src/Pure/thm.ML
author nipkow
Tue Feb 13 17:16:06 1996 +0100 (1996-02-13)
changeset 1495 b8b54847c77f
parent 1493 e936723cb94d
child 1503 7dba648ee25c
permissions -rw-r--r--
Added check for duplicate vars with distinct types/sorts (nodup_Vars)
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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 core of Isabelle's Meta Logic: certified types and terms, meta
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theorems, theories, meta rules (including resolution and
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simplification).
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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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  (*certified types*)
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  type ctyp
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  val rep_ctyp          : ctyp -> {sign: Sign.sg, T: typ}
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  val typ_of            : ctyp -> typ
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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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  (*certified terms*)
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  type cterm
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  exception CTERM of string
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  val rep_cterm         : cterm -> {sign: Sign.sg, t: term, T: typ,
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                                    maxidx: int}
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  val term_of           : cterm -> term
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  val cterm_of          : Sign.sg -> term -> cterm
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  val read_cterm        : Sign.sg -> string * typ -> cterm
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  val read_cterms       : Sign.sg -> string list * typ list -> cterm list
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  val cterm_fun         : (term -> term) -> (cterm -> cterm)
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  val dest_cimplies     : cterm -> cterm * cterm
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  val dest_comb         : cterm -> cterm * cterm
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  val dest_abs          : cterm -> cterm * cterm
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  val mk_prop           : cterm -> cterm
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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 list -> bool -> string * typ -> cterm * (indexname * typ) list
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  (*meta theorems*)
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  type thm
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  exception THM of string * int * thm list
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  val rep_thm           : thm -> {sign: Sign.sg, maxidx: int,
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    shyps: sort list, hyps: term list, prop: term}
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  val stamps_of_thm     : thm -> string ref list
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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 force_strip_shyps : bool ref      (* FIXME tmp *)
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  val strip_shyps       : thm -> thm
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  val implies_intr_shyps: thm -> thm
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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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  (*theories*)
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  type theory
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  exception THEORY of string * theory list
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  val rep_theory        : theory ->
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    {sign: Sign.sg, new_axioms: term Sign.Symtab.table, parents: theory list}
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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_thy     : theory -> string ref list
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  val parents_of        : theory -> 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 get_axiom         : theory -> string -> thm
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  val axioms_of         : theory -> (string * thm) list
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  val proto_pure_thy    : theory
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  val pure_thy          : theory
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  val cpure_thy         : theory
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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     : (string * string) trrule list -> theory -> theory
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    val add_trrules_i   : ast trrule 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 merge_theories    : theory * theory -> theory
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  val merge_thy_list    : bool -> theory list -> theory
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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 flexpair_def      : 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   : cterm -> thm
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  val extensional       : thm -> 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 Sequence.seq
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  val instantiate       :
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    (indexname * 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 freezeT           : thm -> thm
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  val dest_state        : thm * int ->
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    (term * term) list * term list * term * term
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  val lift_rule         : (thm * int) -> thm -> thm
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  val assumption        : int -> thm -> thm Sequence.seq
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  val eq_assumption     : 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 ->
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    int -> thm -> thm Sequence.seq
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  val biresolution      : bool -> (bool * thm) list ->
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    int -> thm -> thm Sequence.seq
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  (*meta simplification*)
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  type meta_simpset
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  exception SIMPLIFIER of string * thm
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  val empty_mss         : meta_simpset
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  val add_simps         : meta_simpset * thm list -> meta_simpset
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  val del_simps         : meta_simpset * thm list -> meta_simpset
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  val mss_of            : thm list -> meta_simpset
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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 prems_of_mss      : meta_simpset -> thm list
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  val set_mk_rews       : meta_simpset * (thm -> thm list) -> meta_simpset
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  val mk_rews_of_mss    : meta_simpset -> thm -> thm list
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  val trace_simp        : bool ref
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  val rewrite_cterm     : bool * bool -> meta_simpset ->
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    (meta_simpset -> thm -> thm option) -> cterm -> 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;
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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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exception CTERM of string;
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(*Destruct application in cterms*)
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fun dest_comb (Cterm{sign, 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 {sign=sign, maxidx=maxidx, t=A, T=typeA},
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       Cterm {sign=sign, 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 (Cterm{sign, T, maxidx, t = tm as Abs(s,ty,M)}) = 
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      let fun mk_var{Name,Ty} = Free(Name,Ty);
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          val v = mk_var{Name = s, Ty = ty};
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          val ty2 =
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            case T of Type("fun",[_,S]) => S
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                    | _ => error "Function type expected in dest_abs";
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      in (Cterm{sign = sign, T = ty, maxidx = maxidx, t = v},
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          Cterm{sign = sign, T = ty2, maxidx = maxidx, t = betapply (tm,v)})
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      end
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  | dest_abs _ = raise CTERM "dest_abs";
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(*Convert cterm of type "o" to "prop" by using Trueprop*)
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fun mk_prop (ct as Cterm{sign, T, maxidx, t = Const("Trueprop",_) $ _}) = ct
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  | mk_prop (Cterm{sign, T, maxidx, t}) =
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      if T = Type("o",[]) then
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        Cterm{sign = sign, T = Type("prop",[]), maxidx = maxidx,
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              t = Const("Trueprop", Type("o",[]) --> Type("prop",[])) $ t}
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      else error "Type o expected in mk_prop";
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(** read cterms **)   (*exception ERROR*)
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(*read term, infer types, certify term*)
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fun read_def_cterm (sign, types, sorts) used freeze (a, T) =
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  let
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    val T' = Sign.certify_typ sign T
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      handle TYPE (msg, _, _) => error msg;
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    val ts = Syntax.read (#syn (Sign.rep_sg sign)) T' a;
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    val (_, t', tye) =
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          Sign.infer_types sign types sorts used freeze (ts, T');
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    val ct = cterm_of sign t'
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      handle TYPE arg => error (Sign.exn_type_msg sign arg)
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	   | 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) [] true;
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(*read a list of terms, matching them against a list of expected types.
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  NO disambiguation of alternative parses via type-checking -- it is just
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  not practical.*)
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fun read_cterms sign (bs, Ts) =
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  let
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    val {tsig, syn, ...} = Sign.rep_sg sign
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    fun read (b,T) =
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	case Syntax.read syn T b of
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	    [t] => t
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	  | _   => error("Error or ambiguity in parsing of " ^ b)
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    val (us,_) = Type.infer_types(tsig, Sign.const_type sign, 
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				  K None, K None, 
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				  [], true, 
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				  map (Sign.certify_typ sign) Ts, 
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				  map read (bs~~Ts))
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  in  map (cterm_of sign) us  end
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  handle TYPE arg => error (Sign.exn_type_msg sign arg)
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       | TERM (msg, _) => error msg;
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(*** Meta theorems ***)
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datatype thm = Thm of
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  {sign: Sign.sg,		(*signature for hyps and prop*)
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   maxidx: int,			(*maximum index of any Var or TVar*)
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   shyps: sort list,		(* FIXME comment *)
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   hyps: term list,		(*hypotheses*)
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   prop: term};			(*conclusion*)
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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 (msg, _) => raise THM (msg, 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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   319
  Logic.count_prems (Logic.skip_flexpairs prop, 0);
clasohm@0
   320
wenzelm@387
   321
(*maps object-rule to conclusion*)
wenzelm@387
   322
fun concl_of (Thm {prop, ...}) = Logic.strip_imp_concl prop;
clasohm@0
   323
wenzelm@387
   324
(*the statement of any thm is a cterm*)
wenzelm@1160
   325
fun cprop_of (Thm {sign, maxidx, prop, ...}) =
wenzelm@387
   326
  Cterm {sign = sign, maxidx = maxidx, T = propT, t = prop};
lcp@229
   327
wenzelm@387
   328
clasohm@0
   329
wenzelm@1238
   330
(** sort contexts of theorems **)
wenzelm@1238
   331
wenzelm@1238
   332
(* basic utils *)
wenzelm@1238
   333
wenzelm@1238
   334
(*accumulate sorts suppressing duplicates; these are coded low level
wenzelm@1238
   335
  to improve efficiency a bit*)
wenzelm@1238
   336
wenzelm@1238
   337
fun add_typ_sorts (Type (_, Ts), Ss) = add_typs_sorts (Ts, Ss)
wenzelm@1238
   338
  | add_typ_sorts (TFree (_, S), Ss) = S ins Ss
wenzelm@1238
   339
  | add_typ_sorts (TVar (_, S), Ss) = S ins Ss
wenzelm@1238
   340
and add_typs_sorts ([], Ss) = Ss
wenzelm@1238
   341
  | add_typs_sorts (T :: Ts, Ss) = add_typs_sorts (Ts, add_typ_sorts (T, Ss));
wenzelm@1238
   342
wenzelm@1238
   343
fun add_term_sorts (Const (_, T), Ss) = add_typ_sorts (T, Ss)
wenzelm@1238
   344
  | add_term_sorts (Free (_, T), Ss) = add_typ_sorts (T, Ss)
wenzelm@1238
   345
  | add_term_sorts (Var (_, T), Ss) = add_typ_sorts (T, Ss)
wenzelm@1238
   346
  | add_term_sorts (Bound _, Ss) = Ss
wenzelm@1238
   347
  | add_term_sorts (Abs (_, T, t), Ss) = add_term_sorts (t, add_typ_sorts (T, Ss))
wenzelm@1238
   348
  | add_term_sorts (t $ u, Ss) = add_term_sorts (t, add_term_sorts (u, Ss));
wenzelm@1238
   349
wenzelm@1238
   350
fun add_terms_sorts ([], Ss) = Ss
wenzelm@1238
   351
  | add_terms_sorts (t :: ts, Ss) = add_terms_sorts (ts, add_term_sorts (t, Ss));
wenzelm@1238
   352
wenzelm@1258
   353
fun env_codT (Envir.Envir {iTs, ...}) = map snd iTs;
wenzelm@1258
   354
wenzelm@1258
   355
fun add_env_sorts (env, Ss) =
wenzelm@1258
   356
  add_terms_sorts (map snd (Envir.alist_of env),
wenzelm@1258
   357
    add_typs_sorts (env_codT env, Ss));
wenzelm@1258
   358
wenzelm@1238
   359
fun add_thm_sorts (Thm {hyps, prop, ...}, Ss) =
wenzelm@1238
   360
  add_terms_sorts (hyps, add_term_sorts (prop, Ss));
wenzelm@1238
   361
wenzelm@1238
   362
fun add_thms_shyps ([], Ss) = Ss
wenzelm@1238
   363
  | add_thms_shyps (Thm {shyps, ...} :: ths, Ss) =
wenzelm@1238
   364
      add_thms_shyps (ths, shyps union Ss);
wenzelm@1238
   365
wenzelm@1238
   366
wenzelm@1238
   367
(*get 'dangling' sort constraints of a thm*)
wenzelm@1238
   368
fun extra_shyps (th as Thm {shyps, ...}) =
wenzelm@1238
   369
  shyps \\ add_thm_sorts (th, []);
wenzelm@1238
   370
wenzelm@1238
   371
paulson@1416
   372
(*Compression of theorems -- a separate rule, not integrated with the others,
paulson@1416
   373
  as it could be slow.*)
paulson@1416
   374
fun compress (Thm {sign, maxidx, shyps, hyps, prop}) = 
paulson@1416
   375
    Thm {sign = sign, 
clasohm@1460
   376
	 maxidx = maxidx,
clasohm@1460
   377
	 shyps = shyps, 
clasohm@1460
   378
	 hyps = map Term.compress_term hyps, 
clasohm@1460
   379
	 prop = Term.compress_term prop};
paulson@1416
   380
paulson@1416
   381
wenzelm@1238
   382
(* fix_shyps *)
wenzelm@1238
   383
wenzelm@1238
   384
(*preserve sort contexts of rule premises and substituted types*)
wenzelm@1238
   385
fun fix_shyps thms Ts thm =
wenzelm@1238
   386
  let
wenzelm@1238
   387
    val Thm {sign, maxidx, hyps, prop, ...} = thm;
wenzelm@1238
   388
    val shyps =
wenzelm@1238
   389
      add_thm_sorts (thm, add_typs_sorts (Ts, add_thms_shyps (thms, [])));
wenzelm@1238
   390
  in
wenzelm@1238
   391
    Thm {sign = sign, maxidx = maxidx,
wenzelm@1238
   392
      shyps = shyps, hyps = hyps, prop = prop}
wenzelm@1238
   393
  end;
wenzelm@1238
   394
wenzelm@1238
   395
wenzelm@1238
   396
(* strip_shyps *)       (* FIXME improve? (e.g. only minimal extra sorts) *)
wenzelm@1238
   397
wenzelm@1238
   398
val force_strip_shyps = ref true;  (* FIXME tmp *)
wenzelm@1238
   399
wenzelm@1238
   400
(*remove extra sorts that are known to be syntactically non-empty*)
wenzelm@1238
   401
fun strip_shyps thm =
wenzelm@1238
   402
  let
wenzelm@1238
   403
    val Thm {sign, maxidx, shyps, hyps, prop} = thm;
wenzelm@1238
   404
    val sorts = add_thm_sorts (thm, []);
wenzelm@1238
   405
    val maybe_empty = not o Sign.nonempty_sort sign sorts;
wenzelm@1238
   406
    val shyps' = filter (fn S => S mem sorts orelse maybe_empty S) shyps;
wenzelm@1238
   407
  in
wenzelm@1238
   408
    Thm {sign = sign, maxidx = maxidx,
wenzelm@1238
   409
      shyps =
wenzelm@1238
   410
       (if eq_set (shyps', sorts) orelse not (! force_strip_shyps) then shyps'
wenzelm@1238
   411
        else    (* FIXME tmp *)
wenzelm@1238
   412
         (writeln ("WARNING Removed sort hypotheses: " ^
wenzelm@1238
   413
           commas (map Type.str_of_sort (shyps' \\ sorts)));
wenzelm@1238
   414
           writeln "WARNING Let's hope these sorts are non-empty!";
wenzelm@1238
   415
           sorts)),
wenzelm@1238
   416
      hyps = hyps, prop = prop}
wenzelm@1238
   417
  end;
wenzelm@1238
   418
wenzelm@1238
   419
wenzelm@1238
   420
(* implies_intr_shyps *)
wenzelm@1238
   421
wenzelm@1238
   422
(*discharge all extra sort hypotheses*)
wenzelm@1238
   423
fun implies_intr_shyps thm =
wenzelm@1238
   424
  (case extra_shyps thm of
wenzelm@1238
   425
    [] => thm
wenzelm@1238
   426
  | xshyps =>
wenzelm@1238
   427
      let
wenzelm@1238
   428
        val Thm {sign, maxidx, shyps, hyps, prop} = thm;
wenzelm@1238
   429
        val shyps' = logicS ins (shyps \\ xshyps);
wenzelm@1238
   430
        val used_names = foldr add_term_tfree_names (prop :: hyps, []);
wenzelm@1238
   431
        val names =
wenzelm@1238
   432
          tl (variantlist (replicate (length xshyps + 1) "'", used_names));
wenzelm@1238
   433
        val tfrees = map (TFree o rpair logicS) names;
wenzelm@1238
   434
wenzelm@1238
   435
        fun mk_insort (T, S) = map (Logic.mk_inclass o pair T) S;
wenzelm@1238
   436
        val sort_hyps = flat (map2 mk_insort (tfrees, xshyps));
wenzelm@1238
   437
      in
wenzelm@1238
   438
        Thm {sign = sign, maxidx = maxidx, shyps = shyps',
wenzelm@1238
   439
          hyps = hyps, prop = Logic.list_implies (sort_hyps, prop)}
wenzelm@1238
   440
      end);
wenzelm@1238
   441
wenzelm@1238
   442
wenzelm@1238
   443
wenzelm@387
   444
(*** Theories ***)
wenzelm@387
   445
clasohm@0
   446
datatype theory =
wenzelm@399
   447
  Theory of {
wenzelm@399
   448
    sign: Sign.sg,
wenzelm@399
   449
    new_axioms: term Symtab.table,
wenzelm@399
   450
    parents: theory list};
clasohm@0
   451
wenzelm@387
   452
fun rep_theory (Theory args) = args;
wenzelm@387
   453
wenzelm@387
   454
(*errors involving theories*)
clasohm@0
   455
exception THEORY of string * theory list;
clasohm@0
   456
clasohm@0
   457
wenzelm@387
   458
val sign_of = #sign o rep_theory;
clasohm@0
   459
val syn_of = #syn o Sign.rep_sg o sign_of;
clasohm@0
   460
wenzelm@387
   461
(*stamps associated with a theory*)
wenzelm@387
   462
val stamps_of_thy = #stamps o Sign.rep_sg o sign_of;
wenzelm@387
   463
wenzelm@387
   464
(*return the immediate ancestors*)
wenzelm@387
   465
val parents_of = #parents o rep_theory;
wenzelm@387
   466
wenzelm@387
   467
wenzelm@387
   468
(*compare theories*)
wenzelm@387
   469
val subthy = Sign.subsig o pairself sign_of;
wenzelm@387
   470
val eq_thy = Sign.eq_sg o pairself sign_of;
wenzelm@387
   471
wenzelm@387
   472
wenzelm@387
   473
(*look up the named axiom in the theory*)
wenzelm@387
   474
fun get_axiom theory name =
wenzelm@387
   475
  let
wenzelm@387
   476
    fun get_ax [] = raise Match
wenzelm@399
   477
      | get_ax (Theory {sign, new_axioms, parents} :: thys) =
wenzelm@399
   478
          (case Symtab.lookup (new_axioms, name) of
wenzelm@1238
   479
            Some t => fix_shyps [] []
wenzelm@1238
   480
              (Thm {sign = sign, maxidx = maxidx_of_term t,
wenzelm@1238
   481
                shyps = [], hyps = [], prop = t})
wenzelm@387
   482
          | None => get_ax parents handle Match => get_ax thys);
wenzelm@387
   483
  in
wenzelm@387
   484
    get_ax [theory] handle Match
wenzelm@387
   485
      => raise THEORY ("get_axiom: no axiom " ^ quote name, [theory])
wenzelm@387
   486
  end;
wenzelm@387
   487
wenzelm@776
   488
(*return additional axioms of this theory node*)
wenzelm@776
   489
fun axioms_of thy =
wenzelm@776
   490
  map (fn (s, _) => (s, get_axiom thy s))
wenzelm@776
   491
    (Symtab.dest (#new_axioms (rep_theory thy)));
wenzelm@776
   492
wenzelm@387
   493
clasohm@922
   494
(* the Pure theories *)
clasohm@922
   495
clasohm@922
   496
val proto_pure_thy =
clasohm@922
   497
  Theory {sign = Sign.proto_pure, new_axioms = Symtab.null, parents = []};
wenzelm@387
   498
wenzelm@387
   499
val pure_thy =
wenzelm@399
   500
  Theory {sign = Sign.pure, new_axioms = Symtab.null, parents = []};
wenzelm@387
   501
clasohm@922
   502
val cpure_thy =
clasohm@922
   503
  Theory {sign = Sign.cpure, new_axioms = Symtab.null, parents = []};
clasohm@922
   504
clasohm@0
   505
wenzelm@387
   506
wenzelm@387
   507
(** extend theory **)
wenzelm@387
   508
wenzelm@387
   509
fun err_dup_axms names =
wenzelm@387
   510
  error ("Duplicate axiom name(s) " ^ commas_quote names);
wenzelm@387
   511
wenzelm@399
   512
fun ext_thy (thy as Theory {sign, new_axioms, parents}) sign1 new_axms =
wenzelm@387
   513
  let
wenzelm@387
   514
    val draft = Sign.is_draft sign;
wenzelm@399
   515
    val new_axioms1 =
wenzelm@399
   516
      Symtab.extend_new (if draft then new_axioms else Symtab.null, new_axms)
wenzelm@387
   517
        handle Symtab.DUPS names => err_dup_axms names;
wenzelm@387
   518
    val parents1 = if draft then parents else [thy];
wenzelm@387
   519
  in
wenzelm@399
   520
    Theory {sign = sign1, new_axioms = new_axioms1, parents = parents1}
wenzelm@387
   521
  end;
wenzelm@387
   522
wenzelm@387
   523
wenzelm@387
   524
(* extend signature of a theory *)
wenzelm@387
   525
wenzelm@387
   526
fun ext_sg extfun decls (thy as Theory {sign, ...}) =
wenzelm@387
   527
  ext_thy thy (extfun decls sign) [];
wenzelm@387
   528
wenzelm@387
   529
val add_classes   = ext_sg Sign.add_classes;
wenzelm@421
   530
val add_classrel  = ext_sg Sign.add_classrel;
wenzelm@387
   531
val add_defsort   = ext_sg Sign.add_defsort;
wenzelm@387
   532
val add_types     = ext_sg Sign.add_types;
wenzelm@387
   533
val add_tyabbrs   = ext_sg Sign.add_tyabbrs;
wenzelm@387
   534
val add_tyabbrs_i = ext_sg Sign.add_tyabbrs_i;
wenzelm@387
   535
val add_arities   = ext_sg Sign.add_arities;
wenzelm@387
   536
val add_consts    = ext_sg Sign.add_consts;
wenzelm@387
   537
val add_consts_i  = ext_sg Sign.add_consts_i;
wenzelm@387
   538
val add_syntax    = ext_sg Sign.add_syntax;
wenzelm@387
   539
val add_syntax_i  = ext_sg Sign.add_syntax_i;
wenzelm@387
   540
val add_trfuns    = ext_sg Sign.add_trfuns;
wenzelm@387
   541
val add_trrules   = ext_sg Sign.add_trrules;
wenzelm@1160
   542
val add_trrules_i = ext_sg Sign.add_trrules_i;
wenzelm@387
   543
val add_thyname   = ext_sg Sign.add_name;
clasohm@0
   544
clasohm@0
   545
wenzelm@387
   546
(* prepare axioms *)
wenzelm@387
   547
wenzelm@387
   548
fun err_in_axm name =
wenzelm@387
   549
  error ("The error(s) above occurred in axiom " ^ quote name);
wenzelm@387
   550
wenzelm@387
   551
fun no_vars tm =
wenzelm@387
   552
  if null (term_vars tm) andalso null (term_tvars tm) then tm
wenzelm@387
   553
  else error "Illegal schematic variable(s) in term";
wenzelm@387
   554
wenzelm@387
   555
fun cert_axm sg (name, raw_tm) =
wenzelm@387
   556
  let
wenzelm@387
   557
    val Cterm {t, T, ...} = cterm_of sg raw_tm
paulson@1394
   558
      handle TYPE arg => error (Sign.exn_type_msg sg arg)
clasohm@1460
   559
	   | TERM (msg, _) => error msg;
wenzelm@387
   560
  in
wenzelm@387
   561
    assert (T = propT) "Term not of type prop";
wenzelm@387
   562
    (name, no_vars t)
wenzelm@387
   563
  end
wenzelm@387
   564
  handle ERROR => err_in_axm name;
wenzelm@387
   565
wenzelm@387
   566
fun read_axm sg (name, str) =
wenzelm@387
   567
  (name, no_vars (term_of (read_cterm sg (str, propT))))
wenzelm@387
   568
    handle ERROR => err_in_axm name;
wenzelm@387
   569
wenzelm@564
   570
fun inferT_axm sg (name, pre_tm) =
clasohm@959
   571
  let val t = #2(Sign.infer_types sg (K None) (K None) [] true
nipkow@949
   572
                                     ([pre_tm], propT))
nipkow@949
   573
  in  (name, no_vars t) end
nipkow@949
   574
  handle ERROR => err_in_axm name;
wenzelm@564
   575
wenzelm@387
   576
wenzelm@387
   577
(* extend axioms of a theory *)
wenzelm@387
   578
wenzelm@387
   579
fun ext_axms prep_axm axms (thy as Theory {sign, ...}) =
wenzelm@387
   580
  let
wenzelm@387
   581
    val sign1 = Sign.make_draft sign;
paulson@1416
   582
    val axioms = map (apsnd (Term.compress_term o Logic.varify) o 
clasohm@1460
   583
		      prep_axm sign) 
clasohm@1460
   584
	         axms;
wenzelm@387
   585
  in
wenzelm@399
   586
    ext_thy thy sign1 axioms
wenzelm@387
   587
  end;
wenzelm@387
   588
wenzelm@387
   589
val add_axioms = ext_axms read_axm;
wenzelm@387
   590
val add_axioms_i = ext_axms cert_axm;
wenzelm@387
   591
wenzelm@387
   592
wenzelm@387
   593
wenzelm@387
   594
(** merge theories **)
wenzelm@387
   595
wenzelm@387
   596
fun merge_thy_list mk_draft thys =
wenzelm@387
   597
  let
wenzelm@387
   598
    fun is_union thy = forall (fn t => subthy (t, thy)) thys;
wenzelm@387
   599
    val is_draft = Sign.is_draft o sign_of;
wenzelm@387
   600
wenzelm@387
   601
    fun add_sign (sg, Theory {sign, ...}) =
wenzelm@387
   602
      Sign.merge (sg, sign) handle TERM (msg, _) => error msg;
wenzelm@387
   603
  in
wenzelm@387
   604
    (case (find_first is_union thys, exists is_draft thys) of
wenzelm@387
   605
      (Some thy, _) => thy
wenzelm@387
   606
    | (None, true) => raise THEORY ("Illegal merge of draft theories", thys)
wenzelm@387
   607
    | (None, false) => Theory {
wenzelm@387
   608
        sign =
wenzelm@387
   609
          (if mk_draft then Sign.make_draft else I)
clasohm@922
   610
          (foldl add_sign (Sign.proto_pure, thys)),
wenzelm@399
   611
        new_axioms = Symtab.null,
wenzelm@387
   612
        parents = thys})
wenzelm@387
   613
  end;
wenzelm@387
   614
wenzelm@387
   615
fun merge_theories (thy1, thy2) = merge_thy_list false [thy1, thy2];
wenzelm@387
   616
clasohm@0
   617
nipkow@1495
   618
(* check that term does not contain same var with different typing/sorting *)
nipkow@1495
   619
fun nodup_Vars(thm as Thm{prop,...}) s =
nipkow@1495
   620
  Sign.nodup_Vars prop handle TYPE(msg,_,_) => raise THM(s^": "^msg,0,[thm]);
nipkow@1495
   621
clasohm@0
   622
wenzelm@1220
   623
(*** Meta rules ***)
wenzelm@1220
   624
wenzelm@1220
   625
(** 'primitive' rules **)
wenzelm@1220
   626
wenzelm@1220
   627
(*discharge all assumptions t from ts*)
clasohm@0
   628
val disch = gen_rem (op aconv);
clasohm@0
   629
wenzelm@1220
   630
(*The assumption rule A|-A in a theory*)
wenzelm@250
   631
fun assume ct : thm =
lcp@229
   632
  let val {sign, t=prop, T, maxidx} = rep_cterm ct
wenzelm@250
   633
  in  if T<>propT then
wenzelm@250
   634
        raise THM("assume: assumptions must have type prop", 0, [])
clasohm@0
   635
      else if maxidx <> ~1 then
wenzelm@250
   636
        raise THM("assume: assumptions may not contain scheme variables",
wenzelm@250
   637
                  maxidx, [])
wenzelm@1238
   638
      else fix_shyps [] []
wenzelm@1238
   639
        (Thm{sign = sign, maxidx = ~1, shyps = [], hyps = [prop], prop = prop})
clasohm@0
   640
  end;
clasohm@0
   641
wenzelm@1220
   642
(*Implication introduction
wenzelm@1220
   643
  A |- B
wenzelm@1220
   644
  -------
wenzelm@1220
   645
  A ==> B
wenzelm@1220
   646
*)
wenzelm@1238
   647
fun implies_intr cA (thB as Thm{sign,maxidx,hyps,prop,...}) : thm =
lcp@229
   648
  let val {sign=signA, t=A, T, maxidx=maxidxA} = rep_cterm cA
clasohm@0
   649
  in  if T<>propT then
wenzelm@250
   650
        raise THM("implies_intr: assumptions must have type prop", 0, [thB])
wenzelm@1238
   651
      else fix_shyps [thB] []
wenzelm@1238
   652
        (Thm{sign= Sign.merge (sign,signA),  maxidx= max[maxidxA, maxidx],
wenzelm@1238
   653
          shyps= [], hyps= disch(hyps,A),  prop= implies$A$prop})
clasohm@0
   654
      handle TERM _ =>
clasohm@0
   655
        raise THM("implies_intr: incompatible signatures", 0, [thB])
clasohm@0
   656
  end;
clasohm@0
   657
wenzelm@1220
   658
(*Implication elimination
wenzelm@1220
   659
  A ==> B    A
wenzelm@1220
   660
  ------------
wenzelm@1220
   661
        B
wenzelm@1220
   662
*)
clasohm@0
   663
fun implies_elim thAB thA : thm =
clasohm@0
   664
    let val Thm{maxidx=maxA, hyps=hypsA, prop=propA,...} = thA
wenzelm@250
   665
        and Thm{sign, maxidx, hyps, prop,...} = thAB;
wenzelm@250
   666
        fun err(a) = raise THM("implies_elim: "^a, 0, [thAB,thA])
clasohm@0
   667
    in  case prop of
wenzelm@250
   668
            imp$A$B =>
wenzelm@250
   669
                if imp=implies andalso  A aconv propA
wenzelm@1220
   670
                then fix_shyps [thAB, thA] []
wenzelm@1220
   671
                       (Thm{sign= merge_thm_sgs(thAB,thA),
wenzelm@250
   672
                          maxidx= max[maxA,maxidx],
wenzelm@1220
   673
                          shyps= [],
wenzelm@250
   674
                          hyps= hypsA union hyps,  (*dups suppressed*)
wenzelm@1220
   675
                          prop= B})
wenzelm@250
   676
                else err("major premise")
wenzelm@250
   677
          | _ => err("major premise")
clasohm@0
   678
    end;
wenzelm@250
   679
wenzelm@1220
   680
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@1220
   681
    A
wenzelm@1220
   682
  -----
wenzelm@1220
   683
  !!x.A
wenzelm@1220
   684
*)
wenzelm@1238
   685
fun forall_intr cx (th as Thm{sign,maxidx,hyps,prop,...}) =
lcp@229
   686
  let val x = term_of cx;
wenzelm@1238
   687
      fun result(a,T) = fix_shyps [th] []
wenzelm@1238
   688
        (Thm{sign= sign, maxidx= maxidx, shyps= [], hyps= hyps,
wenzelm@1238
   689
          prop= all(T) $ Abs(a, T, abstract_over (x,prop))})
clasohm@0
   690
  in  case x of
wenzelm@250
   691
        Free(a,T) =>
wenzelm@250
   692
          if exists (apl(x, Logic.occs)) hyps
wenzelm@250
   693
          then  raise THM("forall_intr: variable free in assumptions", 0, [th])
wenzelm@250
   694
          else  result(a,T)
clasohm@0
   695
      | Var((a,_),T) => result(a,T)
clasohm@0
   696
      | _ => raise THM("forall_intr: not a variable", 0, [th])
clasohm@0
   697
  end;
clasohm@0
   698
wenzelm@1220
   699
(*Forall elimination
wenzelm@1220
   700
  !!x.A
wenzelm@1220
   701
  ------
wenzelm@1220
   702
  A[t/x]
wenzelm@1220
   703
*)
wenzelm@1220
   704
fun forall_elim ct (th as Thm{sign,maxidx,hyps,prop,...}) : thm =
lcp@229
   705
  let val {sign=signt, t, T, maxidx=maxt} = rep_cterm ct
clasohm@0
   706
  in  case prop of
wenzelm@250
   707
          Const("all",Type("fun",[Type("fun",[qary,_]),_])) $ A =>
wenzelm@250
   708
            if T<>qary then
wenzelm@250
   709
                raise THM("forall_elim: type mismatch", 0, [th])
nipkow@1495
   710
            else let val thm = fix_shyps [th] []
nipkow@1495
   711
                      (Thm{sign= Sign.merge(sign,signt),
nipkow@1495
   712
                           maxidx= max[maxidx, maxt],
nipkow@1495
   713
                           shyps= [], hyps= hyps,  prop= betapply(A,t)})
nipkow@1495
   714
                 in nodup_Vars thm "forall_elim"; thm end
wenzelm@250
   715
        | _ => raise THM("forall_elim: not quantified", 0, [th])
clasohm@0
   716
  end
clasohm@0
   717
  handle TERM _ =>
wenzelm@250
   718
         raise THM("forall_elim: incompatible signatures", 0, [th]);
clasohm@0
   719
clasohm@0
   720
wenzelm@1220
   721
(* Equality *)
clasohm@0
   722
wenzelm@1220
   723
(* Definition of the relation =?= *)
wenzelm@1238
   724
val flexpair_def = fix_shyps [] []
wenzelm@1238
   725
  (Thm{sign= Sign.proto_pure, shyps= [], hyps= [], maxidx= 0,
wenzelm@1238
   726
        prop= term_of (read_cterm Sign.proto_pure
wenzelm@1238
   727
                ("(?t =?= ?u) == (?t == ?u::?'a::{})", propT))});
clasohm@0
   728
clasohm@0
   729
(*The reflexivity rule: maps  t   to the theorem   t==t   *)
wenzelm@250
   730
fun reflexive ct =
lcp@229
   731
  let val {sign, t, T, maxidx} = rep_cterm ct
wenzelm@1238
   732
  in  fix_shyps [] []
wenzelm@1238
   733
       (Thm{sign= sign, shyps= [], hyps= [], maxidx= maxidx,
wenzelm@1238
   734
         prop= Logic.mk_equals(t,t)})
clasohm@0
   735
  end;
clasohm@0
   736
clasohm@0
   737
(*The symmetry rule
wenzelm@1220
   738
  t==u
wenzelm@1220
   739
  ----
wenzelm@1220
   740
  u==t
wenzelm@1220
   741
*)
wenzelm@1220
   742
fun symmetric (th as Thm{sign,shyps,hyps,prop,maxidx}) =
clasohm@0
   743
  case prop of
clasohm@0
   744
      (eq as Const("==",_)) $ t $ u =>
wenzelm@1238
   745
        (*no fix_shyps*)
wenzelm@1238
   746
        Thm{sign=sign, shyps=shyps, hyps=hyps, maxidx=maxidx, prop= eq$u$t}
clasohm@0
   747
    | _ => raise THM("symmetric", 0, [th]);
clasohm@0
   748
clasohm@0
   749
(*The transitive rule
wenzelm@1220
   750
  t1==u    u==t2
wenzelm@1220
   751
  --------------
wenzelm@1220
   752
      t1==t2
wenzelm@1220
   753
*)
clasohm@0
   754
fun transitive th1 th2 =
clasohm@0
   755
  let val Thm{maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
clasohm@0
   756
      and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2;
clasohm@0
   757
      fun err(msg) = raise THM("transitive: "^msg, 0, [th1,th2])
clasohm@0
   758
  in case (prop1,prop2) of
clasohm@0
   759
       ((eq as Const("==",_)) $ t1 $ u, Const("==",_) $ u' $ t2) =>
wenzelm@250
   760
          if not (u aconv u') then err"middle term"  else
wenzelm@1220
   761
              fix_shyps [th1, th2] []
wenzelm@1220
   762
                (Thm{sign= merge_thm_sgs(th1,th2), shyps= [],
wenzelm@1220
   763
                  hyps= hyps1 union hyps2,
wenzelm@1220
   764
                  maxidx= max[max1,max2], prop= eq$t1$t2})
clasohm@0
   765
     | _ =>  err"premises"
clasohm@0
   766
  end;
clasohm@0
   767
wenzelm@1160
   768
(*Beta-conversion: maps (%x.t)(u) to the theorem (%x.t)(u) == t[u/x] *)
wenzelm@250
   769
fun beta_conversion ct =
lcp@229
   770
  let val {sign, t, T, maxidx} = rep_cterm ct
clasohm@0
   771
  in  case t of
wenzelm@1238
   772
          Abs(_,_,bodt) $ u => fix_shyps [] []
wenzelm@1238
   773
            (Thm{sign= sign,  shyps= [], hyps= [],
wenzelm@250
   774
                maxidx= maxidx_of_term t,
wenzelm@1238
   775
                prop= Logic.mk_equals(t, subst_bounds([u],bodt))})
wenzelm@250
   776
        | _ =>  raise THM("beta_conversion: not a redex", 0, [])
clasohm@0
   777
  end;
clasohm@0
   778
clasohm@0
   779
(*The extensionality rule   (proviso: x not free in f, g, or hypotheses)
wenzelm@1220
   780
  f(x) == g(x)
wenzelm@1220
   781
  ------------
wenzelm@1220
   782
     f == g
wenzelm@1220
   783
*)
wenzelm@1220
   784
fun extensional (th as Thm{sign,maxidx,shyps,hyps,prop}) =
clasohm@0
   785
  case prop of
clasohm@0
   786
    (Const("==",_)) $ (f$x) $ (g$y) =>
wenzelm@250
   787
      let fun err(msg) = raise THM("extensional: "^msg, 0, [th])
clasohm@0
   788
      in (if x<>y then err"different variables" else
clasohm@0
   789
          case y of
wenzelm@250
   790
                Free _ =>
wenzelm@250
   791
                  if exists (apl(y, Logic.occs)) (f::g::hyps)
wenzelm@250
   792
                  then err"variable free in hyps or functions"    else  ()
wenzelm@250
   793
              | Var _ =>
wenzelm@250
   794
                  if Logic.occs(y,f)  orelse  Logic.occs(y,g)
wenzelm@250
   795
                  then err"variable free in functions"   else  ()
wenzelm@250
   796
              | _ => err"not a variable");
wenzelm@1238
   797
          (*no fix_shyps*)
wenzelm@1220
   798
          Thm{sign=sign, shyps=shyps, hyps=hyps, maxidx=maxidx,
wenzelm@250
   799
              prop= Logic.mk_equals(f,g)}
clasohm@0
   800
      end
clasohm@0
   801
 | _ =>  raise THM("extensional: premise", 0, [th]);
clasohm@0
   802
clasohm@0
   803
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   804
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@1220
   805
     t == u
wenzelm@1220
   806
  ------------
wenzelm@1220
   807
  %x.t == %x.u
wenzelm@1220
   808
*)
wenzelm@1238
   809
fun abstract_rule a cx (th as Thm{sign,maxidx,hyps,prop,...}) =
lcp@229
   810
  let val x = term_of cx;
wenzelm@250
   811
      val (t,u) = Logic.dest_equals prop
wenzelm@250
   812
            handle TERM _ =>
wenzelm@250
   813
                raise THM("abstract_rule: premise not an equality", 0, [th])
wenzelm@1238
   814
      fun result T = fix_shyps [th] []
wenzelm@1238
   815
            (Thm{sign= sign, maxidx= maxidx, shyps= [], hyps= hyps,
wenzelm@250
   816
                prop= Logic.mk_equals(Abs(a, T, abstract_over (x,t)),
wenzelm@1238
   817
                                      Abs(a, T, abstract_over (x,u)))})
clasohm@0
   818
  in  case x of
wenzelm@250
   819
        Free(_,T) =>
wenzelm@250
   820
         if exists (apl(x, Logic.occs)) hyps
wenzelm@250
   821
         then raise THM("abstract_rule: variable free in assumptions", 0, [th])
wenzelm@250
   822
         else result T
clasohm@0
   823
      | Var(_,T) => result T
clasohm@0
   824
      | _ => raise THM("abstract_rule: not a variable", 0, [th])
clasohm@0
   825
  end;
clasohm@0
   826
clasohm@0
   827
(*The combination rule
wenzelm@1220
   828
  f==g    t==u
wenzelm@1220
   829
  ------------
wenzelm@1220
   830
   f(t)==g(u)
wenzelm@1220
   831
*)
clasohm@0
   832
fun combination th1 th2 =
wenzelm@1220
   833
  let val Thm{maxidx=max1, shyps=shyps1, hyps=hyps1, prop=prop1,...} = th1
wenzelm@1220
   834
      and Thm{maxidx=max2, shyps=shyps2, hyps=hyps2, prop=prop2,...} = th2
nipkow@1495
   835
  in case (prop1,prop2)  of
clasohm@0
   836
       (Const("==",_) $ f $ g, Const("==",_) $ t $ u) =>
nipkow@1495
   837
          let val thm = (*no fix_shyps*)
nipkow@1495
   838
             Thm{sign= merge_thm_sgs(th1,th2), shyps= shyps1 union shyps2,
nipkow@1495
   839
                 hyps= hyps1 union hyps2,
nipkow@1495
   840
                 maxidx= max[max1,max2], prop= Logic.mk_equals(f$t, g$u)}
nipkow@1495
   841
          in nodup_Vars thm "combination"; thm end
clasohm@0
   842
     | _ =>  raise THM("combination: premises", 0, [th1,th2])
clasohm@0
   843
  end;
clasohm@0
   844
clasohm@0
   845
clasohm@0
   846
(*The equal propositions rule
wenzelm@1220
   847
  A==B    A
wenzelm@1220
   848
  ---------
wenzelm@1220
   849
      B
wenzelm@1220
   850
*)
clasohm@0
   851
fun equal_elim th1 th2 =
clasohm@0
   852
  let val Thm{maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
clasohm@0
   853
      and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2;
clasohm@0
   854
      fun err(msg) = raise THM("equal_elim: "^msg, 0, [th1,th2])
clasohm@0
   855
  in  case prop1  of
clasohm@0
   856
       Const("==",_) $ A $ B =>
wenzelm@250
   857
          if not (prop2 aconv A) then err"not equal"  else
wenzelm@1220
   858
            fix_shyps [th1, th2] []
wenzelm@1220
   859
              (Thm{sign= merge_thm_sgs(th1,th2), shyps= [],
wenzelm@1220
   860
                  hyps= hyps1 union hyps2,
wenzelm@1220
   861
                  maxidx= max[max1,max2], prop= B})
clasohm@0
   862
     | _ =>  err"major premise"
clasohm@0
   863
  end;
clasohm@0
   864
clasohm@0
   865
clasohm@0
   866
(* Equality introduction
wenzelm@1220
   867
  A==>B    B==>A
wenzelm@1220
   868
  --------------
wenzelm@1220
   869
       A==B
wenzelm@1220
   870
*)
clasohm@0
   871
fun equal_intr th1 th2 =
wenzelm@1220
   872
let val Thm{maxidx=max1, shyps=shyps1, hyps=hyps1, prop=prop1,...} = th1
wenzelm@1220
   873
    and Thm{maxidx=max2, shyps=shyps2, hyps=hyps2, prop=prop2,...} = th2;
clasohm@0
   874
    fun err(msg) = raise THM("equal_intr: "^msg, 0, [th1,th2])
clasohm@0
   875
in case (prop1,prop2) of
clasohm@0
   876
     (Const("==>",_) $ A $ B, Const("==>",_) $ B' $ A')  =>
wenzelm@250
   877
        if A aconv A' andalso B aconv B'
wenzelm@1238
   878
        then
wenzelm@1238
   879
          (*no fix_shyps*)
wenzelm@1238
   880
          Thm{sign= merge_thm_sgs(th1,th2), shyps= shyps1 union shyps2,
wenzelm@1238
   881
                hyps= hyps1 union hyps2,
wenzelm@1238
   882
                maxidx= max[max1,max2], prop= Logic.mk_equals(A,B)}
wenzelm@250
   883
        else err"not equal"
clasohm@0
   884
   | _ =>  err"premises"
clasohm@0
   885
end;
clasohm@0
   886
wenzelm@1220
   887
wenzelm@1220
   888
clasohm@0
   889
(**** Derived rules ****)
clasohm@0
   890
clasohm@0
   891
(*Discharge all hypotheses (need not verify cterms)
clasohm@0
   892
  Repeated hypotheses are discharged only once;  fold cannot do this*)
wenzelm@1220
   893
fun implies_intr_hyps (Thm{sign, maxidx, shyps, hyps=A::As, prop}) =
wenzelm@1238
   894
      implies_intr_hyps (*no fix_shyps*)
wenzelm@1220
   895
            (Thm{sign=sign,  maxidx=maxidx, shyps=shyps,
wenzelm@250
   896
                 hyps= disch(As,A),  prop= implies$A$prop})
clasohm@0
   897
  | implies_intr_hyps th = th;
clasohm@0
   898
clasohm@0
   899
(*Smash" unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@250
   900
  Instantiates the theorem and deletes trivial tpairs.
clasohm@0
   901
  Resulting sequence may contain multiple elements if the tpairs are
clasohm@0
   902
    not all flex-flex. *)
wenzelm@1220
   903
fun flexflex_rule (th as Thm{sign,maxidx,hyps,prop,...}) =
wenzelm@250
   904
  let fun newthm env =
wenzelm@250
   905
          let val (tpairs,horn) =
wenzelm@250
   906
                        Logic.strip_flexpairs (Envir.norm_term env prop)
wenzelm@250
   907
                (*Remove trivial tpairs, of the form t=t*)
wenzelm@250
   908
              val distpairs = filter (not o op aconv) tpairs
wenzelm@250
   909
              val newprop = Logic.list_flexpairs(distpairs, horn)
wenzelm@1220
   910
          in  fix_shyps [th] (env_codT env)
wenzelm@1220
   911
                (Thm{sign= sign, shyps= [], hyps= hyps,
wenzelm@1220
   912
                  maxidx= maxidx_of_term newprop, prop= newprop})
wenzelm@250
   913
          end;
clasohm@0
   914
      val (tpairs,_) = Logic.strip_flexpairs prop
clasohm@0
   915
  in Sequence.maps newthm
wenzelm@250
   916
            (Unify.smash_unifiers(sign, Envir.empty maxidx, tpairs))
clasohm@0
   917
  end;
clasohm@0
   918
clasohm@0
   919
(*Instantiation of Vars
wenzelm@1220
   920
           A
wenzelm@1220
   921
  -------------------
wenzelm@1220
   922
  A[t1/v1,....,tn/vn]
wenzelm@1220
   923
*)
clasohm@0
   924
clasohm@0
   925
(*Check that all the terms are Vars and are distinct*)
clasohm@0
   926
fun instl_ok ts = forall is_Var ts andalso null(findrep ts);
clasohm@0
   927
clasohm@0
   928
(*For instantiate: process pair of cterms, merge theories*)
clasohm@0
   929
fun add_ctpair ((ct,cu), (sign,tpairs)) =
lcp@229
   930
  let val {sign=signt, t=t, T= T, ...} = rep_cterm ct
lcp@229
   931
      and {sign=signu, t=u, T= U, ...} = rep_cterm cu
clasohm@0
   932
  in  if T=U  then (Sign.merge(sign, Sign.merge(signt, signu)), (t,u)::tpairs)
clasohm@0
   933
      else raise TYPE("add_ctpair", [T,U], [t,u])
clasohm@0
   934
  end;
clasohm@0
   935
clasohm@0
   936
fun add_ctyp ((v,ctyp), (sign',vTs)) =
lcp@229
   937
  let val {T,sign} = rep_ctyp ctyp
clasohm@0
   938
  in (Sign.merge(sign,sign'), (v,T)::vTs) end;
clasohm@0
   939
clasohm@0
   940
(*Left-to-right replacements: ctpairs = [...,(vi,ti),...].
clasohm@0
   941
  Instantiates distinct Vars by terms of same type.
clasohm@0
   942
  Normalizes the new theorem! *)
wenzelm@1220
   943
fun instantiate (vcTs,ctpairs)  (th as Thm{sign,maxidx,hyps,prop,...}) =
clasohm@0
   944
  let val (newsign,tpairs) = foldr add_ctpair (ctpairs, (sign,[]));
clasohm@0
   945
      val (newsign,vTs) = foldr add_ctyp (vcTs, (newsign,[]));
wenzelm@250
   946
      val newprop =
wenzelm@250
   947
            Envir.norm_term (Envir.empty 0)
wenzelm@250
   948
              (subst_atomic tpairs
wenzelm@250
   949
               (Type.inst_term_tvars(#tsig(Sign.rep_sg newsign),vTs) prop))
wenzelm@1220
   950
      val newth =
wenzelm@1220
   951
            fix_shyps [th] (map snd vTs)
wenzelm@1220
   952
              (Thm{sign= newsign, shyps= [], hyps= hyps,
wenzelm@1220
   953
                maxidx= maxidx_of_term newprop, prop= newprop})
wenzelm@250
   954
  in  if not(instl_ok(map #1 tpairs))
nipkow@193
   955
      then raise THM("instantiate: variables not distinct", 0, [th])
nipkow@193
   956
      else if not(null(findrep(map #1 vTs)))
nipkow@193
   957
      then raise THM("instantiate: type variables not distinct", 0, [th])
nipkow@1495
   958
      else nodup_Vars newth "instantiate";
nipkow@1495
   959
      newth
clasohm@0
   960
  end
wenzelm@250
   961
  handle TERM _ =>
clasohm@0
   962
           raise THM("instantiate: incompatible signatures",0,[th])
nipkow@193
   963
       | TYPE _ => raise THM("instantiate: type conflict", 0, [th]);
clasohm@0
   964
clasohm@0
   965
(*The trivial implication A==>A, justified by assume and forall rules.
clasohm@0
   966
  A can contain Vars, not so for assume!   *)
wenzelm@250
   967
fun trivial ct : thm =
lcp@229
   968
  let val {sign, t=A, T, maxidx} = rep_cterm ct
wenzelm@250
   969
  in  if T<>propT then
wenzelm@250
   970
            raise THM("trivial: the term must have type prop", 0, [])
wenzelm@1238
   971
      else fix_shyps [] []
wenzelm@1238
   972
        (Thm{sign= sign, maxidx= maxidx, shyps= [], hyps= [],
wenzelm@1238
   973
              prop= implies$A$A})
clasohm@0
   974
  end;
clasohm@0
   975
wenzelm@1160
   976
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)" --
wenzelm@1220
   977
  essentially just an instance of A==>A.*)
wenzelm@399
   978
fun class_triv thy c =
wenzelm@399
   979
  let
wenzelm@399
   980
    val sign = sign_of thy;
wenzelm@399
   981
    val Cterm {t, maxidx, ...} =
wenzelm@399
   982
      cterm_of sign (Logic.mk_inclass (TVar (("'a", 0), [c]), c))
wenzelm@399
   983
        handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@399
   984
  in
wenzelm@1238
   985
    fix_shyps [] []
wenzelm@1238
   986
      (Thm {sign = sign, maxidx = maxidx, shyps = [], hyps = [], prop = t})
wenzelm@399
   987
  end;
wenzelm@399
   988
wenzelm@399
   989
clasohm@0
   990
(* Replace all TFrees not in the hyps by new TVars *)
wenzelm@1220
   991
fun varifyT(Thm{sign,maxidx,shyps,hyps,prop}) =
clasohm@0
   992
  let val tfrees = foldr add_term_tfree_names (hyps,[])
wenzelm@1238
   993
  in (*no fix_shyps*)
wenzelm@1238
   994
    Thm{sign=sign, maxidx=max[0,maxidx], shyps=shyps, hyps=hyps,
wenzelm@1238
   995
        prop= Type.varify(prop,tfrees)}
clasohm@0
   996
  end;
clasohm@0
   997
clasohm@0
   998
(* Replace all TVars by new TFrees *)
wenzelm@1220
   999
fun freezeT(Thm{sign,maxidx,shyps,hyps,prop}) =
nipkow@949
  1000
  let val prop' = Type.freeze prop
wenzelm@1238
  1001
  in (*no fix_shyps*)
wenzelm@1238
  1002
    Thm{sign=sign, maxidx=maxidx_of_term prop', shyps=shyps, hyps=hyps,
wenzelm@1238
  1003
        prop=prop'}
wenzelm@1220
  1004
  end;
clasohm@0
  1005
clasohm@0
  1006
clasohm@0
  1007
(*** Inference rules for tactics ***)
clasohm@0
  1008
clasohm@0
  1009
(*Destruct proof state into constraints, other goals, goal(i), rest *)
clasohm@0
  1010
fun dest_state (state as Thm{prop,...}, i) =
clasohm@0
  1011
  let val (tpairs,horn) = Logic.strip_flexpairs prop
clasohm@0
  1012
  in  case  Logic.strip_prems(i, [], horn) of
clasohm@0
  1013
          (B::rBs, C) => (tpairs, rev rBs, B, C)
clasohm@0
  1014
        | _ => raise THM("dest_state", i, [state])
clasohm@0
  1015
  end
clasohm@0
  1016
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1017
lcp@309
  1018
(*Increment variables and parameters of orule as required for
clasohm@0
  1019
  resolution with goal i of state. *)
clasohm@0
  1020
fun lift_rule (state, i) orule =
wenzelm@1238
  1021
  let val Thm{shyps=sshyps,prop=sprop,maxidx=smax,...} = state;
clasohm@0
  1022
      val (Bi::_, _) = Logic.strip_prems(i, [], Logic.skip_flexpairs sprop)
wenzelm@250
  1023
        handle TERM _ => raise THM("lift_rule", i, [orule,state]);
clasohm@0
  1024
      val (lift_abs,lift_all) = Logic.lift_fns(Bi,smax+1);
wenzelm@1238
  1025
      val (Thm{sign,maxidx,shyps,hyps,prop}) = orule
clasohm@0
  1026
      val (tpairs,As,B) = Logic.strip_horn prop
wenzelm@1238
  1027
  in  (*no fix_shyps*)
wenzelm@1238
  1028
      Thm{hyps=hyps, sign= merge_thm_sgs(state,orule),
wenzelm@1238
  1029
          shyps=sshyps union shyps, maxidx= maxidx+smax+1,
wenzelm@250
  1030
          prop= Logic.rule_of(map (pairself lift_abs) tpairs,
wenzelm@1238
  1031
                              map lift_all As,    lift_all B)}
clasohm@0
  1032
  end;
clasohm@0
  1033
clasohm@0
  1034
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1035
fun assumption i state =
wenzelm@1220
  1036
  let val Thm{sign,maxidx,hyps,prop,...} = state;
clasohm@0
  1037
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
wenzelm@250
  1038
      fun newth (env as Envir.Envir{maxidx, ...}, tpairs) =
wenzelm@1220
  1039
        fix_shyps [state] (env_codT env)
wenzelm@1220
  1040
          (Thm{sign=sign, shyps=[], hyps=hyps, maxidx=maxidx, prop=
wenzelm@250
  1041
            if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@250
  1042
              Logic.rule_of (tpairs, Bs, C)
wenzelm@250
  1043
            else (*normalize the new rule fully*)
wenzelm@1220
  1044
              Envir.norm_term env (Logic.rule_of (tpairs, Bs, C))});
clasohm@0
  1045
      fun addprfs [] = Sequence.null
clasohm@0
  1046
        | addprfs ((t,u)::apairs) = Sequence.seqof (fn()=> Sequence.pull
clasohm@0
  1047
             (Sequence.mapp newth
wenzelm@250
  1048
                (Unify.unifiers(sign,Envir.empty maxidx, (t,u)::tpairs))
wenzelm@250
  1049
                (addprfs apairs)))
clasohm@0
  1050
  in  addprfs (Logic.assum_pairs Bi)  end;
clasohm@0
  1051
wenzelm@250
  1052
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1053
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1054
fun eq_assumption i state =
wenzelm@1220
  1055
  let val Thm{sign,maxidx,hyps,prop,...} = state;
clasohm@0
  1056
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
clasohm@0
  1057
  in  if exists (op aconv) (Logic.assum_pairs Bi)
wenzelm@1220
  1058
      then fix_shyps [state] []
wenzelm@1220
  1059
             (Thm{sign=sign, shyps=[], hyps=hyps, maxidx=maxidx,
wenzelm@1220
  1060
               prop=Logic.rule_of(tpairs, Bs, C)})
clasohm@0
  1061
      else  raise THM("eq_assumption", 0, [state])
clasohm@0
  1062
  end;
clasohm@0
  1063
clasohm@0
  1064
clasohm@0
  1065
(** User renaming of parameters in a subgoal **)
clasohm@0
  1066
clasohm@0
  1067
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1068
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1069
  The names in cs, if distinct, are used for the innermost parameters;
clasohm@0
  1070
   preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1071
fun rename_params_rule (cs, i) state =
wenzelm@1220
  1072
  let val Thm{sign,maxidx,hyps,prop,...} = state
clasohm@0
  1073
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
clasohm@0
  1074
      val iparams = map #1 (Logic.strip_params Bi)
clasohm@0
  1075
      val short = length iparams - length cs
wenzelm@250
  1076
      val newnames =
wenzelm@250
  1077
            if short<0 then error"More names than abstractions!"
wenzelm@250
  1078
            else variantlist(take (short,iparams), cs) @ cs
clasohm@0
  1079
      val freenames = map (#1 o dest_Free) (term_frees prop)
clasohm@0
  1080
      val newBi = Logic.list_rename_params (newnames, Bi)
wenzelm@250
  1081
  in
clasohm@0
  1082
  case findrep cs of
clasohm@0
  1083
     c::_ => error ("Bound variables not distinct: " ^ c)
clasohm@0
  1084
   | [] => (case cs inter freenames of
clasohm@0
  1085
       a::_ => error ("Bound/Free variable clash: " ^ a)
wenzelm@1220
  1086
     | [] => fix_shyps [state] []
wenzelm@1220
  1087
               (Thm{sign=sign, shyps=[], hyps=hyps, maxidx=maxidx, prop=
wenzelm@1220
  1088
                 Logic.rule_of(tpairs, Bs@[newBi], C)}))
clasohm@0
  1089
  end;
clasohm@0
  1090
clasohm@0
  1091
(*** Preservation of bound variable names ***)
clasohm@0
  1092
wenzelm@250
  1093
(*Scan a pair of terms; while they are similar,
clasohm@0
  1094
  accumulate corresponding bound vars in "al"*)
wenzelm@1238
  1095
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
lcp@1195
  1096
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@1238
  1097
                                          else (x,y)::al)
clasohm@0
  1098
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
clasohm@0
  1099
  | match_bvs(_,_,al) = al;
clasohm@0
  1100
clasohm@0
  1101
(* strip abstractions created by parameters *)
clasohm@0
  1102
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
clasohm@0
  1103
clasohm@0
  1104
wenzelm@250
  1105
(* strip_apply f A(,B) strips off all assumptions/parameters from A
clasohm@0
  1106
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
  1107
fun strip_apply f =
clasohm@0
  1108
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@250
  1109
                Const("==>",_)$ _  $ B2) = implies $ A1 $ strip(B1,B2)
wenzelm@250
  1110
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
  1111
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
  1112
        | strip(A,_) = f A
clasohm@0
  1113
  in strip end;
clasohm@0
  1114
clasohm@0
  1115
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1116
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1117
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1118
fun rename_bvs([],_,_,_) = I
clasohm@0
  1119
  | rename_bvs(al,dpairs,tpairs,B) =
wenzelm@250
  1120
    let val vars = foldr add_term_vars
wenzelm@250
  1121
                        (map fst dpairs @ map fst tpairs @ map snd tpairs, [])
wenzelm@250
  1122
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1123
        val vids = map (#1 o #1 o dest_Var) vars;
wenzelm@250
  1124
        fun rename(t as Var((x,i),T)) =
wenzelm@250
  1125
                (case assoc(al,x) of
wenzelm@250
  1126
                   Some(y) => if x mem vids orelse y mem vids then t
wenzelm@250
  1127
                              else Var((y,i),T)
wenzelm@250
  1128
                 | None=> t)
clasohm@0
  1129
          | rename(Abs(x,T,t)) =
wenzelm@250
  1130
              Abs(case assoc(al,x) of Some(y) => y | None => x,
wenzelm@250
  1131
                  T, rename t)
clasohm@0
  1132
          | rename(f$t) = rename f $ rename t
clasohm@0
  1133
          | rename(t) = t;
wenzelm@250
  1134
        fun strip_ren Ai = strip_apply rename (Ai,B)
clasohm@0
  1135
    in strip_ren end;
clasohm@0
  1136
clasohm@0
  1137
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
  1138
fun rename_bvars(dpairs, tpairs, B) =
wenzelm@250
  1139
        rename_bvs(foldr match_bvars (dpairs,[]), dpairs, tpairs, B);
clasohm@0
  1140
clasohm@0
  1141
clasohm@0
  1142
(*** RESOLUTION ***)
clasohm@0
  1143
lcp@721
  1144
(** Lifting optimizations **)
lcp@721
  1145
clasohm@0
  1146
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
  1147
  identical because of lifting*)
wenzelm@250
  1148
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
  1149
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
  1150
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
  1151
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
  1152
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
  1153
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
  1154
  | strip_assums2 BB = BB;
clasohm@0
  1155
clasohm@0
  1156
lcp@721
  1157
(*Faster normalization: skip assumptions that were lifted over*)
lcp@721
  1158
fun norm_term_skip env 0 t = Envir.norm_term env t
lcp@721
  1159
  | norm_term_skip env n (Const("all",_)$Abs(a,T,t)) =
lcp@721
  1160
        let val Envir.Envir{iTs, ...} = env
wenzelm@1238
  1161
            val T' = typ_subst_TVars iTs T
wenzelm@1238
  1162
            (*Must instantiate types of parameters because they are flattened;
lcp@721
  1163
              this could be a NEW parameter*)
lcp@721
  1164
        in  all T' $ Abs(a, T', norm_term_skip env n t)  end
lcp@721
  1165
  | norm_term_skip env n (Const("==>", _) $ A $ B) =
wenzelm@1238
  1166
        implies $ A $ norm_term_skip env (n-1) B
lcp@721
  1167
  | norm_term_skip env n t = error"norm_term_skip: too few assumptions??";
lcp@721
  1168
lcp@721
  1169
clasohm@0
  1170
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
  1171
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
  1172
  If match then forbid instantiations in proof state
clasohm@0
  1173
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
  1174
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
  1175
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
  1176
  Curried so that resolution calls dest_state only once.
clasohm@0
  1177
*)
clasohm@0
  1178
local open Sequence; exception Bicompose
clasohm@0
  1179
in
wenzelm@250
  1180
fun bicompose_aux match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
  1181
                        (eres_flg, orule, nsubgoal) =
wenzelm@1258
  1182
 let val Thm{maxidx=smax, shyps=sshyps, hyps=shyps, ...} = state
wenzelm@1258
  1183
     and Thm{maxidx=rmax, shyps=rshyps, hyps=rhyps, prop=rprop,...} = orule
wenzelm@1238
  1184
             (*How many hyps to skip over during normalization*)
wenzelm@1238
  1185
     and nlift = Logic.count_prems(strip_all_body Bi,
wenzelm@1238
  1186
                                   if eres_flg then ~1 else 0)
wenzelm@387
  1187
     val sign = merge_thm_sgs(state,orule);
clasohm@0
  1188
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
wenzelm@250
  1189
     fun addth As ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
  1190
       let val normt = Envir.norm_term env;
wenzelm@250
  1191
           (*perform minimal copying here by examining env*)
wenzelm@250
  1192
           val normp =
wenzelm@250
  1193
             if Envir.is_empty env then (tpairs, Bs @ As, C)
wenzelm@250
  1194
             else
wenzelm@250
  1195
             let val ntps = map (pairself normt) tpairs
wenzelm@1238
  1196
             in if the (Envir.minidx env) > smax then
wenzelm@1238
  1197
                  (*no assignments in state; normalize the rule only*)
wenzelm@1238
  1198
                  if lifted
wenzelm@1238
  1199
                  then (ntps, Bs @ map (norm_term_skip env nlift) As, C)
wenzelm@1238
  1200
                  else (ntps, Bs @ map normt As, C)
wenzelm@250
  1201
                else if match then raise Bicompose
wenzelm@250
  1202
                else (*normalize the new rule fully*)
wenzelm@250
  1203
                  (ntps, map normt (Bs @ As), normt C)
wenzelm@250
  1204
             end
wenzelm@1258
  1205
           val th = (*tuned fix_shyps*)
wenzelm@1258
  1206
             Thm{sign=sign,
wenzelm@1258
  1207
               shyps=add_env_sorts (env, rshyps union sshyps),
wenzelm@1258
  1208
               hyps=rhyps union shyps,
wenzelm@1258
  1209
               maxidx=maxidx, prop= Logic.rule_of normp}
clasohm@0
  1210
        in  cons(th, thq)  end  handle Bicompose => thq
clasohm@0
  1211
     val (rtpairs,rhorn) = Logic.strip_flexpairs(rprop);
clasohm@0
  1212
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rhorn)
clasohm@0
  1213
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
  1214
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
  1215
     fun newAs(As0, n, dpairs, tpairs) =
clasohm@0
  1216
       let val As1 = if !Logic.auto_rename orelse not lifted then As0
wenzelm@250
  1217
                     else map (rename_bvars(dpairs,tpairs,B)) As0
clasohm@0
  1218
       in (map (Logic.flatten_params n) As1)
wenzelm@250
  1219
          handle TERM _ =>
wenzelm@250
  1220
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
  1221
       end;
clasohm@0
  1222
     val env = Envir.empty(max[rmax,smax]);
clasohm@0
  1223
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
  1224
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
  1225
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
clasohm@0
  1226
     fun tryasms (_, _, []) = null
clasohm@0
  1227
       | tryasms (As, n, (t,u)::apairs) =
wenzelm@250
  1228
          (case pull(Unify.unifiers(sign, env, (t,u)::dpairs))  of
wenzelm@250
  1229
               None                   => tryasms (As, n+1, apairs)
wenzelm@250
  1230
             | cell as Some((_,tpairs),_) =>
wenzelm@250
  1231
                   its_right (addth (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@250
  1232
                       (seqof (fn()=> cell),
wenzelm@250
  1233
                        seqof (fn()=> pull (tryasms (As, n+1, apairs)))));
clasohm@0
  1234
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
clasohm@0
  1235
       | eres (A1::As) = tryasms (As, 1, Logic.assum_pairs A1);
clasohm@0
  1236
     (*ordinary resolution*)
clasohm@0
  1237
     fun res(None) = null
wenzelm@250
  1238
       | res(cell as Some((_,tpairs),_)) =
wenzelm@250
  1239
             its_right (addth(newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@250
  1240
                       (seqof (fn()=> cell), null)
clasohm@0
  1241
 in  if eres_flg then eres(rev rAs)
clasohm@0
  1242
     else res(pull(Unify.unifiers(sign, env, dpairs)))
clasohm@0
  1243
 end;
clasohm@0
  1244
end;  (*open Sequence*)
clasohm@0
  1245
clasohm@0
  1246
clasohm@0
  1247
fun bicompose match arg i state =
clasohm@0
  1248
    bicompose_aux match (state, dest_state(state,i), false) arg;
clasohm@0
  1249
clasohm@0
  1250
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1251
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1252
fun could_bires (Hs, B, eres_flg, rule) =
clasohm@0
  1253
    let fun could_reshyp (A1::_) = exists (apl(A1,could_unify)) Hs
wenzelm@250
  1254
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@250
  1255
    in  could_unify(concl_of rule, B) andalso
wenzelm@250
  1256
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1257
    end;
clasohm@0
  1258
clasohm@0
  1259
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1260
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1261
fun biresolution match brules i state =
clasohm@0
  1262
    let val lift = lift_rule(state, i);
wenzelm@250
  1263
        val (stpairs, Bs, Bi, C) = dest_state(state,i)
wenzelm@250
  1264
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1265
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@250
  1266
        val comp = bicompose_aux match (state, (stpairs, Bs, Bi, C), true);
wenzelm@250
  1267
        fun res [] = Sequence.null
wenzelm@250
  1268
          | res ((eres_flg, rule)::brules) =
wenzelm@250
  1269
              if could_bires (Hs, B, eres_flg, rule)
wenzelm@1160
  1270
              then Sequence.seqof (*delay processing remainder till needed*)
wenzelm@250
  1271
                  (fn()=> Some(comp (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1272
                               res brules))
wenzelm@250
  1273
              else res brules
clasohm@0
  1274
    in  Sequence.flats (res brules)  end;
clasohm@0
  1275
clasohm@0
  1276
clasohm@0
  1277
clasohm@0
  1278
(*** Meta simp sets ***)
clasohm@0
  1279
nipkow@288
  1280
type rrule = {thm:thm, lhs:term, perm:bool};
nipkow@288
  1281
type cong = {thm:thm, lhs:term};
clasohm@0
  1282
datatype meta_simpset =
nipkow@405
  1283
  Mss of {net:rrule Net.net, congs:(string * cong)list, bounds:string list,
clasohm@0
  1284
          prems: thm list, mk_rews: thm -> thm list};
clasohm@0
  1285
clasohm@0
  1286
(*A "mss" contains data needed during conversion:
clasohm@0
  1287
  net: discrimination net of rewrite rules
clasohm@0
  1288
  congs: association list of congruence rules
nipkow@405
  1289
  bounds: names of bound variables already used;
nipkow@405
  1290
          for generating new names when rewriting under lambda abstractions
clasohm@0
  1291
  mk_rews: used when local assumptions are added
clasohm@0
  1292
*)
clasohm@0
  1293
nipkow@405
  1294
val empty_mss = Mss{net= Net.empty, congs= [], bounds=[], prems= [],
clasohm@0
  1295
                    mk_rews = K[]};
clasohm@0
  1296
clasohm@0
  1297
exception SIMPLIFIER of string * thm;
clasohm@0
  1298
lcp@229
  1299
fun prtm a sign t = (writeln a; writeln(Sign.string_of_term sign t));
clasohm@0
  1300
nipkow@209
  1301
val trace_simp = ref false;
nipkow@209
  1302
lcp@229
  1303
fun trace_term a sign t = if !trace_simp then prtm a sign t else ();
nipkow@209
  1304
nipkow@209
  1305
fun trace_thm a (Thm{sign,prop,...}) = trace_term a sign prop;
nipkow@209
  1306
nipkow@427
  1307
fun vperm(Var _, Var _) = true
nipkow@427
  1308
  | vperm(Abs(_,_,s), Abs(_,_,t)) = vperm(s,t)
nipkow@427
  1309
  | vperm(t1$t2, u1$u2) = vperm(t1,u1) andalso vperm(t2,u2)
nipkow@427
  1310
  | vperm(t,u) = (t=u);
nipkow@288
  1311
nipkow@427
  1312
fun var_perm(t,u) = vperm(t,u) andalso
nipkow@427
  1313
                    eq_set(add_term_vars(t,[]), add_term_vars(u,[]))
nipkow@288
  1314
clasohm@0
  1315
(*simple test for looping rewrite*)
clasohm@0
  1316
fun loops sign prems (lhs,rhs) =
nipkow@1023
  1317
   is_Var(lhs)
nipkow@1023
  1318
  orelse
nipkow@1023
  1319
   (exists (apl(lhs, Logic.occs)) (rhs::prems))
nipkow@1023
  1320
  orelse
nipkow@1023
  1321
   (null(prems) andalso
nipkow@1023
  1322
    Pattern.matches (#tsig(Sign.rep_sg sign)) (lhs,rhs));
nipkow@1028
  1323
(* the condition "null(prems)" in the last case is necessary because
nipkow@1028
  1324
   conditional rewrites with extra variables in the conditions may terminate
nipkow@1028
  1325
   although the rhs is an instance of the lhs. Example:
nipkow@1028
  1326
   ?m < ?n ==> f(?n) == f(?m)
nipkow@1028
  1327
*)
clasohm@0
  1328
wenzelm@1238
  1329
fun mk_rrule raw_thm =
wenzelm@1238
  1330
  let
wenzelm@1258
  1331
      val thm = strip_shyps raw_thm;
wenzelm@1238
  1332
      val Thm{sign,prop,maxidx,...} = thm;
wenzelm@1238
  1333
      val prems = Logic.strip_imp_prems prop
nipkow@678
  1334
      val concl = Logic.strip_imp_concl prop
nipkow@678
  1335
      val (lhs,_) = Logic.dest_equals concl handle TERM _ =>
clasohm@0
  1336
                      raise SIMPLIFIER("Rewrite rule not a meta-equality",thm)
nipkow@678
  1337
      val econcl = Pattern.eta_contract concl
nipkow@678
  1338
      val (elhs,erhs) = Logic.dest_equals econcl
nipkow@678
  1339
      val perm = var_perm(elhs,erhs) andalso not(elhs aconv erhs)
nipkow@678
  1340
                                     andalso not(is_Var(elhs))
wenzelm@1220
  1341
  in
wenzelm@1258
  1342
     if not perm andalso loops sign prems (elhs,erhs) then
wenzelm@1220
  1343
       (prtm "Warning: ignoring looping rewrite rule" sign prop; None)
nipkow@288
  1344
     else Some{thm=thm,lhs=lhs,perm=perm}
clasohm@0
  1345
  end;
clasohm@0
  1346
nipkow@87
  1347
local
nipkow@87
  1348
 fun eq({thm=Thm{prop=p1,...},...}:rrule,
nipkow@87
  1349
        {thm=Thm{prop=p2,...},...}:rrule) = p1 aconv p2
nipkow@87
  1350
in
nipkow@87
  1351
nipkow@405
  1352
fun add_simp(mss as Mss{net,congs,bounds,prems,mk_rews},
clasohm@0
  1353
             thm as Thm{sign,prop,...}) =
nipkow@87
  1354
  case mk_rrule thm of
nipkow@87
  1355
    None => mss
nipkow@87
  1356
  | Some(rrule as {lhs,...}) =>
nipkow@209
  1357
      (trace_thm "Adding rewrite rule:" thm;
nipkow@209
  1358
       Mss{net= (Net.insert_term((lhs,rrule),net,eq)
nipkow@209
  1359
                 handle Net.INSERT =>
nipkow@87
  1360
                  (prtm "Warning: ignoring duplicate rewrite rule" sign prop;
nipkow@87
  1361
                   net)),
nipkow@405
  1362
           congs=congs, bounds=bounds, prems=prems,mk_rews=mk_rews});
nipkow@87
  1363
nipkow@405
  1364
fun del_simp(mss as Mss{net,congs,bounds,prems,mk_rews},
nipkow@87
  1365
             thm as Thm{sign,prop,...}) =
nipkow@87
  1366
  case mk_rrule thm of
nipkow@87
  1367
    None => mss
nipkow@87
  1368
  | Some(rrule as {lhs,...}) =>
nipkow@87
  1369
      Mss{net= (Net.delete_term((lhs,rrule),net,eq)
nipkow@87
  1370
                handle Net.INSERT =>
nipkow@87
  1371
                 (prtm "Warning: rewrite rule not in simpset" sign prop;
nipkow@87
  1372
                  net)),
nipkow@405
  1373
             congs=congs, bounds=bounds, prems=prems,mk_rews=mk_rews}
nipkow@87
  1374
nipkow@87
  1375
end;
clasohm@0
  1376
clasohm@0
  1377
val add_simps = foldl add_simp;
nipkow@87
  1378
val del_simps = foldl del_simp;
clasohm@0
  1379
clasohm@0
  1380
fun mss_of thms = add_simps(empty_mss,thms);
clasohm@0
  1381
nipkow@405
  1382
fun add_cong(Mss{net,congs,bounds,prems,mk_rews},thm) =
clasohm@0
  1383
  let val (lhs,_) = Logic.dest_equals(concl_of thm) handle TERM _ =>
clasohm@0
  1384
                    raise SIMPLIFIER("Congruence not a meta-equality",thm)
nipkow@678
  1385
(*      val lhs = Pattern.eta_contract lhs*)
clasohm@0
  1386
      val (a,_) = dest_Const (head_of lhs) handle TERM _ =>
clasohm@0
  1387
                  raise SIMPLIFIER("Congruence must start with a constant",thm)
nipkow@405
  1388
  in Mss{net=net, congs=(a,{lhs=lhs,thm=thm})::congs, bounds=bounds,
clasohm@0
  1389
         prems=prems, mk_rews=mk_rews}
clasohm@0
  1390
  end;
clasohm@0
  1391
clasohm@0
  1392
val (op add_congs) = foldl add_cong;
clasohm@0
  1393
nipkow@405
  1394
fun add_prems(Mss{net,congs,bounds,prems,mk_rews},thms) =
nipkow@405
  1395
  Mss{net=net, congs=congs, bounds=bounds, prems=thms@prems, mk_rews=mk_rews};
clasohm@0
  1396
clasohm@0
  1397
fun prems_of_mss(Mss{prems,...}) = prems;
clasohm@0
  1398
nipkow@405
  1399
fun set_mk_rews(Mss{net,congs,bounds,prems,...},mk_rews) =
nipkow@405
  1400
  Mss{net=net, congs=congs, bounds=bounds, prems=prems, mk_rews=mk_rews};
clasohm@0
  1401
fun mk_rews_of_mss(Mss{mk_rews,...}) = mk_rews;
clasohm@0
  1402
clasohm@0
  1403
wenzelm@250
  1404
(*** Meta-level rewriting
clasohm@0
  1405
     uses conversions, omitting proofs for efficiency.  See
wenzelm@250
  1406
        L C Paulson, A higher-order implementation of rewriting,
wenzelm@250
  1407
        Science of Computer Programming 3 (1983), pages 119-149. ***)
clasohm@0
  1408
clasohm@0
  1409
type prover = meta_simpset -> thm -> thm option;
clasohm@0
  1410
type termrec = (Sign.sg * term list) * term;
clasohm@0
  1411
type conv = meta_simpset -> termrec -> termrec;
clasohm@0
  1412
nipkow@305
  1413
datatype order = LESS | EQUAL | GREATER;
nipkow@288
  1414
nipkow@305
  1415
fun stringord(a,b:string) = if a<b then LESS  else
nipkow@305
  1416
                            if a=b then EQUAL else GREATER;
nipkow@305
  1417
nipkow@305
  1418
fun intord(i,j:int) = if i<j then LESS  else
nipkow@305
  1419
                      if i=j then EQUAL else GREATER;
nipkow@288
  1420
nipkow@427
  1421
(* NB: non-linearity of the ordering is not a soundness problem *)
nipkow@427
  1422
nipkow@305
  1423
(* FIXME: "***ABSTRACTION***" is a hack and makes the ordering non-linear *)
nipkow@305
  1424
fun string_of_hd(Const(a,_)) = a
nipkow@305
  1425
  | string_of_hd(Free(a,_))  = a
nipkow@305
  1426
  | string_of_hd(Var(v,_))   = Syntax.string_of_vname v
nipkow@305
  1427
  | string_of_hd(Bound i)    = string_of_int i
nipkow@305
  1428
  | string_of_hd(Abs _)      = "***ABSTRACTION***";
nipkow@288
  1429
nipkow@305
  1430
(* a strict (not reflexive) linear well-founded AC-compatible ordering
nipkow@305
  1431
 * for terms:
nipkow@305
  1432
 * s < t <=> 1. size(s) < size(t) or
nipkow@305
  1433
             2. size(s) = size(t) and s=f(...) and t = g(...) and f<g or
nipkow@305
  1434
             3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
nipkow@305
  1435
                (s1..sn) < (t1..tn) (lexicographically)
nipkow@305
  1436
 *)
nipkow@288
  1437
nipkow@288
  1438
(* FIXME: should really take types into account as well.
nipkow@427
  1439
 * Otherwise non-linear *)
nipkow@622
  1440
fun termord(Abs(_,_,t),Abs(_,_,u)) = termord(t,u)
nipkow@622
  1441
  | termord(t,u) =
nipkow@305
  1442
      (case intord(size_of_term t,size_of_term u) of
nipkow@305
  1443
         EQUAL => let val (f,ts) = strip_comb t and (g,us) = strip_comb u
nipkow@305
  1444
                  in case stringord(string_of_hd f, string_of_hd g) of
nipkow@305
  1445
                       EQUAL => lextermord(ts,us)
nipkow@305
  1446
                     | ord   => ord
nipkow@305
  1447
                  end
nipkow@305
  1448
       | ord => ord)
nipkow@305
  1449
and lextermord(t::ts,u::us) =
nipkow@305
  1450
      (case termord(t,u) of
nipkow@305
  1451
         EQUAL => lextermord(ts,us)
nipkow@305
  1452
       | ord   => ord)
nipkow@305
  1453
  | lextermord([],[]) = EQUAL
nipkow@305
  1454
  | lextermord _ = error("lextermord");
nipkow@288
  1455
nipkow@305
  1456
fun termless tu = (termord tu = LESS);
nipkow@288
  1457
wenzelm@1258
  1458
fun check_conv(thm as Thm{shyps,hyps,prop,sign,maxidx,...}, prop0) =
nipkow@432
  1459
  let fun err() = (trace_thm "Proved wrong thm (Check subgoaler?)" thm;
nipkow@432
  1460
                   trace_term "Should have proved" sign prop0;
nipkow@432
  1461
                   None)
clasohm@0
  1462
      val (lhs0,_) = Logic.dest_equals(Logic.strip_imp_concl prop0)
clasohm@0
  1463
  in case prop of
clasohm@0
  1464
       Const("==",_) $ lhs $ rhs =>
clasohm@0
  1465
         if (lhs = lhs0) orelse
nipkow@427
  1466
            (lhs aconv Envir.norm_term (Envir.empty 0) lhs0)
wenzelm@1258
  1467
         then (trace_thm "SUCCEEDED" thm; Some(shyps,hyps,maxidx,rhs))
clasohm@0
  1468
         else err()
clasohm@0
  1469
     | _ => err()
clasohm@0
  1470
  end;
clasohm@0
  1471
nipkow@659
  1472
fun ren_inst(insts,prop,pat,obj) =
nipkow@659
  1473
  let val ren = match_bvs(pat,obj,[])
nipkow@659
  1474
      fun renAbs(Abs(x,T,b)) =
nipkow@659
  1475
            Abs(case assoc(ren,x) of None => x | Some(y) => y, T, renAbs(b))
nipkow@659
  1476
        | renAbs(f$t) = renAbs(f) $ renAbs(t)
nipkow@659
  1477
        | renAbs(t) = t
nipkow@659
  1478
  in subst_vars insts (if null(ren) then prop else renAbs(prop)) end;
nipkow@678
  1479
wenzelm@1258
  1480
fun add_insts_sorts ((iTs, is), Ss) =
wenzelm@1258
  1481
  add_typs_sorts (map snd iTs, add_terms_sorts (map snd is, Ss));
wenzelm@1258
  1482
nipkow@659
  1483
clasohm@0
  1484
(*Conversion to apply the meta simpset to a term*)
wenzelm@1258
  1485
fun rewritec (prover,signt) (mss as Mss{net,...}) (shypst,hypst,maxidxt,t) =
nipkow@678
  1486
  let val etat = Pattern.eta_contract t;
wenzelm@1258
  1487
      fun rew {thm as Thm{sign,shyps,hyps,maxidx,prop,...}, lhs, perm} =
wenzelm@250
  1488
        let val unit = if Sign.subsig(sign,signt) then ()
clasohm@446
  1489
                  else (trace_thm"Warning: rewrite rule from different theory"
clasohm@446
  1490
                          thm;
nipkow@208
  1491
                        raise Pattern.MATCH)
nipkow@1065
  1492
            val rprop = if maxidxt = ~1 then prop
nipkow@1065
  1493
                        else Logic.incr_indexes([],maxidxt+1) prop;
nipkow@1065
  1494
            val rlhs = if maxidxt = ~1 then lhs
nipkow@1065
  1495
                       else fst(Logic.dest_equals(Logic.strip_imp_concl rprop))
nipkow@1065
  1496
            val insts = Pattern.match (#tsig(Sign.rep_sg signt)) (rlhs,etat)
nipkow@1065
  1497
            val prop' = ren_inst(insts,rprop,rlhs,t);
clasohm@0
  1498
            val hyps' = hyps union hypst;
wenzelm@1258
  1499
            val shyps' = add_insts_sorts (insts, shyps union shypst);
nipkow@1065
  1500
            val maxidx' = maxidx_of_term prop'
wenzelm@1258
  1501
            val thm' = Thm{sign=signt, shyps=shyps', hyps=hyps',
wenzelm@1258
  1502
                           prop=prop', maxidx=maxidx'}
nipkow@427
  1503
            val (lhs',rhs') = Logic.dest_equals(Logic.strip_imp_concl prop')
nipkow@427
  1504
        in if perm andalso not(termless(rhs',lhs')) then None else
nipkow@427
  1505
           if Logic.count_prems(prop',0) = 0
wenzelm@1258
  1506
           then (trace_thm "Rewriting:" thm'; Some(shyps',hyps',maxidx',rhs'))
clasohm@0
  1507
           else (trace_thm "Trying to rewrite:" thm';
clasohm@0
  1508
                 case prover mss thm' of
clasohm@0
  1509
                   None       => (trace_thm "FAILED" thm'; None)
nipkow@112
  1510
                 | Some(thm2) => check_conv(thm2,prop'))
clasohm@0
  1511
        end
clasohm@0
  1512
nipkow@225
  1513
      fun rews [] = None
nipkow@225
  1514
        | rews (rrule::rrules) =
nipkow@225
  1515
            let val opt = rew rrule handle Pattern.MATCH => None
nipkow@225
  1516
            in case opt of None => rews rrules | some => some end;
clasohm@0
  1517
nipkow@678
  1518
  in case etat of
wenzelm@1258
  1519
       Abs(_,_,body) $ u => Some(shypst, hypst, maxidxt, subst_bounds([u], body))
nipkow@678
  1520
     | _                 => rews(Net.match_term net etat)
clasohm@0
  1521
  end;
clasohm@0
  1522
clasohm@0
  1523
(*Conversion to apply a congruence rule to a term*)
wenzelm@1258
  1524
fun congc (prover,signt) {thm=cong,lhs=lhs} (shypst,hypst,maxidxt,t) =
wenzelm@1258
  1525
  let val Thm{sign,shyps,hyps,maxidx,prop,...} = cong
nipkow@208
  1526
      val unit = if Sign.subsig(sign,signt) then ()
nipkow@208
  1527
                 else error("Congruence rule from different theory")
nipkow@208
  1528
      val tsig = #tsig(Sign.rep_sg signt)
nipkow@1065
  1529
      val rprop = if maxidxt = ~1 then prop
nipkow@1065
  1530
                  else Logic.incr_indexes([],maxidxt+1) prop;
nipkow@1065
  1531
      val rlhs = if maxidxt = ~1 then lhs
nipkow@1065
  1532
                 else fst(Logic.dest_equals(Logic.strip_imp_concl rprop))
nipkow@1065
  1533
      val insts = Pattern.match tsig (rlhs,t) handle Pattern.MATCH =>
clasohm@0
  1534
                  error("Congruence rule did not match")
nipkow@1065
  1535
      val prop' = ren_inst(insts,rprop,rlhs,t);
wenzelm@1258
  1536
      val shyps' = add_insts_sorts (insts, shyps union shypst);
wenzelm@1258
  1537
      val thm' = Thm{sign=signt, shyps=shyps', hyps=hyps union hypst,
wenzelm@1258
  1538
                     prop=prop', maxidx=maxidx_of_term prop'};
clasohm@0
  1539
      val unit = trace_thm "Applying congruence rule" thm';
nipkow@112
  1540
      fun err() = error("Failed congruence proof!")
clasohm@0
  1541
clasohm@0
  1542
  in case prover thm' of
nipkow@112
  1543
       None => err()
nipkow@112
  1544
     | Some(thm2) => (case check_conv(thm2,prop') of
nipkow@405
  1545
                        None => err() | some => some)
clasohm@0
  1546
  end;
clasohm@0
  1547
clasohm@0
  1548
nipkow@405
  1549
nipkow@214
  1550
fun bottomc ((simprem,useprem),prover,sign) =
nipkow@405
  1551
  let fun botc fail mss trec =
nipkow@405
  1552
            (case subc mss trec of
nipkow@405
  1553
               some as Some(trec1) =>
nipkow@405
  1554
                 (case rewritec (prover,sign) mss trec1 of
nipkow@405
  1555
                    Some(trec2) => botc false mss trec2
nipkow@405
  1556
                  | None => some)
nipkow@405
  1557
             | None =>
nipkow@405
  1558
                 (case rewritec (prover,sign) mss trec of
nipkow@405
  1559
                    Some(trec2) => botc false mss trec2
nipkow@405
  1560
                  | None => if fail then None else Some(trec)))
clasohm@0
  1561
nipkow@405
  1562
      and try_botc mss trec = (case botc true mss trec of
nipkow@405
  1563
                                 Some(trec1) => trec1
nipkow@405
  1564
                               | None => trec)
nipkow@405
  1565
nipkow@405
  1566
      and subc (mss as Mss{net,congs,bounds,prems,mk_rews})
wenzelm@1258
  1567
               (trec as (shyps,hyps,maxidx,t)) =
clasohm@0
  1568
        (case t of
clasohm@0
  1569
            Abs(a,T,t) =>
nipkow@405
  1570
              let val b = variant bounds a
nipkow@405
  1571
                  val v = Free("." ^ b,T)
nipkow@405
  1572
                  val mss' = Mss{net=net, congs=congs, bounds=b::bounds,
clasohm@0
  1573
                                 prems=prems,mk_rews=mk_rews}
wenzelm@1258
  1574
              in case botc true mss' (shyps,hyps,maxidx,subst_bounds([v],t)) of
wenzelm@1258
  1575
                   Some(shyps',hyps',maxidx',t') =>
wenzelm@1258
  1576
                     Some(shyps', hyps', maxidx', Abs(a, T, abstract_over(v,t')))
nipkow@405
  1577
                 | None => None
nipkow@405
  1578
              end
clasohm@0
  1579
          | t$u => (case t of
wenzelm@1258
  1580
              Const("==>",_)$s  => Some(impc(shyps,hyps,maxidx,s,u,mss))
nipkow@405
  1581
            | Abs(_,_,body) =>
wenzelm@1258
  1582
                let val trec = (shyps,hyps,maxidx,subst_bounds([u], body))
nipkow@405
  1583
                in case subc mss trec of
nipkow@405
  1584
                     None => Some(trec)
nipkow@405
  1585
                   | trec => trec
nipkow@405
  1586
                end
nipkow@405
  1587
            | _  =>
nipkow@405
  1588
                let fun appc() =
wenzelm@1258
  1589
                          (case botc true mss (shyps,hyps,maxidx,t) of
wenzelm@1258
  1590
                             Some(shyps1,hyps1,maxidx1,t1) =>
wenzelm@1258
  1591
                               (case botc true mss (shyps1,hyps1,maxidx,u) of
wenzelm@1258
  1592
                                  Some(shyps2,hyps2,maxidx2,u1) =>
wenzelm@1258
  1593
                                    Some(shyps2,hyps2,max[maxidx1,maxidx2],t1$u1)
nipkow@1065
  1594
                                | None =>
wenzelm@1258
  1595
                                    Some(shyps1,hyps1,max[maxidx1,maxidx],t1$u))
nipkow@405
  1596
                           | None =>
wenzelm@1258
  1597
                               (case botc true mss (shyps,hyps,maxidx,u) of
wenzelm@1258
  1598
                                  Some(shyps1,hyps1,maxidx1,u1) =>
wenzelm@1258
  1599
                                    Some(shyps1,hyps1,max[maxidx,maxidx1],t$u1)
nipkow@405
  1600
                                | None => None))
clasohm@0
  1601
                    val (h,ts) = strip_comb t
clasohm@0
  1602
                in case h of
clasohm@0
  1603
                     Const(a,_) =>
clasohm@0
  1604
                       (case assoc(congs,a) of
clasohm@0
  1605
                          None => appc()
nipkow@208
  1606
                        | Some(cong) => congc (prover mss,sign) cong trec)
clasohm@0
  1607
                   | _ => appc()
clasohm@0
  1608
                end)
nipkow@405
  1609
          | _ => None)
clasohm@0
  1610
wenzelm@1258
  1611
      and impc(shyps,hyps,maxidx,s,u,mss as Mss{mk_rews,...}) =
wenzelm@1258
  1612
        let val (shyps1,hyps1,_,s1) =
wenzelm@1258
  1613
              if simprem then try_botc mss (shyps,hyps,maxidx,s)
wenzelm@1258
  1614
              else (shyps,hyps,0,s);
nipkow@1065
  1615
            val maxidx1 = maxidx_of_term s1
nipkow@405
  1616
            val mss1 =
nipkow@1065
  1617
              if not useprem orelse maxidx1 <> ~1 then mss
wenzelm@1258
  1618
              else let val thm =
wenzelm@1258
  1619
                     Thm{sign=sign,shyps=add_term_sorts(s1,[]),
wenzelm@1258
  1620
                         hyps=[s1],prop=s1,maxidx= ~1}
nipkow@214
  1621
                   in add_simps(add_prems(mss,[thm]), mk_rews thm) end
wenzelm@1258
  1622
            val (shyps2,hyps2,maxidx2,u1) = try_botc mss1 (shyps1,hyps1,maxidx,u)
nipkow@405
  1623
            val hyps3 = if s1 mem hyps1 then hyps2 else hyps2\s1
wenzelm@1258
  1624
        in (shyps2, hyps3, max[maxidx1,maxidx2], Logic.mk_implies(s1,u1)) end
clasohm@0
  1625
nipkow@405
  1626
  in try_botc end;
clasohm@0
  1627
clasohm@0
  1628
clasohm@0
  1629
(*** Meta-rewriting: rewrites t to u and returns the theorem t==u ***)
clasohm@0
  1630
(* Parameters:
wenzelm@250
  1631
   mode = (simplify A, use A in simplifying B) when simplifying A ==> B
clasohm@0
  1632
   mss: contains equality theorems of the form [|p1,...|] ==> t==u
clasohm@0
  1633
   prover: how to solve premises in conditional rewrites and congruences
clasohm@0
  1634
*)
nipkow@405
  1635
(*** FIXME: check that #bounds(mss) does not "occur" in ct alread ***)
nipkow@214
  1636
fun rewrite_cterm mode mss prover ct =
lcp@229
  1637
  let val {sign, t, T, maxidx} = rep_cterm ct;
wenzelm@1258
  1638
      val (shyps,hyps,maxidxu,u) =
wenzelm@1258
  1639
        bottomc (mode,prover,sign) mss (add_term_sorts(t,[]),[],maxidx,t);
clasohm@0
  1640
      val prop = Logic.mk_equals(t,u)
wenzelm@1258
  1641
  in
wenzelm@1258
  1642
      Thm{sign= sign, shyps= shyps, hyps= hyps, maxidx= max[maxidx,maxidxu],
wenzelm@1258
  1643
          prop= prop}
clasohm@0
  1644
  end
clasohm@0
  1645
clasohm@0
  1646
end;