ITEC 380 2021fall ibarland

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Interpreting Z
(as developed in lecture)

The language Z0

Z0:
Expr    ::= Num | Paren | BinOp | IfZero
Paren   ::= < Expr >                          Interpretation: a parenthesized expression
BinOp   ::= [ Op Expr Expr ]                    Interpretation: apply a binary operator
Op      ::= add | sub | mul                Interpretation: addition, subtraction, multiplication (resp.)
IfZero  ::= zero Expr ? Expr : Expr       Interpretation: if 1st-expr is 0, eval to 2nd-expr, else 3rd-expr.  Mnemonic: branch iff … zero,ok? … else if :t: …

Z1:see ../Z2.rkt for details
Op      ::= … | mod                       Interpretation: “exponentiation”, “remainder1”
Expr    ::= … | IfGT                            Interpretation: “if greater than”
IfGT    ::= grtr Expr Expr ? Expr : Expr  Interpretation: if first Expr is greater than second, result is the third Expr else the fourth.

Z2:see ../Z2.rkt for details
Expr    ::= … | Id | LetExpr                    Interpretation: identifier; let
LetExpr ::= let Id := Expr in Expr           Interpretation: bind Id to (result of) first Expr; then eval 2nd Expr w/ that binding

 
Z4:see ../Z4.rkt for details
 Expr ::= … | FuncExpr | FuncApplyExpr

 FuncExpr ::= fun Id -> Expr          Interpretation: a function-value, with parameter Id and body-Expr.
 FuncApplyExpr ::= pass Expr |> Expr   Interpretation: apply a function (2nd expr) to an argument (1st expr)

Semantics (interpretation):

• A Paren is a parenthesized expression (used for grouping only);
• A Binop is a (prefix) binary operator expression; add means addition; sub means subtraction (the 2nd arg from the 1st); mul 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).

Some similar(??) languages:

• emojicode
• Arnold[Schwarzenegger]C

Discussion

• Give five example programs (Exprs) written in Z0.
• 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,
  and
  • eval, which actually interprets the program, returning a value (a number for Z0-Z2, and a number-or-function in Z3).
  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.

Z0 Implementations

• Z0.rkt, with helper files scanner.rkt (and, scanner-demo.rkt); test cases Z0-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: Z0-java/ (browse the directory), or see the .jar.

  Got JDK17?: If you have Java JDK 17 installed, records can simplify our classes: Z0-java17/ (browse the Java17 directory), or see the Java17 .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 Z0.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 Z0-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 Z0-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 Z0 grammar/datatype-definition.
  • This is called “recursive descent” parsing.

    Note: Parsing Z0 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)
    
    

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