Questions tagged [semantics]
Semantics formally describe the meaning of some syntax.
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How to evaluate an arbitrary mathematical expression
For Instance, if I allowed the user to pass in expressions like "35 + 2 * 5" as strings, how would I go about writing such a program?
Also, what topics does this question fall under?
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Does lambda calculus become covariant if you fix the base type instead of the lambda calculus term?
In category theory, we are taught that polymorphic functions correspond to dinatural transformations, a k a multivariant natural transformations between functors of mixed variance
$\operatorname{G} \...
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Rationale behind prefix-closure in CSP trace semantics
I'm currently studying Hoare's "Communicating Sequential Processes" (1) and I've come across a concept that I find a bit puzzling. In CSP trace semantics, a process's semantics are described ...
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Definition of "deterministic" semantics in While language
I came across this definition in my book but I'm not sure that I understand it correctly.
Isn't this the same as saying: $\langle S, s\rangle \rightarrow s = \langle S, s\rangle \rightarrow s$ ...
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What is the definition of a redex and what are they for in programming languages literature?
I saw the word "redex" in the context of proramming language theory/semantics in 2018 and now when I was reading a neurosymbolic research paper (machine learning with neural nets + symbolic ...
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When is a stuck state not final and when is a maximal sequence not complete in transition systems?
Reading the book Practical Foundations for Programming Language.
In section 5.1 Transition Systems, the author said that
Whereas all final states are, by convention, stuck, there may be stuck states ...
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Semantics and implementation of side effects
From a practical point of view, how do functional languages with formally specified semantics (like ML) handle side effects like printing? I'm aware of things like the IO monad in Haskell but I'm ...
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How do you justify making algorithm subroutines more efficient when Big-O notation only includes the dominant term?
I don't really understand time complexity, and wanted some clarification in this hypothetical situation.
If I were being given items one by one, and I wanted a list of them all in the reverse order I ...
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Resources for implementing dependent type theory
I want to implement Martin Löf's intuitionistic type theory in a functional language such as Haskell, preferably also implementing a lexer/parser for the language. How should I start approaching it? ...
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Relation between programming languages requiring declaration of variables before use and using the token class $\text{id}$ while parsing
I was going through the text Compilers: Principles, Techniques and Tools by Ullman et. al. where I came across the following excerpt.
Example 4.11. Consider the abstract language $L_1 = \text{ { $wcw$...
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Break keyword outside a loop is syntax error or semantic error?
I am designing a simple compiler for my university project. In my programming language, the break keyword is allowed.
I want to know whether break keyword occurs outside a loop should be a syntax ...
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Why process algebras à la chemical abstract machine are not common?
I recently read the Berry and Boudol's chemical abstract machine [1, 2]. I found the way they describe the semantic really nice and quite intuitive for a process calculus.
The aspect that really ...
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Proving equivalence of two substitutions by induction
I'm trying to prove the following reduction:
$$
t\{x:=u\}\{y:=v\} = t\{y:=v\}\{x:=u\{y:=v\}\}
$$
under the following assumptions:
$x \neq y$
$x$ is not a free variable of $v$ (in symbols, $x \...
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Semantics of "write-once" variables for complex data structures
Question
My use case for what is described below is not a language or compiler implementation, but finding a reasonable semantics for this feature in a an abstract calculus.
Ideally, you give me a ...
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What does it mean by putting (\alpha-\beta) in front of the authors of a paper
When I was searching the publication list of some CS researchers, I sometimes saw them putting a ($\alpha-\beta$) or ($\alpha-\beta$ order) in front of the authors of a paper. What does this mean?
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Denotational semantics of command sequencing
Moved from cstheory.stackexchange upon request
Winskel, in his book The formal semantics of programming languages, on page 58, writes:
C[c0;c1] = C[c1] o C[c0] a composition of relations, the ...
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What should I read to understand semantics of programming languages?
I would like to have a good conceptual understanding of the semantics of programming languages: operational-, denotational-, axiomatic-, categorical-.
Is there a good (standard?) textbook for this?
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Is type-checking "syntactic" or "semantic"?
On the wikipedia page on compilers, it says:
Semantic analysis adds semantic information to the parse tree and builds the symbol table. This phase performs semantic checks such as type checking (...
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Why is the assignment rule the way it is in Hoare Logic?
Why is the assignment rule the way it is in Hoare Logic/Axiomatic Semantics?
I can't wrap my head around why the assignment rule is backwards from what I expected.
I understand Hoare logic is use to ...
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Is the problem of deciding whether two programs have the same semantics decidable?
If I have program and I want to check whether other programs have the exact same semantics or not, could I always build a machine that could make that decision?
This is a question relevant to ...
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Analogue of the topology-computability correspondence for computational complexity
There is an interesting correspondence between notions of topology and notions of computability theory originating from the ingenious idea of Dana Scott to identify computable functions with ...
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What is the denotation for identifiers?
I am trying to understand what is the domain for denotational semantics.
Right now the way I understand denotational semantics is that given some syntax of a program that maps to some mathematical ...
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Finding two store typings that make the same store valid (lambda-calculus with references)
Problem 13.5.2 of Pierce's TAPL's book (page 167) asks:
Can you find a context $\Gamma$, a store $\mu$ and two different store typings $\Sigma_1,\Sigma_2$ such that both $\Gamma | \Sigma_1 \vdash \...
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What is meant by a full abstract model of a lambda-calculus like language?
The simply typed lambda-calculus with numbers and fix has long been a favorite experimental subject for programming language researchers, since it is the simplest language in which a range of subtle ...
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How “logic-based symbolic reasoning” and “ontology” are related?
I have a basic understanding of knowledge representation systems, semantic networks and ontologies. But I can not relate my understanding to the reasoning.
How the reasoning is applied on ontologies ...
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Why there is forward chaining inference engine (reasoner) for description logics only and not for other logics?
Reasoner is forward chaining inference engine (https://en.wikipedia.org/wiki/Semantic_reasoner) as opposite to Prolog backward chaining SAT solver (for queries). Why there is reasoner for description ...
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Why algebraic semantics of programming languages have died out and have not used today?
Algebraic semantics is one type of semantics that uses algebraic expressions for connecting the formal descriptions of initial and final states of some operation of some operation that is defined in ...
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Do the following concepts belong to syntax or semantics?
I am not very sure about the difference between syntax and semantics.
Does each of the following concepts belong to syntax or semantics?
terms
values: terms that are possible final results of ...
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Is natural semantics a total or partial function
I have the following def's
Sns : Stm → (State ֒→ State)
Sns[S] = s' (if <S,s> -> s') else undefined
I'm wondering if ...
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Prooving equations are non derivable in Sigma algebra
Let Σ be the signature made up from the following symbols.
e: 0 arguments function (constant symbol)
f: 2 arguments function
g: 1 argument function
Variable set Var is made up from x,y,z
Let E be ...
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What is the relation between an algorithm and its implementation at the level of code?
Is there any isomorphism or equivalence relation? What strictly bind these two together?
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Formal semantics of a mutable/imperative stack
When introducing formal semantics for data structures, immutable stacks are a nice simple example :
$\mathit{is\_empty}(\mathit{create()})=\mathrm{True}$
$\mathit{is\_empty}(\mathit{push}(e, s))=\...
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Small step vs big step semantics for static analysis?
To be an honest question poster I do not yet fully grasp the difference between small step and big step semantics. There was a good discussion here
My question is if I were to do static analysis on ...
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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 ...
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Negation of the semantics of the Until operator in LTL
I have been looking at the Until operator and the release operator and when introduced to the release operator it was suggested that it is equivalent to:
$\phi R \psi \equiv \neg(\neg\phi U \neg \psi)...
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What is a "model" of lambda calculus?
I know about the concept of the "model" of a logical proposition in the context of mathematical logic: It is a mathematical structure in which that proposition is true.
However, it's not clear to me ...
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The definition of weakest precondition for a non-deterministic language
In the classical IMP language, the definition of weakest precondition is:
definition "wp c Q s ≡ ∃t. (c,s) ⇒ t ∧ Q t"
This is stating that from state s, after ...
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The Law of Excluded Miracle in the language of guarded commands
The definition of weakest precondition is familiar (let me use Isabelle's syntax here):
definition "wp c Q s ≡ ∃t. (c,s) ⇒ t ∧ Q t"
the weakest precondition ...
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How does one prove that Big Step semantics and Small Step semantics are equivalent for IMP?
I know there is this paper but I wanted to do a special case proof for just IMP for fun. So the theorem is:
$$ \langle P , \sigma \rangle \to_{Big} \langle \{ \} , \sigma' \rangle \iff \exists N \...
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Examples of interesting semantics to study during a small project for a graduate Semantics course
I have been following the course Concrete Semantics with Isabelle/HOL. At some point we are given the task to verify a program/extend some semantic construction/prove some mathematical fact. I ...
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What are $(S,\Sigma)$-CCCs?
I was reading this and I was trying to understand the definition of $(S,\Sigma)$-CCC. The first requirement says:
a mapping [[_]] : S → |C|, associating some object [[s]] ∈ |C| to
any s ∈ S;
...
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How is it that programs can be identified with partial functions for programming language semantics?
I was reading about denotational semantics
Broadly speaking, denotational semantics is concerned with finding mathematical objects called domains that represent what programs do. For example, ...
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Proving parametricity for Gallina functions
I have the following definitions
Definition nat'' {X : Type} := (X -> X) -> X -> X.
Definition nat' := forall (X : Type), @nat'' X.
And when I wanted to ...
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How does topic or tag suggestion algorithms work?
I know it's a keyword based search. But sites like Quora have some good suggesting algorithms where the algorithm understands the intent of question asked rather than just the keywords meanings.
For ...
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Unclear logic notation for PFX program rules
I'm very new to this so please bear with me.
I found this document describing the PFX language, a stack-oriented language where the instructions act on a stack and replace the arguments with the ...
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Formal basis for "peephole reasoning" about code
The approaches I've seen to abstractly talking about the semantics of a programming language like Turing machines, various lambda calculi, and Hoare logic seem to be talking about the behavior of ...
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Evaluation semantics: reduction rule for a split statement
Assume a language with statements such as $x := e$, $\text{assume}(e)$, etc., and particularly a $\text{split}\ stmt_1 ... stmt_n$ statement, constructed from $n$ statements. Informally, the semantics ...
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Programmatically checking equivalence of statements
So as part of a theorem-prover/checker, I'm using Prolog to try to determine the equivalence of statements that have been parsed into tree form, e.g. $x=2$ is represented as ...
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Why does substitution terminate?
I'm formalizing some properties of lambda calculus in Coq and I have some problems proving termination of substitution. My terms are defined as:
...
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Semantic/DRT methods for conversational agents / chatbots / dialogue systems - reference request?
The wiki pages about chabots mention that statistical methods, keyword search and precompiled answers are used for the chatbots. But I feel that there should exist different - semantical approach for ...
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