Please provide code in Lisp: Use LOCAL variables within functions $($e$.$g$.,$ introduced by $\text{'}$ let'$)$

except for truly global parameters $($such as a hash table$)$ that multiple

functions need to access.

Unless stated otherwise, include type checking in your functions; i$.$e$.,$

if the user gives an argument which is not of the specified type or form

of the corresponding parameter, your function should return $.$

$($More generally one might print more specific error messages.$)$

PREPARING FOR BUILDING BLOCK STRUCTURES

Preamble

The "Blocks World", where an AI system builds structures with children's

blocks on a table is a long$-$standing experimental domain in AI$,$ e$.$g$.,$

going back to Terry Winograd's "SHRDLU" $($a name based on letter frequencies$)$

in $1968-71($e$.$g$.,$ low$-$res demo,

Georgiy Platonov and Ben Kane,

experimented in

a physical blocks world, focusing on question answering about spatial

relations $($e$.$g$.,$ "Which blocks are to the left of a red block?"$),$ as well

as about past situations, and enabling structural concept learning, etc.

The Blocks World domain is interesting from a reasoning and planning

perspective, because it involves precisely the kinds of problems for

which current LLMs fail miserably. However, neural$-$net$-$based systems

specifically designed for virtual Blocks World problems have been built

successfully. Once suitable data structures and models of possible

moves and relationships in such a virtual domain have been engineered,

a DNN can be "let loose", experimenting with millions of moves and

configurations, thereby learning what moves lead to what configurations.

But one feels that with more reasoning power and spatial conceptualization,

success should not depend on such massive experimentation.

We will be working towards the ability to create block structures in

a $2-$D Blocks World, given descriptions of those structures. In Lisp$1$

we'll do some preliminary programming to enable this. Here is an example

of a block structure $($call it a "springboard"$)$:

$($CUBE A$)($CUBE B$)$

$($CUBE C$)($CUBE D$)$

$($BAR G$)($BAR H$)$

$($VERTICAL G$)$

$($HORIZONTAL H$)$

$($ON G $)$

$($ON A $)$

$($NEAR A G$)$; $"$A is one unit to the right

of $G$; valid only for blocks on

$($ON B A$)$

$($ON C B$),$

$($ON H C$)$; This is "symmetrical"$-$ON

For now, assume that we have exactly $6$ unit "cubes", $\{A,B,C,D,E,F\}$

and $2$ "bars" $\{G,H\}$ of length $3.$ Our eventual aim $($not yet in this

assignment!$)$ will be to specify how structures like the one above can be

built step by step, one block at a time. For the example this might be:

$($TURN$-$VERTICAL G$)$; applicable to horizontal bars

$($PUT$-$ON G $)$

$($PUT$-$NEAR A G$)$; Assume this means "put A on $,1$ unit right of G$"$

$($PUT$-$ON B A$)$

$($PUT$-$ON C B$)$

$($PUT$-$ON D G$)$

$($PUT$-$ON H C$)$; for horizontal H$,$ this means "put the middle of $H$ on $C^{.}$