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Questions tagged [operational-semantics]

Operational semantics is a category of formal programming language semantics in which certain desired properties of a program, such as correctness, safety or security, are verified by constructing proofs from logical statements about its execution and procedures, rather than by attaching mathematical meanings to its terms.

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Difference Between Small and Big-step Operational Semantics

What's the fundamental difference(s) between small and big-step operational semantics? I'm having a hard time grasping what it is and the motivation for having the two.
Simon Morgan
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What is this fraction-like "discrete mathematics"–style notation used for formal rules?

In the paper "A Conflict-Free Replicated JSON Datatype", I encountered this notation for formally defining "rules": What is this notation called? How do I read it? For example: the DOC rule doesn't have anything in its "numerator" — why not? the…
natevw
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What questions can denotational semantics answer that operational semantics can't?

I am familiar with operational semantics (both small-step and big-step) for defining programming languages. I'm interested in learning denotational semantics as well, but I'm not sure if it will be worth the effort. Will I just be learning the same…
gardenhead
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What's the difference between a calculus and a programming language?

I think I'm pretty confused about what's called a calculus and what's called a programming language. I tend to think, and might have been told, that a calculus is a formal system for reasoning about the equivalence of programs. Programs have an…
Guido
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What's the difference between: operational, denotational and axiomatic semantics?

Recap of the terms from the dictionary: semantics: the study of meaning in a language (words, phrases, etc) and of language constructs in programming languages (basically any syntactically valid part of a program that generates an instruction or a…
George
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Why does the state remain unchanged in the small-step operational semantics of a while loop?

Usually I see that in the structural operational semantics representation for the while loop, the program state don't change: $(while \> B \> do \>S, \sigma) \rightarrow (if \>B \> then \>S; (while \> B \> do \>S) \> else \> SKIP, \sigma)$ For me,…
El Marce
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TAPL: Explanation and example(s) for satisfied

This question arises from my reading of "Types and Programming Languages" (WorldCat) by Benjamin C. Pierce. On page 36 is the definition for satisfied A rule is satisfied by a relation if, for each instance of the rule, either the conclusion is…
Guy Coder
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Formal model of execution for Java (or general imperative language)

I'm trying to prove some statements about execution in Java programs under some heavy restrictions (basically I have a conjecture that if two methods satisfy a set of constraints for a given input then the are they equivalent - i.e., that return…
Ben Kushigian
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Reduction rule for IF?

I'm working through Simon Peyton Jones' "The Implementation of Functional Programming Languages" and on page 20 I see: IF TRUE ((λp.p) 3) ↔ IF TRUE 3 (per β red) (1) ↔ (λx.IF TRUE 3 x) (per η red) (2) …
galaxybeing
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How are observational equivalence, contextual equivalence, and extensional equality related?

First, some context: I'm reading this blog post by Andrej Bauer. So, I stumbled in these terms: "observational equivalence" and "contextual equivalence". I know almost nothing about operational semantics ... I know it gives meaning for terms by it's…
Rafael Castro
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When would one use equational dynamics?

I'm trying to sort out in my mind the different ways of assigning semantics to a programming language. There are two main methodologies: operational semantics and denotational semantics (I asked a previous question on the relationship between the…
gardenhead
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Is there relation between K-Framework and structural operational semantics?

K-framework strives to give one (instead of two - operational and denotational) semantics for industrial programming languages. The same unification is done by structural operational semantic as well. Are those two frameworks related somehow? Such…
TomR
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What does ⊢ mean in operational semantics?

I have been reading a couple of texts on operational semantics. In [1], the evaluation of expressions is done as in this rule: $\frac{\;\Rightarrow \;n_1\;\;\;\;\Rightarrow \;n_2} { \;\Rightarrow \; n_3}$, where $n_3 =…
josh
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Notation for operational semantics that can be used in code comments

I'm defining an intermediate language for a multi-backend code generator that I'm writing. I want to document the operational semantics for this intermediate language in a way that is readable both from within the source code and generated…
Mike Samuel
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How to decide between operational, denotational, and axiomatic semantics?

Context I'm designing a language which implements lambda calculus and (first-order) predicate calculus, where lambdas behave as the abstraction encapsulating logic, compositionally forming a computational model for higher-order logic. Question How…
Phizo
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