# CS322 Fall 1999

Module 8 (Metainterpreters)

Assignment 8

## Solution.

In this assignment you will implement, in CILog, a new programming language **ArLog** that allows for adjustable parameters in arithmetic expressions
and user-defined arithmetic functions.
An ArLog program is a set of clauses of the form:

H <= B.

where *H* is an atom and *B* is a body.
A body is either of the form:

`true`

`A & B `

where *A* and *B* are bodies
`A `

where *A* is an atom defined by rules
`X is Exp `

where *X* is a number and *Exp* is a
parametrized arithmetic expression. This is true if *X* is the value
of the expression *Exp*.
`assign(P,Exp) `

where *P* is a parameter and *Exp* is a
parametrized arithmetic expression. This assigns the value of *Exp* to
the parameter *P*.
`E1 > E2 `

where *E1* and *E2* are
parametrized arithmetic expressions. (This, "assign" and "is" are the only
built-in relations).

Parametrized expressions are of the form:

`A+B`

, `A*B`

, `A-B`

, `A/B`

where *A* and
*B* are parametrized expressions
`N `

where *N* is a number
`P `

where *P* is a parameter (a CILog constant).
- a user-defined function

Parametrized expressions are always evaluated in an environment, where
an environment is a list of terms of the form `val(P,V)`

where
*P* is a parameter and *V* is a number.

We always prove goals within an environment, but the environment can
be updated with an *assign* goal. In a conjunction, the rightmost
conjunct is evaluated in the environment that is the result of the
evaluation of the leftmost conjunct.

As well as normal clauses defining atoms, the user can define
functions using:

F=Exp <= B.

Where *F* is a user-defined function and *Exp* is an expression. If
*B* is true, the value of *Exp* is the value that *F* evaluates to.
You can also download a CILog implementation of
ArLog, as well as a sample ArLog program.

David Poole