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authorJack Sangdahl <[email protected]>2024-12-12 21:02:58 -0700
committerJack Sangdahl <[email protected]>2024-12-12 21:02:58 -0700
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Unit 3
Signed-off-by: Jack Sangdahl <[email protected]>
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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "7ec161ff",
+ "metadata": {},
+ "source": [
+ "Before you turn this problem in, make sure everything runs as expected. First, **restart the kernel** (in the menubar, select Kernel $\\rightarrow$ Restart) and then **run all cells** (in the menubar, select Cell $\\rightarrow$ Run All).\n",
+ "\n",
+ "Make sure you fill in any place that says `???`, `YOUR CODE HERE`, \"???\", \"YOUR ANSWER HERE\", as well as your name and collaborators below:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "3d65dedf",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "val NAME = \"\"\n",
+ "val COLLABORATORS = \"\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "74474148",
+ "metadata": {},
+ "source": [
+ "---"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4d8f8547-4bad-42d0-8621-75e17d4b6741",
+ "metadata": {},
+ "source": [
+ "$\\newcommand{\\TirName}[1]{\\text{#1}}\n",
+ "\\newcommand{\\inferrule}[3][]{\n",
+ " \\let\\and\\qquad\n",
+ " \\begin{array}{@{}l@{}}\n",
+ " \\TirName{#1}\n",
+ " \\\\\n",
+ " \\displaystyle\n",
+ " \\frac{#2}{#3}\n",
+ " \\end{array}\n",
+ "}\n",
+ "\\newcommand{\\infer}[3][]{\\inferrule[#1]{#2}{#3}}\n",
+ "$\n",
+ "\n",
+ "# Lab: Small-Step Operational Semantics\n",
+ "\n",
+ "<!-- 3 Expressions -->\n",
+ "\n",
+ "<!-- 4 Binding and Scope -->\n",
+ "\n",
+ "<!-- 8 Recursion -->\n",
+ "\n",
+ "<!-- 9 Inductive Data Types -->\n",
+ "\n",
+ "<!-- 11 Concrete Syntax -->\n",
+ "\n",
+ "<!-- 12 Abstract Syntax and Parsing -->\n",
+ "\n",
+ "<!-- 13 Exercise: Syntax -->\n",
+ "\n",
+ "<!-- 14 Static Scoping -->\n",
+ "\n",
+ "<!-- 15 Judgments -->\n",
+ "\n",
+ "<!-- 16 Variables, Basic Values, and Judgments Lab -->\n",
+ "\n",
+ "<!-- 18 Operational Semantics -->\n",
+ "\n",
+ "<!-- 19 Functions and Dynamic Scoping -->\n",
+ "\n",
+ "<!-- 20 Big-Step Exercise -->\n",
+ "\n",
+ "<!-- 21 Evaluation Order -->\n",
+ "\n",
+ "### Learning Goals\n",
+ "\n",
+ "The primary learning goals of this assignment are to build intuition for\n",
+ "the following:\n",
+ "\n",
+ "- the distinction between a big-step and a small-step operational\n",
+ " semantics;\n",
+ "- evaluation order; and\n",
+ "- substitution and program transformation.\n",
+ "\n",
+ "Functional Programming Skills \n",
+ "Iteration. Introduction to higher-order functions.\n",
+ "\n",
+ "Programming Language Ideas \n",
+ "Semantics: evaluation order. Small-step operational semantics.\n",
+ "Substitution and program transformation.\n",
+ "\n",
+ "### Instructions\n",
+ "\n",
+ "A version of project files for this lab resides in the public\n",
+ "[pppl-lab3](https://github.com/csci3155/pppl-lab3) repository. Please\n",
+ "follow separate instructions to get a private clone of this repository\n",
+ "for your work.\n",
+ "\n",
+ "You will be replacing `???` or `case _ => ???` in the `Lab3.scala` file\n",
+ "with solutions to the coding exercises described below.\n",
+ "\n",
+ "**Your lab will not be graded if it does not compile**. You may check\n",
+ "compilation with your IDE, `sbt compile`, or with the “sbt compile”\n",
+ "GitHub Action provided for you. Comment out any code that does not\n",
+ "compile or causes a failing assert. Put in `???` as needed to get\n",
+ "something that compiles without error.\n",
+ "\n",
+ "You may add additional tests to the `Lab3Spec.scala` file. In the\n",
+ "`Lab3Spec.scala`, there is empty test class `Lab3StudentSpec` that you\n",
+ "can use to separate your tests from the given tests in the `Lab3Spec`\n",
+ "class. You are also likely to edit `Lab3.worksheet.sc` for any scratch\n",
+ "work. You can also use `Lab3.worksheet.js` to write and experiment in a\n",
+ "JavaScript file that you can then parse into a JavaScripty AST (see\n",
+ "`Lab3.worksheet.sc`).\n",
+ "\n",
+ "If you like, you may use this notebook for experimentation. However,\n",
+ "**please make sure your code is in `Lab3.scala`; code in this notebook\n",
+ "will not graded.**\n",
+ "\n",
+ "Note that there is a section with concept exercises\n",
+ "(<a href=\"#sec-concept-exercises-small-step-lab\"\n",
+ "class=\"quarto-xref\">Section 6</a>). Make sure to complete the concept\n",
+ "exercises in that section and **turn in this file as part of your\n",
+ "submission for the concept exercises**. However, all code and testing\n",
+ "exercises from other sections are submitted in `Lab3.scala` or\n",
+ "`Lab3Spec.scala`.\n",
+ "\n",
+ "Recall that you need to switch kernels between running JavaScript and\n",
+ "Scala cells.\n",
+ "\n",
+ "## Small-Step Interpreter: JavaScripty Functions\n",
+ "\n",
+ "We consider the same JavaScripty variant as in the previous exercise on\n",
+ "big-step operational semantics (**?@sec-big-step-interpreter-exercise**)\n",
+ "where the interesting language feature are first-class functions:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "52da72d3",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "trait Expr\n",
+ "case class Fun(xopt: Option[String], y: String, e1: Expr) extends Expr // e ::= x?(y) => e1\n",
+ "case class Call(e1: Expr, e2: Expr) extends Expr // e ::= e1(e2) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8fcd8270-9c1f-45de-a144-5658d132eeb9",
+ "metadata": {},
+ "source": [
+ "We consider a `Fun` constructor for representing JavaScripty function\n",
+ "literals. This version of `Fun` allows for named functions. When a\n",
+ "function expression\n",
+ "$x\\texttt{(}y\\texttt{)} \\mathrel{\\texttt{=}\\!\\texttt{>}} e'$ has a name,\n",
+ "then it is can be recursive. As noted previously about recursive\n",
+ "functions (**?@sec-recursive-functions**), variable $x$ is an additional\n",
+ "formal parameter, and the function body $e'$ may have free variable uses\n",
+ "of $x$. The variable $x$ gets bound to itself (i.e., the function value\n",
+ "for $x\\texttt{(}y\\texttt{)} \\mathrel{\\texttt{=}\\!\\texttt{>}} e'$) on a\n",
+ "function call.\n",
+ "\n",
+ "In the abstract syntax representation, the `xopt: Option[String]`\n",
+ "parameter in our `Fun` constructor is `None` if there is no identifier\n",
+ "present (cannot be used recursively), or `Some(x: String)` if there is\n",
+ "an identifier, `x`, present (can be used recursively).\n",
+ "\n",
+ "In this lab, we will do two things. First, we will move to implementing\n",
+ "a small-step interpreter with a function `step` that takes an `e: Expr`\n",
+ "and returns a one-step reduction of `e`. A small-step interpreter makes\n",
+ "explicit the evaluation order of expressions. Second, we will remove\n",
+ "environments and instead use a language semantics based on substitution.\n",
+ "This change will result in static, lexical scoping without needing\n",
+ "closures, thus demonstrating another way to fix dynamical scoping.\n",
+ "\n",
+ "These two changes are orthogonal, that is, one could implement a\n",
+ "big-step interpreter using substitution (as in\n",
+ "**?@sec-big-step-substitution**) or a small-step interpreter using\n",
+ "environments. Substitution is a fairly simple way to get lexical\n",
+ "scoping, but in practice, it is rarely used because it is not the most\n",
+ "efficient implementation.\n",
+ "\n",
+ "## Static Scoping\n",
+ "\n",
+ "<span class=\"theorem-title\">**Exercise 1 (Substitute)**</span> Since our\n",
+ "implementation requires substitution, we begin by implementing\n",
+ "`substitute`, which substitutes value `v` for all *free* occurrences of\n",
+ "variable `x` in expression `e`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2b7556f9",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def substitute(e: Expr, v: Expr, x: String): Expr = ???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "55d4fa8c-6cbc-4798-9f06-477ebfc236fc",
+ "metadata": {},
+ "source": [
+ "We advise defining `substitute` by induction on `e`. The cases to be\n",
+ "careful about are `ConstDecl` and `Fun` because these are the variable\n",
+ "binding constructs (as discussed in the reading on substitution in\n",
+ "**?@sec-substitution**). In particular, calling `substitute` on\n",
+ "expression\n",
+ "\n",
+ "``` typescript\n",
+ "a; { const a = 4; a }\n",
+ "```\n",
+ "\n",
+ "with value `3` for variable `a` should return\n",
+ "\n",
+ "``` typescript\n",
+ "3; { const a = 4; a }\n",
+ "```\n",
+ "\n",
+ "not\n",
+ "\n",
+ "``` typescript\n",
+ "3; { const a = 4; 3 }\n",
+ "```\n",
+ "\n",
+ "This function is a helper for the `step` function, but you might want to\n",
+ "implement all of the cases of `step` that do not require `substitute`\n",
+ "first.\n",
+ "\n",
+ "## Iteration\n",
+ "\n",
+ "Our `step` performs a single reduction step. We may want to test it by\n",
+ "repeatedly calling it with an expression until reducing to value. Thus,\n",
+ "from a software engineering standpoint, you might want to evolve the\n",
+ "`iterate` function described below together with your implementation of\n",
+ "`step`.\n",
+ "\n",
+ "This idea of repeatedly performing an action until some condition is\n",
+ "satisfied is a loop or iteration. We have seen that we can iterate with\n",
+ "a tail-recursive helper function. For example, consider the `sumTo`\n",
+ "function that sums the integers from `0` to `n`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "4c8c6cd3",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def sumTo(n: Int): Int = {\n",
+ " def loop(acc: Int, i: Int): Int = {\n",
+ " require(n >= 0)\n",
+ " if (i > n) acc\n",
+ " else loop(acc + i, i + 1)\n",
+ " }\n",
+ " loop(0, 0)\n",
+ "}\n",
+ "sumTo(100)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8add8f1e-fc70-4f2e-8198-76fbfd8b00b0",
+ "metadata": {},
+ "source": [
+ "<span class=\"theorem-title\">**Exercise 2 (Iterate with Error\n",
+ "Side-Effects)**</span> Because this pattern is so common, we want to get\n",
+ "practice refactoring this pattern into a higher-order function. We are\n",
+ "implementing a library function that a client like `sumTo` can use:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "79d0ad51",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def iterateBasic[A](acc0: A)(stepi: (A, Int) => Option[A]): A = {\n",
+ " def loop(acc: A, i: Int): A = ???\n",
+ " loop(acc0, 0)\n",
+ "}\n",
+ "\n",
+ "def sumTo(n: Int) = {\n",
+ " iterate(0) { case (acc, i) =>\n",
+ " require(n >= 0)\n",
+ " if (i > n) None\n",
+ " else Some(acc + i)\n",
+ " }\n",
+ "}\n",
+ "sumTo(100)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5bbddb8d-9f02-4123-b7da-6427b0f8fbef",
+ "metadata": {},
+ "source": [
+ "The `iterate` function calls iterates (i.e., repeatedly calls) the\n",
+ "callback `stepi` until it returns `None` starting from `acc0: A`. Note\n",
+ "that `iterate` is a generic in the accumulation type `A`. The `stepi`\n",
+ "callback takes the current accumulator of type `A` and the iteration\n",
+ "number as an `Int` and indicates continuing by returning `Some(acc)` for\n",
+ "some next accumulator value `acc`. We see how `sumTo` can use `iterate`.\n",
+ "\n",
+ "<span class=\"theorem-title\">**Exercise 3 (Iterate with Error\n",
+ "Values)**</span> One unfortunate aspect of the above is that `sumTo`\n",
+ "“exits `iterate` with an error” by throwing an exception (i.e., with the\n",
+ "`require(n >= 0)`). Let us refactor `iterate` to allow for explicit\n",
+ "error values using `Either[Err, A]`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "cd23905f",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def iterate[Err, A](acc0: A)(stepi: (A, Int) => Option[Either[Err, A]]): Either[Err, A] = {\n",
+ " def loop(acc: A, i: Int): Either[Err, A] = ???\n",
+ " loop(acc0, 0)\n",
+ "}\n",
+ "\n",
+ "def sumTo(n: Int): Either[IllegalArgumentException, Int] = {\n",
+ " iterate(0) { case (acc, i) =>\n",
+ " if (n < 0) Some(Left(new IllegalArgumentException(\"requirement failed\")))\n",
+ " else if (i > n) None\n",
+ " else Some(Right(acc + i))\n",
+ " }\n",
+ "}\n",
+ "sumTo(100)\n",
+ "sumTo(-1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "bbbe0657-2fe0-4c51-b135-b7a1a6969049",
+ "metadata": {},
+ "source": [
+ "The `iterate` is now parametrized by an error type `Err` and returns an\n",
+ "`Either[Err, A]`. The `stepi` callback should return `None` if it wants\n",
+ "to stop normally, `Some(Left(err))` if it wants to stop with an error,\n",
+ "and `Some(Right(acc)` if it wants to continue with an accumulator value\n",
+ "`acc`.\n",
+ "\n",
+ "We can imagine that we can imagine how we can use `iterate` as a library\n",
+ "function to iterate your `step` implementation. In particular, this is\n",
+ "how `iterate` will be used to iterate `step` while adding some debugging\n",
+ "output:\n",
+ "\n",
+ "``` scala\n",
+ "def iterateStep(e: Expr) = {\n",
+ " require(closed(e), s\"iterateStep: ${e} not closed\")\n",
+ " if (debug) {\n",
+ " println(\"------------------------------------------------------------\")\n",
+ " println(\"Evaluating with step ...\")\n",
+ " }\n",
+ " val v = iterate(e) { (e: Expr, n: Int) =>\n",
+ " if (debug) { println(s\"Step $n: $e\") }\n",
+ " if (isValue(e)) None else Some(step(e))\n",
+ " }\n",
+ " if (debug) { println(\"Value: \" + v) }\n",
+ " v\n",
+ "}\n",
+ "```\n",
+ "\n",
+ "Of particular interest is the anonymous function passed to `iterate`\n",
+ "that calls your implementation of `step`.\n",
+ "\n",
+ "## Small-Step Interpreter\n",
+ "\n",
+ "In this section, we implement the one-step evaluation judgment form\n",
+ "$e \\longrightarrow r$ that says, “Expression $e$ can take one step of\n",
+ "evaluation to a step-result $r$.”\n",
+ "\n",
+ "$$\n",
+ "\\begin{array}{rrrl}\n",
+ "\\text{step-results} & r& \\mathrel{::=}& \\mathop{\\mathsf{typeerror}}e \\mid e'\n",
+ "\\end{array}\n",
+ "$$\n",
+ "\n",
+ "A step-result $r$ is either a $\\mathop{\\mathsf{typeerror}}e$ indicating\n",
+ "a dynamic type error in attempting to reduce $e$ or a successful\n",
+ "one-step reduction to an expression $e'$.\n",
+ "\n",
+ "We represent a step-result $r$ in Scala using a type\n",
+ "`Either[DynamicTypeError, Expr]`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "25bea4a5",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "case class DynamicTypeError(e: Expr) {\n",
+ " override def toString = s\"TypeError: in expression $e\"\n",
+ "}\n",
+ "type Result = Either[DynamicTypeError, Expr] // r ::= typeerror e | e"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "45af4baf-ce37-41a5-9eaf-4f12c47627d7",
+ "metadata": {},
+ "source": [
+ "Note that unlike before, `DynamicTypeError` is not an `Exception`, so it\n",
+ "cannot be `throw`n.\n",
+ "\n",
+ "The small-step semantics that we should implement are given in the\n",
+ "section below (<a href=\"#sec-small-step-operational-semantics\"\n",
+ "class=\"quarto-xref\">Section 5</a>). The language we implement is\n",
+ "JavaScripty with numbers, booleans, strings, $\\mathbf{undefined}$,\n",
+ "printing, and first-class functions. It is a simpler language than the\n",
+ "previous lab because we remove type coercions (except to booleans) and\n",
+ "replace most coercion cases with dynamic type error\n",
+ "$\\mathop{\\mathsf{typeerror}}e$.\n",
+ "\n",
+ "<span class=\"theorem-title\">**Exercise 4 (Step without Dynamic Type\n",
+ "Checking)**</span> We advise first implementing the cases restricted to\n",
+ "judgments of the form $e \\longrightarrow e'$, that is, implement the\n",
+ "$\\TirName{Do}$ and $\\TirName{Search}$ rules while ignoring the\n",
+ "$\\TirName{TypeError}$ and $\\TirName{Propagate}$ rules. Start with\n",
+ "implementing a `stepBasic` function with type:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2fa3e363",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def stepBasic(e: Expr): Expr = ???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "706787b6-5fe2-406f-9a50-0d6ad8ea04ea",
+ "metadata": {},
+ "source": [
+ "That is, just crash with a `MatchError` exception if your `step`\n",
+ "encounters any ill-typed expression `e`.\n",
+ "\n",
+ "The suggested practice here is to read some rules, write a few tests for\n",
+ "those rules, and implement the cases for those tests.\n",
+ "\n",
+ "<span class=\"theorem-title\">**Exercise 5 (Step with Dynamic Type\n",
+ "Checking)**</span> Then, copy your code from `stepBasic` to `stepCheck`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "d7aa264c",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def stepCheck(e: Expr): Either[DynamicTypeError, Expr] = ???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1ba099a1-963d-4319-b463-73f302d883d4",
+ "metadata": {},
+ "source": [
+ "to then add dynamic type checking. You will likely need to refactor your\n",
+ "code to satisfy the new types before implementing the\n",
+ "$\\TirName{TypeError}$ and $\\TirName{Propagate}$ rules.\n",
+ "\n",
+ "<span class=\"theorem-title\">**Exercise 6 (To Boolean)**</span> You will\n",
+ "need to implement a `toBoolean` function to convert JavaScripty values\n",
+ "to booleans, following the $\\TirName{ToBoolean}$ rules in\n",
+ "<a href=\"#sec-small-step-operational-semantics\"\n",
+ "class=\"quarto-xref\">Section 5</a>."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "681e068d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def toBoolean(e: Expr): Boolean = ???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4b64c82f-2cc5-4520-b729-10c8aca232c4",
+ "metadata": {},
+ "source": [
+ "However, you will not need any other type coercion functions here.\n",
+ "\n",
+ "#### Notes\n",
+ "\n",
+ "- Note that the tests call the `step` function that is originally\n",
+ " defined as:\n",
+ "\n",
+ " ``` scala\n",
+ " //def step(e: Expr): Either[DynamicTypeError, Expr] = Right(stepBasic(e))\n",
+ " def step(e: Expr): Either[DynamicTypeError, Expr] = stepCheck(e)\n",
+ " ```\n",
+ "\n",
+ " You can first test `stepBasic` by uncommenting the first line and\n",
+ " commenting out the second line.\n",
+ "\n",
+ "- Note that the provided tests are minimal. You will want to add your\n",
+ " own tests to cover most language features.\n",
+ "\n",
+ "## Small-Step Operational Semantics\n",
+ "\n",
+ "In this section, we give the small-step operational semantics for\n",
+ "JavaScripty with numbers, booleans, strings, $\\mathbf{undefined}$,\n",
+ "printing, and first-class functions. We have type coercions to booleans\n",
+ "but otherwise use dynamic type error for other cases.\n",
+ "\n",
+ "We write ${}[v/x]e$ for substituting value $v$ for all free occurrences\n",
+ "of the variable $x$ in expression $e$ (i.e., a call to `substitute`).\n",
+ "\n",
+ "It is informative to compare the small-step semantics used in this lab\n",
+ "and the big-step semantics from last homework.\n",
+ "\n",
+ "### Do Rules\n",
+ "\n",
+ "$\\fbox{$e \\longrightarrow e'$}$\n",
+ "\n",
+ "$\\inferrule[DoNeg]{\n",
+ " n' = - n_1\n",
+ "}{\n",
+ " \\mathop{\\texttt{-}} n_1 \\longrightarrow n'\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoArith]{\n",
+ " n' = n_1 \\mathbin{\\mathit{bop}}n_2\n",
+ " \\and\n",
+ " \\mathit{bop}\\in \\left\\{ \\texttt{+}, \\texttt{-}, \\texttt{*}, \\texttt{/} \\right\\}\n",
+ "}{\n",
+ " n_1 \\mathbin{\\mathit{bop}}n_2 \\longrightarrow n'\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoPlusString]{\n",
+ " \\mathit{str}' = \\mathit{str}_1 \\mathit{str}_2\n",
+ "}{\n",
+ " \\mathit{str}_1 \\mathbin{\\texttt{+}} \\mathit{str}_2 \\longrightarrow\\mathit{str}'\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoInequalityNumber]{\n",
+ " b' = n_1 \\mathbin{\\mathit{bop}}n_2\n",
+ " \\and\n",
+ " \\mathit{bop}\\in \\left\\{ \\texttt{<}, \\texttt{<=}, \\texttt{>}, \\texttt{>=} \\right\\}\n",
+ "}{\n",
+ " n_1 \\mathbin{\\mathit{bop}}n_2 \\longrightarrow b'\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoInequalityString]{\n",
+ " b' = \\mathit{str}_1 \\mathbin{\\mathit{bop}}\\mathit{str}_2\n",
+ " \\and\n",
+ " \\mathit{bop}\\in \\left\\{ \\texttt{<}, \\texttt{<=}, \\texttt{>}, \\texttt{>=} \\right\\}\n",
+ "}{\n",
+ " \\mathit{str}_1 \\mathbin{\\mathit{bop}}\\mathit{str}_2 \\longrightarrow b'\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoEquality]{\n",
+ " b' = (v_1 \\mathbin{\\mathit{bop}}v_2)\n",
+ " \\and\n",
+ " \\mathit{bop}\\in \\left\\{ \\texttt{===}, \\texttt{!==} \\right\\}\n",
+ "}{\n",
+ " v_1 \\mathbin{\\mathit{bop}}v_2 \\longrightarrow b'\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoNot]{\n",
+ " v_1 \\rightsquigarrow b_1\n",
+ "}{\n",
+ " \\mathop{\\texttt{!}} v_1 \\longrightarrow\\neg b_1\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoAndTrue]{\n",
+ " v_1 \\rightsquigarrow \\mathbf{true}\n",
+ "}{\n",
+ " v_1 \\mathbin{\\texttt{\\&\\&}} e_2 \\longrightarrow e_2\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoAndFalse]{\n",
+ " v_1 \\rightsquigarrow \\mathbf{false}\n",
+ "}{\n",
+ " v_1 \\mathbin{\\texttt{\\&\\&}} e_2 \\longrightarrow v_1\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoOrTrue]{\n",
+ " v_1 \\rightsquigarrow \\mathbf{true}\n",
+ "}{\n",
+ " v_1 \\mathbin{\\texttt{||}} e_2 \\longrightarrow v_1\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoOrFalse]{\n",
+ " v_1 \\rightsquigarrow \\mathbf{false}\n",
+ "}{\n",
+ " v_1 \\mathbin{\\texttt{||}} e_2 \\longrightarrow e_2\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoIfTrue]{\n",
+ " v_1 \\rightsquigarrow \\mathbf{true}\n",
+ "}{\n",
+ " v_1\\;\\texttt{?}\\;e_2\\;\\texttt{:}\\;e_3 \\longrightarrow e_2\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoIfFalse]{\n",
+ " v_1 \\rightsquigarrow \\mathbf{false}\n",
+ "}{\n",
+ " v_1\\;\\texttt{?}\\;e_2\\;\\texttt{:}\\;e_3 \\longrightarrow e_3\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoSeq]{\n",
+ "}{\n",
+ " v_1 \\mathbin{\\texttt{,}} e_2 \\longrightarrow e_2\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoPrint]{\n",
+ " \\text{$v_1$ printed}\n",
+ "}{\n",
+ " \\texttt{console}\\texttt{.}\\texttt{log}\\texttt{(}v_1\\texttt{)} \\longrightarrow\\mathbf{undefined}\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoConst]{\n",
+ "}{\n",
+ " \\mathbf{const}\\;x\\;\\texttt{=}\\;v_1\\texttt{;}\\;e_2 \\longrightarrow[v_1/x]e_2\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoCall]{\n",
+ "}{\n",
+ " (\\texttt{(}x\\texttt{)} \\mathrel{\\texttt{=}\\!\\texttt{>}} e_1) \\texttt{(}v_2\\texttt{)} \\longrightarrow{}[v_2/x]e_1\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[DoCallRec]{\n",
+ " v_1 = (x_1\\texttt{(}x_2\\texttt{)} \\mathrel{\\texttt{=}\\!\\texttt{>}} e_1)\n",
+ "}{\n",
+ " v_1\\texttt{(}v_2\\texttt{)} \\longrightarrow {}[v_1/x_1] {}[v_2/x_2]e_1 \n",
+ "}$\n",
+ "\n",
+ "Figure 1: The $\\TirName{Do}$ rules for JavaScripty with numbers,\n",
+ "booleans, strings, $\\mathbf{undefined}$, printing, and first-class\n",
+ "functions.\n",
+ "\n",
+ "### Search Rules\n",
+ "\n",
+ "$\\fbox{$e \\longrightarrow e'$}$\n",
+ "\n",
+ "$\\inferrule[SearchUnary]{\n",
+ " e_1 \\longrightarrow e_1'\n",
+ "}{\n",
+ " \\mathop{\\mathit{uop}}e_1 \\longrightarrow\\mathop{\\mathit{uop}}e_1'\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[SearchBinary1]{\n",
+ " e_1 \\longrightarrow e_1'\n",
+ "}{\n",
+ " e_1 \\mathbin{\\mathit{bop}}e_2 \\longrightarrow e_1' \\mathbin{\\mathit{bop}}e_2\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[SearchBinary2]{\n",
+ " e_2 \\longrightarrow e_2'\n",
+ "}{\n",
+ " v_1 \\mathbin{\\mathit{bop}}e_2 \\longrightarrow v_1 \\mathbin{\\mathit{bop}}e_2'\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[SearchIf]{\n",
+ " e_1 \\longrightarrow e_1'\n",
+ "}{\n",
+ " e_1\\;\\texttt{?}\\;e_2\\;\\texttt{:}\\;e_3 \\longrightarrow e_1'\\;\\texttt{?}\\;e_2\\;\\texttt{:}\\;e_3\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[SearchPrint]{\n",
+ " e_1 \\longrightarrow e_1'\n",
+ "}{\n",
+ " \\texttt{console}\\texttt{.}\\texttt{log}\\texttt{(}e_1\\texttt{)} \\longrightarrow\\texttt{console}\\texttt{.}\\texttt{log}\\texttt{(}e_1'\\texttt{)}\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[SearchConst]{\n",
+ " e_1 \\longrightarrow e_1'\n",
+ "}{\n",
+ " \\mathbf{const}\\;x\\;\\texttt{=}\\;e_1\\texttt{;}\\;e_2 \\longrightarrow\\mathbf{const}\\;x\\;\\texttt{=}\\;e_1'\\texttt{;}\\;e_2 \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[SearchCall1]{\n",
+ " e_1 \\longrightarrow e_1'\n",
+ "}{\n",
+ " e_1\\texttt{(}e_2\\texttt{)} \\longrightarrow e_1'\\texttt{(}e_2\\texttt{)}\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[SearchCall2]{\n",
+ " e_2 \\longrightarrow e_2'\n",
+ "}{\n",
+ " v_1 \\texttt{(}e_2\\texttt{)} \\longrightarrow v_1 \\texttt{(}e_2'\\texttt{)}\n",
+ "}$\n",
+ "\n",
+ "Figure 2: The $\\TirName{Search}$ rules for JavaScripty with numbers,\n",
+ "booleans, strings, $\\mathbf{undefined}$, printing and first-class\n",
+ "functions.\n",
+ "\n",
+ "### Coercing to Boolean\n",
+ "\n",
+ "$\\fbox{$v \\rightsquigarrow b$}$\n",
+ "\n",
+ "$\\inferrule[ToBooleanNumFalse]{\n",
+ " n= 0.0 \\lor n= -0.0 \\lor n= \\mathsf{NaN}\n",
+ "}{\n",
+ " n \\rightsquigarrow \\mathbf{false}\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[ToBooleanNumTrue]{\n",
+ " n\\neq 0.0 \\and n\\neq -0.0 \\and n\\neq \\mathsf{NaN}\n",
+ "}{\n",
+ " n \\rightsquigarrow \\mathbf{true}\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[ToBooleanBoolean]{\n",
+ "}{\n",
+ " b \\rightsquigarrow b\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[ToBooleanStrFalse]{\n",
+ "}{\n",
+ " \\texttt{\"\"} \\rightsquigarrow \\mathbf{false}\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[ToBooleanStrTrue]{\n",
+ " \\mathit{str}\\neq \\texttt{\"\"}\n",
+ "}{\n",
+ " \\mathit{str} \\rightsquigarrow \\mathbf{true}\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[ToBooleanUndefined]{\n",
+ "}{\n",
+ " \\mathbf{undefined} \\rightsquigarrow \\mathbf{false}\n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[ToBooleanFun]{\n",
+ "}{\n",
+ " x^{?}\\texttt{(}y\\texttt{)} \\mathrel{\\texttt{=}\\!\\texttt{>}} e \\rightsquigarrow \\mathbf{true}\n",
+ "}$\n",
+ "\n",
+ "Figure 3: The $\\TirName{ToBoolean}$ rules for JavaScripty with numbers,\n",
+ "booleans, strings, $\\mathbf{undefined}$, and first-class functions.\n",
+ "\n",
+ "### Dynamic Typing Rules\n",
+ "\n",
+ "$\\fbox{$e \\longrightarrow r$}$\n",
+ "\n",
+ "$\\inferrule[TypeErrorNeg]{\n",
+ " v_1 \\neq n_1\n",
+ "}{\n",
+ " \\mathop{\\texttt{-}} n_1 \\longrightarrow \\mathop{\\mathsf{typeerror}}(\\mathop{\\texttt{-}} n_1) \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[TypeErrorNot]{\n",
+ " v_1 \\neq n_1\n",
+ "}{\n",
+ " \\mathop{\\texttt{!}} n_1 \\longrightarrow \\mathop{\\mathsf{typeerror}}(\\mathop{\\texttt{!}} n_1) \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[TypeErrorArith2]{\n",
+ " v_2 \\neq n_2\n",
+ " \\and \n",
+ " \\mathit{bop}\\in \\left\\{ \\texttt{+}, \\texttt{-}, \\texttt{*}, \\texttt{/} \\right\\}\n",
+ "}{\n",
+ " n_1 \\mathbin{\\mathit{bop}}v_2 \\longrightarrow \\mathop{\\mathsf{typeerror}}(n_1 \\mathbin{\\mathit{bop}}v_2) \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[TypeErrorArith1]{\n",
+ " v_1 \\neq n_1\n",
+ " \\and\n",
+ " \\mathit{bop}\\in \\left\\{ \\texttt{+}, \\texttt{-}, \\texttt{*}, \\texttt{/} \\right\\}\n",
+ "}{\n",
+ " v_1 \\mathbin{\\mathit{bop}}e_2 \\longrightarrow \\mathop{\\mathsf{typeerror}}(v_1 \\mathbin{\\mathit{bop}}e_2) \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[TypeErrorPlusString2]{\n",
+ " v_2 \\neq \\mathit{str}_2\n",
+ "}{\n",
+ " \\mathit{str}_1 \\mathbin{\\texttt{+}} v_2 \\longrightarrow \\mathop{\\mathsf{typeerror}}(\\mathit{str}_1 \\mathbin{\\texttt{+}} v_2) \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[TypeErrorPlusString1]{\n",
+ " v_1 \\neq \\mathit{str}_1\n",
+ "}{\n",
+ " v_1 \\mathbin{\\texttt{+}} e_2 \\longrightarrow \\mathop{\\mathsf{typeerror}}(v_1 \\mathbin{\\texttt{+}} e_2) \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[TypeErrorInequalityNumber2]{\n",
+ " v_2 \\neq n_2\n",
+ " \\and \n",
+ " \\mathit{bop}\\in \\left\\{ \\texttt{<}, \\texttt{<=}, \\texttt{>}, \\texttt{>=} \\right\\}\n",
+ "}{\n",
+ " n_1 \\mathbin{\\mathit{bop}}v_2 \\longrightarrow \\mathop{\\mathsf{typeerror}}(n_1 \\mathbin{\\mathit{bop}}v_2) \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[TypeErrorInequalityNumber1]{\n",
+ " v_1 \\neq n_1\n",
+ " \\and\n",
+ " \\mathit{bop}\\in \\left\\{ \\texttt{<}, \\texttt{<=}, \\texttt{>}, \\texttt{>=} \\right\\}\n",
+ "}{\n",
+ " v_1 \\mathbin{\\mathit{bop}}e_2 \\longrightarrow \\mathop{\\mathsf{typeerror}}(v_1 \\mathbin{\\mathit{bop}}e_2) \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[TypeErrorInequalityString2]{\n",
+ " v_2 \\neq \\mathit{str}_2\n",
+ " \\and\n",
+ " \\mathit{bop}\\in \\left\\{ \\texttt{<}, \\texttt{<=}, \\texttt{>}, \\texttt{>=} \\right\\}\n",
+ "}{\n",
+ " \\mathit{str}_1 \\mathbin{\\mathit{bop}}v_2 \\longrightarrow \\mathop{\\mathsf{typeerror}}(\\mathit{str}_1 \\mathbin{\\mathit{bop}}v_2 ) \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[TypeErrorInequalityString1]{\n",
+ " v_1 \\neq \\mathit{str}_1\n",
+ " \\and\n",
+ " \\mathit{bop}\\in \\left\\{ \\texttt{<}, \\texttt{<=}, \\texttt{>}, \\texttt{>=} \\right\\}\n",
+ "}{\n",
+ " v_1 \\mathbin{\\mathit{bop}}e_2 \\longrightarrow \\mathop{\\mathsf{typeerror}}(v_1 \\mathbin{\\mathit{bop}}e_2 ) \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[TypeErrorCall]{\n",
+ " v_1 \\neq x^{?}\\texttt{(}x\\texttt{)} \\mathrel{\\texttt{=}\\!\\texttt{>}} e_1\n",
+ "}{\n",
+ " v_1\\texttt{(}e_2\\texttt{)} \\longrightarrow \\mathop{\\mathsf{typeerror}} (v_1\\texttt{(}e_2\\texttt{)}) \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[PropagateUnary]{\n",
+ " e_1 \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}{\n",
+ " \\mathop{\\mathit{uop}} e_1 \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[PropagateBinary1]{\n",
+ " e_1 \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}{\n",
+ " e_1 \\mathbin{\\mathit{bop}} e_2 \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[PropagateBinary2]{\n",
+ " e_2 \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}{\n",
+ " v_1 \\mathbin{\\mathit{bop}} e_2 \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[PropagateIf]{\n",
+ " e_1 \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}{\n",
+ " e_1\\;\\texttt{?}\\;e_2\\;\\texttt{:}\\;e_3 \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[PropagatePrint]{\n",
+ " e_1 \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}{\n",
+ " \\texttt{console}\\texttt{.}\\texttt{log}\\texttt{(}e_1\\texttt{)} \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[PropagateConst]{\n",
+ " e_1 \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}{\n",
+ " \\mathbf{const}\\;x\\;\\texttt{=}\\;e_1\\texttt{;}\\;e_2 \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[PropagateCall1]{\n",
+ " e_1 \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}{\n",
+ " e_1\\texttt{(}e_2\\texttt{)} \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}$\n",
+ "\n",
+ "$\\inferrule[PropagateCall2]{\n",
+ " e_2 \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}{\n",
+ " v_1\\texttt{(}e_2\\texttt{)} \\longrightarrow \\mathop{\\mathsf{typeerror}}e \n",
+ "}$\n",
+ "\n",
+ "Figure 4: The $\\TirName{TypeError}$ and $\\TirName{Propagate}$ rules for\n",
+ "JavaScripty with numbers, booleans, strings, $\\mathbf{undefined}$,\n",
+ "printing, and first-class functions.\n",
+ "\n",
+ "## Concept Exercises\n",
+ "\n",
+ "Make sure to complete the concept exercises in this section and turn in\n",
+ "this file as part of your submission. However, all code and testing\n",
+ "exercises from other sections are submitted in `Lab3.scala` or\n",
+ "`Lab3Spec.scala`.\n",
+ "\n",
+ "<span class=\"theorem-title\">**Exercise 7 (Evaluation Order)**</span>\n",
+ "Consider the small-step operational semantics shown in\n",
+ "<a href=\"#sec-small-step-operational-semantics\"\n",
+ "class=\"quarto-xref\">Section 5</a>. What is the evaluation order for\n",
+ "$e_1 \\mathbin{\\texttt{+}} e_2$? Explain.\n",
+ "\n",
+ "**Edit this cell:**"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7f776bde-b6d9-4fda-9a42-a1bd2d05357f",
+ "metadata": {},
+ "source": [
+ "???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f6430bd4-aa33-4d31-8ab2-08c78eaa3390",
+ "metadata": {},
+ "source": [
+ "<span class=\"theorem-title\">**Exercise 8 (Changing Evaluation\n",
+ "Order)**</span> How do we change the rules to obtain the opposite\n",
+ "evaluation order?\n",
+ "\n",
+ "**Edit this cell:**"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "27e97fb3-e0b7-45c3-8cf2-9b9603719076",
+ "metadata": {},
+ "source": [
+ "???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0db10e5a-00cb-4360-9e6b-b3ad88719fed",
+ "metadata": {},
+ "source": [
+ "<span class=\"theorem-title\">**Exercise 9 (Using Short-Circuit\n",
+ "Evaluation)**</span> Give an example that illustrates the usefulness of\n",
+ "short-circuit evaluation. Explain your example.\n",
+ "\n",
+ "**Edit this cell:**"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "323a2822-45d2-48f0-9e08-a44a717af6c3",
+ "metadata": {},
+ "source": [
+ "???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1b84a9cd-025f-4e6b-8451-88700db1c441",
+ "metadata": {},
+ "source": [
+ "<span class=\"theorem-title\">**Exercise 10 (Removing Short-Circuit\n",
+ "Evaluation)**</span> Consider the small-step operational semantics shown\n",
+ "in <a href=\"#sec-small-step-operational-semantics\"\n",
+ "class=\"quarto-xref\">Section 5</a>. Does\n",
+ "$e_1 \\mathbin{\\texttt{\\&\\&}} e_2$ short circuit? Explain. If\n",
+ "$e_1 \\mathbin{\\texttt{\\&\\&}} e_2$ short circuits, give rules to\n",
+ "eliminatesshort circuiting. If it does not short circuit, give the\n",
+ "short-circuiting rules.\n",
+ "\n",
+ "**Edit this cell:**"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ef2e3b86-efd9-44e8-ada5-fd6d123e737c",
+ "metadata": {},
+ "source": [
+ "???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6fd4e9a9-fc95-42de-ab66-90aa6f6daa4e",
+ "metadata": {},
+ "source": [
+ "## Testing\n",
+ "\n",
+ "This section has some space to write some tests in our subset of\n",
+ "JavaScript. You might want to work on these tests while you are\n",
+ "implementing `step`. As before, you will add your tests to\n",
+ "`Lab3StudentSpec`. Your interpreter will run the tests against the\n",
+ "expected result you provide. We will write three tests, all of these\n",
+ "tests must properly parse.\n",
+ "\n",
+ "<span class=\"theorem-title\">**Exercise 11 (Test 1: Higher-Order\n",
+ "Function)**</span> Write a test case that has a function that takes a\n",
+ "function value as an argument (i.e., is a higher order function):"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "1adbdab3-bdfa-4f5a-86e0-761adc7c1501",
+ "metadata": {
+ "deletable": false,
+ "nbgrader": {
+ "cell_type": "code",
+ "checksum": "1555b8553ead2a857b18c9afd0b6db41",
+ "grade": false,
+ "grade_id": "test1-higher-order-function",
+ "locked": false,
+ "schema_version": 3,
+ "solution": true,
+ "task": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7e138cea-488d-4395-a908-9721db43e4fe",
+ "metadata": {},
+ "source": [
+ "<span class=\"theorem-title\">**Exercise 12 (Test 2: Recursion)**</span>\n",
+ "Write a test case that uses recursion"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "7b8788b0-fddc-4221-9d04-dfb9e6cb407c",
+ "metadata": {
+ "deletable": false,
+ "nbgrader": {
+ "cell_type": "code",
+ "checksum": "914962b49a6beefb2f6d7313b0b52a87",
+ "grade": false,
+ "grade_id": "test2-recursion",
+ "locked": false,
+ "schema_version": 3,
+ "solution": true,
+ "task": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6afa15bb-a8cc-493b-923b-8e345b60047e",
+ "metadata": {},
+ "source": [
+ "<span class=\"theorem-title\">**Exercise 13 (Test 3: Any Test in this\n",
+ "variant of JavaScripty)**</span> Write another test"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "a7d9f58b-858f-4af6-967b-3c91a58fba92",
+ "metadata": {
+ "deletable": false,
+ "nbgrader": {
+ "cell_type": "code",
+ "checksum": "3fca668afe5d69ccb211d30b0571ee11",
+ "grade": false,
+ "grade_id": "test3-anytest",
+ "locked": false,
+ "schema_version": 3,
+ "solution": true,
+ "task": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a66dc716-10f3-400d-9248-fe3bc26e144a",
+ "metadata": {},
+ "source": [
+ "#### Notes\n",
+ "\n",
+ "- Remember to add these to `Lab3StudentSpec` in `Lab3Spec.scala`.\n",
+ "- Add the JavaScripty code as a string in `jsyStr` and the expected\n",
+ " result in `answer`.\n",
+ "\n",
+ "## Accelerated Component\n",
+ "\n",
+ "For the accelerated component of this lab, we will give rules and\n",
+ "implement the behavior that enables us to match JavaScript semantics. In\n",
+ "particular, we will give rules and implement type coercions for numbers\n",
+ "and strings, and we will update our small-step operational semantics to\n",
+ "use them.\n",
+ "\n",
+ "### Additional Type Coercions\n",
+ "\n",
+ "<span class=\"theorem-title\">**Exercise 14**</span> Give the inference\n",
+ "rules defining the judgment form for coercing a value to a number\n",
+ "$v \\rightsquigarrow n$\n",
+ "\n",
+ "**Edit this cell:**"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "eae0bbfd-22bd-4716-9735-82b855628fa6",
+ "metadata": {},
+ "source": [
+ "???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6030af49-acee-4600-be79-a3475b3c3a2e",
+ "metadata": {},
+ "source": [
+ "<span class=\"theorem-title\">**Exercise 15**</span> Give the inference\n",
+ "rules defining the judgment form for coercing a value to a string\n",
+ "$v \\rightsquigarrow \\mathit{str}$\n",
+ "\n",
+ "**Edit this cell:**"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a709b005-1042-48a4-b9b7-0dbd52ceed1c",
+ "metadata": {},
+ "source": [
+ "???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0a6d8753-a62e-4c3f-a4d9-cdea983e3486",
+ "metadata": {},
+ "source": [
+ "<span class=\"theorem-title\">**Exercise 16**</span> Implement the\n",
+ "`toNumber` and `toStr`coercions."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "1287f427",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def toNumber(v: Expr): Double = ???\n",
+ "def toStr(v: Expr): String = ???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e350fa53-d98f-4ec7-b3e7-dc9f09943ce3",
+ "metadata": {},
+ "source": [
+ "#### Notes\n",
+ "\n",
+ "- If your recall Lab 2, we implemented these functions. They will be\n",
+ " the same here, except we must add the rules for functions.\n",
+ "\n",
+ "### Updating the Small-Step Operational Semantics\n",
+ "\n",
+ "Now that we are allowing type coersions, our operational semantics will\n",
+ "change. For example, consider the following $\\TirName{Do}$ rule:\n",
+ "\n",
+ "$\\inferrule[DoNeg]{\n",
+ " v \\rightsquigarrow n\n",
+ "}{\n",
+ " \\mathop{\\texttt{-}} v \\longrightarrow-n\n",
+ "}$\n",
+ "\n",
+ "This is a new rule for $\\TirName{DoNeg}$, which is read as if $v$\n",
+ "coerces to $n$, then $\\mathop{\\texttt{-}} v$ steps to $-n$. Now that we\n",
+ "are allowing non-numbers to be coerced and then negated, we no longer\n",
+ "have our $\\TirName{TypeErrorNeg}$ rule.\n",
+ "\n",
+ "Note that we only need to update $\\TirName{Do}$ rules with coercions and\n",
+ "remove $\\TirName{TypeError}$ rules. We do not need to update the\n",
+ "$\\TirName{Search}$ or $\\TirName{Propagage}$ rules.\n",
+ "\n",
+ "<span class=\"theorem-title\">**Exercise 17**</span> Explain why we only\n",
+ "need to update the $\\TirName{Do}$ rules with coercions and remove\n",
+ "$\\TirName{TypeError}$ rules, and we do not need to update the\n",
+ "$\\TirName{Search}$ or $\\TirName{Propagage}$ rules.\n",
+ "\n",
+ "**Edit this cell:**"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "dab04724-501e-43b6-9e8b-42a98f57a8ed",
+ "metadata": {},
+ "source": [
+ "???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "27f17dc9-86e6-4b9e-89fb-831e377080a5",
+ "metadata": {},
+ "source": [
+ "One rule of particular interest is $\\TirName{DoArith}$, which we need to\n",
+ "split to account for $e_1 \\mathbin{\\texttt{+}} e_2$ being overloaded for\n",
+ "numbers and strings. Given this, we need to rewrite $\\TirName{DoArith}$\n",
+ "so it does not include $\\texttt{+}$ (and adds coersions), add the rule\n",
+ "$\\TirName{DoPlusNumber}$, and alter $\\TirName{DoPlusString}$ to become\n",
+ "two rules.\n",
+ "\n",
+ "<span class=\"theorem-title\">**Exercise 18**</span> Give these new\n",
+ "$\\TirName{Do}$ rules\n",
+ "\n",
+ "***Edit this cell:***"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "45b4dc5e-15b8-40e0-8c64-678055a78564",
+ "metadata": {},
+ "source": [
+ "???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "71bab51c-f791-418b-a9bc-852fe06aa1ff",
+ "metadata": {},
+ "source": [
+ "Similar to this, our $\\TirName{DoInequalityNumber}$ rule must be split\n",
+ "into two and altered:\n",
+ "\n",
+ "<span class=\"theorem-title\">**Exercise 19**</span> Give the two new\n",
+ "$\\TirName{DoInequalityNumber\\(_1\\)}$ and\n",
+ "$\\TirName{DoInequalityNumber\\(_2\\)}$ rules:\n",
+ "\n",
+ "***Edit this cell:***"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c7ca71c0-6f30-48a6-85e8-91f018d723ac",
+ "metadata": {},
+ "source": [
+ "???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "64400b28-73e0-43ee-a733-01036957fa13",
+ "metadata": {},
+ "source": [
+ "Once we have all of these rules defined, we notice that most of our\n",
+ "$\\mathsf{typeerror}$ rules no longer result in type errors. Therefore,\n",
+ "most of them should be deleted. In fact, the only non-propagate rule\n",
+ "left for type errors is $\\TirName{TypeErrorCall}$, since we are still\n",
+ "not allowed to call something that is not a function (in JavaScript).\n",
+ "\n",
+ "### Update Step\n",
+ "\n",
+ "<span class=\"theorem-title\">**Exercise 20**</span> Now that we have our\n",
+ "type conversion functions implemented and our new rules defined, we are\n",
+ "ready to update `step`. Implement `stepCoerce` by first copying your\n",
+ "code from `stepCheck` and then update based on your new rules."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "bd11e062",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def stepCoerce(e: Expr): Either[DynamicTypeError,Expr] = ???"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0677bd36-105b-499b-9e07-97ee98f41f82",
+ "metadata": {},
+ "source": [
+ "As before, let the rules guide your implementation.\n",
+ "\n",
+ "### Notes\n",
+ "\n",
+ "- None of your other functions should need to be altered.\n",
+ "\n",
+ "## Submission\n",
+ "\n",
+ "If you are a University of Colorado Boulder student, we use Gradescope\n",
+ "for assignment submission. In summary,\n",
+ "\n",
+ "- [ ] Create a private GitHub repository by clicking on a GitHub\n",
+ " Classroom link from the corresponding Canvas assignment entry.\n",
+ "- [ ] Clone your private GitHub repository to your development\n",
+ " environment (using the `<> Code` button on GitHub to get the\n",
+ " repository URL).\n",
+ "- [ ] Work on this lab from your cloned repository. Use Git to save\n",
+ " versions on GitHub (e.g., `git add`, `git commit`, `git push` on the\n",
+ " command line or via VSCode).\n",
+ "- [ ] Submit to the corresponding Gradescope assignment entry for\n",
+ " grading by choosing GitHub as the submission method.\n",
+ "\n",
+ "You need to have a GitHub identity and must have your full name in your\n",
+ "GitHub profile in case we need to associate you with your submissions."
+ ]
+ }
+ ],
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