Interpreting X
(as chosen in class)

The language X0

  X0:
  Expr       ::= Num | Paren | BinOp | IfZero
  Paren      ::= [ Expr ]                            Interpretation: a parenthesized expression
  BinOp      ::= ~ Expr Op Expr !                    Interpretation: apply a binary operator  
  Op         ::= add | sub | mlt                   Interpretation: addition, subtraction, multiplication (resp.) 
  IfZero     ::= if0 Expr thn Expr els Expr ;        Interpretation: if 1st expr is zero, answer is the 2nd expr, else use the 3rd expr

where Num is any numeric literal (as written in either Java or Racket, your choice ¹). For the provided parsers to work, whitespace is required between all terminals with the exception of punctuation.

Semantics (interpretation):

A Paren is a parenthesized expression (used for grouping only);
A Binop is a binary operator expression, in infix; add means addition; sub means subtraction (the 2nd arg from the 1st); mlt means multiplication.
A IfZero evaluates its first expressions; if it's zero then then the result is is the second expression (evaluated), else the result is the last expression (evaluated).

Discussion

Give five example programs (Exprs) written in X0.
Give their parse trees.
How should we represent these trees, internally? (In Racket, and equivalently in Java).

Where we're headed

For interpreting this language, we will implement three methods:
- parse, which turns source-code into an internal representation,
- toString which turns internal representation back into source-code,
- eval, which actually interprets the program, returning a value (a number for X0-X2, and a number-or-function in V3).
I recommend implementing and testing the methods in this order. Some test-cases will be provided. There might be other helper functions to implement as well.

X0 Implementations

X0.rkt, with helper files scanner.rkt (and, scanner-demo.rkt); test cases X0-tests.rkt, and student-extras.rkt.
Note: Download the racket files, and then choose Open… from DrRacket. Do not copy/paste into an empty DrRacket window, since that window is probably using a student-language, and some of the files below use full racket.
Java: X0-java/ (browse the directory), or see the .jar.
Note the composite pattern to implement union-types, in Java: The classes Expr and its four variants Num/BinOp/IfZero/Paren are organized in the same way AncTree and its two variants Child/Unknown were.

Discuss the implementation

Once we've talked in class about internal-representation (and given examples of the W programs and corresponding internal-data), then we can discuss the provided-implementation, including recursive-descent parsing:

2018 version: The videos below are based on 2018fall's language, T0. So details of the syntax are different than this semester, and some statements might have different semantics, but overall the content is extremely similar to this semester's language.

Look over expr->string, eval in X0.rkt (or T0.rkt, the exact version from the video). The code directly follows the design recipe. video (9m13s)
Look over the same code in X0-java/ (or T0-java/, the exact version from the video). The code is equivalent to the racket — still just following the design recipe. video (13m04s)
parse — recursive-descent parsing: video (17m21s)
- It does not exactly follow the the design recipe (because it processes a string/scanner, not Exprs), yet the code's shape is still extremely correlated to the X0 grammar/data-definition.
- This is called “recursive descent” parsing.
  Note: Parsing X0 is particularly easy because each expression-type's leading-token lets us know exactly what to expect, removing the need for look-ahead, backtracking, or cleverer algorithms.
- The Java code is essentially the same, up to class Scanner working a bit differently. video (12m19s)
  
  .
Optional, but helpful for your own test cases:
- Writing test-cases the regular, same-ol’ same-ol’ way, and then realizing what we can re-factor into easier-to-write tests, via an “test-harness” specific to this assignment. In racket: video (14m14s)
- The same test-harness, in Java (slightly more involved, and less flexible): video (8m08s)

¹ This is so we can just use our language's built-in number-parsing functions, without getting bogged down in tokening input. So racket implementations will allow exactly those strings recognized by number?, (including +nan.0, -inf.0, and 2+3i).

Similarly, if using Java, the semantics of X0's arithmetic will be similar to IEEE floating point arithmetic (rather than perfectly-correct arithmetic).

Don't confuse X0's class Num (which extends Expr) with the existing java.lang.Number, which doesn't extend Expr.

↩

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Interpreting X (as chosen in class)