src/Sequents/Sequents.thy

Sara Kalvala: moving the <<...>> notation from LK to Sequents

(*  Title: 	Sequents/Sequents.thy
    ID:         $Id$
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1993  University of Cambridge

Basis theory for parsing and pretty-printing of sequences to be used in
Sequent Calculi. 
*)

Sequents = Pure +

global

types
  o 

arities
  o :: logic


(* Sequences *)

types
 seq'

consts
 SeqO'         :: [o,seq']=>seq'
 Seq1'         :: o=>seq'
    

(* concrete syntax *)

types
  seq seqobj seqcont


syntax
 SeqEmp         :: seq                                ("")
 SeqApp         :: [seqobj,seqcont] => seq            ("__")

 SeqContEmp     :: seqcont                            ("")
 SeqContApp     :: [seqobj,seqcont] => seqcont        (",/ __")
  
 SeqO           :: o => seqobj                        ("_")
 SeqId          :: 'a => seqobj                       ("$_")

types
    
 single_seqe = [seq,seqobj] => prop
 single_seqi = [seq'=>seq',seq'=>seq'] => prop
 two_seqi    = [seq'=>seq', seq'=>seq'] => prop
 two_seqe    = [seq, seq] => prop
 three_seqi  = [seq'=>seq', seq'=>seq', seq'=>seq'] => prop
 three_seqe  = [seq, seq, seq] => prop
 four_seqi   = [seq'=>seq', seq'=>seq', seq'=>seq', seq'=>seq'] => prop
 four_seqe   = [seq, seq, seq, seq] => prop


 sequence_name = seq'=>seq'


consts
  (*Constant to allow definitions of SEQUENCES of formulas*)
  "@Side"        :: seq=>(seq'=>seq')     ("<<(_)>>")

end

ML

(* parse translation for sequences *)

fun abs_seq' t = Abs("s", Type("seq'",[]), t);

fun seqobj_tr(Const("SeqO",_) $ f) = Const("SeqO'",dummyT) $ f |
    seqobj_tr(_ $ i) = i;
    
fun seqcont_tr(Const("SeqContEmp",_)) = Bound 0 |
    seqcont_tr(Const("SeqContApp",_) $ so $ sc) = 
      (seqobj_tr so) $ (seqcont_tr sc);

fun seq_tr(Const("SeqEmp",_)) = abs_seq'(Bound 0) |
    seq_tr(Const("SeqApp",_) $ so $ sc) = 
      abs_seq'(seqobj_tr(so) $ seqcont_tr(sc));


fun singlobj_tr(Const("SeqO",_) $ f) =
    abs_seq' ((Const("SeqO'",dummyT) $ f) $ Bound 0);
    

    
(* print translation for sequences *)

fun seqcont_tr' (Bound 0) = 
      Const("SeqContEmp",dummyT) |
    seqcont_tr' (Const("SeqO'",_) $ f $ s) =
      Const("SeqContApp",dummyT) $ 
      (Const("SeqO",dummyT) $ f) $ 
      (seqcont_tr' s) |
(*    seqcont_tr' ((a as Abs(_,_,_)) $ s)= 
      seqcont_tr'(betapply(a,s)) | *)
    seqcont_tr' (i $ s) = 
      Const("SeqContApp",dummyT) $ 
      (Const("SeqId",dummyT) $ i) $ 
      (seqcont_tr' s);

fun seq_tr' s =
    let fun seq_itr' (Bound 0) = 
              Const("SeqEmp",dummyT) |
            seq_itr' (Const("SeqO'",_) $ f $ s) =
              Const("SeqApp",dummyT) $ 
              (Const("SeqO",dummyT) $ f) $ (seqcont_tr' s) |
(*            seq_itr' ((a as Abs(_,_,_)) $ s) =
              seq_itr'(betapply(a,s)) |    *)
            seq_itr' (i $ s) =
              Const("SeqApp",dummyT) $ 
              (Const("SeqId",dummyT) $ i) $ 
              (seqcont_tr' s)
    in case s of 
         Abs(_,_,t) => seq_itr' t |
         _ => s $ (Bound 0)
    end;




fun single_tr c [s1,s2] =
    Const(c,dummyT) $ seq_tr s1 $ singlobj_tr s2;

fun two_seq_tr c [s1,s2] =
    Const(c,dummyT) $ seq_tr s1 $ seq_tr s2;

fun three_seq_tr c [s1,s2,s3] =
    Const(c,dummyT) $ seq_tr s1 $ seq_tr s2 $ seq_tr s3;

fun four_seq_tr c [s1,s2,s3,s4] =
    Const(c,dummyT) $ seq_tr s1 $ seq_tr s2 $ seq_tr s3 $ seq_tr s4;


fun singlobj_tr'(Const("SeqO'",_) $ fm) = fm |
    singlobj_tr'(id) = Const("@SeqId",dummyT) $ id;


fun single_tr' c [s1, s2] =
(Const (c, dummyT) $ seq_tr' s1 $ seq_tr' s2 ); 


fun two_seq_tr' c [s1, s2] =
  Const (c, dummyT) $ seq_tr' s1 $ seq_tr' s2; 

fun three_seq_tr' c [s1, s2, s3] =
  Const (c, dummyT) $ seq_tr' s1 $ seq_tr' s2 $ seq_tr' s3; 

fun four_seq_tr' c [s1, s2, s3, s4] =
  Const (c, dummyT) $ seq_tr' s1 $ seq_tr' s2 $ seq_tr' s3 $ seq_tr' s4; 


			 
(** for the <<...>> notation **)
  
fun side_tr [s1] = seq_tr s1;

val parse_translation = [("@Side", side_tr)];