Module 3: Parsing and Unparsing: Assembly Language and Virtual Object Code

try <* and *> and <$ combinators (<$ for lab), ask Q about algebraic laws

consider merging REGS and REGSLIT forms in object code (but given how unparsing works, it might be a bad plan)


(This module is also available in PDF, in two-column and one-column formats.)

This week you’ll design your assembly language and implement an unparser for it. And you’ll start learning about parsing combinators and about the Universal Forward Translator. The parsing stuff is a lot to swallow, but you’ll have two weeks to assimilate it; your full parser isn’t due until module 4.

The theme for the week is designing concrete syntax that promotes readability.

The module step by step

Before lab

  1. Review ML. Review your knowledge of Standard ML. Or if you are preparing to write the UFT in Haskell or in some other functional language, review that. Especially review pattern matching, Curried function application, lists, and the option type with its SOME and NONE constructors.

  2. Learn about error monads. Read about the baby error monad and complete the algebraic laws.

    We’ll look at your laws before other lab work. If you want to maximize your lab time, DM your laws to me before lab starts (by 1:00, please).

  3. Start your syntax design. Design concrete syntax for a fragment of your assembly language. Following the design guidelines, write a grammar that can express at least these three instructions:

    • Add two registers and put the sum in a third
    • Load a literal value in a register
    • Print a register
  4. Learn what parsing combinators can do for us. To learn what problems parsing combinators solve for us, you have your choice of two videos. Each will give you a different perspective. Watching both would be reasonable, but a single one suffices.

    The professional video, which starts at 28:14, needs a little explanation:

    • Although higher-order functions have been used for parsing for almost thirty years, new techniques are still being developed. This presentation, from the 2020 International Conference on Functional Programming, describes a new technique that is used to make combinator parsers very, very efficient.

    • The talk begins with a great, accessible introduction, which runs for about three and a half minutes. Then around 31:44 it accelerates into hyperspace (a parsing machine based on continuations). In my opinion, the typed machine at 35:00 is very cool.

    • If you want to follow along with the talk, here is a translation table:

      Talk code Our code
      pure succeed
      (:) curry op ::
      runParser    produce (roughly)
      some many1
      satisfy sat
  5. Learn how parsing combinators work. Read my handout on how parsing combinators work.


Lab proceeds in three parts. I will keep time and will move people along in lock step.

  1. Combinators as functions. From the parsing handout, review the type of 'a producer and the three possible forms of its result type:

    • Failure: NONE
    • Success: SOME (OK a, remaining_inputs)
    • Error: SOME (ERROR msg, remaining_inputs)

    Now define the parsing combinator for choice:

    val <|> : 'a producer * 'a producer -> 'a producer

    You may define an ML function using fun, or you may complete this algebraic law:

    (p1 <|> p2) ts == ...

    Plan on writing one case for each form of result from p1 ts.

    If you finish before I move the group to step 7, define the parsing combinator for satisfaction:

    val sat : ('a -> bool) -> 'a producer -> 'a producer

    Again you may write code or you may complete this law:

    sat predicate p ts = ...

    Again you will have to consider all possible forms of p ts.

  2. Combinators as abstractions. Although an 'a producer is represented as an ML function, we usually treat a producer as an abstraction. In the next part of the lab, you will define higher-order functions that make new combinators from old combinators. Your code will not acknowledge that a parsing combinator is a function. Instead, you will build new combinators using operations like <$>, <*>, and <|>. Function curry will also be useful.

    The first group of producers you will define are the ones that implement classic notations of extended BNF: “zero or one,” “zero or more,” and “one or more.” You’ll also implement a notation found in Internet protocols and other odd corners: “exactly N.”

    val optional : 'a producer -> 'a option producer  (* zero or one *)

    Remember the definition of 'a option:

    datatype 'a option = SOME of 'a | NONE

    To show optional in action, I use it to get the optional else clause in a C if statement:

    the "if" >> curry3 C_IF <$>
                    (the "(" >> exp <~> the ")") <*>
                    statement <*>
                    optional (the "else" >> statement)

    Now write algebraic laws for optional:

    optional p == ...

    The next two combinators recognize lists:

    val many  : 'a producer -> 'a list producer       (* zero or more *)
    val many1 : 'a producer -> 'a list producer       (* one or more *)

    For example, a Scheme function application is an expression followed by zero or more arguments, all in brackets:1

    the "(" >> curry APPLY <$> exp <*> many exp <~> the ")"

    The algebraic laws for many and many1 are analogous to the structure of the outputs they produce. You may recognize some laws from CS 105:

    • Parser many p may succeed by reading no input and producing the empty list, or it may succeed by producing a single input from p, followed by a list of zero or more p’s.

    • Parser many1 p may succeed by producing a single input from p, followed by a list of zero or more p’s.

    Complete these algebraic laws:

    many  p == ...
    many1 p == ...

    If you finish before I move the group on to step 8, try one of the following:

    • Analogously with many and many1, define a count combinator that produces a list of exactly \(N\) values of type 'a:

      val count : int -> 'a producer -> 'a list producer (* exactly N *)
      count 0     p == ...
      count (n+1) p == ...
    • Define two more combinators that help deal with concrete syntax that must be parsed, but that does not contribute anything to a result of type 'a in an 'a producer. Such syntax usually includes keywords as well as syntactic particles like brackets and commas. This kind of syntax can be ignored by using the following combinators:

      val <~> : 'a producer * 'b producer -> 'a producer
      val >>  : 'a producer * 'b producer -> 'b producer

      In the first combinator, the result from the 'a producer is used and the result from the 'b producer is ignored; in the second combinator, the result from the 'b producer is used and the result from the 'a producer is ignored. Using <$>, <*>, and curry, among other functions, complete the following algebraic laws:

      p <~> q == ...
      p >>  q == ...
    • Define a combinator

      val bracketed : 'a producer -> 'a producer

      where bracketed p recognizes whatever p recognizes, but enclosed in the matching brackets of your choice.

  3. Writing parsers. The last step of lab is to use what you’ve written, together with what I provide, to write a very simple parser.

    Each token of assembly language can be recognized by a parser dedicated to that token. The parsers I provide for this lab recognize, register numbers, literals, and names. Plus the can recognize any single given token, like a comma or a bracket.

    type reg = int
    val reg    : reg producer             (* parses a register number *)
    val int    : int producer             (* parses an integer literal *)
    val string : string producer          (* parses a string literal *)
    val name   : string producer          (* parses a name *)
    val the    : string -> unit producer  (* one token, like a comma or bracket *)

    As functions you can use with <$>, I provide these encoders:

    type opcode = string
    type instr (* instruction *)
    val eR0 : opcode -> instr
    val eR1 : opcode -> reg -> instr
    val eR2 : opcode -> reg -> reg -> instr
    val eR3 : opcode -> reg -> reg -> reg -> instr

    The parsers and functions above are meant to be combined with <$>, <*>, <~>, <|>, and the other parsing combinators. As an example, here’s a parser that recognizes the assembly-language instruction r3 := r1 + r2:

    eR3 "add" <$> reg <~> the ":=" <*> reg <~> the "+" <*> reg

    Emulating this example, write a parser for one of the syntactic forms you defined before lab in step 3.

After lab


  1. Set up your computer for ML programming. Read the handout on “Software development in Standard ML”, and get set up with some ML compilers. (It sounds crazy, but I recommend that you use a mix of three ML compilers. If this sounds awful, you can limp along with just Moscow ML or MLton.)

    If you’re comfortable working on the department servers, you can skip this step.

  2. Download infrastructure for universal forward translation. Update your git repository in two steps:

    1. Be sure all your own code is committed. Confirm using git status.

    2. Update your working tree by running git pull (or you might possibly need git pull origin main).

    If git gives you trouble, please post on the #git-fu channel in Slack.

  3. Verify that the code builds. Assuming you have Moscow ML, change to the src/uft directory, run make, then ../../bin/uft. Running the UFT should name seven languages, of which only two are implemented so far:

    > make
    > ../../bin/uft
      ../../bin/uft <from>-<to> [file]
    where <from> and <to> are one of these languages:
      ho!  Higher-order vScheme with mutation
      ho   Pure, higher-order vScheme
      fo   Pure, first-order vScheme
      cl   Pure, first-order vScheme with closure and capture forms
      kn   K-Normal form
      vs   VM assembly language
      vo   VM object code

    If you don’t have Moscow ML but you do have MLton, try make mlton and then run ../../bin/uft.opt.

    If you haven’t done so already, add the project bin directory to your Unix PATH.

  4. Verify that the Universal Forward Translator behaves as expected. Close study of the UFT is going to wait until we have more languages to work with. For now, confirm that you can activate two translations:

    • Verify that you can use my escape-hatch parser to translate some assembly code into object code:

      > echo '@ print 33' | uft vs-vo | svm
      .load module 1
      print 33
    • Verify that you can unparse code from the escape-hatch parser, but that unparsed assembly language is just a placeholder.

      > echo '@ print 33' | uft vs-vs
      an unknown assembly-code instruction

    If you compiled with MLton, you’ll use uft.opt instead of uft.

  5. Familiarize yourself with the big picture. Still in the src/uft directory, have a quick look at these files:

    List of all source files (except main.sml)

    object-code.sml and asm.sml

    Internal representations of object code and assembly code.


    Toy parser and unparser for assembly code, including example cases for three demonstration instructions

    More details can be found in the code overview.

Syntax design

  1. Decide on concrete syntax for register names. I ship a lexical analyzer that accepts both $rk and rk as register numbers, where k is an integer literal in the range 0 to 255. If that works for you, you’re done. Otherwise, you’ll have to edit asmlex.sml (the registerNum function, the token parser, or both).

  2. Decide if you want floating-point literals. If so, you’ll need to extend asmlex.sml. If not, you can live nicely without them.

  3. Finish your grammar. In this step, which can be interleaved with with step 17, you finish designing the assembly-language syntax you started in step 3.

    • Make sure there is concrete syntax for each of the five forms of assembly-language instruction defined in file asm.sml.

    • Make sure the concrete syntax for LOADFUNC does not require a count of the instructions in the body (instr list). Instead, make sure that the concrete syntax includes some sort of unambiguous terminator, so a parser can tell where the body of the function stops. (The terminator must look different from an instruction!)

    • Make sure there is concrete syntax for each of the instructions your VM recognizes (all of which will take the OBJECT_CODE form in asm.sml).

    • Follow the design guidelines.


  1. Write unparsers for your assembly language. Using the grammar you defined in steps 3 and 16, and possibly concurrently with step 16, define unparsing functions so that every instruction and every assembly-language form can be rendered in the concrete syntax you have chosen.

    In file asmparse.sml, you will find a prototype unparser unparse1, which is meant to unparse any instruction except LOADFUNC. The prototype knows how to unparse three VM instructions:

    • Opcode + adds two registers and places the sum in a third.
    • Opcode swap swaps the contents of two registers.
    • Opcode +imm adds a register and an immediate constant and places the sum in a register. The immediate constant is “offset-coded”; an 8-bit byte \(z\) codes for the number \(z-128\).

    The concrete syntax I use for these instructions is described in step 18.

    File asmparse.sml also includes a prototype unparse, but once LOADFUNC enters the picture, this prototype will have to be rewritten.

    Complete both steps:

    1. In file asmparse.sml, replace prototypes unparse and unparse1 with a real unparser for assembly code.

      • Write unparse1, which should handle every form except LOADFUNC. (Each of those cases produces one line of output.)

      • Write unparse, which handles both forms of LOADFUNC.2 A function load generally requires multiple lines of assembly code to express the body of the function. Those lines should be indented.

      Function unparse1 requires a ton of case analysis: pattern matching on opcode names. Every instruction your VM accepts must unparse to a readable assembly-language syntax.

    2. Test your unparser by creating a test file unparse.vs. In this file, using my “passthrough parser”, or using your own parser if you have completed step 18, write at least half the instructions that your VM recognizes. (If you use my passthrough parser, you will be limited to instructions in formats R0 through R3, like halt and print but not loadliteral or check.) Test that these instructions unparse correctly by running

      uft vs-vs unparse.vs

      and comparing the output with what you expect from your grammar.

      The other half of your instructions should be implemented in your unparser, but they can remain untested until next week.

One step toward parsing

  1. Extend my placeholder parser with at least one new syntactic form. In file asmparse.sml, I define a simple parser for assembly instructions. This parser, one_line_instr, recognizes these forms:

    • From the form @ opcode { int }, it generates an object-code instruction with the given opcode and registers. This form basically works as a “passthrough” to be able to write some virtual object code after the @ sign.

    • From the form reg := reg + reg, it generates an add instruction (opcode +).

    • From the form reg := reg + int, it generates an add-immediate instruction (opcode +imm).

    • From the form reg := reg - int, it also generates an add-immediate instruction—subtracting a small integer is the same as adding a negative small integer.

    • From the form regreg’ := reg’reg, it generates a swap instruction (opcode swap). The concrete syntax is “multiple assignment,” which is found in Python, Lua, and other languages.

    Extend one_line_instr with at least one case of concrete syntax in your assembly language. A good case to implement would be concrete syntax for loading a literal value into a register. You’ll add more cases next week.

  2. That’s it! Next week you’ll complete your parser, and you’ll write the label-elimination pass that translates assembly code to virtual object code. But for now, you’re done.

What and how to submit

  1. On Monday, submit the homework. In the src/uft directory you’ll find a file SUBMIT.03. That file needs to be edited to answer the same questions you answer every week.

    From now on, you’ll be submitting your full src tree, including both the UFT and the SVM.

    To submit, you’ll need to copy your working tree to the department servers. We recommend using rsync, but scp also works.

    Now log into a department server, change to your working tree, and submit your entire src directory:

    provide cs106 hw03 src
  2. On Tuesday, submit your reflection. Create a plain text file REFLECTION, which will hold your claims for project points and depth points.

    For each project point you claim, write the number of the point, plus whatever is called for in the section “How to claim the project points”—usually a few sentences.

    Now copy your REFLECTION file to a department server and submit it using provide:

    provide cs106 reflection03 REFLECTION

Reading in depth

Occasionally I’ll suggest reading that may enrich your view of programming-language implementation. This week I suggest three works on combinator parsing:

Learning outcomes

Outcomes available for points

Learning outcomes available for project points:

  1. Algebraic laws. You can write algebraic laws for particular monads.

  2. Parsing combinators. You can write new parsing combinators.

  3. Syntax design. You can explain how the design of your concrete syntax promotes readability.

  4. Costs of design. You can argue whether a well-designed concrete syntax is unreasonably expensive.

  5. Unparsing. At least half the instructions your VM recognizes can be unparsed by your UFT.

  6. Parsing in theory. You understand when your parser needs to see multiple tokens before making a choice.

  7. Parsing in practice. Using a parser you wrote yourself, your UFT can successfully parse one assembly-language instruction.

  8. Embedding and projection. You understand how assembly-language abstract syntax and concrete syntax are related by embedding and projection.

Learning outcome available for depth points:

  1. Assembler macro [1 point]. You make check-expect look like a single assembly instruction, but it expands to multiple VM instructions. You can assemble and run a .vs file that contains a check-expect. The point can be redeemed with this module or the next module; after that, it expires.

How to claim the project points

Each of the numbered learning outcomes 1 to N is worth one point, and the points can be claimed as follows:

  1. In lab you wrote algebraic laws for Kleisli composition using the baby error monad. To claim this point, write algebraic laws for Kleisli composition using the full error monad.

  2. To claim this point, define this parsing combinator:

    val commaSep : 'a producer -> 'a list producer
      (* `commaSep p` returns a parser that parses a sequence
          of zero or more p's separated by commas *)

    You may include the definition in your REFLECTION file or in your Monday night submission (in which case, please point to it).

  3. To claim this point, identify examples of two different syntactic forms of virtual object code, and compare those examples side by side with the corresponding forms of your assembly language. Explain why you believe that the assembly-language examples are more readable.

  4. It’s good if the assembly language is easy to read and write, but it’s also good if the code inside the UFT is short. To claim this point, argue at least one of the following positions:

    • These are competing concerns.
    • Both can be accomplished in a single design.

    To earn the point, every argument must be supported by pointing to specific line numbers within your unparser.

  5. To claim this point, make sure your Monday night submission includes test file unparse.vs and that it passes the test described in step 17B above.

  6. To claim this point, identify a choice point in your grammar (that is, an alternative between two syntactic forms), where making the choice requires looking at more than one token. If all your choices can be made by looking at a single token—that is, if your grammar is LL(1)—then explain what you did to make that so.

  7. To claim this point, you will show assembly syntax that your UFT successfully parses and unparses, using code you wrote yourself (or with a partner). You may use the parser you wrote in lab in step 8, or you may use another parser of your choice. Demonstrate that it works with your unparser by feeding an assembly language instruction to the UFT, parsing it, and unparsing it back to the original string, as in this example from my own code:

    > echo "r1 := r2 + r3" | uft vs-vs
    r1 := r2 + r3
  8. To claim this point,

    • Explain whether and how the embedding/projection concept applies to the abstract syntax and concrete syntax of assembly language.

    • Point to where in your code embedding and/or projection are implemented.

    • If projection is implemented, say how projection failure is manifested.

Concrete syntax of the week

Your most interesting design choice will probably be the notation you want to use for global variables. Here are your options:

Choose wisely!

  1. Examples not typechecked!

  2. There is not only Asm.LOADFUNC, but also Asm.OBJECT_CODE applied to ObjectCode.LOADFUNC.