(*  Title:      quotient_def.thy+
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    Author:     Cezary Kaliszyk and Christian Urban+
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+
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    Definitions for constants on quotient types.+
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+
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*)+
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+
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signature QUOTIENT_DEF =+
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sig +
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  val quotient_def: mixfix -> Attrib.binding -> term -> term ->+
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    local_theory -> (term * thm) * local_theory+
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+
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  val quotdef_cmd: (Attrib.binding * string) * (mixfix * string) ->+
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    local_theory -> local_theory+
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end;+
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+
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structure Quotient_Def: QUOTIENT_DEF =+
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struct+
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+
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open Quotient_Info;+
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open Quotient_Term;+
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+
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(* wrapper for define *)+
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fun define name mx attr rhs lthy =+
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let+
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  val ((rhs, (_ , thm)), lthy') =+
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     Local_Theory.define ((name, mx), (attr, rhs)) lthy+
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in+
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  ((rhs, thm), lthy')+
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end+
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+
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+
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(** Interface and Syntax Setup **)+
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+
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(* The ML-interface for a quotient definition takes +
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   as argument:+
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+
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    - the mixfix annotation+
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    - name and attributes+
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    - the new constant as term+
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    - the rhs of the definition as term+
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+
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   It returns the defined constant and its definition+
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   theorem; stores the data in the qconsts data slot. +
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+
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   Restriction: At the moment the right-hand side must+
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   be a terms composed of constant. Similarly the +
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   left-hand side must be a single constant.   +
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*)+
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fun quotient_def mx attr lhs rhs lthy =+
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let+
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  val (lhs_str, lhs_ty) = dest_Free lhs handle TERM _ => error "Constant already defined."+
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  val _ = if null (strip_abs_vars rhs) then () else error "The definiens cannot be an abstraction"+
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+
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  val qconst_bname = Binding.name lhs_str+
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  val absrep_trm = absrep_fun absF lthy (fastype_of rhs, lhs_ty) $ rhs+
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  val prop = Logic.mk_equals (lhs, Syntax.check_term lthy absrep_trm)+
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  val (_, prop') = LocalDefs.cert_def lthy prop+
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  val (_, newrhs) = Primitive_Defs.abs_def prop'+
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+
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  val ((trm, thm), lthy') = define qconst_bname mx attr newrhs lthy+
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+
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  (* data storage *)+
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  fun qcinfo phi = transform_qconsts phi {qconst = trm, rconst = rhs, def = thm}+
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  fun trans_name phi = (fst o dest_Const o #qconst) (qcinfo phi)+
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  val lthy'' = Local_Theory.declaration true+
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                 (fn phi => qconsts_update_gen (trans_name phi) (qcinfo phi)) lthy'+
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in+
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  ((trm, thm), lthy'')+
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end+
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+
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fun quotdef_cmd ((attr, lhs_str), (mx, rhs_str)) lthy =+
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let+
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  val lhs = Syntax.read_term lthy lhs_str+
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  val rhs = Syntax.read_term lthy rhs_str+
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  (* FIXME: Relating the reads will cause errors. *) +
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in+
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  quotient_def mx attr lhs rhs lthy |> snd+
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end+
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+
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val _ = OuterKeyword.keyword "as";+
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+
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val quotdef_parser =+
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  (SpecParse.opt_thm_name ":" --+
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     OuterParse.term) --+
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      (OuterParse.opt_mixfix' --| OuterParse.$$$ "as" --+
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         OuterParse.term)+
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+
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val _ = OuterSyntax.local_theory "quotient_definition" +
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	  "definition for constants over the quotient type"+
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             OuterKeyword.thy_decl (quotdef_parser >> quotdef_cmd)+
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+
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end; (* structure *)+
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