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There are many depending on where you want to start and what exactly you want. Usually textbook start with giving semantics to the While or IMP language and then give references to semantics of lambda calculus (typed untyped) unless you are reading Gunter. I am listing down a few below that I have referenced a number of times: Operational Denotational and ...


3

The simplest proof is giving a model where types are interpreted as propositions, and terms as proofs, then observing that $\forall \alpha.\alpha$ is interpreted as the false proposition, so any $\cdot \vdash t : \forall \alpha.\alpha$ would be a proof of falsehood. It is important to remember that $\forall \alpha.\alpha$ is only uninhabited for sure in the ...


2

The WebAssembly has a formal specification, a reference interpreter implemented in OCaml, and a bunch of advanced tools. And it's the Real Thing. If you're looking for something educational and do not care about usability, you can have a look at my Programming Langauges Zoo. Two languages have VMs and compilers: The functional language MiniML has a virtual ...


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I think something somewhat trivial is happening here, that is if the let binding is not used, then you can let bind an ill-typed term, e.g. if: $t =\ $let x = (if 3 then 4 else false) in 5 then $t^* =\ $ 5 which is well-typed in $\mathrm{HM}$, even though t is not. If every let-binding is used, though, then this pathology can't happen.


2

The short answer to your question is "for productivity and portability". Let me expand on this. The very first generation of computers were indeed programmed directly in binary, either by entering each binary instruction using physical switches on the computer itself or by some simple bulk loading mechanism such a reading and loading instructions from a ...


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(I might be wrong, but this is my understanding.) Callbacks, especially as seen in JS, are analogous to a semantic model known as Continuation-passing style (CPS). In CPS, a program’s flow is modeled as a series of functions, each of which takes in a continuation, and calls the continuation with the function’s result when finished. As stated, this is also ...


1

Yes, callbacks belong to to the family of Higer-order functions. Because they're one of the simplest members of the family, they're often encountered in practice.


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Your (let (x) 'x) will just return the atom x, and obviously all of those are the same. That you define variables called x (and give them no value whatsoever, and never use them) is just confusing the issue. I.e., your code is a roundabout way to write (eq 'x 'x). How could a name "escape" from a lexical scope? The scope is precisely where the name has a ...


1

You ask a good question. Why doesn't a CPU just execute say C++ directly? Why go to the trouble of translating it first (i.e. compiling or interpreting) into some arcane machine language (Intel x86)? The answer is all to do with flexibility. Computer hardware architectures are designed to be able to execute a broad range of programs. To enable this ...


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The first rule T-Typetest is a type-checking rule. Let's read it together. Firstly, $\Gamma$ is not important (on a first reading at least). We have the following premises: $t_1$ has type $S$ if $x$ has type $T$ then $T_2$ has type $U$ $t_3$ has type $U$ The conclusions is, that we get an expression of type $U$ (I think your transcription should have "$: U$...


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I'm going to go against every other answer posted so far; they were reasonable at the time, but are now somewhat obsolete. I posit that true answer is, in fact: It's totally possible, and some very big companies went ahead and did exactly that. WebAssembly (abbreviated Wasm) is a binary instruction format for a stack-based virtual machine. Wasm is ...


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