(*  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: (binding * mixfix) option * (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: (binding * mixfix) option * (Attrib.binding * (string * string)) ->+
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    local_theory -> (term * thm) * 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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(** 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 (bindmx, (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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  val der_bname = Binding.name lhs_str+
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  val (qconst_bname, mx) =+
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    case bindmx of+
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      SOME (bname, mx) =>+
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        let+
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          val _ = (Name.of_binding bname = lhs_str) orelse error ("Head of quotient_definition " ^ +
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            (quote lhs_str) ^ " differs from declaration " ^ (Binding.name_of bname) ^+
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            Position.str_of (Binding.pos_of bname))+
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        in+
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          (der_bname, mx)+
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        end+
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      | NONE => (der_bname, NoSyn)+
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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') = Local_Theory.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 (bindmx, (attr, (lhs_str, 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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  val lthy' = Variable.declare_term lhs lthy+
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  val lthy'' = Variable.declare_term rhs lthy'+
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in+
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  quotient_def (bindmx, (attr, (lhs, rhs))) lthy''+
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end+
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+
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val binding_mixfix_parser = OuterParse.binding -- OuterParse.opt_mixfix' --| OuterParse.$$$ "where"+
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val quotdef_parser =+
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  (Scan.option binding_mixfix_parser) --+
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    OuterParse.!!! (SpecParse.opt_thm_name ":" -- ((OuterParse.term --| OuterParse.$$$ "is") -- OuterParse.term))+
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+
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val _ =+
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  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 >> (snd oo quotdef_cmd))+
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+
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end; (* structure *)+
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