src/Pure/thm.ML
author wenzelm
Tue Aug 23 19:31:05 1994 +0200 (1994-08-23)
changeset 573 2fa5ef27bd0a
parent 564 eec3a9222b50
child 574 810da101bad2
permissions -rw-r--r--
removed constant _constrain from Pure sig;
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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 abstract types "theory" and "thm".
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Also "cterm" / "ctyp" (certified terms / typs under a signature).
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*)
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signature THM =
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sig
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  structure Envir : ENVIR
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  structure Sequence : SEQUENCE
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  structure Sign : SIGN
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  type ctyp
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  type cterm
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  type thm
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  type theory
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  type meta_simpset
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  exception THM of string * int * thm list
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  exception THEORY of string * theory list
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  exception SIMPLIFIER of string * thm
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  (*certified terms/types; previously in sign.ML*)
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  val cterm_of: Sign.sg -> term -> cterm
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  val ctyp_of: Sign.sg -> typ -> ctyp
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  val read_ctyp: Sign.sg -> string -> ctyp
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  val read_cterm: Sign.sg -> string * typ -> cterm
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  val rep_cterm: cterm -> {T: typ, t: term, sign: Sign.sg, maxidx: int}
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  val rep_ctyp: ctyp -> {T: typ, sign: Sign.sg}
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  val term_of: cterm -> term
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  val typ_of: ctyp -> typ
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  val cterm_fun: (term -> term) -> (cterm -> cterm)
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  (*end of cterm/ctyp functions*)
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  local open Sign.Syntax in
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    val add_classes: (class * class list) list -> theory -> theory
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    val add_classrel: (class * class) list -> theory -> theory
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    val add_defsort: sort -> theory -> theory
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    val add_types: (string * int * mixfix) list -> theory -> theory
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    val add_tyabbrs: (string * string list * string * mixfix) list
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      -> theory -> theory
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    val add_tyabbrs_i: (string * string list * typ * mixfix) list
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      -> theory -> theory
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    val add_arities: (string * sort list * sort) list -> theory -> theory
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    val add_consts: (string * string * mixfix) list -> theory -> theory
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    val add_consts_i: (string * typ * mixfix) list -> theory -> theory
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    val add_syntax: (string * string * mixfix) list -> theory -> theory
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    val add_syntax_i: (string * typ * mixfix) list -> theory -> theory
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    val add_trfuns:
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      (string * (ast list -> ast)) list *
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      (string * (term list -> term)) list *
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      (string * (term list -> term)) list *
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      (string * (ast list -> ast)) list -> theory -> theory
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    val add_trrules: xrule list -> theory -> theory
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    val add_axioms: (string * string) list -> theory -> theory
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    val add_axioms_i: (string * term) list -> theory -> theory
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    val add_thyname: string -> theory -> theory
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  end
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  val cert_axm: Sign.sg -> string * term -> string * term
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  val read_axm: Sign.sg -> string * string -> string * term
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  val inferT_axm: Sign.sg -> string * term -> string * term
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  val abstract_rule: string -> cterm -> thm -> thm
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  val add_congs: meta_simpset * thm list -> meta_simpset
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  val add_prems: meta_simpset * thm list -> meta_simpset
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  val add_simps: meta_simpset * thm list -> meta_simpset
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  val assume: cterm -> thm
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  val assumption: int -> thm -> thm Sequence.seq
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  val axioms_of: theory -> (string * term) list
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  val beta_conversion: cterm -> thm
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  val bicompose: bool -> bool * thm * int -> int -> thm -> thm Sequence.seq
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  val biresolution: bool -> (bool*thm)list -> int -> thm -> thm Sequence.seq
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  val combination: thm -> thm -> thm
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  val concl_of: thm -> term
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  val cprop_of: thm -> cterm
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  val del_simps: meta_simpset * thm list -> meta_simpset
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  val dest_cimplies: cterm -> cterm*cterm
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  val dest_state: thm * int -> (term*term)list * term list * term * term
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  val empty_mss: meta_simpset
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  val eq_assumption: int -> 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 extensional: thm -> thm
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  val flexflex_rule: thm -> thm Sequence.seq
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  val flexpair_def: thm
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  val forall_elim: cterm -> thm -> thm
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  val forall_intr: cterm -> thm -> thm
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  val freezeT: thm -> thm
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  val get_axiom: theory -> string -> thm
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  val implies_elim: thm -> thm -> thm
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  val implies_intr: cterm -> thm -> thm
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  val implies_intr_hyps: thm -> thm
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  val instantiate: (indexname*ctyp)list * (cterm*cterm)list
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                   -> thm -> thm
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  val lift_rule: (thm * int) -> thm -> thm
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  val merge_theories: theory * theory -> theory
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  val merge_thy_list: bool -> theory list -> theory
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  val mk_rews_of_mss: meta_simpset -> thm -> thm list
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  val mss_of: thm list -> meta_simpset
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  val nprems_of: thm -> int
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  val parents_of: theory -> theory list
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  val prems_of: thm -> term list
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  val prems_of_mss: meta_simpset -> thm list
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  val pure_thy: theory
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  val read_def_cterm :
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         Sign.sg * (indexname -> typ option) * (indexname -> sort option) ->
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         string * typ -> cterm * (indexname * typ) list
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   val reflexive: cterm -> thm
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  val rename_params_rule: string list * int -> thm -> thm
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  val rep_thm: thm -> {prop: term, hyps: term list, maxidx: int, sign: Sign.sg}
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  val rewrite_cterm:
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         bool*bool -> meta_simpset -> (meta_simpset -> thm -> thm option)
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           -> cterm -> thm
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  val set_mk_rews: meta_simpset * (thm -> thm list) -> meta_simpset
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  val rep_theory: theory -> {sign: Sign.sg, new_axioms: term Sign.Symtab.table,
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    parents: theory list}
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  val subthy: theory * theory -> bool
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  val eq_thy: theory * theory -> bool
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  val sign_of: theory -> Sign.sg
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  val syn_of: theory -> Sign.Syntax.syntax
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  val stamps_of_thm: thm -> string ref list
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  val stamps_of_thy: theory -> string ref list
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  val symmetric: thm -> thm
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  val tpairs_of: thm -> (term*term)list
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  val trace_simp: bool ref
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  val transitive: thm -> 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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end;
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functor ThmFun (structure Logic: LOGIC and Unify: UNIFY and Pattern: PATTERN
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  and Net:NET sharing type Pattern.type_sig = Unify.Sign.Type.type_sig): THM =
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struct
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structure Sequence = Unify.Sequence;
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structure Envir = Unify.Envir;
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structure Sign = Unify.Sign;
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structure Type = Sign.Type;
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structure Syntax = Sign.Syntax;
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structure Symtab = Sign.Symtab;
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(*** Certified terms and types ***)
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(** certified types **)
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(*certified typs under a signature*)
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datatype ctyp = Ctyp of {sign: Sign.sg, T: typ};
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fun rep_ctyp (Ctyp args) = args;
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fun typ_of (Ctyp {T, ...}) = T;
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fun ctyp_of sign T =
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  Ctyp {sign = sign, T = Sign.certify_typ sign T};
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fun read_ctyp sign s =
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  Ctyp {sign = sign, T = Sign.read_typ (sign, K None) s};
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(** certified terms **)
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(*certified terms under a signature, with checked typ and maxidx of Vars*)
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datatype cterm = Cterm of {sign: Sign.sg, t: term, T: typ, maxidx: int};
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fun rep_cterm (Cterm args) = args;
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fun term_of (Cterm {t, ...}) = t;
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(*create a cterm by checking a "raw" term with respect to a signature*)
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fun cterm_of sign tm =
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  let val (t, T, maxidx) = Sign.certify_term sign tm
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  in Cterm {sign = sign, t = t, T = T, maxidx = maxidx}
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  end handle TYPE (msg, _, _)
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    => raise TERM ("Term not in signature\n" ^ msg, [tm]);
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fun cterm_fun f (Cterm {sign, t, ...}) = cterm_of sign (f t);
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(*dest_implies for cterms. Note T=prop below*)
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fun dest_cimplies (Cterm{sign, T, maxidx, t=Const("==>", _) $ A $ B}) =
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       (Cterm{sign=sign, T=T, maxidx=maxidx, t=A},
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        Cterm{sign=sign, T=T, maxidx=maxidx, t=B})
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  | dest_cimplies ct = raise TERM ("dest_cimplies", [term_of ct]);
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(** read cterms **)   (*exception ERROR*)     (* FIXME check *)
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(*read term, infer types, certify term*)
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fun read_def_cterm (sign, types, sorts) (a, T) =
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  let
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    val t = Syntax.read (#syn (Sign.rep_sg sign)) T a;
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    val (t', tye) = Sign.infer_types sign types sorts (t, T);
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    val ct = cterm_of sign t' handle TERM (msg, _) => error msg;
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  in (ct, tye) end;
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fun read_cterm sign = #1 o read_def_cterm (sign, K None, K None);
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(*** Meta theorems ***)
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datatype thm = Thm of
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  {sign: Sign.sg, maxidx: int, hyps: term list, prop: term};
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fun rep_thm (Thm args) = args;
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(*errors involving theorems*)
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exception THM of string * int * thm list;
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val sign_of_thm = #sign o rep_thm;
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val stamps_of_thm = #stamps o Sign.rep_sg o sign_of_thm;
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(*merge signatures of two theorems; raise exception if incompatible*)
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fun merge_thm_sgs (th1, th2) =
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  Sign.merge (pairself sign_of_thm (th1, th2))
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    handle TERM _ => raise THM ("incompatible signatures", 0, [th1, th2]);
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(*maps object-rule to tpairs*)
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fun tpairs_of (Thm {prop, ...}) = #1 (Logic.strip_flexpairs prop);
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(*maps object-rule to premises*)
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fun prems_of (Thm {prop, ...}) =
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  Logic.strip_imp_prems (Logic.skip_flexpairs prop);
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(*counts premises in a rule*)
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fun nprems_of (Thm {prop, ...}) =
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  Logic.count_prems (Logic.skip_flexpairs prop, 0);
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(*maps object-rule to conclusion*)
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fun concl_of (Thm {prop, ...}) = Logic.strip_imp_concl prop;
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(*the statement of any thm is a cterm*)
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fun cprop_of (Thm {sign, maxidx, hyps, prop}) =
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  Cterm {sign = sign, maxidx = maxidx, T = propT, t = prop};
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(*** Theories ***)
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datatype theory =
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  Theory of {
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    sign: Sign.sg,
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    new_axioms: term Symtab.table,
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    parents: theory list};
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fun rep_theory (Theory args) = args;
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(*errors involving theories*)
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exception THEORY of string * theory list;
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val sign_of = #sign o rep_theory;
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val syn_of = #syn o Sign.rep_sg o sign_of;
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(*stamps associated with a theory*)
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val stamps_of_thy = #stamps o Sign.rep_sg o sign_of;
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(*return additional axioms of this theory node*)
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val axioms_of = Symtab.dest o #new_axioms o rep_theory;
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(*return the immediate ancestors*)
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val parents_of = #parents o rep_theory;
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(*compare theories*)
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val subthy = Sign.subsig o pairself sign_of;
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val eq_thy = Sign.eq_sg o pairself sign_of;
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(*look up the named axiom in the theory*)
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fun get_axiom theory name =
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  let
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    fun get_ax [] = raise Match
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      | get_ax (Theory {sign, new_axioms, parents} :: thys) =
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          (case Symtab.lookup (new_axioms, name) of
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            Some t =>
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              Thm {sign = sign, maxidx = maxidx_of_term t, hyps = [], prop = t}
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          | None => get_ax parents handle Match => get_ax thys);
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  in
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    get_ax [theory] handle Match
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      => raise THEORY ("get_axiom: no axiom " ^ quote name, [theory])
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  end;
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(* the Pure theory *)
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val pure_thy =
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  Theory {sign = Sign.pure, new_axioms = Symtab.null, parents = []};
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(** extend theory **)
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fun err_dup_axms names =
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  error ("Duplicate axiom name(s) " ^ commas_quote names);
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fun ext_thy (thy as Theory {sign, new_axioms, parents}) sign1 new_axms =
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  let
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    val draft = Sign.is_draft sign;
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    val new_axioms1 =
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      Symtab.extend_new (if draft then new_axioms else Symtab.null, new_axms)
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        handle Symtab.DUPS names => err_dup_axms names;
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    val parents1 = if draft then parents else [thy];
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  in
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    Theory {sign = sign1, new_axioms = new_axioms1, parents = parents1}
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  end;
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(* extend signature of a theory *)
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fun ext_sg extfun decls (thy as Theory {sign, ...}) =
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  ext_thy thy (extfun decls sign) [];
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val add_classes   = ext_sg Sign.add_classes;
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val add_classrel  = ext_sg Sign.add_classrel;
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val add_defsort   = ext_sg Sign.add_defsort;
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val add_types     = ext_sg Sign.add_types;
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val add_tyabbrs   = ext_sg Sign.add_tyabbrs;
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val add_tyabbrs_i = ext_sg Sign.add_tyabbrs_i;
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val add_arities   = ext_sg Sign.add_arities;
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val add_consts    = ext_sg Sign.add_consts;
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val add_consts_i  = ext_sg Sign.add_consts_i;
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val add_syntax    = ext_sg Sign.add_syntax;
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val add_syntax_i  = ext_sg Sign.add_syntax_i;
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val add_trfuns    = ext_sg Sign.add_trfuns;
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val add_trrules   = ext_sg Sign.add_trrules;
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val add_thyname   = ext_sg Sign.add_name;
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(* prepare axioms *)
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fun err_in_axm name =
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  error ("The error(s) above occurred in axiom " ^ quote name);
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fun no_vars tm =
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  if null (term_vars tm) andalso null (term_tvars tm) then tm
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  else error "Illegal schematic variable(s) in term";
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   343
fun cert_axm sg (name, raw_tm) =
wenzelm@387
   344
  let
wenzelm@387
   345
    val Cterm {t, T, ...} = cterm_of sg raw_tm
wenzelm@387
   346
      handle TERM (msg, _) => error msg;
wenzelm@387
   347
  in
wenzelm@387
   348
    assert (T = propT) "Term not of type prop";
wenzelm@387
   349
    (name, no_vars t)
wenzelm@387
   350
  end
wenzelm@387
   351
  handle ERROR => err_in_axm name;
wenzelm@387
   352
wenzelm@387
   353
fun read_axm sg (name, str) =
wenzelm@387
   354
  (name, no_vars (term_of (read_cterm sg (str, propT))))
wenzelm@387
   355
    handle ERROR => err_in_axm name;
wenzelm@387
   356
wenzelm@564
   357
fun inferT_axm sg (name, pre_tm) =
wenzelm@564
   358
  (name, no_vars (#1 (Sign.infer_types sg (K None) (K None) (pre_tm, propT))))
wenzelm@564
   359
    handle ERROR => err_in_axm name;
wenzelm@564
   360
wenzelm@387
   361
wenzelm@387
   362
(* extend axioms of a theory *)
wenzelm@387
   363
wenzelm@387
   364
fun ext_axms prep_axm axms (thy as Theory {sign, ...}) =
wenzelm@387
   365
  let
wenzelm@387
   366
    val sign1 = Sign.make_draft sign;
wenzelm@399
   367
    val axioms = map (apsnd Logic.varify o prep_axm sign) axms;
wenzelm@387
   368
  in
wenzelm@399
   369
    ext_thy thy sign1 axioms
wenzelm@387
   370
  end;
wenzelm@387
   371
wenzelm@387
   372
val add_axioms = ext_axms read_axm;
wenzelm@387
   373
val add_axioms_i = ext_axms cert_axm;
wenzelm@387
   374
wenzelm@387
   375
wenzelm@387
   376
wenzelm@387
   377
(** merge theories **)
wenzelm@387
   378
wenzelm@387
   379
fun merge_thy_list mk_draft thys =
wenzelm@387
   380
  let
wenzelm@387
   381
    fun is_union thy = forall (fn t => subthy (t, thy)) thys;
wenzelm@387
   382
    val is_draft = Sign.is_draft o sign_of;
wenzelm@387
   383
wenzelm@387
   384
    fun add_sign (sg, Theory {sign, ...}) =
wenzelm@387
   385
      Sign.merge (sg, sign) handle TERM (msg, _) => error msg;
wenzelm@387
   386
  in
wenzelm@387
   387
    (case (find_first is_union thys, exists is_draft thys) of
wenzelm@387
   388
      (Some thy, _) => thy
wenzelm@387
   389
    | (None, true) => raise THEORY ("Illegal merge of draft theories", thys)
wenzelm@387
   390
    | (None, false) => Theory {
wenzelm@387
   391
        sign =
wenzelm@387
   392
          (if mk_draft then Sign.make_draft else I)
wenzelm@387
   393
          (foldl add_sign (Sign.pure, thys)),
wenzelm@399
   394
        new_axioms = Symtab.null,
wenzelm@387
   395
        parents = thys})
wenzelm@387
   396
  end;
wenzelm@387
   397
wenzelm@387
   398
fun merge_theories (thy1, thy2) = merge_thy_list false [thy1, thy2];
wenzelm@387
   399
clasohm@0
   400
clasohm@0
   401
clasohm@0
   402
(**** Primitive rules ****)
clasohm@0
   403
clasohm@0
   404
(* discharge all assumptions t from ts *)
clasohm@0
   405
val disch = gen_rem (op aconv);
clasohm@0
   406
clasohm@0
   407
(*The assumption rule A|-A in a theory  *)
wenzelm@250
   408
fun assume ct : thm =
lcp@229
   409
  let val {sign, t=prop, T, maxidx} = rep_cterm ct
wenzelm@250
   410
  in  if T<>propT then
wenzelm@250
   411
        raise THM("assume: assumptions must have type prop", 0, [])
clasohm@0
   412
      else if maxidx <> ~1 then
wenzelm@250
   413
        raise THM("assume: assumptions may not contain scheme variables",
wenzelm@250
   414
                  maxidx, [])
clasohm@0
   415
      else Thm{sign = sign, maxidx = ~1, hyps = [prop], prop = prop}
clasohm@0
   416
  end;
clasohm@0
   417
wenzelm@250
   418
(* Implication introduction
wenzelm@250
   419
              A |- B
wenzelm@250
   420
              -------
wenzelm@250
   421
              A ==> B    *)
clasohm@0
   422
fun implies_intr cA (thB as Thm{sign,maxidx,hyps,prop}) : thm =
lcp@229
   423
  let val {sign=signA, t=A, T, maxidx=maxidxA} = rep_cterm cA
clasohm@0
   424
  in  if T<>propT then
wenzelm@250
   425
        raise THM("implies_intr: assumptions must have type prop", 0, [thB])
wenzelm@250
   426
      else Thm{sign= Sign.merge (sign,signA),  maxidx= max[maxidxA, maxidx],
wenzelm@250
   427
             hyps= disch(hyps,A),  prop= implies$A$prop}
clasohm@0
   428
      handle TERM _ =>
clasohm@0
   429
        raise THM("implies_intr: incompatible signatures", 0, [thB])
clasohm@0
   430
  end;
clasohm@0
   431
clasohm@0
   432
(* Implication elimination
wenzelm@250
   433
        A ==> B       A
wenzelm@250
   434
        ---------------
wenzelm@250
   435
                B      *)
clasohm@0
   436
fun implies_elim thAB thA : thm =
clasohm@0
   437
    let val Thm{maxidx=maxA, hyps=hypsA, prop=propA,...} = thA
wenzelm@250
   438
        and Thm{sign, maxidx, hyps, prop,...} = thAB;
wenzelm@250
   439
        fun err(a) = raise THM("implies_elim: "^a, 0, [thAB,thA])
clasohm@0
   440
    in  case prop of
wenzelm@250
   441
            imp$A$B =>
wenzelm@250
   442
                if imp=implies andalso  A aconv propA
wenzelm@387
   443
                then  Thm{sign= merge_thm_sgs(thAB,thA),
wenzelm@250
   444
                          maxidx= max[maxA,maxidx],
wenzelm@250
   445
                          hyps= hypsA union hyps,  (*dups suppressed*)
wenzelm@250
   446
                          prop= B}
wenzelm@250
   447
                else err("major premise")
wenzelm@250
   448
          | _ => err("major premise")
clasohm@0
   449
    end;
wenzelm@250
   450
clasohm@0
   451
(* Forall introduction.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   452
     A
clasohm@0
   453
   ------
clasohm@0
   454
   !!x.A       *)
clasohm@0
   455
fun forall_intr cx (th as Thm{sign,maxidx,hyps,prop}) =
lcp@229
   456
  let val x = term_of cx;
clasohm@0
   457
      fun result(a,T) = Thm{sign= sign, maxidx= maxidx, hyps= hyps,
wenzelm@250
   458
                            prop= all(T) $ Abs(a, T, abstract_over (x,prop))}
clasohm@0
   459
  in  case x of
wenzelm@250
   460
        Free(a,T) =>
wenzelm@250
   461
          if exists (apl(x, Logic.occs)) hyps
wenzelm@250
   462
          then  raise THM("forall_intr: variable free in assumptions", 0, [th])
wenzelm@250
   463
          else  result(a,T)
clasohm@0
   464
      | Var((a,_),T) => result(a,T)
clasohm@0
   465
      | _ => raise THM("forall_intr: not a variable", 0, [th])
clasohm@0
   466
  end;
clasohm@0
   467
clasohm@0
   468
(* Forall elimination
wenzelm@250
   469
              !!x.A
wenzelm@250
   470
             --------
wenzelm@250
   471
              A[t/x]     *)
clasohm@0
   472
fun forall_elim ct (th as Thm{sign,maxidx,hyps,prop}) : thm =
lcp@229
   473
  let val {sign=signt, t, T, maxidx=maxt} = rep_cterm ct
clasohm@0
   474
  in  case prop of
wenzelm@250
   475
          Const("all",Type("fun",[Type("fun",[qary,_]),_])) $ A =>
wenzelm@250
   476
            if T<>qary then
wenzelm@250
   477
                raise THM("forall_elim: type mismatch", 0, [th])
wenzelm@250
   478
            else Thm{sign= Sign.merge(sign,signt),
wenzelm@250
   479
                     maxidx= max[maxidx, maxt],
wenzelm@250
   480
                     hyps= hyps,  prop= betapply(A,t)}
wenzelm@250
   481
        | _ => raise THM("forall_elim: not quantified", 0, [th])
clasohm@0
   482
  end
clasohm@0
   483
  handle TERM _ =>
wenzelm@250
   484
         raise THM("forall_elim: incompatible signatures", 0, [th]);
clasohm@0
   485
clasohm@0
   486
clasohm@0
   487
(*** Equality ***)
clasohm@0
   488
clasohm@0
   489
(*Definition of the relation =?= *)
clasohm@0
   490
val flexpair_def =
wenzelm@250
   491
  Thm{sign= Sign.pure, hyps= [], maxidx= 0,
wenzelm@250
   492
      prop= term_of
wenzelm@250
   493
              (read_cterm Sign.pure
wenzelm@250
   494
                 ("(?t =?= ?u) == (?t == ?u::?'a::{})", propT))};
clasohm@0
   495
clasohm@0
   496
(*The reflexivity rule: maps  t   to the theorem   t==t   *)
wenzelm@250
   497
fun reflexive ct =
lcp@229
   498
  let val {sign, t, T, maxidx} = rep_cterm ct
clasohm@0
   499
  in  Thm{sign= sign, hyps= [], maxidx= maxidx, prop= Logic.mk_equals(t,t)}
clasohm@0
   500
  end;
clasohm@0
   501
clasohm@0
   502
(*The symmetry rule
clasohm@0
   503
    t==u
clasohm@0
   504
    ----
clasohm@0
   505
    u==t         *)
clasohm@0
   506
fun symmetric (th as Thm{sign,hyps,prop,maxidx}) =
clasohm@0
   507
  case prop of
clasohm@0
   508
      (eq as Const("==",_)) $ t $ u =>
wenzelm@250
   509
          Thm{sign=sign, hyps=hyps, maxidx=maxidx, prop= eq$u$t}
clasohm@0
   510
    | _ => raise THM("symmetric", 0, [th]);
clasohm@0
   511
clasohm@0
   512
(*The transitive rule
clasohm@0
   513
    t1==u    u==t2
clasohm@0
   514
    ------------
clasohm@0
   515
        t1==t2      *)
clasohm@0
   516
fun transitive th1 th2 =
clasohm@0
   517
  let val Thm{maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
clasohm@0
   518
      and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2;
clasohm@0
   519
      fun err(msg) = raise THM("transitive: "^msg, 0, [th1,th2])
clasohm@0
   520
  in case (prop1,prop2) of
clasohm@0
   521
       ((eq as Const("==",_)) $ t1 $ u, Const("==",_) $ u' $ t2) =>
wenzelm@250
   522
          if not (u aconv u') then err"middle term"  else
wenzelm@387
   523
              Thm{sign= merge_thm_sgs(th1,th2), hyps= hyps1 union hyps2,
wenzelm@250
   524
                  maxidx= max[max1,max2], prop= eq$t1$t2}
clasohm@0
   525
     | _ =>  err"premises"
clasohm@0
   526
  end;
clasohm@0
   527
clasohm@0
   528
(*Beta-conversion: maps (%(x)t)(u) to the theorem  (%(x)t)(u) == t[u/x]   *)
wenzelm@250
   529
fun beta_conversion ct =
lcp@229
   530
  let val {sign, t, T, maxidx} = rep_cterm ct
clasohm@0
   531
  in  case t of
wenzelm@250
   532
          Abs(_,_,bodt) $ u =>
wenzelm@250
   533
            Thm{sign= sign,  hyps= [],
wenzelm@250
   534
                maxidx= maxidx_of_term t,
wenzelm@250
   535
                prop= Logic.mk_equals(t, subst_bounds([u],bodt))}
wenzelm@250
   536
        | _ =>  raise THM("beta_conversion: not a redex", 0, [])
clasohm@0
   537
  end;
clasohm@0
   538
clasohm@0
   539
(*The extensionality rule   (proviso: x not free in f, g, or hypotheses)
clasohm@0
   540
    f(x) == g(x)
clasohm@0
   541
    ------------
clasohm@0
   542
       f == g    *)
clasohm@0
   543
fun extensional (th as Thm{sign,maxidx,hyps,prop}) =
clasohm@0
   544
  case prop of
clasohm@0
   545
    (Const("==",_)) $ (f$x) $ (g$y) =>
wenzelm@250
   546
      let fun err(msg) = raise THM("extensional: "^msg, 0, [th])
clasohm@0
   547
      in (if x<>y then err"different variables" else
clasohm@0
   548
          case y of
wenzelm@250
   549
                Free _ =>
wenzelm@250
   550
                  if exists (apl(y, Logic.occs)) (f::g::hyps)
wenzelm@250
   551
                  then err"variable free in hyps or functions"    else  ()
wenzelm@250
   552
              | Var _ =>
wenzelm@250
   553
                  if Logic.occs(y,f)  orelse  Logic.occs(y,g)
wenzelm@250
   554
                  then err"variable free in functions"   else  ()
wenzelm@250
   555
              | _ => err"not a variable");
wenzelm@250
   556
          Thm{sign=sign, hyps=hyps, maxidx=maxidx,
wenzelm@250
   557
              prop= Logic.mk_equals(f,g)}
clasohm@0
   558
      end
clasohm@0
   559
 | _ =>  raise THM("extensional: premise", 0, [th]);
clasohm@0
   560
clasohm@0
   561
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   562
  The bound variable will be named "a" (since x will be something like x320)
clasohm@0
   563
          t == u
clasohm@0
   564
    ----------------
clasohm@0
   565
      %(x)t == %(x)u     *)
clasohm@0
   566
fun abstract_rule a cx (th as Thm{sign,maxidx,hyps,prop}) =
lcp@229
   567
  let val x = term_of cx;
wenzelm@250
   568
      val (t,u) = Logic.dest_equals prop
wenzelm@250
   569
            handle TERM _ =>
wenzelm@250
   570
                raise THM("abstract_rule: premise not an equality", 0, [th])
clasohm@0
   571
      fun result T =
clasohm@0
   572
            Thm{sign= sign, maxidx= maxidx, hyps= hyps,
wenzelm@250
   573
                prop= Logic.mk_equals(Abs(a, T, abstract_over (x,t)),
wenzelm@250
   574
                                      Abs(a, T, abstract_over (x,u)))}
clasohm@0
   575
  in  case x of
wenzelm@250
   576
        Free(_,T) =>
wenzelm@250
   577
         if exists (apl(x, Logic.occs)) hyps
wenzelm@250
   578
         then raise THM("abstract_rule: variable free in assumptions", 0, [th])
wenzelm@250
   579
         else result T
clasohm@0
   580
      | Var(_,T) => result T
clasohm@0
   581
      | _ => raise THM("abstract_rule: not a variable", 0, [th])
clasohm@0
   582
  end;
clasohm@0
   583
clasohm@0
   584
(*The combination rule
clasohm@0
   585
    f==g    t==u
clasohm@0
   586
    ------------
clasohm@0
   587
     f(t)==g(u)      *)
clasohm@0
   588
fun combination th1 th2 =
clasohm@0
   589
  let val Thm{maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
clasohm@0
   590
      and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2
clasohm@0
   591
  in  case (prop1,prop2)  of
clasohm@0
   592
       (Const("==",_) $ f $ g, Const("==",_) $ t $ u) =>
wenzelm@387
   593
              Thm{sign= merge_thm_sgs(th1,th2), hyps= hyps1 union hyps2,
wenzelm@250
   594
                  maxidx= max[max1,max2], prop= Logic.mk_equals(f$t, g$u)}
clasohm@0
   595
     | _ =>  raise THM("combination: premises", 0, [th1,th2])
clasohm@0
   596
  end;
clasohm@0
   597
clasohm@0
   598
clasohm@0
   599
(*The equal propositions rule
clasohm@0
   600
    A==B    A
clasohm@0
   601
    ---------
clasohm@0
   602
        B          *)
clasohm@0
   603
fun equal_elim th1 th2 =
clasohm@0
   604
  let val Thm{maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
clasohm@0
   605
      and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2;
clasohm@0
   606
      fun err(msg) = raise THM("equal_elim: "^msg, 0, [th1,th2])
clasohm@0
   607
  in  case prop1  of
clasohm@0
   608
       Const("==",_) $ A $ B =>
wenzelm@250
   609
          if not (prop2 aconv A) then err"not equal"  else
wenzelm@387
   610
              Thm{sign= merge_thm_sgs(th1,th2), hyps= hyps1 union hyps2,
wenzelm@250
   611
                  maxidx= max[max1,max2], prop= B}
clasohm@0
   612
     | _ =>  err"major premise"
clasohm@0
   613
  end;
clasohm@0
   614
clasohm@0
   615
clasohm@0
   616
(* Equality introduction
clasohm@0
   617
    A==>B    B==>A
clasohm@0
   618
    -------------
clasohm@0
   619
         A==B            *)
clasohm@0
   620
fun equal_intr th1 th2 =
clasohm@0
   621
let val Thm{maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
clasohm@0
   622
    and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2;
clasohm@0
   623
    fun err(msg) = raise THM("equal_intr: "^msg, 0, [th1,th2])
clasohm@0
   624
in case (prop1,prop2) of
clasohm@0
   625
     (Const("==>",_) $ A $ B, Const("==>",_) $ B' $ A')  =>
wenzelm@250
   626
        if A aconv A' andalso B aconv B'
wenzelm@387
   627
        then Thm{sign= merge_thm_sgs(th1,th2), hyps= hyps1 union hyps2,
wenzelm@250
   628
                 maxidx= max[max1,max2], prop= Logic.mk_equals(A,B)}
wenzelm@250
   629
        else err"not equal"
clasohm@0
   630
   | _ =>  err"premises"
clasohm@0
   631
end;
clasohm@0
   632
clasohm@0
   633
(**** Derived rules ****)
clasohm@0
   634
clasohm@0
   635
(*Discharge all hypotheses (need not verify cterms)
clasohm@0
   636
  Repeated hypotheses are discharged only once;  fold cannot do this*)
clasohm@0
   637
fun implies_intr_hyps (Thm{sign, maxidx, hyps=A::As, prop}) =
clasohm@0
   638
      implies_intr_hyps
wenzelm@250
   639
            (Thm{sign=sign,  maxidx=maxidx,
wenzelm@250
   640
                 hyps= disch(As,A),  prop= implies$A$prop})
clasohm@0
   641
  | implies_intr_hyps th = th;
clasohm@0
   642
clasohm@0
   643
(*Smash" unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@250
   644
  Instantiates the theorem and deletes trivial tpairs.
clasohm@0
   645
  Resulting sequence may contain multiple elements if the tpairs are
clasohm@0
   646
    not all flex-flex. *)
clasohm@0
   647
fun flexflex_rule (Thm{sign,maxidx,hyps,prop}) =
wenzelm@250
   648
  let fun newthm env =
wenzelm@250
   649
          let val (tpairs,horn) =
wenzelm@250
   650
                        Logic.strip_flexpairs (Envir.norm_term env prop)
wenzelm@250
   651
                (*Remove trivial tpairs, of the form t=t*)
wenzelm@250
   652
              val distpairs = filter (not o op aconv) tpairs
wenzelm@250
   653
              val newprop = Logic.list_flexpairs(distpairs, horn)
wenzelm@250
   654
          in  Thm{sign= sign, hyps= hyps,
wenzelm@250
   655
                  maxidx= maxidx_of_term newprop, prop= newprop}
wenzelm@250
   656
          end;
clasohm@0
   657
      val (tpairs,_) = Logic.strip_flexpairs prop
clasohm@0
   658
  in Sequence.maps newthm
wenzelm@250
   659
            (Unify.smash_unifiers(sign, Envir.empty maxidx, tpairs))
clasohm@0
   660
  end;
clasohm@0
   661
clasohm@0
   662
(*Instantiation of Vars
wenzelm@250
   663
                      A
wenzelm@250
   664
             --------------------
wenzelm@250
   665
              A[t1/v1,....,tn/vn]     *)
clasohm@0
   666
clasohm@0
   667
(*Check that all the terms are Vars and are distinct*)
clasohm@0
   668
fun instl_ok ts = forall is_Var ts andalso null(findrep ts);
clasohm@0
   669
clasohm@0
   670
(*For instantiate: process pair of cterms, merge theories*)
clasohm@0
   671
fun add_ctpair ((ct,cu), (sign,tpairs)) =
lcp@229
   672
  let val {sign=signt, t=t, T= T, ...} = rep_cterm ct
lcp@229
   673
      and {sign=signu, t=u, T= U, ...} = rep_cterm cu
clasohm@0
   674
  in  if T=U  then (Sign.merge(sign, Sign.merge(signt, signu)), (t,u)::tpairs)
clasohm@0
   675
      else raise TYPE("add_ctpair", [T,U], [t,u])
clasohm@0
   676
  end;
clasohm@0
   677
clasohm@0
   678
fun add_ctyp ((v,ctyp), (sign',vTs)) =
lcp@229
   679
  let val {T,sign} = rep_ctyp ctyp
clasohm@0
   680
  in (Sign.merge(sign,sign'), (v,T)::vTs) end;
clasohm@0
   681
clasohm@0
   682
(*Left-to-right replacements: ctpairs = [...,(vi,ti),...].
clasohm@0
   683
  Instantiates distinct Vars by terms of same type.
clasohm@0
   684
  Normalizes the new theorem! *)
wenzelm@250
   685
fun instantiate (vcTs,ctpairs)  (th as Thm{sign,maxidx,hyps,prop}) =
clasohm@0
   686
  let val (newsign,tpairs) = foldr add_ctpair (ctpairs, (sign,[]));
clasohm@0
   687
      val (newsign,vTs) = foldr add_ctyp (vcTs, (newsign,[]));
wenzelm@250
   688
      val newprop =
wenzelm@250
   689
            Envir.norm_term (Envir.empty 0)
wenzelm@250
   690
              (subst_atomic tpairs
wenzelm@250
   691
               (Type.inst_term_tvars(#tsig(Sign.rep_sg newsign),vTs) prop))
clasohm@0
   692
      val newth = Thm{sign= newsign, hyps= hyps,
wenzelm@250
   693
                      maxidx= maxidx_of_term newprop, prop= newprop}
wenzelm@250
   694
  in  if not(instl_ok(map #1 tpairs))
nipkow@193
   695
      then raise THM("instantiate: variables not distinct", 0, [th])
nipkow@193
   696
      else if not(null(findrep(map #1 vTs)))
nipkow@193
   697
      then raise THM("instantiate: type variables not distinct", 0, [th])
nipkow@193
   698
      else (*Check types of Vars for agreement*)
nipkow@193
   699
      case findrep (map (#1 o dest_Var) (term_vars newprop)) of
wenzelm@250
   700
          ix::_ => raise THM("instantiate: conflicting types for variable " ^
wenzelm@250
   701
                             Syntax.string_of_vname ix ^ "\n", 0, [newth])
wenzelm@250
   702
        | [] =>
wenzelm@250
   703
             case findrep (map #1 (term_tvars newprop)) of
wenzelm@250
   704
             ix::_ => raise THM
wenzelm@250
   705
                    ("instantiate: conflicting sorts for type variable " ^
wenzelm@250
   706
                     Syntax.string_of_vname ix ^ "\n", 0, [newth])
nipkow@193
   707
        | [] => newth
clasohm@0
   708
  end
wenzelm@250
   709
  handle TERM _ =>
clasohm@0
   710
           raise THM("instantiate: incompatible signatures",0,[th])
nipkow@193
   711
       | TYPE _ => raise THM("instantiate: type conflict", 0, [th]);
clasohm@0
   712
clasohm@0
   713
(*The trivial implication A==>A, justified by assume and forall rules.
clasohm@0
   714
  A can contain Vars, not so for assume!   *)
wenzelm@250
   715
fun trivial ct : thm =
lcp@229
   716
  let val {sign, t=A, T, maxidx} = rep_cterm ct
wenzelm@250
   717
  in  if T<>propT then
wenzelm@250
   718
            raise THM("trivial: the term must have type prop", 0, [])
clasohm@0
   719
      else Thm{sign= sign, maxidx= maxidx, hyps= [], prop= implies$A$A}
clasohm@0
   720
  end;
clasohm@0
   721
wenzelm@480
   722
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)".
wenzelm@399
   723
  Is weaker than some definition of c_class, e.g. "c_class == %x.T";
wenzelm@399
   724
  may be interpreted as an instance of A==>A.*)
wenzelm@399
   725
fun class_triv thy c =
wenzelm@399
   726
  let
wenzelm@399
   727
    val sign = sign_of thy;
wenzelm@399
   728
    val Cterm {t, maxidx, ...} =
wenzelm@399
   729
      cterm_of sign (Logic.mk_inclass (TVar (("'a", 0), [c]), c))
wenzelm@399
   730
        handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@399
   731
  in
wenzelm@399
   732
    Thm {sign = sign, maxidx = maxidx, hyps = [], prop = t}
wenzelm@399
   733
  end;
wenzelm@399
   734
wenzelm@399
   735
clasohm@0
   736
(* Replace all TFrees not in the hyps by new TVars *)
clasohm@0
   737
fun varifyT(Thm{sign,maxidx,hyps,prop}) =
clasohm@0
   738
  let val tfrees = foldr add_term_tfree_names (hyps,[])
clasohm@0
   739
  in Thm{sign=sign, maxidx=max[0,maxidx], hyps=hyps,
wenzelm@250
   740
         prop= Type.varify(prop,tfrees)}
clasohm@0
   741
  end;
clasohm@0
   742
clasohm@0
   743
(* Replace all TVars by new TFrees *)
clasohm@0
   744
fun freezeT(Thm{sign,maxidx,hyps,prop}) =
clasohm@0
   745
  let val prop' = Type.freeze (K true) prop
clasohm@0
   746
  in Thm{sign=sign, maxidx=maxidx_of_term prop', hyps=hyps, prop=prop'} end;
clasohm@0
   747
clasohm@0
   748
clasohm@0
   749
(*** Inference rules for tactics ***)
clasohm@0
   750
clasohm@0
   751
(*Destruct proof state into constraints, other goals, goal(i), rest *)
clasohm@0
   752
fun dest_state (state as Thm{prop,...}, i) =
clasohm@0
   753
  let val (tpairs,horn) = Logic.strip_flexpairs prop
clasohm@0
   754
  in  case  Logic.strip_prems(i, [], horn) of
clasohm@0
   755
          (B::rBs, C) => (tpairs, rev rBs, B, C)
clasohm@0
   756
        | _ => raise THM("dest_state", i, [state])
clasohm@0
   757
  end
clasohm@0
   758
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
   759
lcp@309
   760
(*Increment variables and parameters of orule as required for
clasohm@0
   761
  resolution with goal i of state. *)
clasohm@0
   762
fun lift_rule (state, i) orule =
clasohm@0
   763
  let val Thm{prop=sprop,maxidx=smax,...} = state;
clasohm@0
   764
      val (Bi::_, _) = Logic.strip_prems(i, [], Logic.skip_flexpairs sprop)
wenzelm@250
   765
        handle TERM _ => raise THM("lift_rule", i, [orule,state]);
clasohm@0
   766
      val (lift_abs,lift_all) = Logic.lift_fns(Bi,smax+1);
clasohm@0
   767
      val (Thm{sign,maxidx,hyps,prop}) = orule
clasohm@0
   768
      val (tpairs,As,B) = Logic.strip_horn prop
wenzelm@387
   769
  in  Thm{hyps=hyps, sign= merge_thm_sgs(state,orule),
wenzelm@250
   770
          maxidx= maxidx+smax+1,
wenzelm@250
   771
          prop= Logic.rule_of(map (pairself lift_abs) tpairs,
wenzelm@250
   772
                              map lift_all As,    lift_all B)}
clasohm@0
   773
  end;
clasohm@0
   774
clasohm@0
   775
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
   776
fun assumption i state =
clasohm@0
   777
  let val Thm{sign,maxidx,hyps,prop} = state;
clasohm@0
   778
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
wenzelm@250
   779
      fun newth (env as Envir.Envir{maxidx, ...}, tpairs) =
wenzelm@250
   780
          Thm{sign=sign, hyps=hyps, maxidx=maxidx, prop=
wenzelm@250
   781
            if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@250
   782
              Logic.rule_of (tpairs, Bs, C)
wenzelm@250
   783
            else (*normalize the new rule fully*)
wenzelm@250
   784
              Envir.norm_term env (Logic.rule_of (tpairs, Bs, C))};
clasohm@0
   785
      fun addprfs [] = Sequence.null
clasohm@0
   786
        | addprfs ((t,u)::apairs) = Sequence.seqof (fn()=> Sequence.pull
clasohm@0
   787
             (Sequence.mapp newth
wenzelm@250
   788
                (Unify.unifiers(sign,Envir.empty maxidx, (t,u)::tpairs))
wenzelm@250
   789
                (addprfs apairs)))
clasohm@0
   790
  in  addprfs (Logic.assum_pairs Bi)  end;
clasohm@0
   791
wenzelm@250
   792
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
   793
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
   794
fun eq_assumption i state =
clasohm@0
   795
  let val Thm{sign,maxidx,hyps,prop} = state;
clasohm@0
   796
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
clasohm@0
   797
  in  if exists (op aconv) (Logic.assum_pairs Bi)
wenzelm@250
   798
      then Thm{sign=sign, hyps=hyps, maxidx=maxidx,
wenzelm@250
   799
               prop=Logic.rule_of(tpairs, Bs, C)}
clasohm@0
   800
      else  raise THM("eq_assumption", 0, [state])
clasohm@0
   801
  end;
clasohm@0
   802
clasohm@0
   803
clasohm@0
   804
(** User renaming of parameters in a subgoal **)
clasohm@0
   805
clasohm@0
   806
(*Calls error rather than raising an exception because it is intended
clasohm@0
   807
  for top-level use -- exception handling would not make sense here.
clasohm@0
   808
  The names in cs, if distinct, are used for the innermost parameters;
clasohm@0
   809
   preceding parameters may be renamed to make all params distinct.*)
clasohm@0
   810
fun rename_params_rule (cs, i) state =
clasohm@0
   811
  let val Thm{sign,maxidx,hyps,prop} = state
clasohm@0
   812
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
clasohm@0
   813
      val iparams = map #1 (Logic.strip_params Bi)
clasohm@0
   814
      val short = length iparams - length cs
wenzelm@250
   815
      val newnames =
wenzelm@250
   816
            if short<0 then error"More names than abstractions!"
wenzelm@250
   817
            else variantlist(take (short,iparams), cs) @ cs
clasohm@0
   818
      val freenames = map (#1 o dest_Free) (term_frees prop)
clasohm@0
   819
      val newBi = Logic.list_rename_params (newnames, Bi)
wenzelm@250
   820
  in
clasohm@0
   821
  case findrep cs of
clasohm@0
   822
     c::_ => error ("Bound variables not distinct: " ^ c)
clasohm@0
   823
   | [] => (case cs inter freenames of
clasohm@0
   824
       a::_ => error ("Bound/Free variable clash: " ^ a)
clasohm@0
   825
     | [] => Thm{sign=sign, hyps=hyps, maxidx=maxidx, prop=
wenzelm@250
   826
                    Logic.rule_of(tpairs, Bs@[newBi], C)})
clasohm@0
   827
  end;
clasohm@0
   828
clasohm@0
   829
(*** Preservation of bound variable names ***)
clasohm@0
   830
wenzelm@250
   831
(*Scan a pair of terms; while they are similar,
clasohm@0
   832
  accumulate corresponding bound vars in "al"*)
clasohm@0
   833
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = match_bvs(s,t,(x,y)::al)
clasohm@0
   834
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
clasohm@0
   835
  | match_bvs(_,_,al) = al;
clasohm@0
   836
clasohm@0
   837
(* strip abstractions created by parameters *)
clasohm@0
   838
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
clasohm@0
   839
clasohm@0
   840
wenzelm@250
   841
(* strip_apply f A(,B) strips off all assumptions/parameters from A
clasohm@0
   842
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
   843
fun strip_apply f =
clasohm@0
   844
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@250
   845
                Const("==>",_)$ _  $ B2) = implies $ A1 $ strip(B1,B2)
wenzelm@250
   846
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
   847
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
   848
        | strip(A,_) = f A
clasohm@0
   849
  in strip end;
clasohm@0
   850
clasohm@0
   851
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
   852
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
   853
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
   854
fun rename_bvs([],_,_,_) = I
clasohm@0
   855
  | rename_bvs(al,dpairs,tpairs,B) =
wenzelm@250
   856
    let val vars = foldr add_term_vars
wenzelm@250
   857
                        (map fst dpairs @ map fst tpairs @ map snd tpairs, [])
wenzelm@250
   858
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
   859
        val vids = map (#1 o #1 o dest_Var) vars;
wenzelm@250
   860
        fun rename(t as Var((x,i),T)) =
wenzelm@250
   861
                (case assoc(al,x) of
wenzelm@250
   862
                   Some(y) => if x mem vids orelse y mem vids then t
wenzelm@250
   863
                              else Var((y,i),T)
wenzelm@250
   864
                 | None=> t)
clasohm@0
   865
          | rename(Abs(x,T,t)) =
wenzelm@250
   866
              Abs(case assoc(al,x) of Some(y) => y | None => x,
wenzelm@250
   867
                  T, rename t)
clasohm@0
   868
          | rename(f$t) = rename f $ rename t
clasohm@0
   869
          | rename(t) = t;
wenzelm@250
   870
        fun strip_ren Ai = strip_apply rename (Ai,B)
clasohm@0
   871
    in strip_ren end;
clasohm@0
   872
clasohm@0
   873
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
   874
fun rename_bvars(dpairs, tpairs, B) =
wenzelm@250
   875
        rename_bvs(foldr match_bvars (dpairs,[]), dpairs, tpairs, B);
clasohm@0
   876
clasohm@0
   877
clasohm@0
   878
(*** RESOLUTION ***)
clasohm@0
   879
clasohm@0
   880
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
   881
  identical because of lifting*)
wenzelm@250
   882
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
   883
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
   884
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
   885
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
   886
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
   887
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
   888
  | strip_assums2 BB = BB;
clasohm@0
   889
clasohm@0
   890
clasohm@0
   891
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
   892
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
   893
  If match then forbid instantiations in proof state
clasohm@0
   894
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
   895
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
   896
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
   897
  Curried so that resolution calls dest_state only once.
clasohm@0
   898
*)
clasohm@0
   899
local open Sequence; exception Bicompose
clasohm@0
   900
in
wenzelm@250
   901
fun bicompose_aux match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
   902
                        (eres_flg, orule, nsubgoal) =
clasohm@0
   903
 let val Thm{maxidx=smax, hyps=shyps, ...} = state
clasohm@0
   904
     and Thm{maxidx=rmax, hyps=rhyps, prop=rprop,...} = orule;
wenzelm@387
   905
     val sign = merge_thm_sgs(state,orule);
clasohm@0
   906
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
wenzelm@250
   907
     fun addth As ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
   908
       let val normt = Envir.norm_term env;
wenzelm@250
   909
           (*perform minimal copying here by examining env*)
wenzelm@250
   910
           val normp =
wenzelm@250
   911
             if Envir.is_empty env then (tpairs, Bs @ As, C)
wenzelm@250
   912
             else
wenzelm@250
   913
             let val ntps = map (pairself normt) tpairs
wenzelm@250
   914
             in if the (Envir.minidx env) > smax then (*no assignments in state*)
wenzelm@250
   915
                  (ntps, Bs @ map normt As, C)
wenzelm@250
   916
                else if match then raise Bicompose
wenzelm@250
   917
                else (*normalize the new rule fully*)
wenzelm@250
   918
                  (ntps, map normt (Bs @ As), normt C)
wenzelm@250
   919
             end
wenzelm@250
   920
           val th = Thm{sign=sign, hyps=rhyps union shyps, maxidx=maxidx,
wenzelm@250
   921
                        prop= Logic.rule_of normp}
clasohm@0
   922
        in  cons(th, thq)  end  handle Bicompose => thq
clasohm@0
   923
     val (rtpairs,rhorn) = Logic.strip_flexpairs(rprop);
clasohm@0
   924
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rhorn)
clasohm@0
   925
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
   926
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
   927
     fun newAs(As0, n, dpairs, tpairs) =
clasohm@0
   928
       let val As1 = if !Logic.auto_rename orelse not lifted then As0
wenzelm@250
   929
                     else map (rename_bvars(dpairs,tpairs,B)) As0
clasohm@0
   930
       in (map (Logic.flatten_params n) As1)
wenzelm@250
   931
          handle TERM _ =>
wenzelm@250
   932
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
   933
       end;
clasohm@0
   934
     val env = Envir.empty(max[rmax,smax]);
clasohm@0
   935
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
   936
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
   937
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
clasohm@0
   938
     fun tryasms (_, _, []) = null
clasohm@0
   939
       | tryasms (As, n, (t,u)::apairs) =
wenzelm@250
   940
          (case pull(Unify.unifiers(sign, env, (t,u)::dpairs))  of
wenzelm@250
   941
               None                   => tryasms (As, n+1, apairs)
wenzelm@250
   942
             | cell as Some((_,tpairs),_) =>
wenzelm@250
   943
                   its_right (addth (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@250
   944
                       (seqof (fn()=> cell),
wenzelm@250
   945
                        seqof (fn()=> pull (tryasms (As, n+1, apairs)))));
clasohm@0
   946
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
clasohm@0
   947
       | eres (A1::As) = tryasms (As, 1, Logic.assum_pairs A1);
clasohm@0
   948
     (*ordinary resolution*)
clasohm@0
   949
     fun res(None) = null
wenzelm@250
   950
       | res(cell as Some((_,tpairs),_)) =
wenzelm@250
   951
             its_right (addth(newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@250
   952
                       (seqof (fn()=> cell), null)
clasohm@0
   953
 in  if eres_flg then eres(rev rAs)
clasohm@0
   954
     else res(pull(Unify.unifiers(sign, env, dpairs)))
clasohm@0
   955
 end;
clasohm@0
   956
end;  (*open Sequence*)
clasohm@0
   957
clasohm@0
   958
clasohm@0
   959
fun bicompose match arg i state =
clasohm@0
   960
    bicompose_aux match (state, dest_state(state,i), false) arg;
clasohm@0
   961
clasohm@0
   962
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
   963
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
   964
fun could_bires (Hs, B, eres_flg, rule) =
clasohm@0
   965
    let fun could_reshyp (A1::_) = exists (apl(A1,could_unify)) Hs
wenzelm@250
   966
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@250
   967
    in  could_unify(concl_of rule, B) andalso
wenzelm@250
   968
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
   969
    end;
clasohm@0
   970
clasohm@0
   971
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
   972
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
   973
fun biresolution match brules i state =
clasohm@0
   974
    let val lift = lift_rule(state, i);
wenzelm@250
   975
        val (stpairs, Bs, Bi, C) = dest_state(state,i)
wenzelm@250
   976
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
   977
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@250
   978
        val comp = bicompose_aux match (state, (stpairs, Bs, Bi, C), true);
wenzelm@250
   979
        fun res [] = Sequence.null
wenzelm@250
   980
          | res ((eres_flg, rule)::brules) =
wenzelm@250
   981
              if could_bires (Hs, B, eres_flg, rule)
wenzelm@250
   982
              then Sequence.seqof (*delay processing remainder til needed*)
wenzelm@250
   983
                  (fn()=> Some(comp (eres_flg, lift rule, nprems_of rule),
wenzelm@250
   984
                               res brules))
wenzelm@250
   985
              else res brules
clasohm@0
   986
    in  Sequence.flats (res brules)  end;
clasohm@0
   987
clasohm@0
   988
clasohm@0
   989
clasohm@0
   990
(*** Meta simp sets ***)
clasohm@0
   991
nipkow@288
   992
type rrule = {thm:thm, lhs:term, perm:bool};
nipkow@288
   993
type cong = {thm:thm, lhs:term};
clasohm@0
   994
datatype meta_simpset =
nipkow@405
   995
  Mss of {net:rrule Net.net, congs:(string * cong)list, bounds:string list,
clasohm@0
   996
          prems: thm list, mk_rews: thm -> thm list};
clasohm@0
   997
clasohm@0
   998
(*A "mss" contains data needed during conversion:
clasohm@0
   999
  net: discrimination net of rewrite rules
clasohm@0
  1000
  congs: association list of congruence rules
nipkow@405
  1001
  bounds: names of bound variables already used;
nipkow@405
  1002
          for generating new names when rewriting under lambda abstractions
clasohm@0
  1003
  mk_rews: used when local assumptions are added
clasohm@0
  1004
*)
clasohm@0
  1005
nipkow@405
  1006
val empty_mss = Mss{net= Net.empty, congs= [], bounds=[], prems= [],
clasohm@0
  1007
                    mk_rews = K[]};
clasohm@0
  1008
clasohm@0
  1009
exception SIMPLIFIER of string * thm;
clasohm@0
  1010
lcp@229
  1011
fun prtm a sign t = (writeln a; writeln(Sign.string_of_term sign t));
clasohm@0
  1012
nipkow@209
  1013
val trace_simp = ref false;
nipkow@209
  1014
lcp@229
  1015
fun trace_term a sign t = if !trace_simp then prtm a sign t else ();
nipkow@209
  1016
nipkow@209
  1017
fun trace_thm a (Thm{sign,prop,...}) = trace_term a sign prop;
nipkow@209
  1018
nipkow@427
  1019
fun vperm(Var _, Var _) = true
nipkow@427
  1020
  | vperm(Abs(_,_,s), Abs(_,_,t)) = vperm(s,t)
nipkow@427
  1021
  | vperm(t1$t2, u1$u2) = vperm(t1,u1) andalso vperm(t2,u2)
nipkow@427
  1022
  | vperm(t,u) = (t=u);
nipkow@288
  1023
nipkow@427
  1024
fun var_perm(t,u) = vperm(t,u) andalso
nipkow@427
  1025
                    eq_set(add_term_vars(t,[]), add_term_vars(u,[]))
nipkow@288
  1026
clasohm@0
  1027
(*simple test for looping rewrite*)
clasohm@0
  1028
fun loops sign prems (lhs,rhs) =
nipkow@427
  1029
  is_Var(lhs) orelse
nipkow@427
  1030
  (null(prems) andalso
nipkow@427
  1031
   Pattern.eta_matches (#tsig(Sign.rep_sg sign)) (lhs,rhs));
clasohm@0
  1032
clasohm@0
  1033
fun mk_rrule (thm as Thm{hyps,sign,prop,maxidx,...}) =
clasohm@0
  1034
  let val prems = Logic.strip_imp_prems prop
clasohm@0
  1035
      val concl = Pattern.eta_contract (Logic.strip_imp_concl prop)
clasohm@0
  1036
      val (lhs,rhs) = Logic.dest_equals concl handle TERM _ =>
clasohm@0
  1037
                      raise SIMPLIFIER("Rewrite rule not a meta-equality",thm)
nipkow@427
  1038
      val perm = var_perm(lhs,rhs) andalso not(lhs=rhs orelse is_Var(lhs))
nipkow@288
  1039
  in if not perm andalso loops sign prems (lhs,rhs)
clasohm@0
  1040
     then (prtm "Warning: ignoring looping rewrite rule" sign prop; None)
nipkow@288
  1041
     else Some{thm=thm,lhs=lhs,perm=perm}
clasohm@0
  1042
  end;
clasohm@0
  1043
nipkow@87
  1044
local
nipkow@87
  1045
 fun eq({thm=Thm{prop=p1,...},...}:rrule,
nipkow@87
  1046
        {thm=Thm{prop=p2,...},...}:rrule) = p1 aconv p2
nipkow@87
  1047
in
nipkow@87
  1048
nipkow@405
  1049
fun add_simp(mss as Mss{net,congs,bounds,prems,mk_rews},
clasohm@0
  1050
             thm as Thm{sign,prop,...}) =
nipkow@87
  1051
  case mk_rrule thm of
nipkow@87
  1052
    None => mss
nipkow@87
  1053
  | Some(rrule as {lhs,...}) =>
nipkow@209
  1054
      (trace_thm "Adding rewrite rule:" thm;
nipkow@209
  1055
       Mss{net= (Net.insert_term((lhs,rrule),net,eq)
nipkow@209
  1056
                 handle Net.INSERT =>
nipkow@87
  1057
                  (prtm "Warning: ignoring duplicate rewrite rule" sign prop;
nipkow@87
  1058
                   net)),
nipkow@405
  1059
           congs=congs, bounds=bounds, prems=prems,mk_rews=mk_rews});
nipkow@87
  1060
nipkow@405
  1061
fun del_simp(mss as Mss{net,congs,bounds,prems,mk_rews},
nipkow@87
  1062
             thm as Thm{sign,prop,...}) =
nipkow@87
  1063
  case mk_rrule thm of
nipkow@87
  1064
    None => mss
nipkow@87
  1065
  | Some(rrule as {lhs,...}) =>
nipkow@87
  1066
      Mss{net= (Net.delete_term((lhs,rrule),net,eq)
nipkow@87
  1067
                handle Net.INSERT =>
nipkow@87
  1068
                 (prtm "Warning: rewrite rule not in simpset" sign prop;
nipkow@87
  1069
                  net)),
nipkow@405
  1070
             congs=congs, bounds=bounds, prems=prems,mk_rews=mk_rews}
nipkow@87
  1071
nipkow@87
  1072
end;
clasohm@0
  1073
clasohm@0
  1074
val add_simps = foldl add_simp;
nipkow@87
  1075
val del_simps = foldl del_simp;
clasohm@0
  1076
clasohm@0
  1077
fun mss_of thms = add_simps(empty_mss,thms);
clasohm@0
  1078
nipkow@405
  1079
fun add_cong(Mss{net,congs,bounds,prems,mk_rews},thm) =
clasohm@0
  1080
  let val (lhs,_) = Logic.dest_equals(concl_of thm) handle TERM _ =>
clasohm@0
  1081
                    raise SIMPLIFIER("Congruence not a meta-equality",thm)
clasohm@0
  1082
      val lhs = Pattern.eta_contract lhs
clasohm@0
  1083
      val (a,_) = dest_Const (head_of lhs) handle TERM _ =>
clasohm@0
  1084
                  raise SIMPLIFIER("Congruence must start with a constant",thm)
nipkow@405
  1085
  in Mss{net=net, congs=(a,{lhs=lhs,thm=thm})::congs, bounds=bounds,
clasohm@0
  1086
         prems=prems, mk_rews=mk_rews}
clasohm@0
  1087
  end;
clasohm@0
  1088
clasohm@0
  1089
val (op add_congs) = foldl add_cong;
clasohm@0
  1090
nipkow@405
  1091
fun add_prems(Mss{net,congs,bounds,prems,mk_rews},thms) =
nipkow@405
  1092
  Mss{net=net, congs=congs, bounds=bounds, prems=thms@prems, mk_rews=mk_rews};
clasohm@0
  1093
clasohm@0
  1094
fun prems_of_mss(Mss{prems,...}) = prems;
clasohm@0
  1095
nipkow@405
  1096
fun set_mk_rews(Mss{net,congs,bounds,prems,...},mk_rews) =
nipkow@405
  1097
  Mss{net=net, congs=congs, bounds=bounds, prems=prems, mk_rews=mk_rews};
clasohm@0
  1098
fun mk_rews_of_mss(Mss{mk_rews,...}) = mk_rews;
clasohm@0
  1099
clasohm@0
  1100
wenzelm@250
  1101
(*** Meta-level rewriting
clasohm@0
  1102
     uses conversions, omitting proofs for efficiency.  See
wenzelm@250
  1103
        L C Paulson, A higher-order implementation of rewriting,
wenzelm@250
  1104
        Science of Computer Programming 3 (1983), pages 119-149. ***)
clasohm@0
  1105
clasohm@0
  1106
type prover = meta_simpset -> thm -> thm option;
clasohm@0
  1107
type termrec = (Sign.sg * term list) * term;
clasohm@0
  1108
type conv = meta_simpset -> termrec -> termrec;
clasohm@0
  1109
nipkow@305
  1110
datatype order = LESS | EQUAL | GREATER;
nipkow@288
  1111
nipkow@305
  1112
fun stringord(a,b:string) = if a<b then LESS  else
nipkow@305
  1113
                            if a=b then EQUAL else GREATER;
nipkow@305
  1114
nipkow@305
  1115
fun intord(i,j:int) = if i<j then LESS  else
nipkow@305
  1116
                      if i=j then EQUAL else GREATER;
nipkow@288
  1117
nipkow@427
  1118
(* NB: non-linearity of the ordering is not a soundness problem *)
nipkow@427
  1119
nipkow@305
  1120
(* FIXME: "***ABSTRACTION***" is a hack and makes the ordering non-linear *)
nipkow@305
  1121
fun string_of_hd(Const(a,_)) = a
nipkow@305
  1122
  | string_of_hd(Free(a,_))  = a
nipkow@305
  1123
  | string_of_hd(Var(v,_))   = Syntax.string_of_vname v
nipkow@305
  1124
  | string_of_hd(Bound i)    = string_of_int i
nipkow@305
  1125
  | string_of_hd(Abs _)      = "***ABSTRACTION***";
nipkow@288
  1126
nipkow@305
  1127
(* a strict (not reflexive) linear well-founded AC-compatible ordering
nipkow@305
  1128
 * for terms:
nipkow@305
  1129
 * s < t <=> 1. size(s) < size(t) or
nipkow@305
  1130
             2. size(s) = size(t) and s=f(...) and t = g(...) and f<g or
nipkow@305
  1131
             3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
nipkow@305
  1132
                (s1..sn) < (t1..tn) (lexicographically)
nipkow@305
  1133
 *)
nipkow@288
  1134
nipkow@288
  1135
(* FIXME: should really take types into account as well.
nipkow@427
  1136
 * Otherwise non-linear *)
nipkow@305
  1137
fun termord(t,u) =
nipkow@305
  1138
      (case intord(size_of_term t,size_of_term u) of
nipkow@305
  1139
         EQUAL => let val (f,ts) = strip_comb t and (g,us) = strip_comb u
nipkow@305
  1140
                  in case stringord(string_of_hd f, string_of_hd g) of
nipkow@305
  1141
                       EQUAL => lextermord(ts,us)
nipkow@305
  1142
                     | ord   => ord
nipkow@305
  1143
                  end
nipkow@305
  1144
       | ord => ord)
nipkow@305
  1145
and lextermord(t::ts,u::us) =
nipkow@305
  1146
      (case termord(t,u) of
nipkow@305
  1147
         EQUAL => lextermord(ts,us)
nipkow@305
  1148
       | ord   => ord)
nipkow@305
  1149
  | lextermord([],[]) = EQUAL
nipkow@305
  1150
  | lextermord _ = error("lextermord");
nipkow@288
  1151
nipkow@305
  1152
fun termless tu = (termord tu = LESS);
nipkow@288
  1153
nipkow@432
  1154
fun check_conv(thm as Thm{hyps,prop,sign,...}, prop0) =
nipkow@432
  1155
  let fun err() = (trace_thm "Proved wrong thm (Check subgoaler?)" thm;
nipkow@432
  1156
                   trace_term "Should have proved" sign prop0;
nipkow@432
  1157
                   None)
clasohm@0
  1158
      val (lhs0,_) = Logic.dest_equals(Logic.strip_imp_concl prop0)
clasohm@0
  1159
  in case prop of
clasohm@0
  1160
       Const("==",_) $ lhs $ rhs =>
clasohm@0
  1161
         if (lhs = lhs0) orelse
nipkow@427
  1162
            (lhs aconv Envir.norm_term (Envir.empty 0) lhs0)
nipkow@208
  1163
         then (trace_thm "SUCCEEDED" thm; Some(hyps,rhs))
clasohm@0
  1164
         else err()
clasohm@0
  1165
     | _ => err()
clasohm@0
  1166
  end;
clasohm@0
  1167
clasohm@0
  1168
(*Conversion to apply the meta simpset to a term*)
nipkow@208
  1169
fun rewritec (prover,signt) (mss as Mss{net,...}) (hypst,t) =
nipkow@225
  1170
  let val t = Pattern.eta_contract t;
nipkow@288
  1171
      fun rew {thm as Thm{sign,hyps,maxidx,prop,...}, lhs, perm} =
wenzelm@250
  1172
        let val unit = if Sign.subsig(sign,signt) then ()
clasohm@446
  1173
                  else (trace_thm"Warning: rewrite rule from different theory"
clasohm@446
  1174
                          thm;
nipkow@208
  1175
                        raise Pattern.MATCH)
nipkow@208
  1176
            val insts = Pattern.match (#tsig(Sign.rep_sg signt)) (lhs,t)
clasohm@0
  1177
            val prop' = subst_vars insts prop;
clasohm@0
  1178
            val hyps' = hyps union hypst;
nipkow@208
  1179
            val thm' = Thm{sign=signt, hyps=hyps', prop=prop', maxidx=maxidx}
nipkow@427
  1180
            val (lhs',rhs') = Logic.dest_equals(Logic.strip_imp_concl prop')
nipkow@427
  1181
        in if perm andalso not(termless(rhs',lhs')) then None else
nipkow@427
  1182
           if Logic.count_prems(prop',0) = 0
nipkow@427
  1183
           then (trace_thm "Rewriting:" thm'; Some(hyps',rhs'))
clasohm@0
  1184
           else (trace_thm "Trying to rewrite:" thm';
clasohm@0
  1185
                 case prover mss thm' of
clasohm@0
  1186
                   None       => (trace_thm "FAILED" thm'; None)
nipkow@112
  1187
                 | Some(thm2) => check_conv(thm2,prop'))
clasohm@0
  1188
        end
clasohm@0
  1189
nipkow@225
  1190
      fun rews [] = None
nipkow@225
  1191
        | rews (rrule::rrules) =
nipkow@225
  1192
            let val opt = rew rrule handle Pattern.MATCH => None
nipkow@225
  1193
            in case opt of None => rews rrules | some => some end;
clasohm@0
  1194
clasohm@0
  1195
  in case t of
nipkow@208
  1196
       Abs(_,_,body) $ u => Some(hypst,subst_bounds([u], body))
nipkow@225
  1197
     | _                 => rews(Net.match_term net t)
clasohm@0
  1198
  end;
clasohm@0
  1199
clasohm@0
  1200
(*Conversion to apply a congruence rule to a term*)
nipkow@208
  1201
fun congc (prover,signt) {thm=cong,lhs=lhs} (hypst,t) =
clasohm@0
  1202
  let val Thm{sign,hyps,maxidx,prop,...} = cong
nipkow@208
  1203
      val unit = if Sign.subsig(sign,signt) then ()
nipkow@208
  1204
                 else error("Congruence rule from different theory")
nipkow@208
  1205
      val tsig = #tsig(Sign.rep_sg signt)
clasohm@0
  1206
      val insts = Pattern.match tsig (lhs,t) handle Pattern.MATCH =>
clasohm@0
  1207
                  error("Congruence rule did not match")
clasohm@0
  1208
      val prop' = subst_vars insts prop;
nipkow@208
  1209
      val thm' = Thm{sign=signt, hyps=hyps union hypst,
clasohm@0
  1210
                     prop=prop', maxidx=maxidx}
clasohm@0
  1211
      val unit = trace_thm "Applying congruence rule" thm';
nipkow@112
  1212
      fun err() = error("Failed congruence proof!")
clasohm@0
  1213
clasohm@0
  1214
  in case prover thm' of
nipkow@112
  1215
       None => err()
nipkow@112
  1216
     | Some(thm2) => (case check_conv(thm2,prop') of
nipkow@405
  1217
                        None => err() | some => some)
clasohm@0
  1218
  end;
clasohm@0
  1219
clasohm@0
  1220
nipkow@405
  1221
nipkow@214
  1222
fun bottomc ((simprem,useprem),prover,sign) =
nipkow@405
  1223
  let fun botc fail mss trec =
nipkow@405
  1224
            (case subc mss trec of
nipkow@405
  1225
               some as Some(trec1) =>
nipkow@405
  1226
                 (case rewritec (prover,sign) mss trec1 of
nipkow@405
  1227
                    Some(trec2) => botc false mss trec2
nipkow@405
  1228
                  | None => some)
nipkow@405
  1229
             | None =>
nipkow@405
  1230
                 (case rewritec (prover,sign) mss trec of
nipkow@405
  1231
                    Some(trec2) => botc false mss trec2
nipkow@405
  1232
                  | None => if fail then None else Some(trec)))
clasohm@0
  1233
nipkow@405
  1234
      and try_botc mss trec = (case botc true mss trec of
nipkow@405
  1235
                                 Some(trec1) => trec1
nipkow@405
  1236
                               | None => trec)
nipkow@405
  1237
nipkow@405
  1238
      and subc (mss as Mss{net,congs,bounds,prems,mk_rews})
nipkow@208
  1239
               (trec as (hyps,t)) =
clasohm@0
  1240
        (case t of
clasohm@0
  1241
            Abs(a,T,t) =>
nipkow@405
  1242
              let val b = variant bounds a
nipkow@405
  1243
                  val v = Free("." ^ b,T)
nipkow@405
  1244
                  val mss' = Mss{net=net, congs=congs, bounds=b::bounds,
clasohm@0
  1245
                                 prems=prems,mk_rews=mk_rews}
nipkow@405
  1246
              in case botc true mss' (hyps,subst_bounds([v],t)) of
nipkow@405
  1247
                   Some(hyps',t') =>
nipkow@405
  1248
                     Some(hyps', Abs(a, T, abstract_over(v,t')))
nipkow@405
  1249
                 | None => None
nipkow@405
  1250
              end
clasohm@0
  1251
          | t$u => (case t of
nipkow@405
  1252
              Const("==>",_)$s  => Some(impc(hyps,s,u,mss))
nipkow@405
  1253
            | Abs(_,_,body) =>
nipkow@405
  1254
                let val trec = (hyps,subst_bounds([u], body))
nipkow@405
  1255
                in case subc mss trec of
nipkow@405
  1256
                     None => Some(trec)
nipkow@405
  1257
                   | trec => trec
nipkow@405
  1258
                end
nipkow@405
  1259
            | _  =>
nipkow@405
  1260
                let fun appc() =
nipkow@405
  1261
                          (case botc true mss (hyps,t) of
nipkow@405
  1262
                             Some(hyps1,t1) =>
nipkow@405
  1263
                               (case botc true mss (hyps1,u) of
nipkow@405
  1264
                                  Some(hyps2,u1) => Some(hyps2,t1$u1)
nipkow@405
  1265
                                | None => Some(hyps1,t1$u))
nipkow@405
  1266
                           | None =>
nipkow@405
  1267
                               (case botc true mss (hyps,u) of
nipkow@405
  1268
                                  Some(hyps1,u1) => Some(hyps1,t$u1)
nipkow@405
  1269
                                | None => None))
clasohm@0
  1270
                    val (h,ts) = strip_comb t
clasohm@0
  1271
                in case h of
clasohm@0
  1272
                     Const(a,_) =>
clasohm@0
  1273
                       (case assoc(congs,a) of
clasohm@0
  1274
                          None => appc()
nipkow@208
  1275
                        | Some(cong) => congc (prover mss,sign) cong trec)
clasohm@0
  1276
                   | _ => appc()
clasohm@0
  1277
                end)
nipkow@405
  1278
          | _ => None)
clasohm@0
  1279
nipkow@208
  1280
      and impc(hyps,s,u,mss as Mss{mk_rews,...}) =
nipkow@405
  1281
        let val (hyps1,s1) = if simprem then try_botc mss (hyps,s)
nipkow@405
  1282
                             else (hyps,s)
nipkow@405
  1283
            val mss1 =
nipkow@405
  1284
              if not useprem orelse maxidx_of_term s1 <> ~1 then mss
nipkow@405
  1285
              else let val thm = Thm{sign=sign,hyps=[s1],prop=s1,maxidx= ~1}
nipkow@214
  1286
                   in add_simps(add_prems(mss,[thm]), mk_rews thm) end
nipkow@405
  1287
            val (hyps2,u1) = try_botc mss1 (hyps1,u)
nipkow@405
  1288
            val hyps3 = if s1 mem hyps1 then hyps2 else hyps2\s1
nipkow@405
  1289
        in (hyps3, Logic.mk_implies(s1,u1)) end
clasohm@0
  1290
nipkow@405
  1291
  in try_botc end;
clasohm@0
  1292
clasohm@0
  1293
clasohm@0
  1294
(*** Meta-rewriting: rewrites t to u and returns the theorem t==u ***)
clasohm@0
  1295
(* Parameters:
wenzelm@250
  1296
   mode = (simplify A, use A in simplifying B) when simplifying A ==> B
clasohm@0
  1297
   mss: contains equality theorems of the form [|p1,...|] ==> t==u
clasohm@0
  1298
   prover: how to solve premises in conditional rewrites and congruences
clasohm@0
  1299
*)
clasohm@0
  1300
nipkow@405
  1301
(*** FIXME: check that #bounds(mss) does not "occur" in ct alread ***)
nipkow@214
  1302
fun rewrite_cterm mode mss prover ct =
lcp@229
  1303
  let val {sign, t, T, maxidx} = rep_cterm ct;
nipkow@214
  1304
      val (hyps,u) = bottomc (mode,prover,sign) mss ([],t);
clasohm@0
  1305
      val prop = Logic.mk_equals(t,u)
nipkow@208
  1306
  in  Thm{sign= sign, hyps= hyps, maxidx= maxidx_of_term prop, prop= prop}
clasohm@0
  1307
  end
clasohm@0
  1308
clasohm@0
  1309
end;
wenzelm@250
  1310