In this assignment, you will write a simple parser for the "object language" being a simple logic programming language $($similar e$.$g$.,$ to a subset of Prolog$).$

The parser itself has to be written using the OCaml version of Yacc.

Below is an abstract definition of the logic programming language's syntax.

You should use your learning of Prolog $($Assignments $1$ and $2)$ to write a concrete grammatical specification for the logic programming language corresponding to the abstract formulation below. The objective of the exercise is for you to define the grammar as well as the lexical tokens for your surface language. You will be evaluated on your design of the surface syntax as well as the implementation of the parser.

You may e$.$g$.,$ deviate from the standard Prolog syntax if you so wish $($in particular, you may want to use the if$-$then$-$else construction or a generalisation of it$).$

You will need to represent an abstract syntax of the logic programming language as a data type in OCaml. Abstract syntax trees $($terms in this data type$)$ will be the output of your parser.

The abstract structure of a Prolog program is the following:

A program is a sequence of clauses.

A clause can either be a fact or a rule.

A fact has a head but no body. A rule has a head and a body.

The head is a single atomic formula.

A body is a sequence of atomic formulas.

An atomic formula is a $k-$ary predicate symbol followed by $k$ terms.

A term is either a variable, a constant, or a $k-$ary function symbol with $k$ subterms.

A goal is a sequence of atomic formulas.