src/Pure/term_xml.scala
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/*  Title:      Pure/term_xml.scala
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    Author:     Makarius
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XML data representation of lambda terms.
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*/
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package isabelle
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object Term_XML
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{
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  import Term._
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  object Encode
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  {
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    import XML.Encode._
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    val indexname: P[Indexname] =
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      { case Indexname(a, 0) => List(a)
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        case Indexname(a, b) => List(a, int_atom(b)) }
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    val sort: T[Sort] = list(string)
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    def typ: T[Typ] =
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      variant[Typ](List(
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        { case Type(a, b) => (List(a), list(typ)(b)) },
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        { case TFree(a, b) => (List(a), sort(b)) },
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        { case TVar(a, b) => (indexname(a), sort(b)) }))
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    val typ_body: T[Typ] = (t: Typ) => if (t == dummyT) Nil else typ(t)
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    def term: T[Term] =
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      variant[Term](List(
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        { case Const(a, b) => (List(a), list(typ)(b)) },
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        { case Free(a, b) => (List(a), typ_body(b)) },
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        { case Var(a, b) => (indexname(a), typ_body(b)) },
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        { case Bound(a) => (Nil, int(a)) },
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        { case Abs(a, b, c) => (List(a), pair(typ, term)(b, c)) },
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        { case App(a, b) => (Nil, pair(term, term)(a, b)) }))
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  }
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  object Decode
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  {
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    import XML.Decode._
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    val indexname: P[Indexname] =
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      { case List(a) => Indexname(a, 0)
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        case List(a, b) => Indexname(a, int_atom(b)) }
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    val sort: T[Sort] = list(string)
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    def typ: T[Typ] =
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      variant[Typ](List(
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        { case (List(a), b) => Type(a, list(typ)(b)) },
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        { case (List(a), b) => TFree(a, sort(b)) },
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        { case (a, b) => TVar(indexname(a), sort(b)) }))
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    val typ_body: T[Typ] = { case Nil => dummyT case body => typ(body) }
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    def term: T[Term] =
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      variant[Term](List(
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        { case (List(a), b) => Const(a, list(typ)(b)) },
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        { case (List(a), b) => Free(a, typ_body(b)) },
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        { case (a, b) => Var(indexname(a), typ_body(b)) },
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        { case (Nil, a) => Bound(int(a)) },
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        { case (List(a), b) => val (c, d) = pair(typ, term)(b); Abs(a, c, d) },
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        { case (Nil, a) => val (b, c) = pair(term, term)(a); App(b, c) }))
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    def term_env(env: Map[String, Typ]): T[Term] =
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    {
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      def env_type(x: String, t: Typ): Typ =
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        if (t == dummyT && env.isDefinedAt(x)) env(x) else t
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      def term: T[Term] =
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        variant[Term](List(
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          { case (List(a), b) => Const(a, list(typ)(b)) },
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          { case (List(a), b) => Free(a, env_type(a, typ_body(b))) },
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          { case (a, b) => Var(indexname(a), typ_body(b)) },
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          { case (Nil, a) => Bound(int(a)) },
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          { case (List(a), b) => val (c, d) = pair(typ, term)(b); Abs(a, c, d) },
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          { case (Nil, a) => val (b, c) = pair(term, term)(a); App(b, c) }))
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      term
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    }
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    def proof_env(env: Map[String, Typ]): T[Proof] =
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    {
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      val term = term_env(env)
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      def proof: T[Proof] =
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        variant[Proof](List(
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          { case (Nil, Nil) => MinProof },
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          { case (Nil, a) => PBound(int(a)) },
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          { case (List(a), b) => val (c, d) = pair(typ, proof)(b); Abst(a, c, d) },
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          { case (List(a), b) => val (c, d) = pair(term, proof)(b); AbsP(a, c, d) },
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          { case (Nil, a) => val (b, c) = pair(proof, term)(a); Appt(b, c) },
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          { case (Nil, a) => val (b, c) = pair(proof, proof)(a); AppP(b, c) },
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          { case (Nil, a) => Hyp(term(a)) },
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          { case (List(a), b) => PAxm(a, list(typ)(b)) },
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          { case (List(a), b) => PClass(typ(b), a) },
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          { case (List(a), b) => val (c, d) = pair(term, list(typ))(b); Oracle(a, c, d) },
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          { case (List(a, b, c), d) => PThm(long_atom(a), b, c, list(typ)(d)) }))
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      proof
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    }
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    val proof: T[Proof] = proof_env(Map.empty)
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  }
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}