File: test4.ott

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metavar ident , x  ::= {{ coq-equality auto with arith. }}
  {{ isa string }} {{ coq nat }}  {{ lex alphanum }}

indexvar index , j , n ::=
  {{ isa nat }} {{ coq nat }}  {{ lex numeral }}

grammar

 expr , e  :: Expr_ ::=   
                     |  x                            ::   :: var   {{ com ident }}
                     |  ()                           ::   :: unit  {{ com unit }} 
                     |  ( e1 : t1 , .... , en : tn ) ::   :: tuple 
%{{ com typed tuple }}
                     |   e . j                       ::   :: proj
                     |   e1 e2 :: :: foo

 type , t :: Typ_ ::=
                     | () :: :: unit
                     | ( t1 , .... , tn ) :: :: tuple

 foo1expr  :: Foo1Expr_ ::=   
                     |  x ( @@ e1 : t1 , .... ,  @@ en : tn ) ::   :: tuple 
(+ b=t1....tn +)

 foo2expr  :: Foo2Expr_ ::=   
                     |  x ( e1 @@ e'1 : t1 , .... , en @@ e'n : tn ) ::   :: tuple 

 foo3expr  :: Foo3Expr_ ::=   
                     |  x ( e_0 : t_0 , .... , e_n-1 : t_n-1 ) ::   :: tuple 

% foo4expr  :: Foo4Expr_ ::=   
%                     |  x ( e0 @@ e1 : t1 , .... , em @@ en : tn ) ::   :: tuple 




 formula :: formula_ ::=          
                      |   judgement             ::   :: judgement
                      |   formula1 .. formulan    ::   :: dotdot 
%                                           {{ isa list_all (%(b).b)  [[formula1 .. formulan ]] }}

terminals :: terminals_ ::=
%        |  \                     ::   :: lambda  {{ tex  \lambda }}
%        |  ->                    ::   :: arrow {{ tex  \rightarrow }}
%        |  =>                    ::   :: Arrow {{ tex  \Rightarrow }}
%        |  __                    ::   :: hole {{ tex \_ }}
        | |-                     ::   :: turnstile {{ tex \vdash }}
        | -->                    ::   :: red {{ tex \longrightarrow }}
%        | Forall                 ::   :: forall {{ tex \forall }}
%        | <:                     ::   :: subtype {{ tex <: }}
%        | |->                    ::   :: mapsto {{ tex \mapsto }}
%         | gives                  ::   :: gives {{ tex \vartriangleright }}


substitutions
  single e x :: subst
substitutions
  multiple e x :: m_subst 



defns
Jin :: '' ::=


defn
|- e ok ::  :: eok :: eok_  by 


---------------- :: unit
|- () ok


%|- e1 ok .... |- en ok
------------------------------- :: tuple
|- (e1:t1,....,en:tn) ok 


defn
e --> e' :: :: ered :: ered_ by

--------------------------- :: proj
(e1:t1,....,en:tn).j --> ej

>>
not sure if we should isa that ej as a "(%(e,t).e) (List.nth ets j)" or as an
"(%(e,t).e) et  where List.mem et ets "

the former.


How do we recognise that we need to do that special thing for the ej?

try to merge all the None nt_or_mv's with each bound, and if we find
one record it in the symterm pp environment?

<<