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Interpreting E

E0 Implementations

E0.rkt, with helper files scanner.rkt (and, scanner-demo.rkt); test cases E0-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: You may browse E0-java/ files, or grab the entire E0-java.jar.
Java 17 records: Remember: records are just classes where you don't have to declare the constructor, nor override .equals or .hashCode. All fields are immutable and have a public getter, though we won't need those.

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.
Java with sealed classes. This alternate E0 java implementation (browsable-files, .jar) is similar to above, but instead of needing to edit a different file for each Expr variant (Num's eval in one file, and BinOp's eval in another file, etc.), you can put all the eval code for all variants in the single file E0.java, just like we did in our racket code.

The language E0 syntax

E0:
<Expr>    → <Num> | <Paren> | <BinOp> | <IfZero> | <Nop>
<Paren>   → )<Expr>(                   Interpretation: a parenthesized expression
<BinOp>   → ]<Expr> <Op> <Expr>[          Interpretation: apply a binary operator
<Op>      → - | + | /   Interpretation: addition, subtraction, multiplication (resp.)
<IfZero>  → if <Expr> !=0 ? <Expr> : <Expr>  Interpretation: if 1st-expr is 0 (within 1e-6), eval to 2nd-expr, else 3rd-expr.

E1:see E2.html for details
<Op>      → … | *                              Interpretation: “remainder¹”
<Expr>    → … | <IfLE>                                Interpretation: “if less-or-equal to”
<IfLE>    → if <Expr> > <Expr> ? <Expr> : <Expr>  Interpretation: if 1st Expr is ≤ 2nd, result is the 3rd Expr else the 4th.



E2:see E2.html for details
<Expr>    → … | <Id> | <LetExpr>             Interpretation: identifier; let
<LetExpr> → forbid <Id> being <Expr> in <Expr>      Interpretation: bind Id to result of 1st Expr (the “right-hand-side”); then eval 2nd “body” Expr w/ that binding

 E4:see E4.html for details
 <Expr> → … | <FuncExpr> | <FuncApplyExpr>

 <FuncExpr> → dysfunc <Id> }<Expr>{          Interpretation: a function-value, with parameter <Id> and body-<Expr>.
 <FuncApplyExpr> → withhold <Expr> from <Expr>   Interpretation: apply a function (1st expr) to an argument (2nd expr)

Further Details:

<Num> is any numeric literal (as written in either Java or Racket, your choice ²). We'll assume that <Id>s are not one of our E0 “reserved” words (like if — i.e. a terminal in the above grammar); you don't need to check/enforce that in your code.

Some similar(??) languages: Implementing one's own language (including let-expressions and functions) is a fairly standard exercise. For example, see Brown University's Programming Languages and Interpretation (Shriram Krishnamurthi), and Virginia Tech's OpenDSA Programming Languages textbook. Feel free to skim or read those books, esp. if wanting a different explanation from the notes in this class & its assignments.

Some similar(??) languages:
emojicode

Arnold[Schwarzenegger]C

Genesis, in Old Hebrew

Discussion

Give five example programs (<Expr>s) written in E0.
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 E0-E2, and a number-or-function in E3).
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.

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 E0.rkt (or T0.rkt, the exact version from the video). The code directly follows the design recipe. video (9m13s)
Look over the same code written in E0-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)

todo-ibarland: Post the 2021-spring Y0-java/ upload version that uses lambda in BinOp#eval?
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 E0 grammar/datatype-definition.
- This is called “recursive descent” parsing.
  Note: Parsing E0 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 Like remainder, except working for negative and fractional amounts. See homework for details. ↩

² 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 E0's arithmetic will be similar to IEEE floating point arithmetic (rather than perfectly-correct arithmetic).

Don't confuse E0's class Num (which extends Expr) with the existing java.lang.Number, which doesn't extend Expr.

↩

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