thm: THM =
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struct
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(*** Certified terms and types ***)
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(** certified types **)
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datatype ctyp = Ctyp of {thy_ref: theory_ref, T: typ};
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fun rep_ctyp (Ctyp {thy_ref, T}) =
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  let val thy = Theory.deref thy_ref
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  in {thy = thy, sign = thy, T = T} end;
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val theory_of_ctyp = #thy o rep_ctyp;
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fun typ_of (Ctyp {T, ...}) = T;
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fun ctyp_of thy T =
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  Ctyp {thy_ref = Theory.self_ref thy, T = Sign.certify_typ thy T};
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fun read_ctyp thy s =
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  Ctyp {thy_ref = Theory.self_ref thy, T = Sign.read_typ (thy, K NONE) s};
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fun dest_ctyp (Ctyp {thy_ref, T = Type (s, Ts)}) =
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      map (fn T => Ctyp {thy_ref = thy_ref, T = T}) Ts
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  | dest_ctyp ct = [ct];
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(** certified terms **)
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(*certified terms with checked typ and maxidx of Vars/TVars*)
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datatype cterm = Cterm of {thy_ref: theory_ref, t: term, T: typ, maxidx: int};
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fun rep_cterm (Cterm {thy_ref, t, T, maxidx}) =
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  let val thy =  Theory.deref thy_ref
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  in {thy = thy, sign = thy, t = t, T = T, maxidx = maxidx} end;
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fun crep_cterm (Cterm {thy_ref, t, T, maxidx}) =
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  let val thy = Theory.deref thy_ref in
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    {thy = thy, sign = thy, t = t, T = Ctyp {thy_ref = thy_ref, T = T}, maxidx = maxidx}
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  end;
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fun theory_of_cterm (Cterm {thy_ref, ...}) = Theory.deref thy_ref;
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val sign_of_cterm = theory_of_cterm;
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fun term_of (Cterm {t, ...}) = t;
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fun ctyp_of_term (Cterm {thy_ref, T, ...}) = Ctyp {thy_ref = thy_ref, T = T};
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fun cterm_of thy tm =
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  let val (t, T, maxidx) = Sign.certify_term (Sign.pp thy) thy tm
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  in  Cterm {thy_ref = Theory.self_ref thy, t = t, T = T, maxidx = maxidx}
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  end;
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exception CTERM of string;
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(*Destruct application in cterms*)
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fun dest_comb (Cterm {thy_ref, T, maxidx, t = A $ B}) =
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      let val typeA = fastype_of A;
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          val typeB =
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            case typeA of Type("fun",[S,T]) => S
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                        | _ => error "Function type expected in dest_comb";
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      in
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      (Cterm {thy_ref=thy_ref, maxidx=maxidx, t=A, T=typeA},
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       Cterm {thy_ref=thy_ref, maxidx=maxidx, t=B, T=typeB})
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      end
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  | dest_comb _ = raise CTERM "dest_comb";
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(*Destruct abstraction in cterms*)
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fun dest_abs a (Cterm {thy_ref, T as Type("fun",[_,S]), maxidx, t=Abs(x,ty,M)}) =
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      let val (y,N) = variant_abs (if_none a x, ty, M)
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      in (Cterm {thy_ref = thy_ref, T = ty, maxidx = 0, t = Free(y,ty)},
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          Cterm {thy_ref = thy_ref, T = S, maxidx = maxidx, t = N})
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      end
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  | dest_abs _ _ = raise CTERM "dest_abs";
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(*Makes maxidx precise: it is often too big*)
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fun adjust_maxidx (ct as Cterm {thy_ref, T, t, maxidx, ...}) =
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  if maxidx = ~1 then ct
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  else  Cterm {thy_ref = thy_ref, T = T, maxidx = maxidx_of_term t, t = t};
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(*Form cterm out of a function and an argument*)
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fun capply (Cterm {t=f, thy_ref=thy_ref1, T=Type("fun",[dty,rty]), maxidx=maxidx1})
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           (Cterm {t=x, thy_ref=thy_ref2, T, maxidx=maxidx2}) =
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      if T = dty then
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        Cterm{t = f $ x,
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          thy_ref=Theory.merge_refs(thy_ref1,thy_ref2), T=rty,
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          maxidx=Int.max(maxidx1, maxidx2)}
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      else raise CTERM "capply: types don't agree"
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  | capply _ _ = raise CTERM "capply: first arg is not a function"
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fun cabs (Cterm {t=t1, thy_ref=thy_ref1, T=T1, maxidx=maxidx1})
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         (Cterm {t=t2, thy_ref=thy_ref2, T=T2, maxidx=maxidx2}) =
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      Cterm {t = lambda t1 t2, thy_ref = Theory.merge_refs (thy_ref1,thy_ref2),
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             T = T1 --> T2, maxidx=Int.max(maxidx1, maxidx2)}
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      handle TERM _ => raise CTERM "cabs: first arg is not a variable";
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(*Matching of cterms*)
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fun gen_cterm_match mtch
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      (Cterm {thy_ref = thy_ref1, maxidx = maxidx1, t = t1, ...},
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       Cterm {thy_ref = thy_ref2, maxidx = maxidx2, t = t2, ...}) =
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  let
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    val thy_ref = Theory.merge_refs (thy_ref1, thy_ref2);
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    val tsig = Sign.tsig_of (Theory.deref thy_ref);
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    val (Tinsts, tinsts) = mtch tsig (t1, t2);
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    val maxidx = Int.max (maxidx1, maxidx2);
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    fun mk_cTinsts (ixn, (S, T)) =
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      (Ctyp {thy_ref = thy_ref, T = TVar (ixn, S)},
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       Ctyp {thy_ref = thy_ref, T = T});
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    fun mk_ctinsts (ixn, (T, t)) =
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      let val T = Envir.typ_subst_TVars Tinsts T
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      in
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        (Cterm {thy_ref = thy_ref, maxidx = maxidx, T = T, t = Var (ixn, T)},
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         Cterm {thy_ref = thy_ref, maxidx = maxidx, T = T, t = t})
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      end;
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  in (map mk_cTinsts (Vartab.dest Tinsts),
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    map mk_ctinsts (Vartab.dest tinsts))
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  end;
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val cterm_match = gen_cterm_match Pattern.match;
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val cterm_first_order_match = gen_cterm_match Pattern.first_order_match;
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(*Incrementing indexes*)
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fun cterm_incr_indexes i (ct as Cterm {thy_ref, maxidx, t, T}) =
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  if i < 0 then raise CTERM "negative increment" else
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  if i = 0 then ct else
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    Cterm {thy_ref = thy_ref, maxidx = maxidx + i,
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      t = Logic.incr_indexes ([], i) t, T = Term.incr_tvar i T};
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(** read cterms **)   (*exception ERROR*)
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(*read terms, infer types, certify terms*)
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fun read_def_cterms (thy, types, sorts) used freeze sTs =
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  let
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    val (ts', tye) = Sign.read_def_terms (thy, types, sorts) used freeze sTs;
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    val cts = map (cterm_of thy) ts'
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      handle TYPE (msg, _, _) => error msg
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           | TERM (msg, _) => error msg;
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  in (cts, tye) end;
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(*read term, infer types, certify term*)
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fun read_def_cterm args used freeze aT =
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  let val ([ct],tye) = read_def_cterms args used freeze [aT]
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  in (ct,tye) end;
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fun read_cterm thy = #1 o read_def_cterm (thy, K NONE, K NONE) [] true;
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(*tags provide additional comment, apart from the axiom/theorem name*)
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type tag = string * string list;
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(*** Meta theorems ***)
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structure Pt = Proofterm;
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datatype thm = Thm of
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 {thy_ref: theory_ref,         (*dynamic reference to theory*)
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  der: bool * Pt.proof,        (*derivation*)
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  maxidx: int,                 (*maximum index of any Var or TVar*)
wenzelm@3967
   310
  shyps: sort list,            (*sort hypotheses*)
wenzelm@3967
   311
  hyps: term list,             (*hypotheses*)
berghofe@13658
   312
  tpairs: (term * term) list,  (*flex-flex pairs*)
wenzelm@3967
   313
  prop: term};                 (*conclusion*)
clasohm@0
   314
wenzelm@16024
   315
fun terms_of_tpairs tpairs = List.concat (map (fn (t, u) => [t, u]) tpairs);
berghofe@13658
   316
berghofe@13658
   317
fun attach_tpairs tpairs prop =
berghofe@13658
   318
  Logic.list_implies (map Logic.mk_equals tpairs, prop);
berghofe@13658
   319
wenzelm@16425
   320
fun rep_thm (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   321
  let val thy = Theory.deref thy_ref in
wenzelm@16425
   322
   {thy = thy, sign = thy, der = der, maxidx = maxidx,
wenzelm@16425
   323
    shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@16425
   324
  end;
clasohm@0
   325
wenzelm@16425
   326
(*version of rep_thm returning cterms instead of terms*)
wenzelm@16425
   327
fun crep_thm (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   328
  let
wenzelm@16425
   329
    val thy = Theory.deref thy_ref;
wenzelm@16425
   330
    fun cterm max t = Cterm {thy_ref = thy_ref, t = t, T = propT, maxidx = max};
wenzelm@16425
   331
  in
wenzelm@16425
   332
   {thy = thy, sign = thy, der = der, maxidx = maxidx, shyps = shyps,
wenzelm@16425
   333
    hyps = map (cterm ~1) hyps,
wenzelm@16425
   334
    tpairs = map (pairself (cterm maxidx)) tpairs,
wenzelm@16425
   335
    prop = cterm maxidx prop}
clasohm@1517
   336
  end;
clasohm@1517
   337
wenzelm@387
   338
(*errors involving theorems*)
clasohm@0
   339
exception THM of string * int * thm list;
clasohm@0
   340
wenzelm@16425
   341
(*attributes subsume any kind of rules or context modifiers*)
wenzelm@6089
   342
type 'a attribute = 'a * thm -> 'a * thm;
wenzelm@6089
   343
wenzelm@6089
   344
fun no_attributes x = (x, []);
wenzelm@6089
   345
fun apply_attributes (x_th, atts) = Library.apply atts x_th;
wenzelm@6089
   346
fun applys_attributes (x_ths, atts) = foldl_map (Library.apply atts) x_ths;
wenzelm@6089
   347
wenzelm@3994
   348
fun eq_thm (th1, th2) =
wenzelm@3994
   349
  let
wenzelm@16425
   350
    val {thy = thy1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1, prop = prop1, ...} =
wenzelm@9031
   351
      rep_thm th1;
wenzelm@16425
   352
    val {thy = thy2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2, prop = prop2, ...} =
wenzelm@9031
   353
      rep_thm th2;
wenzelm@3994
   354
  in
wenzelm@16425
   355
    (subthy (thy1, thy2) orelse subthy (thy2, thy1)) andalso
wenzelm@14791
   356
    Sorts.eq_set_sort (shyps1, shyps2) andalso
wenzelm@3994
   357
    aconvs (hyps1, hyps2) andalso
berghofe@13658
   358
    aconvs (terms_of_tpairs tpairs1, terms_of_tpairs tpairs2) andalso
wenzelm@3994
   359
    prop1 aconv prop2
wenzelm@3994
   360
  end;
wenzelm@387
   361
wenzelm@16135
   362
val eq_thms = Library.equal_lists eq_thm;
wenzelm@16135
   363
wenzelm@16425
   364
fun theory_of_thm (Thm {thy_ref, ...}) = Theory.deref thy_ref;
wenzelm@16425
   365
val sign_of_thm = theory_of_thm;
wenzelm@16425
   366
wenzelm@12803
   367
fun prop_of (Thm {prop, ...}) = prop;
wenzelm@13528
   368
fun proof_of (Thm {der = (_, proof), ...}) = proof;
clasohm@0
   369
wenzelm@16425
   370
(*merge theories of two theorems; raise exception if incompatible*)
wenzelm@16425
   371
fun merge_thm_thys
wenzelm@16425
   372
    (th1 as Thm {thy_ref = r1, ...}, th2 as Thm {thy_ref = r2, ...}) =
wenzelm@16425
   373
  Theory.merge_refs (r1, r2) handle TERM (msg, _) => raise THM (msg, 0, [th1, th2]);
wenzelm@387
   374
wenzelm@3967
   375
(*transfer thm to super theory (non-destructive)*)
wenzelm@16425
   376
fun transfer thy' thm =
wenzelm@3895
   377
  let
wenzelm@16425
   378
    val Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop} = thm;
wenzelm@16425
   379
    val thy = Theory.deref thy_ref;
wenzelm@3895
   380
  in
wenzelm@16425
   381
    if eq_thy (thy, thy') then thm
wenzelm@16425
   382
    else if subthy (thy, thy') then
wenzelm@16425
   383
      Thm {thy_ref = Theory.self_ref thy', der = der, maxidx = maxidx,
berghofe@13658
   384
        shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@3895
   385
    else raise THM ("transfer: not a super theory", 0, [thm])
wenzelm@3895
   386
  end;
wenzelm@387
   387
wenzelm@387
   388
(*maps object-rule to tpairs*)
berghofe@13658
   389
fun tpairs_of (Thm {tpairs, ...}) = tpairs;
wenzelm@387
   390
wenzelm@387
   391
(*maps object-rule to premises*)
wenzelm@387
   392
fun prems_of (Thm {prop, ...}) =
berghofe@13658
   393
  Logic.strip_imp_prems prop;
clasohm@0
   394
clasohm@0
   395
(*counts premises in a rule*)
wenzelm@387
   396
fun nprems_of (Thm {prop, ...}) =
berghofe@13658
   397
  Logic.count_prems (prop, 0);
clasohm@0
   398
wenzelm@8299
   399
fun major_prem_of thm =
wenzelm@8299
   400
  (case prems_of thm of
wenzelm@11692
   401
    prem :: _ => Logic.strip_assums_concl prem
wenzelm@8299
   402
  | [] => raise THM ("major_prem_of: rule with no premises", 0, [thm]));
wenzelm@8299
   403
wenzelm@7534
   404
fun no_prems thm = nprems_of thm = 0;
wenzelm@7534
   405
wenzelm@387
   406
(*maps object-rule to conclusion*)
wenzelm@387
   407
fun concl_of (Thm {prop, ...}) = Logic.strip_imp_concl prop;
clasohm@0
   408
wenzelm@387
   409
(*the statement of any thm is a cterm*)
wenzelm@16425
   410
fun cprop_of (Thm {thy_ref, maxidx, prop, ...}) =
wenzelm@16425
   411
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, t = prop};
lcp@229
   412
wenzelm@387
   413
clasohm@0
   414
wenzelm@1238
   415
(** sort contexts of theorems **)
wenzelm@1238
   416
wenzelm@1238
   417
(* basic utils *)
wenzelm@1238
   418
wenzelm@2163
   419
(*accumulate sorts suppressing duplicates; these are coded low levelly
wenzelm@1238
   420
  to improve efficiency a bit*)
wenzelm@1238
   421
wenzelm@1238
   422
fun add_typ_sorts (Type (_, Ts), Ss) = add_typs_sorts (Ts, Ss)
wenzelm@14791
   423
  | add_typ_sorts (TFree (_, S), Ss) = Sorts.ins_sort(S,Ss)
wenzelm@14791
   424
  | add_typ_sorts (TVar (_, S), Ss) = Sorts.ins_sort(S,Ss)
wenzelm@1238
   425
and add_typs_sorts ([], Ss) = Ss
wenzelm@1238
   426
  | add_typs_sorts (T :: Ts, Ss) = add_typs_sorts (Ts, add_typ_sorts (T, Ss));
wenzelm@1238
   427
wenzelm@1238
   428
fun add_term_sorts (Const (_, T), Ss) = add_typ_sorts (T, Ss)
wenzelm@1238
   429
  | add_term_sorts (Free (_, T), Ss) = add_typ_sorts (T, Ss)
wenzelm@1238
   430
  | add_term_sorts (Var (_, T), Ss) = add_typ_sorts (T, Ss)
wenzelm@1238
   431
  | add_term_sorts (Bound _, Ss) = Ss
paulson@2177
   432
  | add_term_sorts (Abs (_,T,t), Ss) = add_term_sorts (t, add_typ_sorts (T,Ss))
wenzelm@1238
   433
  | add_term_sorts (t $ u, Ss) = add_term_sorts (t, add_term_sorts (u, Ss));
wenzelm@1238
   434
wenzelm@1238
   435
fun add_terms_sorts ([], Ss) = Ss
paulson@2177
   436
  | add_terms_sorts (t::ts, Ss) = add_terms_sorts (ts, add_term_sorts (t,Ss));
wenzelm@1238
   437
berghofe@15797
   438
fun env_codT (Envir.Envir {iTs, ...}) = map (snd o snd) (Vartab.dest iTs);
wenzelm@1258
   439
berghofe@8407
   440
fun add_env_sorts (Envir.Envir {iTs, asol, ...}, Ss) =
berghofe@15797
   441
  Vartab.foldl (add_term_sorts o swap o apsnd (snd o snd))
berghofe@15797
   442
    (Vartab.foldl (add_typ_sorts o swap o apsnd (snd o snd)) (Ss, iTs), asol);
wenzelm@1258
   443
berghofe@10416
   444
fun add_insts_sorts ((iTs, is), Ss) =
berghofe@10416
   445
  add_typs_sorts (map snd iTs, add_terms_sorts (map snd is, Ss));
berghofe@10416
   446
berghofe@13658
   447
fun add_thm_sorts (Thm {hyps, tpairs, prop, ...}, Ss) =
berghofe@13658
   448
  add_terms_sorts (hyps @ terms_of_tpairs tpairs, add_term_sorts (prop, Ss));
wenzelm@1238
   449
wenzelm@1238
   450
fun add_thms_shyps ([], Ss) = Ss
wenzelm@1238
   451
  | add_thms_shyps (Thm {shyps, ...} :: ths, Ss) =
wenzelm@14791
   452
      add_thms_shyps (ths, Sorts.union_sort (shyps, Ss));
wenzelm@1238
   453
wenzelm@1238
   454
wenzelm@1238
   455
(*get 'dangling' sort constraints of a thm*)
wenzelm@1238
   456
fun extra_shyps (th as Thm {shyps, ...}) =
wenzelm@14791
   457
  Sorts.rems_sort (shyps, add_thm_sorts (th, []));
wenzelm@1238
   458
wenzelm@1238
   459
wenzelm@1238
   460
(* fix_shyps *)
wenzelm@1238
   461
wenzelm@16425
   462
val all_sorts_nonempty = is_some o Sign.universal_witness o Theory.deref;
wenzelm@7642
   463
wenzelm@1238
   464
(*preserve sort contexts of rule premises and substituted types*)
wenzelm@16425
   465
fun fix_shyps thms Ts (thm as Thm {thy_ref, der, maxidx, hyps, tpairs, prop, ...}) =
wenzelm@7642
   466
  Thm
wenzelm@16425
   467
   {thy_ref = thy_ref,
wenzelm@7642
   468
    der = der,             (*no new derivation, as other rules call this*)
wenzelm@7642
   469
    maxidx = maxidx,
wenzelm@7642
   470
    shyps =
wenzelm@16425
   471
      if all_sorts_nonempty thy_ref then []
wenzelm@7642
   472
      else add_thm_sorts (thm, add_typs_sorts (Ts, add_thms_shyps (thms, []))),
berghofe@13658
   473
    hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@1238
   474
wenzelm@1238
   475
wenzelm@7642
   476
(* strip_shyps *)
wenzelm@1238
   477
wenzelm@7642
   478
(*remove extra sorts that are non-empty by virtue of type signature information*)
wenzelm@7642
   479
fun strip_shyps (thm as Thm {shyps = [], ...}) = thm
wenzelm@16425
   480
  | strip_shyps (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@7642
   481
      let
wenzelm@16425
   482
        val thy = Theory.deref thy_ref;
wenzelm@7642
   483
        val present_sorts = add_thm_sorts (thm, []);
wenzelm@14791
   484
        val extra_shyps = Sorts.rems_sort (shyps, present_sorts);
wenzelm@16425
   485
        val witnessed_shyps = Sign.witness_sorts thy present_sorts extra_shyps;
wenzelm@7642
   486
      in
wenzelm@16425
   487
        Thm {thy_ref = thy_ref, der = der, maxidx = maxidx,
wenzelm@14791
   488
             shyps = Sorts.rems_sort (shyps, map #2 witnessed_shyps),
berghofe@13658
   489
             hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@7642
   490
      end;
wenzelm@1238
   491
wenzelm@1238
   492
wenzelm@1238
   493
paulson@1529
   494
(** Axioms **)
wenzelm@387
   495
wenzelm@16425
   496
(*look up the named axiom in the theory or its ancestors*)
wenzelm@15672
   497
fun get_axiom_i theory name =
wenzelm@387
   498
  let
wenzelm@16425
   499
    fun get_ax thy =
wenzelm@16425
   500
      Symtab.lookup (#2 (#axioms (Theory.rep_theory thy)), name)
wenzelm@16425
   501
      |> Option.map (fn t =>
wenzelm@16425
   502
          fix_shyps [] []
wenzelm@16425
   503
            (Thm {thy_ref = Theory.self_ref thy,
wenzelm@16425
   504
              der = Pt.infer_derivs' I (false, Pt.axm_proof name t),
wenzelm@16425
   505
              maxidx = maxidx_of_term t,
wenzelm@16425
   506
              shyps = [],
wenzelm@16425
   507
              hyps = [],
wenzelm@16425
   508
              tpairs = [],
wenzelm@16425
   509
              prop = t}));
wenzelm@387
   510
  in
wenzelm@16425
   511
    (case get_first get_ax (theory :: Theory.ancestors_of theory) of
skalberg@15531
   512
      SOME thm => thm
skalberg@15531
   513
    | NONE => raise THEORY ("No axiom " ^ quote name, [theory]))
wenzelm@387
   514
  end;
wenzelm@387
   515
wenzelm@16352
   516
fun get_axiom thy =
wenzelm@16425
   517
  get_axiom_i thy o NameSpace.intern (Theory.axiom_space thy);
wenzelm@15672
   518
wenzelm@6368
   519
fun def_name name = name ^ "_def";
wenzelm@6368
   520
fun get_def thy = get_axiom thy o def_name;
wenzelm@4847
   521
paulson@1529
   522
wenzelm@776
   523
(*return additional axioms of this theory node*)
wenzelm@776
   524
fun axioms_of thy =
wenzelm@776
   525
  map (fn (s, _) => (s, get_axiom thy s))
wenzelm@16352
   526
    (Symtab.dest (#2 (#axioms (Theory.rep_theory thy))));
wenzelm@776
   527
wenzelm@6089
   528
wenzelm@6089
   529
(* name and tags -- make proof objects more readable *)
wenzelm@6089
   530
wenzelm@12923
   531
fun get_name_tags (Thm {hyps, prop, der = (_, prf), ...}) =
wenzelm@12923
   532
  Pt.get_name_tags hyps prop prf;
wenzelm@4018
   533
wenzelm@16425
   534
fun put_name_tags x (Thm {thy_ref, der = (ora, prf), maxidx,
wenzelm@16425
   535
      shyps, hyps, tpairs = [], prop}) = Thm {thy_ref = thy_ref,
wenzelm@16425
   536
        der = (ora, Pt.thm_proof (Theory.deref thy_ref) x hyps prop prf),
berghofe@13658
   537
        maxidx = maxidx, shyps = shyps, hyps = hyps, tpairs = [], prop = prop}
berghofe@13658
   538
  | put_name_tags _ thm =
berghofe@13658
   539
      raise THM ("put_name_tags: unsolved flex-flex constraints", 0, [thm]);
wenzelm@6089
   540
wenzelm@6089
   541
val name_of_thm = #1 o get_name_tags;
wenzelm@6089
   542
val tags_of_thm = #2 o get_name_tags;
wenzelm@6089
   543
wenzelm@6089
   544
fun name_thm (name, thm) = put_name_tags (name, tags_of_thm thm) thm;
clasohm@0
   545
clasohm@0
   546
paulson@1529
   547
(*Compression of theorems -- a separate rule, not integrated with the others,
paulson@1529
   548
  as it could be slow.*)
wenzelm@16425
   549
fun compress (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   550
    Thm {thy_ref = thy_ref,
wenzelm@2386
   551
         der = der,     (*No derivation recorded!*)
wenzelm@2386
   552
         maxidx = maxidx,
wenzelm@16425
   553
         shyps = shyps,
wenzelm@16425
   554
         hyps = map Term.compress_term hyps,
berghofe@13658
   555
         tpairs = map (pairself Term.compress_term) tpairs,
wenzelm@2386
   556
         prop = Term.compress_term prop};
wenzelm@564
   557
wenzelm@387
   558
wenzelm@2509
   559
paulson@1529
   560
(*** Meta rules ***)
clasohm@0
   561
wenzelm@1220
   562
(** 'primitive' rules **)
wenzelm@1220
   563
wenzelm@1220
   564
(*discharge all assumptions t from ts*)
clasohm@0
   565
val disch = gen_rem (op aconv);
clasohm@0
   566
wenzelm@1220
   567
(*The assumption rule A|-A in a theory*)
wenzelm@5344
   568
fun assume raw_ct : thm =
wenzelm@16425
   569
  let val ct as Cterm {thy_ref, t=prop, T, maxidx} = adjust_maxidx raw_ct
wenzelm@250
   570
  in  if T<>propT then
wenzelm@250
   571
        raise THM("assume: assumptions must have type prop", 0, [])
clasohm@0
   572
      else if maxidx <> ~1 then
wenzelm@250
   573
        raise THM("assume: assumptions may not contain scheme variables",
wenzelm@250
   574
                  maxidx, [])
wenzelm@16425
   575
      else Thm{thy_ref   = thy_ref,
berghofe@11518
   576
               der    = Pt.infer_derivs' I (false, Pt.Hyp prop),
wenzelm@16425
   577
               maxidx = ~1,
wenzelm@16425
   578
               shyps  = add_term_sorts(prop,[]),
wenzelm@16425
   579
               hyps   = [prop],
berghofe@13658
   580
               tpairs = [],
wenzelm@2386
   581
               prop   = prop}
clasohm@0
   582
  end;
clasohm@0
   583
wenzelm@1220
   584
(*Implication introduction
wenzelm@3529
   585
    [A]
wenzelm@3529
   586
     :
wenzelm@3529
   587
     B
wenzelm@1220
   588
  -------
wenzelm@1220
   589
  A ==> B
wenzelm@1220
   590
*)
wenzelm@16425
   591
fun implies_intr cA (thB as Thm{thy_ref,der,maxidx,hyps,shyps,tpairs,prop}) : thm =
wenzelm@16425
   592
  let val Cterm {thy_ref=thy_refA, t=A, T, maxidx=maxidxA} = cA
clasohm@0
   593
  in  if T<>propT then
wenzelm@250
   594
        raise THM("implies_intr: assumptions must have type prop", 0, [thB])
berghofe@10416
   595
      else
wenzelm@16425
   596
         Thm{thy_ref = Theory.merge_refs (thy_ref,thy_refA),
berghofe@11518
   597
             der = Pt.infer_derivs' (Pt.implies_intr_proof A) der,
wenzelm@2386
   598
             maxidx = Int.max(maxidxA, maxidx),
berghofe@10416
   599
             shyps = add_term_sorts (A, shyps),
wenzelm@2386
   600
             hyps = disch(hyps,A),
berghofe@13658
   601
             tpairs = tpairs,
berghofe@10416
   602
             prop = implies$A$prop}
clasohm@0
   603
      handle TERM _ =>
wenzelm@16425
   604
        raise THM("implies_intr: incompatible theories", 0, [thB])
clasohm@0
   605
  end;
clasohm@0
   606
paulson@1529
   607
wenzelm@1220
   608
(*Implication elimination
wenzelm@1220
   609
  A ==> B    A
wenzelm@1220
   610
  ------------
wenzelm@1220
   611
        B
wenzelm@1220
   612
*)
clasohm@0
   613
fun implies_elim thAB thA : thm =
berghofe@13658
   614
    let val Thm{maxidx=maxA, der=derA, hyps=hypsA, shyps=shypsA, tpairs=tpairsA, prop=propA, ...} = thA
berghofe@13658
   615
        and Thm{der, maxidx, hyps, shyps, tpairs, prop, ...} = thAB;
wenzelm@250
   616
        fun err(a) = raise THM("implies_elim: "^a, 0, [thAB,thA])
clasohm@0
   617
    in  case prop of
wenzelm@250
   618
            imp$A$B =>
wenzelm@250
   619
                if imp=implies andalso  A aconv propA
berghofe@10416
   620
                then
wenzelm@16425
   621
                  Thm{thy_ref= merge_thm_thys (thAB, thA),
berghofe@11612
   622
                      der = Pt.infer_derivs (curry Pt.%%) der derA,
berghofe@10416
   623
                      maxidx = Int.max(maxA,maxidx),
wenzelm@14791
   624
                      shyps = Sorts.union_sort (shypsA, shyps),
berghofe@10416
   625
                      hyps = union_term(hypsA,hyps),  (*dups suppressed*)
berghofe@13658
   626
                      tpairs = tpairsA @ tpairs,
berghofe@10416
   627
                      prop = B}
wenzelm@250
   628
                else err("major premise")
wenzelm@250
   629
          | _ => err("major premise")
clasohm@0
   630
    end;
wenzelm@250
   631
wenzelm@1220
   632
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@1220
   633
    A
wenzelm@1220
   634
  -----
wenzelm@1220
   635
  !!x.A
wenzelm@1220
   636
*)
wenzelm@16425
   637
fun forall_intr cx (th as Thm{thy_ref,der,maxidx,hyps,tpairs,prop,...}) =
lcp@229
   638
  let val x = term_of cx;
berghofe@13658
   639
      fun result a T = fix_shyps [th] []
wenzelm@16425
   640
        (Thm{thy_ref = thy_ref,
berghofe@11518
   641
             der = Pt.infer_derivs' (Pt.forall_intr_proof x a) der,
wenzelm@2386
   642
             maxidx = maxidx,
wenzelm@2386
   643
             shyps = [],
wenzelm@2386
   644
             hyps = hyps,
berghofe@13658
   645
             tpairs = tpairs,
wenzelm@2386
   646
             prop = all(T) $ Abs(a, T, abstract_over (x,prop))})
berghofe@13658
   647
      fun check_occs x ts =
berghofe@13658
   648
        if exists (apl(x, Logic.occs)) ts
berghofe@13658
   649
        then raise THM("forall_intr: variable free in assumptions", 0, [th])
berghofe@13658
   650
        else ()
clasohm@0
   651
  in  case x of
berghofe@13658
   652
        Free(a,T) => (check_occs x (hyps @ terms_of_tpairs tpairs); result a T)
berghofe@13658
   653
      | Var((a,_),T) => (check_occs x (terms_of_tpairs tpairs); result a T)
clasohm@0
   654
      | _ => raise THM("forall_intr: not a variable", 0, [th])
clasohm@0
   655
  end;
clasohm@0
   656
wenzelm@1220
   657
(*Forall elimination
wenzelm@1220
   658
  !!x.A
wenzelm@1220
   659
  ------
wenzelm@1220
   660
  A[t/x]
wenzelm@1220
   661
*)
wenzelm@16425
   662
fun forall_elim ct (th as Thm{thy_ref,der,maxidx,hyps,tpairs,prop,...}) : thm =
wenzelm@16425
   663
  let val Cterm {thy_ref=thy_reft, t, T, maxidx=maxt} = ct
clasohm@0
   664
  in  case prop of
wenzelm@2386
   665
        Const("all",Type("fun",[Type("fun",[qary,_]),_])) $ A =>
wenzelm@2386
   666
          if T<>qary then
wenzelm@2386
   667
              raise THM("forall_elim: type mismatch", 0, [th])
berghofe@15797
   668
          else fix_shyps [th] []
wenzelm@16425
   669
                    (Thm{thy_ref= Theory.merge_refs(thy_ref,thy_reft),
skalberg@15531
   670
                         der = Pt.infer_derivs' (Pt.% o rpair (SOME t)) der,
wenzelm@2386
   671
                         maxidx = Int.max(maxidx, maxt),
wenzelm@2386
   672
                         shyps = [],
wenzelm@16425
   673
                         hyps = hyps,
berghofe@13658
   674
                         tpairs = tpairs,
wenzelm@2386
   675
                         prop = betapply(A,t)})
paulson@2147
   676
      | _ => raise THM("forall_elim: not quantified", 0, [th])
clasohm@0
   677
  end
clasohm@0
   678
  handle TERM _ =>
wenzelm@16425
   679
         raise THM("forall_elim: incompatible theories", 0, [th]);
clasohm@0
   680
clasohm@0
   681
wenzelm@1220
   682
(* Equality *)
clasohm@0
   683
clasohm@0
   684
(*The reflexivity rule: maps  t   to the theorem   t==t   *)
wenzelm@250
   685
fun reflexive ct =
wenzelm@16425
   686
  let val Cterm {thy_ref, t, T, maxidx} = ct
wenzelm@16425
   687
  in Thm{thy_ref= thy_ref,
berghofe@11518
   688
         der = Pt.infer_derivs' I (false, Pt.reflexive),
berghofe@10416
   689
         shyps = add_term_sorts (t, []),
wenzelm@16425
   690
         hyps = [],
berghofe@10416
   691
         maxidx = maxidx,
berghofe@13658
   692
         tpairs = [],
berghofe@10416
   693
         prop = Logic.mk_equals(t,t)}
clasohm@0
   694
  end;
clasohm@0
   695
clasohm@0
   696
(*The symmetry rule
wenzelm@1220
   697
  t==u
wenzelm@1220
   698
  ----
wenzelm@1220
   699
  u==t
wenzelm@1220
   700
*)
wenzelm@16425
   701
fun symmetric (th as Thm{thy_ref,der,maxidx,shyps,hyps,tpairs,prop}) =
clasohm@0
   702
  case prop of
berghofe@11518
   703
      (eq as Const("==", Type (_, [T, _]))) $ t $ u =>
wenzelm@1238
   704
        (*no fix_shyps*)
wenzelm@16425
   705
          Thm{thy_ref = thy_ref,
berghofe@11518
   706
              der = Pt.infer_derivs' Pt.symmetric der,
wenzelm@2386
   707
              maxidx = maxidx,
wenzelm@2386
   708
              shyps = shyps,
wenzelm@2386
   709
              hyps = hyps,
berghofe@13658
   710
              tpairs = tpairs,
wenzelm@2386
   711
              prop = eq$u$t}
clasohm@0
   712
    | _ => raise THM("symmetric", 0, [th]);
clasohm@0
   713
clasohm@0
   714
(*The transitive rule
wenzelm@1220
   715
  t1==u    u==t2
wenzelm@1220
   716
  --------------
wenzelm@1220
   717
      t1==t2
wenzelm@1220
   718
*)
clasohm@0
   719
fun transitive th1 th2 =
berghofe@13658
   720
  let val Thm{der=der1, maxidx=max1, hyps=hyps1, shyps=shyps1, tpairs=tpairs1, prop=prop1,...} = th1
berghofe@13658
   721
      and Thm{der=der2, maxidx=max2, hyps=hyps2, shyps=shyps2, tpairs=tpairs2, prop=prop2,...} = th2;
wenzelm@16425
   722
      fun err msg = raise THM("transitive: "^msg, 0, [th1,th2])
clasohm@0
   723
  in case (prop1,prop2) of
berghofe@11518
   724
       ((eq as Const("==", Type (_, [T, _]))) $ t1 $ u, Const("==",_) $ u' $ t2) =>
nipkow@1634
   725
          if not (u aconv u') then err"middle term"
berghofe@15797
   726
          else
wenzelm@16425
   727
                 Thm{thy_ref= merge_thm_thys (th1, th2),
berghofe@11518
   728
                     der = Pt.infer_derivs (Pt.transitive u T) der1 der2,
wenzelm@16425
   729
                     maxidx = Int.max(max1,max2),
wenzelm@14791
   730
                     shyps = Sorts.union_sort (shyps1, shyps2),
wenzelm@2386
   731
                     hyps = union_term(hyps1,hyps2),
berghofe@13658
   732
                     tpairs = tpairs1 @ tpairs2,
berghofe@10416
   733
                     prop = eq$t1$t2}
clasohm@0
   734
     | _ =>  err"premises"
clasohm@0
   735
  end;
clasohm@0
   736
berghofe@10416
   737
(*Beta-conversion: maps (%x.t)(u) to the theorem (%x.t)(u) == t[u/x]
berghofe@10416
   738
  Fully beta-reduces the term if full=true
berghofe@10416
   739
*)
berghofe@10416
   740
fun beta_conversion full ct =
wenzelm@16425
   741
  let val Cterm {thy_ref, t, T, maxidx} = ct
berghofe@10416
   742
  in Thm
wenzelm@16425
   743
    {thy_ref = thy_ref,
berghofe@11518
   744
     der = Pt.infer_derivs' I (false, Pt.reflexive),
berghofe@10416
   745
     maxidx = maxidx,
berghofe@10416
   746
     shyps = add_term_sorts (t, []),
berghofe@10416
   747
     hyps = [],
berghofe@13658
   748
     tpairs = [],
wenzelm@10486
   749
     prop = Logic.mk_equals (t, if full then Envir.beta_norm t
berghofe@10416
   750
       else case t of
berghofe@10416
   751
          Abs(_, _, bodt) $ u => subst_bound (u, bodt)
berghofe@10416
   752
        | _ => raise THM ("beta_conversion: not a redex", 0, []))}
berghofe@10416
   753
  end;
berghofe@10416
   754
berghofe@10416
   755
fun eta_conversion ct =
wenzelm@16425
   756
  let val Cterm {thy_ref, t, T, maxidx} = ct
berghofe@10416
   757
  in Thm
wenzelm@16425
   758
    {thy_ref = thy_ref,
berghofe@11518
   759
     der = Pt.infer_derivs' I (false, Pt.reflexive),
berghofe@10416
   760
     maxidx = maxidx,
berghofe@10416
   761
     shyps = add_term_sorts (t, []),
berghofe@10416
   762
     hyps = [],
berghofe@13658
   763
     tpairs = [],
berghofe@10416
   764
     prop = Logic.mk_equals (t, Pattern.eta_contract t)}
clasohm@0
   765
  end;
clasohm@0
   766
clasohm@0
   767
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   768
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@1220
   769
     t == u
wenzelm@1220
   770
  ------------
wenzelm@1220
   771
  %x.t == %x.u
wenzelm@1220
   772
*)
wenzelm@16425
   773
fun abstract_rule a cx (th as Thm{thy_ref,der,maxidx,hyps,shyps,tpairs,prop}) =
lcp@229
   774
  let val x = term_of cx;
wenzelm@250
   775
      val (t,u) = Logic.dest_equals prop
wenzelm@250
   776
            handle TERM _ =>
wenzelm@250
   777
                raise THM("abstract_rule: premise not an equality", 0, [th])
berghofe@10416
   778
      fun result T =
wenzelm@16425
   779
           Thm{thy_ref = thy_ref,
berghofe@11518
   780
               der = Pt.infer_derivs' (Pt.abstract_rule x a) der,
wenzelm@16425
   781
               maxidx = maxidx,
wenzelm@16425
   782
               shyps = add_typ_sorts (T, shyps),
wenzelm@2386
   783
               hyps = hyps,
berghofe@13658
   784
               tpairs = tpairs,
wenzelm@2386
   785
               prop = Logic.mk_equals(Abs(a, T, abstract_over (x,t)),
berghofe@10416
   786
                                      Abs(a, T, abstract_over (x,u)))}
berghofe@13658
   787
      fun check_occs x ts =
berghofe@13658
   788
         if exists (apl(x, Logic.occs)) ts
berghofe@13658
   789
         then raise THM("abstract_rule: variable free in assumptions", 0, [th])
berghofe@13658
   790
         else ()
clasohm@0
   791
  in  case x of
berghofe@13658
   792
        Free(_,T) => (check_occs x (hyps @ terms_of_tpairs tpairs); result T)
berghofe@13658
   793
      | Var(_,T) => (check_occs x (terms_of_tpairs tpairs); result T)
clasohm@0
   794
      | _ => raise THM("abstract_rule: not a variable", 0, [th])
clasohm@0
   795
  end;
clasohm@0
   796
clasohm@0
   797
(*The combination rule
wenzelm@3529
   798
  f == g  t == u
wenzelm@3529
   799
  --------------
wenzelm@3529
   800
   f(t) == g(u)
wenzelm@1220
   801
*)
clasohm@0
   802
fun combination th1 th2 =
wenzelm@16425
   803
  let val Thm{der=der1, maxidx=max1, shyps=shyps1, hyps=hyps1,
berghofe@13658
   804
              tpairs=tpairs1, prop=prop1,...} = th1
wenzelm@16425
   805
      and Thm{der=der2, maxidx=max2, shyps=shyps2, hyps=hyps2,
berghofe@13658
   806
              tpairs=tpairs2, prop=prop2,...} = th2
berghofe@10416
   807
      fun chktypes fT tT =
berghofe@10416
   808
            (case fT of
wenzelm@16425
   809
                Type("fun",[T1,T2]) =>
berghofe@10416
   810
                    if T1 <> tT then
wenzelm@2386
   811
                         raise THM("combination: types", 0, [th1,th2])
wenzelm@2386
   812
                    else ()
wenzelm@16425
   813
                | _ => raise THM("combination: not function type", 0,
wenzelm@2386
   814
                                 [th1,th2]))
nipkow@1495
   815
  in case (prop1,prop2)  of
berghofe@10416
   816
       (Const ("==", Type ("fun", [fT, _])) $ f $ g,
berghofe@10416
   817
        Const ("==", Type ("fun", [tT, _])) $ t $ u) =>
berghofe@15797
   818
          (chktypes fT tT;
berghofe@15797
   819
                        (*no fix_shyps*)
wenzelm@16425
   820
                        Thm{thy_ref = merge_thm_thys(th1,th2),
berghofe@11518
   821
                            der = Pt.infer_derivs
berghofe@11518
   822
                              (Pt.combination f g t u fT) der1 der2,
wenzelm@16425
   823
                            maxidx = Int.max(max1,max2),
wenzelm@14791
   824
                            shyps = Sorts.union_sort(shyps1,shyps2),
wenzelm@2386
   825
                            hyps = union_term(hyps1,hyps2),
berghofe@13658
   826
                            tpairs = tpairs1 @ tpairs2,
berghofe@15797
   827
                            prop = Logic.mk_equals(f$t, g$u)})
clasohm@0
   828
     | _ =>  raise THM("combination: premises", 0, [th1,th2])
clasohm@0
   829
  end;
clasohm@0
   830
clasohm@0
   831
clasohm@0
   832
(* Equality introduction
wenzelm@3529
   833
  A ==> B  B ==> A
wenzelm@3529
   834
  ----------------
wenzelm@3529
   835
       A == B
wenzelm@1220
   836
*)
clasohm@0
   837
fun equal_intr th1 th2 =
wenzelm@16425
   838
  let val Thm{der=der1, maxidx=max1, shyps=shyps1, hyps=hyps1,
berghofe@13658
   839
              tpairs=tpairs1, prop=prop1,...} = th1
wenzelm@16425
   840
      and Thm{der=der2, maxidx=max2, shyps=shyps2, hyps=hyps2,
berghofe@13658
   841
              tpairs=tpairs2, prop=prop2,...} = th2;
paulson@1529
   842
      fun err(msg) = raise THM("equal_intr: "^msg, 0, [th1,th2])
paulson@1529
   843
  in case (prop1,prop2) of
paulson@1529
   844
       (Const("==>",_) $ A $ B, Const("==>",_) $ B' $ A')  =>
wenzelm@2386
   845
          if A aconv A' andalso B aconv B'
wenzelm@2386
   846
          then
wenzelm@2386
   847
            (*no fix_shyps*)
wenzelm@16425
   848
              Thm{thy_ref = merge_thm_thys(th1,th2),
berghofe@11518
   849
                  der = Pt.infer_derivs (Pt.equal_intr A B) der1 der2,
wenzelm@2386
   850
                  maxidx = Int.max(max1,max2),
wenzelm@14791
   851
                  shyps = Sorts.union_sort(shyps1,shyps2),
wenzelm@2386
   852
                  hyps = union_term(hyps1,hyps2),
berghofe@13658
   853
                  tpairs = tpairs1 @ tpairs2,
wenzelm@2386
   854
                  prop = Logic.mk_equals(A,B)}
wenzelm@2386
   855
          else err"not equal"
paulson@1529
   856
     | _ =>  err"premises"
paulson@1529
   857
  end;
paulson@1529
   858
paulson@1529
   859
paulson@1529
   860
(*The equal propositions rule
wenzelm@3529
   861
  A == B  A
paulson@1529
   862
  ---------
paulson@1529
   863
      B
paulson@1529
   864
*)
paulson@1529
   865
fun equal_elim th1 th2 =
berghofe@13658
   866
  let val Thm{der=der1, maxidx=max1, hyps=hyps1, tpairs=tpairs1, prop=prop1,...} = th1
berghofe@13658
   867
      and Thm{der=der2, maxidx=max2, hyps=hyps2, tpairs=tpairs2, prop=prop2,...} = th2;
paulson@1529
   868
      fun err(msg) = raise THM("equal_elim: "^msg, 0, [th1,th2])
paulson@1529
   869
  in  case prop1  of
paulson@1529
   870
       Const("==",_) $ A $ B =>
paulson@1529
   871
          if not (prop2 aconv A) then err"not equal"  else
paulson@1529
   872
            fix_shyps [th1, th2] []
wenzelm@16425
   873
              (Thm{thy_ref= merge_thm_thys(th1,th2),
berghofe@11518
   874
                   der = Pt.infer_derivs (Pt.equal_elim A B) der1 der2,
wenzelm@2386
   875
                   maxidx = Int.max(max1,max2),
wenzelm@2386
   876
                   shyps = [],
wenzelm@2386
   877
                   hyps = union_term(hyps1,hyps2),
berghofe@13658
   878
                   tpairs = tpairs1 @ tpairs2,
wenzelm@2386
   879
                   prop = B})
paulson@1529
   880
     | _ =>  err"major premise"
paulson@1529
   881
  end;
clasohm@0
   882
wenzelm@1220
   883
wenzelm@1220
   884
clasohm@0
   885
(**** Derived rules ****)
clasohm@0
   886
paulson@1503
   887
(*Discharge all hypotheses.  Need not verify cterms or call fix_shyps.
clasohm@0
   888
  Repeated hypotheses are discharged only once;  fold cannot do this*)
wenzelm@16425
   889
fun implies_intr_hyps (Thm{thy_ref, der, maxidx, shyps, hyps=A::As, tpairs, prop}) =
wenzelm@1238
   890
      implies_intr_hyps (*no fix_shyps*)
wenzelm@16425
   891
            (Thm{thy_ref = thy_ref,
berghofe@11518
   892
                 der = Pt.infer_derivs' (Pt.implies_intr_proof A) der,
wenzelm@16425
   893
                 maxidx = maxidx,
wenzelm@2386
   894
                 shyps = shyps,
wenzelm@16425
   895
                 hyps = disch(As,A),
berghofe@13658
   896
                 tpairs = tpairs,
wenzelm@2386
   897
                 prop = implies$A$prop})
clasohm@0
   898
  | implies_intr_hyps th = th;
clasohm@0
   899
clasohm@0
   900
(*Smash" unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@250
   901
  Instantiates the theorem and deletes trivial tpairs.
clasohm@0
   902
  Resulting sequence may contain multiple elements if the tpairs are
clasohm@0
   903
    not all flex-flex. *)
wenzelm@16425
   904
fun flexflex_rule (th as Thm{thy_ref, der, maxidx, hyps, tpairs, prop, ...}) =
wenzelm@250
   905
  let fun newthm env =
paulson@1529
   906
          if Envir.is_empty env then th
paulson@1529
   907
          else
berghofe@13658
   908
          let val ntpairs = map (pairself (Envir.norm_term env)) tpairs;
berghofe@13658
   909
              val newprop = Envir.norm_term env prop;
wenzelm@250
   910
                (*Remove trivial tpairs, of the form t=t*)
skalberg@15570
   911
              val distpairs = List.filter (not o op aconv) ntpairs
wenzelm@1220
   912
          in  fix_shyps [th] (env_codT env)
wenzelm@16425
   913
                (Thm{thy_ref = thy_ref,
berghofe@11518
   914
                     der = Pt.infer_derivs' (Pt.norm_proof' env) der,
berghofe@13658
   915
                     maxidx = maxidx_of_terms (newprop ::
berghofe@13658
   916
                       terms_of_tpairs distpairs),
wenzelm@16425
   917
                     shyps = [],
wenzelm@2386
   918
                     hyps = hyps,
berghofe@13658
   919
                     tpairs = distpairs,
wenzelm@2386
   920
                     prop = newprop})
wenzelm@250
   921
          end;
wenzelm@4270
   922
  in Seq.map newthm
wenzelm@16425
   923
            (Unify.smash_unifiers(Theory.deref thy_ref, Envir.empty maxidx, tpairs))
clasohm@0
   924
  end;
clasohm@0
   925
clasohm@0
   926
(*Instantiation of Vars
wenzelm@1220
   927
           A
wenzelm@1220
   928
  -------------------
wenzelm@1220
   929
  A[t1/v1,....,tn/vn]
wenzelm@1220
   930
*)
clasohm@0
   931
wenzelm@6928
   932
local
wenzelm@6928
   933
clasohm@0
   934
(*Check that all the terms are Vars and are distinct*)
clasohm@0
   935
fun instl_ok ts = forall is_Var ts andalso null(findrep ts);
clasohm@0
   936
wenzelm@16425
   937
fun pretty_typing thy t T =
wenzelm@16425
   938
  Pretty.block [Sign.pretty_term thy t, Pretty.str " ::", Pretty.brk 1, Sign.pretty_typ thy T];
berghofe@15797
   939
clasohm@0
   940
(*For instantiate: process pair of cterms, merge theories*)
wenzelm@16425
   941
fun add_ctpair ((ct,cu), (thy_ref,tpairs)) =
wenzelm@6928
   942
  let
wenzelm@16425
   943
    val Cterm {thy_ref=thy_reft, t=t, T= T, ...} = ct
wenzelm@16425
   944
    and Cterm {thy_ref=thy_refu, t=u, T= U, ...} = cu;
wenzelm@16425
   945
    val thy_ref_merged = Theory.merge_refs (thy_ref, Theory.merge_refs (thy_reft, thy_refu));
wenzelm@16425
   946
    val thy_merged = Theory.deref thy_ref_merged;
wenzelm@3967
   947
  in
wenzelm@16425
   948
    if T=U then (thy_ref_merged, (t,u)::tpairs)
wenzelm@6928
   949
    else raise TYPE (Pretty.string_of (Pretty.block [Pretty.str "instantiate: type conflict",
wenzelm@16425
   950
      Pretty.fbrk, pretty_typing thy_merged t T,
wenzelm@16425
   951
      Pretty.fbrk, pretty_typing thy_merged u U]), [T,U], [t,u])
clasohm@0
   952
  end;
clasohm@0
   953
wenzelm@16425
   954
fun add_ctyp ((Ctyp {T = T as TVar (_, S), thy_ref = thy_refT},
wenzelm@16425
   955
      Ctyp {T = U, thy_ref = thy_refU}), (thy_ref, vTs)) =
berghofe@15797
   956
      let
wenzelm@16425
   957
        val thy_ref_merged = Theory.merge_refs
wenzelm@16425
   958
          (thy_ref, Theory.merge_refs (thy_refT, thy_refU));
wenzelm@16425
   959
        val thy_merged = Theory.deref thy_ref_merged
berghofe@15797
   960
      in
wenzelm@16425
   961
        if Type.of_sort (Sign.tsig_of thy_merged) (U, S) then
wenzelm@16425
   962
          (thy_ref_merged, (T, U) :: vTs)
berghofe@15797
   963
        else raise TYPE ("Type not of sort " ^
wenzelm@16425
   964
          Sign.string_of_sort thy_merged S, [U], [])
berghofe@15797
   965
      end
wenzelm@16425
   966
  | add_ctyp ((Ctyp {T, thy_ref}, _), _) =
berghofe@15797
   967
      raise TYPE (Pretty.string_of (Pretty.block
berghofe@15797
   968
        [Pretty.str "instantiate: not a type variable",
wenzelm@16425
   969
         Pretty.fbrk, Sign.pretty_typ (Theory.deref thy_ref) T]), [T], []);
clasohm@0
   970
wenzelm@6928
   971
in
wenzelm@6928
   972
clasohm@0
   973
(*Left-to-right replacements: ctpairs = [...,(vi,ti),...].
clasohm@0
   974
  Instantiates distinct Vars by terms of same type.
paulson@8129
   975
  No longer normalizes the new theorem! *)
paulson@1529
   976
fun instantiate ([], []) th = th
wenzelm@16425
   977
  | instantiate (vcTs,ctpairs) (th as Thm{thy_ref,der,maxidx,hyps,shyps,tpairs=dpairs,prop}) =
wenzelm@16425
   978
  let val (newthy_ref,tpairs) = foldr add_ctpair (thy_ref,[]) ctpairs;
wenzelm@16425
   979
      val (newthy_ref,vTs) = foldr add_ctyp (newthy_ref,[]) vcTs;
wenzelm@14828
   980
      fun subst t =
berghofe@15797
   981
        subst_atomic tpairs (map_term_types (typ_subst_atomic vTs) t);
berghofe@13658
   982
      val newprop = subst prop;
berghofe@13658
   983
      val newdpairs = map (pairself subst) dpairs;
wenzelm@1220
   984
      val newth =
wenzelm@16425
   985
            (Thm{thy_ref = newthy_ref,
berghofe@11518
   986
                 der = Pt.infer_derivs' (Pt.instantiate vTs tpairs) der,
berghofe@13658
   987
                 maxidx = maxidx_of_terms (newprop ::
wenzelm@16425
   988
                   terms_of_tpairs newdpairs),
berghofe@10416
   989
                 shyps = add_insts_sorts ((vTs, tpairs), shyps),
berghofe@10416
   990
                 hyps = hyps,
berghofe@13658
   991
                 tpairs = newdpairs,
berghofe@10416
   992
                 prop = newprop})
wenzelm@250
   993
  in  if not(instl_ok(map #1 tpairs))
nipkow@193
   994
      then raise THM("instantiate: variables not distinct", 0, [th])
nipkow@193
   995
      else if not(null(findrep(map #1 vTs)))
nipkow@193
   996
      then raise THM("instantiate: type variables not distinct", 0, [th])
berghofe@15797
   997
      else newth
clasohm@0
   998
  end
wenzelm@16425
   999
  handle TERM _ => raise THM("instantiate: incompatible theories", 0, [th])
wenzelm@6928
  1000
       | TYPE (msg, _, _) => raise THM (msg, 0, [th]);
wenzelm@6928
  1001
wenzelm@6928
  1002
end;
wenzelm@6928
  1003
clasohm@0
  1004
clasohm@0
  1005
(*The trivial implication A==>A, justified by assume and forall rules.
clasohm@0
  1006
  A can contain Vars, not so for assume!   *)
wenzelm@250
  1007
fun trivial ct : thm =
wenzelm@16425
  1008
  let val Cterm {thy_ref, t=A, T, maxidx} = ct
wenzelm@250
  1009
  in  if T<>propT then
wenzelm@250
  1010
            raise THM("trivial: the term must have type prop", 0, [])
wenzelm@1238
  1011
      else fix_shyps [] []
wenzelm@16425
  1012
        (Thm{thy_ref = thy_ref,
skalberg@15531
  1013
             der = Pt.infer_derivs' I (false, Pt.AbsP ("H", NONE, Pt.PBound 0)),
wenzelm@16425
  1014
             maxidx = maxidx,
wenzelm@16425
  1015
             shyps = [],
wenzelm@2386
  1016
             hyps = [],
berghofe@13658
  1017
             tpairs = [],
wenzelm@2386
  1018
             prop = implies$A$A})
clasohm@0
  1019
  end;
clasohm@0
  1020
paulson@1503
  1021
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)" *)
wenzelm@16425
  1022
fun class_triv thy c =
wenzelm@16425
  1023
  let val Cterm {thy_ref, t, maxidx, ...} =
wenzelm@16425
  1024
    cterm_of thy (Logic.mk_inclass (TVar (("'a", 0), [c]), c))
wenzelm@6368
  1025
      handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@399
  1026
  in
wenzelm@1238
  1027
    fix_shyps [] []
wenzelm@16425
  1028
      (Thm {thy_ref = thy_ref,
berghofe@11518
  1029
            der = Pt.infer_derivs' I
skalberg@15531
  1030
              (false, Pt.PAxm ("ProtoPure.class_triv:" ^ c, t, SOME [])),
wenzelm@16425
  1031
            maxidx = maxidx,
wenzelm@16425
  1032
            shyps = [],
wenzelm@16425
  1033
            hyps = [],
berghofe@13658
  1034
            tpairs = [],
wenzelm@2386
  1035
            prop = t})
wenzelm@399
  1036
  end;
wenzelm@399
  1037
wenzelm@399
  1038
wenzelm@6786
  1039
(* Replace all TFrees not fixed or in the hyps by new TVars *)
wenzelm@16425
  1040
fun varifyT' fixed (Thm{thy_ref,der,maxidx,shyps,hyps,tpairs,prop}) =
wenzelm@12500
  1041
  let
berghofe@15797
  1042
    val tfrees = foldr add_term_tfrees fixed hyps;
berghofe@13658
  1043
    val prop1 = attach_tpairs tpairs prop;
berghofe@13658
  1044
    val (prop2, al) = Type.varify (prop1, tfrees);
berghofe@13658
  1045
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2)
berghofe@15797
  1046
  in (*no fix_shyps*)
wenzelm@16425
  1047
   (Thm{thy_ref = thy_ref,
berghofe@11518
  1048
        der = Pt.infer_derivs' (Pt.varify_proof prop tfrees) der,
wenzelm@16425
  1049
        maxidx = Int.max(0,maxidx),
wenzelm@16425
  1050
        shyps = shyps,
wenzelm@2386
  1051
        hyps = hyps,
berghofe@13658
  1052
        tpairs = rev (map Logic.dest_equals ts),
berghofe@15797
  1053
        prop = prop3}, al)
clasohm@0
  1054
  end;
clasohm@0
  1055
wenzelm@12500
  1056
val varifyT = #1 o varifyT' [];
wenzelm@6786
  1057
clasohm@0
  1058
(* Replace all TVars by new TFrees *)
wenzelm@16425
  1059
fun freezeT(Thm{thy_ref,der,maxidx,shyps,hyps,tpairs,prop}) =
berghofe@13658
  1060
  let
berghofe@13658
  1061
    val prop1 = attach_tpairs tpairs prop;
wenzelm@16287
  1062
    val prop2 = Type.freeze prop1;
berghofe@13658
  1063
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2)
wenzelm@1238
  1064
  in (*no fix_shyps*)
wenzelm@16425
  1065
    Thm{thy_ref = thy_ref,
berghofe@13658
  1066
        der = Pt.infer_derivs' (Pt.freezeT prop1) der,
berghofe@13658
  1067
        maxidx = maxidx_of_term prop2,
wenzelm@2386
  1068
        shyps = shyps,
wenzelm@2386
  1069
        hyps = hyps,
berghofe@13658
  1070
        tpairs = rev (map Logic.dest_equals ts),
berghofe@13658
  1071
        prop = prop3}
wenzelm@1220
  1072
  end;
clasohm@0
  1073
clasohm@0
  1074
clasohm@0
  1075
(*** Inference rules for tactics ***)
clasohm@0
  1076
clasohm@0
  1077
(*Destruct proof state into constraints, other goals, goal(i), rest *)
berghofe@13658
  1078
fun dest_state (state as Thm{prop,tpairs,...}, i) =
berghofe@13658
  1079
  (case  Logic.strip_prems(i, [], prop) of
berghofe@13658
  1080
      (B::rBs, C) => (tpairs, rev rBs, B, C)
berghofe@13658
  1081
    | _ => raise THM("dest_state", i, [state]))
clasohm@0
  1082
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1083
lcp@309
  1084
(*Increment variables and parameters of orule as required for
clasohm@0
  1085
  resolution with goal i of state. *)
clasohm@0
  1086
fun lift_rule (state, i) orule =
wenzelm@16425
  1087
  let val Thm{shyps=sshyps, prop=sprop, maxidx=smax, thy_ref=sthy_ref,...} = state
berghofe@13658
  1088
      val (Bi::_, _) = Logic.strip_prems(i, [], sprop)
paulson@1529
  1089
        handle TERM _ => raise THM("lift_rule", i, [orule,state])
wenzelm@16425
  1090
      val ct_Bi = Cterm {thy_ref=sthy_ref, maxidx=smax, T=propT, t=Bi}
paulson@1529
  1091
      val (lift_abs,lift_all) = Logic.lift_fns(Bi,smax+1)
wenzelm@16425
  1092
      val (Thm{thy_ref, der, maxidx,shyps,hyps,tpairs,prop}) = orule
berghofe@13658
  1093
      val (As, B) = Logic.strip_horn prop
wenzelm@1238
  1094
  in  (*no fix_shyps*)
wenzelm@16425
  1095
      Thm{thy_ref = merge_thm_thys(state,orule),
berghofe@11518
  1096
          der = Pt.infer_derivs' (Pt.lift_proof Bi (smax+1) prop) der,
wenzelm@2386
  1097
          maxidx = maxidx+smax+1,
wenzelm@16425
  1098
          shyps = Sorts.union_sort(sshyps,shyps),
wenzelm@16425
  1099
          hyps = hyps,
berghofe@13658
  1100
          tpairs = map (pairself lift_abs) tpairs,
berghofe@13658
  1101
          prop = Logic.list_implies (map lift_all As, lift_all B)}
clasohm@0
  1102
  end;
clasohm@0
  1103
wenzelm@16425
  1104
fun incr_indexes i (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
berghofe@10416
  1105
  if i < 0 then raise THM ("negative increment", 0, [thm]) else
berghofe@10416
  1106
  if i = 0 then thm else
wenzelm@16425
  1107
    Thm {thy_ref = thy_ref,
berghofe@11518
  1108
         der = Pt.infer_derivs' (Pt.map_proof_terms
berghofe@11518
  1109
           (Logic.incr_indexes ([], i)) (incr_tvar i)) der,
berghofe@10416
  1110
         maxidx = maxidx + i,
berghofe@10416
  1111
         shyps = shyps,
berghofe@10416
  1112
         hyps = hyps,
berghofe@13658
  1113
         tpairs = map (pairself (Logic.incr_indexes ([], i))) tpairs,
berghofe@10416
  1114
         prop = Logic.incr_indexes ([], i) prop};
berghofe@10416
  1115
clasohm@0
  1116
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1117
fun assumption i state =
wenzelm@16425
  1118
  let val Thm{thy_ref,der,maxidx,hyps,prop,...} = state;
clasohm@0
  1119
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
berghofe@11518
  1120
      fun newth n (env as Envir.Envir{maxidx, ...}, tpairs) =
wenzelm@1220
  1121
        fix_shyps [state] (env_codT env)
wenzelm@16425
  1122
          (Thm{thy_ref = thy_ref,
berghofe@11518
  1123
               der = Pt.infer_derivs'
berghofe@11518
  1124
                 ((if Envir.is_empty env then I else (Pt.norm_proof' env)) o
berghofe@11518
  1125
                   Pt.assumption_proof Bs Bi n) der,
wenzelm@2386
  1126
               maxidx = maxidx,
wenzelm@2386
  1127
               shyps = [],
wenzelm@2386
  1128
               hyps = hyps,
berghofe@13658
  1129
               tpairs = if Envir.is_empty env then tpairs else
berghofe@13658
  1130
                 map (pairself (Envir.norm_term env)) tpairs,
wenzelm@16425
  1131
               prop =
wenzelm@2386
  1132
               if Envir.is_empty env then (*avoid wasted normalizations*)
berghofe@13658
  1133
                   Logic.list_implies (Bs, C)
wenzelm@2386
  1134
               else (*normalize the new rule fully*)
berghofe@13658
  1135
                   Envir.norm_term env (Logic.list_implies (Bs, C))});
berghofe@11518
  1136
      fun addprfs [] _ = Seq.empty
berghofe@11518
  1137
        | addprfs ((t,u)::apairs) n = Seq.make (fn()=> Seq.pull
berghofe@11518
  1138
             (Seq.mapp (newth n)
wenzelm@16425
  1139
                (Unify.unifiers(Theory.deref thy_ref,Envir.empty maxidx, (t,u)::tpairs))
berghofe@11518
  1140
                (addprfs apairs (n+1))))
paulson@15454
  1141
  in  addprfs (Logic.assum_pairs (~1,Bi)) 1 end;
clasohm@0
  1142
wenzelm@250
  1143
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1144
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1145
fun eq_assumption i state =
wenzelm@16425
  1146
  let val Thm{thy_ref,der,maxidx,hyps,prop,...} = state;
clasohm@0
  1147
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
paulson@15454
  1148
  in  (case find_index (op aconv) (Logic.assum_pairs (~1,Bi)) of
berghofe@11518
  1149
         (~1) => raise THM("eq_assumption", 0, [state])
berghofe@11518
  1150
       | n => fix_shyps [state] []
wenzelm@16425
  1151
                (Thm{thy_ref = thy_ref,
berghofe@11518
  1152
                     der = Pt.infer_derivs'
berghofe@11518
  1153
                       (Pt.assumption_proof Bs Bi (n+1)) der,
berghofe@11518
  1154
                     maxidx = maxidx,
berghofe@11518
  1155
                     shyps = [],
berghofe@11518
  1156
                     hyps = hyps,
berghofe@13658
  1157
                     tpairs = tpairs,
berghofe@13658
  1158
                     prop = Logic.list_implies (Bs, C)}))
clasohm@0
  1159
  end;
clasohm@0
  1160
clasohm@0
  1161
paulson@2671
  1162
(*For rotate_tac: fast rotation of assumptions of subgoal i*)
paulson@2671
  1163
fun rotate_rule k i state =
wenzelm@16425
  1164
  let val Thm{thy_ref,der,maxidx,hyps,prop,shyps,...} = state;
paulson@2671
  1165
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
paulson@8066
  1166
      val params = Term.strip_all_vars Bi
paulson@8066
  1167
      and rest   = Term.strip_all_body Bi
paulson@8066
  1168
      val asms   = Logic.strip_imp_prems rest
paulson@8066
  1169
      and concl  = Logic.strip_imp_concl rest
paulson@2671
  1170
      val n      = length asms
berghofe@11563
  1171
      val m      = if k<0 then n+k else k
berghofe@11563
  1172
      val Bi'    = if 0=m orelse m=n then Bi
wenzelm@16425
  1173
                   else if 0<m andalso m<n
wenzelm@16425
  1174
                   then let val (ps,qs) = splitAt(m,asms)
nipkow@13629
  1175
                        in list_all(params, Logic.list_implies(qs @ ps, concl))
wenzelm@16425
  1176
                        end
wenzelm@16425
  1177
                   else raise THM("rotate_rule", k, [state])
wenzelm@7264
  1178
  in  (*no fix_shyps*)
wenzelm@16425
  1179
      Thm{thy_ref = thy_ref,
berghofe@11563
  1180
          der = Pt.infer_derivs' (Pt.rotate_proof Bs Bi m) der,
wenzelm@16425
  1181
          maxidx = maxidx,
wenzelm@16425
  1182
          shyps = shyps,
wenzelm@16425
  1183
          hyps = hyps,
berghofe@13658
  1184
          tpairs = tpairs,
wenzelm@16425
  1185
          prop = Logic.list_implies (Bs @ [Bi'], C)}
paulson@2671
  1186
  end;
paulson@2671
  1187
paulson@2671
  1188
paulson@7248
  1189
(*Rotates a rule's premises to the left by k, leaving the first j premises
paulson@7248
  1190
  unchanged.  Does nothing if k=0 or if k equals n-j, where n is the
paulson@7248
  1191
  number of premises.  Useful with etac and underlies tactic/defer_tac*)
paulson@7248
  1192
fun permute_prems j k rl =
wenzelm@16425
  1193
  let val Thm{thy_ref,der,maxidx,hyps,tpairs,prop,shyps} = rl
paulson@7248
  1194
      val prems  = Logic.strip_imp_prems prop
paulson@7248
  1195
      and concl  = Logic.strip_imp_concl prop
paulson@7248
  1196
      val moved_prems = List.drop(prems, j)
paulson@7248
  1197
      and fixed_prems = List.take(prems, j)
paulson@7248
  1198
        handle Subscript => raise THM("permute_prems:j", j, [rl])
paulson@7248
  1199
      val n_j    = length moved_prems
berghofe@11563
  1200
      val m = if k<0 then n_j + k else k
berghofe@11563
  1201
      val prop'  = if 0 = m orelse m = n_j then prop
wenzelm@16425
  1202
                   else if 0<m andalso m<n_j
wenzelm@16425
  1203
                   then let val (ps,qs) = splitAt(m,moved_prems)
wenzelm@16425
  1204
                        in Logic.list_implies(fixed_prems @ qs @ ps, concl) end
wenzelm@16425
  1205
                   else raise THM("permute_prems:k", k, [rl])
wenzelm@7264
  1206
  in  (*no fix_shyps*)
wenzelm@16425
  1207
      Thm{thy_ref = thy_ref,
berghofe@11563
  1208
          der = Pt.infer_derivs' (Pt.permute_prems_prf prems j m) der,
wenzelm@16425
  1209
          maxidx = maxidx,
wenzelm@16425
  1210
          shyps = shyps,
wenzelm@16425
  1211
          hyps = hyps,
berghofe@13658
  1212
          tpairs = tpairs,
wenzelm@16425
  1213
          prop = prop'}
paulson@7248
  1214
  end;
paulson@7248
  1215
paulson@7248
  1216
clasohm@0
  1217
(** User renaming of parameters in a subgoal **)
clasohm@0
  1218
clasohm@0
  1219
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1220
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1221
  The names in cs, if distinct, are used for the innermost parameters;
clasohm@0
  1222
   preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1223
fun rename_params_rule (cs, i) state =
wenzelm@16425
  1224
  let val Thm{thy_ref,der,maxidx,hyps,shyps,...} = state
clasohm@0
  1225
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
clasohm@0
  1226
      val iparams = map #1 (Logic.strip_params Bi)
clasohm@0
  1227
      val short = length iparams - length cs
wenzelm@250
  1228
      val newnames =
wenzelm@250
  1229
            if short<0 then error"More names than abstractions!"
skalberg@15570
  1230
            else variantlist(Library.take (short,iparams), cs) @ cs
nipkow@3037
  1231
      val freenames = map (#1 o dest_Free) (term_frees Bi)
clasohm@0
  1232
      val newBi = Logic.list_rename_params (newnames, Bi)
wenzelm@250
  1233
  in
clasohm@0
  1234
  case findrep cs of
wenzelm@16425
  1235
     c::_ => (warning ("Can't rename.  Bound variables not distinct: " ^ c);
wenzelm@16425
  1236
              state)
berghofe@1576
  1237
   | [] => (case cs inter_string freenames of
wenzelm@16425
  1238
       a::_ => (warning ("Can't rename.  Bound/Free variable clash: " ^ a);
wenzelm@16425
  1239
                state)
wenzelm@16425
  1240
     | [] => Thm{thy_ref = thy_ref,
berghofe@13658
  1241
                 der = der,
berghofe@13658
  1242
                 maxidx = maxidx,
berghofe@13658
  1243
                 shyps = shyps,
berghofe@13658
  1244
                 hyps = hyps,
berghofe@13658
  1245
                 tpairs = tpairs,
berghofe@13658
  1246
                 prop = Logic.list_implies (Bs @ [newBi], C)})
clasohm@0
  1247
  end;
clasohm@0
  1248
wenzelm@12982
  1249
clasohm@0
  1250
(*** Preservation of bound variable names ***)
clasohm@0
  1251
wenzelm@16425
  1252
fun rename_boundvars pat obj (thm as Thm {thy_ref, der, maxidx, hyps, shyps, tpairs, prop}) =
wenzelm@12982
  1253
  (case Term.rename_abs pat obj prop of
skalberg@15531
  1254
    NONE => thm
skalberg@15531
  1255
  | SOME prop' => Thm
wenzelm@16425
  1256
      {thy_ref = thy_ref,
wenzelm@12982
  1257
       der = der,
wenzelm@12982
  1258
       maxidx = maxidx,
wenzelm@12982
  1259
       hyps = hyps,
wenzelm@12982
  1260
       shyps = shyps,
berghofe@13658
  1261
       tpairs = tpairs,
wenzelm@12982
  1262
       prop = prop'});
berghofe@10416
  1263
clasohm@0
  1264
wenzelm@250
  1265
(* strip_apply f A(,B) strips off all assumptions/parameters from A
clasohm@0
  1266
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
  1267
fun strip_apply f =
clasohm@0
  1268
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@250
  1269
                Const("==>",_)$ _  $ B2) = implies $ A1 $ strip(B1,B2)
wenzelm@250
  1270
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
  1271
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
  1272
        | strip(A,_) = f A
clasohm@0
  1273
  in strip end;
clasohm@0
  1274
clasohm@0
  1275
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1276
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1277
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1278
fun rename_bvs([],_,_,_) = I
clasohm@0
  1279
  | rename_bvs(al,dpairs,tpairs,B) =
skalberg@15574
  1280
    let val vars = foldr add_term_vars []
skalberg@15574
  1281
                        (map fst dpairs @ map fst tpairs @ map snd tpairs)
wenzelm@250
  1282
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1283
        val vids = map (#1 o #1 o dest_Var) vars;
wenzelm@250
  1284
        fun rename(t as Var((x,i),T)) =
wenzelm@250
  1285
                (case assoc(al,x) of
skalberg@15531
  1286
                   SOME(y) => if x mem_string vids orelse y mem_string vids then t
wenzelm@250
  1287
                              else Var((y,i),T)
skalberg@15531
  1288
                 | NONE=> t)
clasohm@0
  1289
          | rename(Abs(x,T,t)) =
wenzelm@16425
  1290
              Abs (if_none (assoc_string (al, x)) x, T, rename t)
clasohm@0
  1291
          | rename(f$t) = rename f $ rename t
clasohm@0
  1292
          | rename(t) = t;
wenzelm@250
  1293
        fun strip_ren Ai = strip_apply rename (Ai,B)
clasohm@0
  1294
    in strip_ren end;
clasohm@0
  1295
clasohm@0
  1296
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
  1297
fun rename_bvars(dpairs, tpairs, B) =
skalberg@15574
  1298
        rename_bvs(foldr Term.match_bvars [] dpairs, dpairs, tpairs, B);
clasohm@0
  1299
clasohm@0
  1300
clasohm@0
  1301
(*** RESOLUTION ***)
clasohm@0
  1302
lcp@721
  1303
(** Lifting optimizations **)
lcp@721
  1304
clasohm@0
  1305
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
  1306
  identical because of lifting*)
wenzelm@250
  1307
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
  1308
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
  1309
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
  1310
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
  1311
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
  1312
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
  1313
  | strip_assums2 BB = BB;
clasohm@0
  1314
clasohm@0
  1315
lcp@721
  1316
(*Faster normalization: skip assumptions that were lifted over*)
lcp@721
  1317
fun norm_term_skip env 0 t = Envir.norm_term env t
lcp@721
  1318
  | norm_term_skip env n (Const("all",_)$Abs(a,T,t)) =
lcp@721
  1319
        let val Envir.Envir{iTs, ...} = env
berghofe@15797
  1320
            val T' = Envir.typ_subst_TVars iTs T
wenzelm@1238
  1321
            (*Must instantiate types of parameters because they are flattened;
lcp@721
  1322
              this could be a NEW parameter*)
lcp@721
  1323
        in  all T' $ Abs(a, T', norm_term_skip env n t)  end
lcp@721
  1324
  | norm_term_skip env n (Const("==>", _) $ A $ B) =
wenzelm@1238
  1325
        implies $ A $ norm_term_skip env (n-1) B
lcp@721
  1326
  | norm_term_skip env n t = error"norm_term_skip: too few assumptions??";
lcp@721
  1327
lcp@721
  1328
clasohm@0
  1329
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
  1330
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
  1331
  If match then forbid instantiations in proof state
clasohm@0
  1332
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
  1333
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
  1334
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
  1335
  Curried so that resolution calls dest_state only once.
clasohm@0
  1336
*)
wenzelm@4270
  1337
local exception COMPOSE
clasohm@0
  1338
in
wenzelm@250
  1339
fun bicompose_aux match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
  1340
                        (eres_flg, orule, nsubgoal) =
paulson@1529
  1341
 let val Thm{der=sder, maxidx=smax, shyps=sshyps, hyps=shyps, ...} = state
wenzelm@16425
  1342
     and Thm{der=rder, maxidx=rmax, shyps=rshyps, hyps=rhyps,
berghofe@13658
  1343
             tpairs=rtpairs, prop=rprop,...} = orule
paulson@1529
  1344
         (*How many hyps to skip over during normalization*)
wenzelm@1238
  1345
     and nlift = Logic.count_prems(strip_all_body Bi,
wenzelm@1238
  1346
                                   if eres_flg then ~1 else 0)
wenzelm@16425
  1347
     val thy_ref = merge_thm_thys(state,orule);
wenzelm@16425
  1348
     val thy = Theory.deref thy_ref;
clasohm@0
  1349
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
berghofe@11518
  1350
     fun addth A (As, oldAs, rder', n) ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
  1351
       let val normt = Envir.norm_term env;
wenzelm@250
  1352
           (*perform minimal copying here by examining env*)
berghofe@13658
  1353
           val (ntpairs, normp) =
berghofe@13658
  1354
             if Envir.is_empty env then (tpairs, (Bs @ As, C))
wenzelm@250
  1355
             else
wenzelm@250
  1356
             let val ntps = map (pairself normt) tpairs
paulson@2147
  1357
             in if Envir.above (smax, env) then
wenzelm@1238
  1358
                  (*no assignments in state; normalize the rule only*)
wenzelm@1238
  1359
                  if lifted
berghofe@13658
  1360
                  then (ntps, (Bs @ map (norm_term_skip env nlift) As, C))
berghofe@13658
  1361
                  else (ntps, (Bs @ map normt As, C))
paulson@1529
  1362
                else if match then raise COMPOSE
wenzelm@250
  1363
                else (*normalize the new rule fully*)
berghofe@13658
  1364
                  (ntps, (map normt (Bs @ As), normt C))
wenzelm@250
  1365
             end
wenzelm@1258
  1366
           val th = (*tuned fix_shyps*)
wenzelm@16425
  1367
             Thm{thy_ref = thy_ref,
berghofe@11518
  1368
                 der = Pt.infer_derivs
berghofe@11518
  1369
                   ((if Envir.is_empty env then I
berghofe@11518
  1370
                     else if Envir.above (smax, env) then
berghofe@11518
  1371
                       (fn f => fn der => f (Pt.norm_proof' env der))
berghofe@11518
  1372
                     else
berghofe@11518
  1373
                       curry op oo (Pt.norm_proof' env))
berghofe@11518
  1374
                    (Pt.bicompose_proof Bs oldAs As A n)) rder' sder,
wenzelm@2386
  1375
                 maxidx = maxidx,
wenzelm@14791
  1376
                 shyps = add_env_sorts (env, Sorts.union_sort(rshyps,sshyps)),
wenzelm@2386
  1377
                 hyps = union_term(rhyps,shyps),
berghofe@13658
  1378
                 tpairs = ntpairs,
berghofe@13658
  1379
                 prop = Logic.list_implies normp}
berghofe@11518
  1380
        in  Seq.cons(th, thq)  end  handle COMPOSE => thq;
berghofe@13658
  1381
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rprop)
clasohm@0
  1382
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
  1383
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
  1384
     fun newAs(As0, n, dpairs, tpairs) =
berghofe@11518
  1385
       let val (As1, rder') =
berghofe@11518
  1386
         if !Logic.auto_rename orelse not lifted then (As0, rder)
berghofe@11518
  1387
         else (map (rename_bvars(dpairs,tpairs,B)) As0,
berghofe@11518
  1388
           Pt.infer_derivs' (Pt.map_proof_terms
berghofe@11518
  1389
             (rename_bvars (dpairs, tpairs, Bound 0)) I) rder);
berghofe@11518
  1390
       in (map (Logic.flatten_params n) As1, As1, rder', n)
wenzelm@250
  1391
          handle TERM _ =>
wenzelm@250
  1392
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
  1393
       end;
paulson@2147
  1394
     val env = Envir.empty(Int.max(rmax,smax));
clasohm@0
  1395
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
  1396
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
  1397
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
berghofe@11518
  1398
     fun tryasms (_, _, _, []) = Seq.empty
berghofe@11518
  1399
       | tryasms (A, As, n, (t,u)::apairs) =
wenzelm@16425
  1400
          (case Seq.pull(Unify.unifiers(thy, env, (t,u)::dpairs))  of
wenzelm@16425
  1401
              NONE                   => tryasms (A, As, n+1, apairs)
wenzelm@16425
  1402
            | cell as SOME((_,tpairs),_) =>
wenzelm@16425
  1403
                Seq.it_right (addth A (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@16425
  1404
                    (Seq.make(fn()=> cell),
wenzelm@16425
  1405
                     Seq.make(fn()=> Seq.pull (tryasms(A, As, n+1, apairs)))))
clasohm@0
  1406
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
skalberg@15531
  1407
       | eres (A1::As) = tryasms(SOME A1, As, 1, Logic.assum_pairs(nlift+1,A1))
clasohm@0
  1408
     (*ordinary resolution*)
skalberg@15531
  1409
     fun res(NONE) = Seq.empty
skalberg@15531
  1410
       | res(cell as SOME((_,tpairs),_)) =
skalberg@15531
  1411
             Seq.it_right (addth NONE (newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@4270
  1412
                       (Seq.make (fn()=> cell), Seq.empty)
clasohm@0
  1413
 in  if eres_flg then eres(rev rAs)
wenzelm@16425
  1414
     else res(Seq.pull(Unify.unifiers(thy, env, dpairs)))
clasohm@0
  1415
 end;
wenzelm@7528
  1416
end;
clasohm@0
  1417
clasohm@0
  1418
clasohm@0
  1419
fun bicompose match arg i state =
clasohm@0
  1420
    bicompose_aux match (state, dest_state(state,i), false) arg;
clasohm@0
  1421
clasohm@0
  1422
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1423
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1424
fun could_bires (Hs, B, eres_flg, rule) =
clasohm@0
  1425
    let fun could_reshyp (A1::_) = exists (apl(A1,could_unify)) Hs
wenzelm@250
  1426
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@250
  1427
    in  could_unify(concl_of rule, B) andalso
wenzelm@250
  1428
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1429
    end;
clasohm@0
  1430
clasohm@0
  1431
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1432
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1433
fun biresolution match brules i state =
clasohm@0
  1434
    let val lift = lift_rule(state, i);
wenzelm@250
  1435
        val (stpairs, Bs, Bi, C) = dest_state(state,i)
wenzelm@250
  1436
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1437
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@250
  1438
        val comp = bicompose_aux match (state, (stpairs, Bs, Bi, C), true);
wenzelm@4270
  1439
        fun res [] = Seq.empty
wenzelm@250
  1440
          | res ((eres_flg, rule)::brules) =
nipkow@13642
  1441
              if !Pattern.trace_unify_fail orelse
nipkow@13642
  1442
                 could_bires (Hs, B, eres_flg, rule)
wenzelm@4270
  1443
              then Seq.make (*delay processing remainder till needed*)
skalberg@15531
  1444
                  (fn()=> SOME(comp (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1445
                               res brules))
wenzelm@250
  1446
              else res brules
wenzelm@4270
  1447
    in  Seq.flat (res brules)  end;
clasohm@0
  1448
clasohm@0
  1449
wenzelm@2509
  1450
(*** Oracles ***)
wenzelm@2509
  1451
wenzelm@16425
  1452
fun invoke_oracle_i thy1 name =
wenzelm@3812
  1453
  let
wenzelm@3812
  1454
    val oracle =
wenzelm@16425
  1455
      (case Symtab.lookup (#2 (#oracles (Theory.rep_theory thy1)), name) of
skalberg@15531
  1456
        NONE => raise THM ("Unknown oracle: " ^ name, 0, [])
skalberg@15531
  1457
      | SOME (f, _) => f);
wenzelm@3812
  1458
  in
wenzelm@16425
  1459
    fn (thy2, data) =>
wenzelm@3812
  1460
      let
wenzelm@16425
  1461
        val thy' = Theory.merge (thy1, thy2);
wenzelm@14828
  1462
        val (prop, T, maxidx) =
wenzelm@16425
  1463
          Sign.certify_term (Sign.pp thy') thy' (oracle (thy', data));
wenzelm@3812
  1464
      in
wenzelm@3812
  1465
        if T <> propT then
wenzelm@3812
  1466
          raise THM ("Oracle's result must have type prop: " ^ name, 0, [])
wenzelm@3812
  1467
        else fix_shyps [] []
wenzelm@16425
  1468
          (Thm {thy_ref = Theory.self_ref thy',
berghofe@11518
  1469
            der = (true, Pt.oracle_proof name prop),
wenzelm@3812
  1470
            maxidx = maxidx,
wenzelm@16425
  1471
            shyps = [],
wenzelm@16425
  1472
            hyps = [],
berghofe@13658
  1473
            tpairs = [],
wenzelm@3812
  1474
            prop = prop})
wenzelm@3812
  1475
      end
wenzelm@3812
  1476
  end;
wenzelm@3812
  1477
wenzelm@15672
  1478
fun invoke_oracle thy =
wenzelm@16425
  1479
  invoke_oracle_i thy o NameSpace.intern (Theory.oracle_space thy);
wenzelm@15672
  1480
paulson@1539
  1481
clasohm@0
  1482
end;
paulson@1503
  1483
wenzelm@6089
  1484
wenzelm@6089
  1485
structure BasicThm: BASIC_THM = Thm;
wenzelm@6089
  1486
open BasicThm;