\documentclass[preprint,natbib]{sigplanconf}

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%format ^^^^ = "\hspace{1em}"
%format ^^^ = "\;"
%format . = "."
%format signature = "\mathbf{signature}"
%format inputs = "\mathbf{inputs}"
%format outputs = "\mathbf{outputs}"
%format collation = "\mathbf{collation}"
%format sem = "\mathbf{sem}"
%format clause = "\mathbf{clause}"
%format match = "\mathbf{match}"
%format forall = "\mathbf{forall}"
%format partial = "\mathbf{partial}"
%format << = "\langle"
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\begin{document}

% \conferenceinfo{TLDI '10}{January 23, 2010, Madrid.}
% \copyrightyear{2010}
% \copyrightdata{[to be supplied]}

% \titlebanner{banner above paper title}        % These are ignored unless
\preprintfooter{Attribute Grammar Visit Sequences}   % 'preprint' option specified.

\title{Attribute Grammars as Visit Sequences}

\authorinfo{Arie Middelkoop\and Atze Dijkstra\and S. Doaitse Swierstra}
           {Universiteit Utrecht}
           {\{ariem,atze,doaitse\}@@cs.uu.nl}

\maketitle


% \begin{abstract}
% \end{abstract}

% \category{F.3.1}{Logics and Meanings of Programs}{Specifying and Verifying and Reasoning about Programs}
% \terms{Algorithms, Languages}
% \keywords{Type system, type rules, inference algorithm, aspect-oriented programming}

\section{Data Types}

  \subsection{Introduction}
  
  \paragraph{Declaration}
  
  \begin{code}
  data Expr
    | Var  nm    :: Name
    | App  fun   :: Expr
           arg   :: Expr
    | Lam  pat   :: Pat
           body  :: Expr
  \end{code}

  \paragraph{Pattern Match}
  
  \begin{code}
  @loc::Expr:Var
  @e::Expr:App
  \end{code}


\section{Signatures}

  \subsection{Introduction}

  \paragraph{Inputs and Outputs.}
  
  \begin{code}
  signature TypeExpr1
    inputs   env  :: Env
             e    :: Expr
    outputs  ty   :: Type
  \end{code}
  
  \paragraph{Contexts.}

  \begin{code}
  signature TypeExpr2
    inputs     env  :: Env
               e    :: Expr
    Check <<
      inputs   ty :: Ty
    >>
    Infer <<
      outputs  ty :: Ty
    >>
  \end{code}
  
  \paragraph{Visits.}

  \begin{code}
  signature TypePat1
    gather <<
      inputs   p        :: Pat
      outputs  gathEnv  :: Env
    >>

    analyse <<
      inputs   env  :: Env
               ty   :: Type
    >>
  \end{code}

   \paragraph{Mixing contexts and visits.}

   \begin{code}
   signature TypePat2
    gather <<
       inputs   p        :: Pat
       outputs  gathEnv  :: Env
     >>
     analyse <<
       inputs    env     :: Env
       Check <<
         inputs  ty      :: Type
       >>
       Infer <<
         outputs ty      :: Type
       >>
     >>
   \end{code}
  
  \paragraph{Totality.}

  \begin{code}
  signature TypePat1
    gather partial Err <<
      ... 
    >>
  \end{code}

  \paragraph{Type parameters.}
  
  \begin{code}
  forall a . signature Eval
    inputs  e :: {Expr a}
    outputs v :: {a}
  \end{code}


\section{Collations}

  \subsection{Introduction}
  
  \begin{code}
  collation Inference of TypePat2
      gather
      analyse::Check
  \end{code}


\section{Semantics}

  \begin{code}
  typeExpr = <<
    sem :: TypeExpr1
      clause
        match {@loc::Expr:Var} = {@lhs.e}
        {@lhs.ty} = {findWithDefault undefined @loc.nm @lhs.env}
      clause
        match {@loc::Expr:App} = {@lhs.e}
        child f  :: TypeExpr1 = {typeExpr}
        child a  :: TypeExpr1 = {typeExpr}
        {@f.env}  = {@lhs.env}
        {@f.e}    = {@loc.fun}
        {@a.env}  = {@lhs.env}
        {@a.e}    = {@loc.arg}
        {@lhs.ty} = case @f.ty of
                      Arr a r | a == @a.ty  = r
                      _                     = error "type error"
  >>
  \end{code}


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\end{document}