\section{|TIA| --- Type-Indexed Aggregates --- ``Type Information Awareness''}

The original |TIA| module provides aggregates of type-indexed constructions,
somewhat inpired by the heterogeneous list data type |HList| of
\cite{Kiselyov-Laemmel-Schupke-2004}.

\begin{code}
{-# LANGUAGE ScopedTypeVariables, KindSignatures #-}
-- Original module requires more:
-- {-# LANGUAGE ScopedTypeVariables, KindSignatures, MultiParamTypeClasses, FlexibleContexts, FlexibleInstances, TypeSynonymInstances, FunctionalDependencies, UndecidableInstances, Rank2Types, TypeOperators #-}
module TIATest where
\end{code}

\begin{code}
data TIACons1 (i :: *) (r :: (* -> *) -> *) (c :: * -> *) = c i ::: r c
\end{code}

Type-level replication is occasionally useful ---
we provide hard-coded factors as demand arises.

\begin{code}
type TIACons2 t x = TIACons1 t (TIACons1 t x)
type TIACons3 t x = TIACons2 t (TIACons1 t x)
type TIACons4 t x = TIACons2 t (TIACons2 t x)
type TIACons7 t x = TIACons4 t (TIACons3 t x)
type TIACons8 t x = TIACons4 t (TIACons4 t x)
type TIACons15 t x = TIACons8 t (TIACons7 t x)
type TIACons16 t x = TIACons8 t (TIACons8 t x)
type TIACons31 t x = TIACons16 t (TIACons15 t x)
type TIACons32 t x = TIACons16 t (TIACons16 t x)
type TIACons47 t x = TIACons32 t (TIACons15 t x)
type TIACons48 t x = TIACons32 t (TIACons16 t x)
{-
-}
\end{code}
%}}}

Up to 8:

real    0m0.375s
user    0m0.284s
sys     0m0.067s
-rw------- 1 kahl users 2176 Sep 14 16:39 Utils/TIATest.o
-rw------- 1 kahl users  779 Sep 14 16:39 Utils/TIATest.hi

Up to 15:

real    0m0.374s
user    0m0.290s
sys     0m0.065s
-rw------- 1 kahl users 2176 Sep 14 16:39 Utils/TIATest.o
-rw------- 1 kahl users  883 Sep 14 16:39 Utils/TIATest.hi

Up to 16:

real    0m0.368s
user    0m0.298s
sys     0m0.064s
-rw------- 1 kahl users 2176 Sep 14 16:40 Utils/TIATest.o
-rw------- 1 kahl users  961 Sep 14 16:40 Utils/TIATest.hi

Up to 31:

real    0m7.386s
user    0m7.139s
sys     0m0.118s
-rw------- 1 kahl users 2176 Sep 14 16:41 Utils/TIATest.o
-rw------- 1 kahl users 1065 Sep 14 16:41 Utils/TIATest.hi


Up to 32:

real    0m18.570s
user    0m18.301s
sys     0m0.188s
-rw------- 1 kahl users 2176 Sep 14 16:42 Utils/TIATest.o
-rw------- 1 kahl users 1143 Sep 14 16:42 Utils/TIATest.hi



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