Questions tagged [pl.programming-languages]

Programming languages, in particular, focussing on their semantics.

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5 answers
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Is there such a thing as a state-based programming language?

As anyone knows who has read Alan Turing's paper describing the Turing Machine (On Computable Numbers, With an Application to the Entscheidungsproblem), the syntax he uses is vastly different from ...
8 votes
1 answer
344 views

In logic programming, what would a language with second-order model theory gain?

HiLog is described as a logic programming language with higher-order syntax, but first-order model theory. For example, it allows you to define a map over lists: ...
1 vote
0 answers
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Abstract domain monad

I was reading old lecture from a CS course at Cornel and I have some doubts about the following at 2.4 It defines how to transform domains between each other via a Galois Insertion, more formally: ...
2 votes
2 answers
330 views

A few questions about ISWIM

I recently read Landin's paper "The Next 700 Programming Languages". But I was a bit confused by ISWIM. In particular, are functions first-class objects in ISWIM? It seems not because every ...
10 votes
4 answers
7k views

Difference between Strict Consistency and Sequential Consistency

I understand strict and sequential consistency independently fairly well. Strict C basically enforces the actual order in which the instructions ran on the global clock. Sequential Consistency ...
5 votes
0 answers
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Can a positive elementary inductive definition refer to its own stage comparison relation?

Moschovakis' stage comparison theorem says that the stage comparison relation associated with any positive elementary induction is itself definable by (another) positive elementary induction. But what ...
3 votes
1 answer
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Is there a high level (functional) language compiling to Mixed Integer Linear Programming problems?

Many different kinds of optimization problems can be expressed as Mixed Integer Linear Programming (MILP). The translation is usually very direct, and one has to encode invariants as constraints in a ...
4 votes
0 answers
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Description of the CPS transformation for the typed lambda-calculus

Is there somewhere a precise but hopefully readable account of how the CPS (=continuation-passing-style) transformation applies to the typed lambda-calculus? (Say, simply-typed with product and sum ...
-1 votes
1 answer
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Generating grammar from a string

Given a string generated with a valid grammar, how can I find list of all the valid grammar for that particular string? Problem statement - I'm trying to build a code base scanner, and I'd like to ...
7 votes
1 answer
194 views

Can you regain the Church-Rosser property in languages with continuations?

I'm aware that if you naively add continuations to a language, the Church-Rosser property no longer holds. For example, suppose we have some variant of the STLC with basic arithmetic and integer types....
3 votes
1 answer
75 views

Is Linear Evaluation Parametric?

Parametric functions satisfy free theorems which state that they take related arguments to related results. This is formalized by the notion of parametric transformation introduced in section 5 of ...
7 votes
2 answers
339 views

Efficiently ordering typed programs

Sometimes it is useful to enumerate in increasing order programs that have a given type. A simple example is test generation for compilers: we want to test a new optimising phase and are ...
0 votes
1 answer
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Formal differences between emulation and simulation?

Recently this question came up, and I've been unable to find a concrete answer. When I was reading this paper on CRDTs, I was a little perplexed by the notion of emulation here in theorems 3.1 and 3.2....
1 vote
1 answer
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Is data structure necessarily a functor?

The justification of my conjecture is that (seemly) any data structure can have a mapper that applies a given function $f$ to each element of the structure. A data structure in the end is a container ...
14 votes
4 answers
2k views

Where is the model theory in programming language theory?

I have a background in mathematical logic and am trying to learn some programming language theory. In the syntax of, say, first-order logic, one of the first distinctions you learn about is between ...
9 votes
3 answers
333 views

Resumption-based IO systems?

I've been playing around with resumptions lately, mostly from Abramsky's classic paper Retracing Some Paths in Process Algebra. They are quite slick (basically solutions to the domain equation $R = I \...
-1 votes
1 answer
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Typing rule for corresponding `val` and `let` bindings

$\newcommand{\clet}{\texttt{let }} \newcommand{\cval}{\texttt{val }} \newcommand{\cin}{\texttt{ in }} $I have the syntax for a programming language containing both let-bindings of the form $\clet x = ...
6 votes
2 answers
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What's the difference between an invariant and an "inductive" invariant?

I would like to understand this with an example. Also, are there other kinds of invariants related to these? Thanks!
5 votes
2 answers
348 views

Lambda-calculus: Beta-equivalent terms have the same type

In the simply-typed lambda calculus, how do you prove that: If two terms are beta-equivalent, then they have the same type? My guess is that I should use the subject reduction, and maybe the ...
1 vote
0 answers
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Is it possible to define beta reduction for PHOAS?

I'm using Parametric Higher-Order Abstract Syntax (PHOAS) as a representation for untyped lambda calculus in OCaml: ...
6 votes
1 answer
2k views

How can I prove formally semantic equivalence of programming languages?

I would like to compare two languages which are from different programming paradigms. Both languages are object oriented languages, but one of them a multiparadigm language because it supports ...
13 votes
4 answers
834 views

Can any program be implemented mechanically?

Is it possible to build a single purpose (non Turing complete) mechanical implementation of say, Microsoft Word? Is it possible to implement such things as iterators, first-order functions, the whole ...
6 votes
0 answers
114 views

List Functions That Don't Depend on Length

Intuitively, a polymorphic function of type $f : \forall a. [a] \to [a]$ cannot inspect the type of its elements. This intuition can be captured formally using either natural transformations or ...
9 votes
1 answer
172 views

What is known about reduction by "$P_1$ interprets $P_2$" for generalized programming languages?

Inspired by this answer, let's say that a programming language is given by the data $L=(P,ev)$ where $P$ (the set of "valid programs") is a computable subset of $\Sigma^*$ and $ev$ (the "evaluator") ...
8 votes
0 answers
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Does Bellantoni-Cook safe recursion (or any other implicit characterization of P) admit Kleene's second recursion theorem?

Abstractly, by a programming language that operates on binary strings I mean a set $P$ of programs along with a semantics relation $[p](x) = y$, ``the program $p$ on string $x$ halts with output $y$.&...
7 votes
1 answer
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The precise definition of Normalization By Evaluation?

The Wikipedia article suggests that NbE is a technique for obtaining "the normal form of terms" by translating the object language into abstractions of the meta (host) language: The ...
2 votes
1 answer
90 views

Nominal Tree Languages i.e. with Binders and Infinite Symbols?

I'm wondering if there has been any research done into automata that accept languages of trees that can bind arbitrary variables, and are considered equal under alpha equivalence. I've found so far: ...
1 vote
0 answers
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Alternative notions of bisimulation

Suppose $(S, \Lambda, \rightarrow)$ is a labeled transition system. A bisimulation is a relation $R \subseteq S \times S$ s.t. $\forall \alpha \in \Lambda$ and $\forall p, q \in S$ with $R(p,q)$, $\...
1 vote
1 answer
99 views

Extension of primitive recursion, that is as powerful as System-T

I know that System-T restricted to first-order types is exactly as powerful as primitive recursive functions, because I proved it in Agda. I asked myself, if there is a extension of primitive ...
1 vote
0 answers
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Decision vs search problem specification

Let us suppose we have a sort function. One way of specifying it is to say that a sort function is any function where if the input/output are vectors $I, O$, then $O_i \leq O_j \forall i < j$ and ...
7 votes
1 answer
261 views

Has anyone studied "polynomially compact" metric spaces?

A subspace $S$ of a metric space $A$ is compact if it is complete and totally bounded. Here, complete means that every Cauchy sequence in $S$ has a limit also in $S$. For $S$ to be totally bounded, ...
0 votes
0 answers
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Has there already been research done on how data(e.g. runtime) can improve the development environment of a language?

tl;dr; I am being offered a graduate thesis about how to use data about a languages runtime/static analysis of dependencies etc. and feed it back into the development process. And my question is: Has ...
4 votes
1 answer
142 views

Is there a relation between the techniques used by Dan Willard, versus those of Brown and Palsberg, to exclude diagonalization?

This question extends my inquiry from a previous post [0]. Dan Willard's Self-Justifying Axiom Systems/Self-Verifying Theories [1] and Brown and Palsberg's self-interpreter for F-Omega [2] both employ ...
2 votes
0 answers
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Is there a relationship between Brown and Palsberg's Self-Interpreter for F-Omega and Lawvere's Fixed Point Theorem?

Brown and Palsberg [0] demonstrated an self-interpreter for F-Omega. To do so, they perform "a careful analysis of the classical theorem [of the impossibility of self-interpretation by total ...
3 votes
1 answer
405 views

Similarities and differences between Pie and popular languages with dependent types

The book The Little Typer explains dependent types using a toy language called Pie (https://github.com/the-little-typer/pie). How similar is Pie to the popular languages with dependent types: Coq, ...
0 votes
0 answers
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Programming languages with constraints on values of variables?

Hi Theoretical Computer Science Stack Exchange, I have been wondering if there are programming languages where one can have constraints on values variables can have? Have such approach been used in ...
2 votes
1 answer
177 views

Intuitive way to handle variable binding

Suppose we have an algebraic datatype parameterised by a type variable name, e.g. ...
8 votes
3 answers
754 views

What's the logical counterpart to jumps with arguments on CPS terms?

It's well known that the CPS (continuation-passing style) translation often employed in compilers corresponds to double negation translation under the Curry-Howard isomorphism. Though often the target ...
7 votes
0 answers
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Halting problem for finitary PCF

Is the halting problem decidable for finitary PCF? By "halting problem" I mean the problem of deciding whether a closed PCF term evaluates to bottom under the denotational semantics of PCF. ...
4 votes
1 answer
192 views

Is Barbara Liskov's claim that CLU was the first implemented language to provide linguistic support for data abstraction accurate?

According to this paper by Barbara Liskov, CLU was "The first implemented programming language to provide direct linguistic support for data abstraction". She then defines "data ...
4 votes
0 answers
56 views

Coinduction principle for smash products of pointed cpos

In "Relational Properties of Domains", Pitts gives a coinduction principle for pointed cpos (cppos). In corollary 6.13 (below), he specializes it to cppos constructed as fixed points of cppo-...
6 votes
3 answers
2k views

How does type theory change how one thinks about programming?

I have been dabbling in HoTT and I am convinced that dependent type theory is much more suitable than set theory for proof assistants. Now, this made me wonder - how fundamental is Type Theory ...
0 votes
0 answers
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Is BigInteger-based Brainfuck Turing Complete?

All of the proofs of Turing-Completeness I've found for Brainfuck rely on its cells being fixed-width integers that wrap around upon over/underflow. The "parent language" P'' on which ...
2 votes
0 answers
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Reference request: characterisation of simultaneous substitution

For simply typed λ-calculus, a simultaneous substitution from $\Gamma$ to $\Delta$ is concretely a type-preserving map from variables in $\Delta$ to terms in $\Gamma$. See, for example, Programming ...
3 votes
0 answers
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syntax and semantics for transfinite algorithms

Let's say I wanted to informally describe a very simple algorithm for searching through an (undirected) finite connected graph $G = (V,E)$. I could define, for each natural number $n$, a set $S_n$ and ...
10 votes
0 answers
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What is the "standard" lambda-calculus model for bicartesian closed categories?

(I'm familiar with the lambda-calculus, less so with its categorical models.) It is well-known that cartesian-closed categories are in tight correspondence to the simply-typed lambda-calculus with ...
-2 votes
1 answer
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Resource for Understanding this Notation [closed]

I am trying to read this paper: https://arxiv.org/abs/1510.00925. I am familiar with grammars, but I cannot understand the notations in figure 1. Can anyone suggest a resource or book where I can ...
6 votes
1 answer
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What are the pros and cons for type cases in dependent type theories?

Pattern matching on $\cal U$ is allowed in XTT and Idris2 (for unerased types), and that implies the injectivity of type constructors (that's just my intuition, though -- I also wonder how do I prove ...
0 votes
1 answer
153 views

What does x.y notation mean?

In Harper's PFPL (Ed. 2, top of page 8), this notation is used but I don't see a definition. What does $x.y$ mean?
4 votes
1 answer
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Is this variant of bitwise cyclic tag Turing-complete?

Cross-posted to MathOverflow. CT is an extremely minimalist programming language that can simulate arbitrary tag systems, and is therefore Turing-complete. A program consists simply of a string of 3 ...

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