Questions tagged [type-checking]
verifying that a variable, expression or value has the declared type
99
questions
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12 views
What is the meet of two polymorphic function types in “Local Type Inference”
How does one take the meet of two polymorphic function types? The issue I'm finding is that the two function types can have a different number of type variables. Or the same number of variables, but ...
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0answers
45 views
How do program types such as natural numbers figure into the Curry-Howard Isomorphism?
In Coq, the nat, the type of natural numbers, has type Set. By the Curry-Howard Isomorphism, all propositions of type ...
6
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2answers
93 views
Does strong typing contribute to better performance optimization by compiler?
Do guarantees provided by the type systems enable better performance optimizations by the modern compilers? I found a 20+ year article suggesting that it would. Also, intuitively speaking, knowing ...
3
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1answer
124 views
Is occurrence typing (flow-sensitive typing) a form of dependent typing?
I take occurrence typing to be typing that "... allows the type system to ascribe more precise types based on whether a [check] succeeds or fails." (adapted from the Racket docs with "...
3
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1answer
68 views
Which language is used to construct a type system?
Typically, OCaml and Scala seem to be used for designing any programming languages tool. But what features offer them an edge over other languages.
A related question, is a type system for a language ...
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0answers
28 views
Is the borrow checker mechanism in Rust based on quantitative types?
I was trying to understand if the borrow checking mechanism for references is actually a quantitaive type in disguise because it does look very similar. In case these are just similar but unrelated ...
2
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1answer
65 views
How does the undecidability of Extensional Martin-Löf Type Theory apply to real type-checking compilers?
It is claimed in many sources (for example, here) that adding a rule like "if Id(X,Y) then X really equals ...
2
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1answer
70 views
Type-checking function calls with functional subtyping
I'm relatively new to the topic. Suppose that you want to type-check an expression of the form f(a), i.e. a function call. Assuming that all the declarations are ...
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0answers
65 views
Consistency of a set of bidirectional typing rules
Main
Is there any way to algorithmically check the consistency of a set of bidirectional typing rules, e.g. the absence of cycles and the uniqueness of the derivation tree? This problem is naturally ...
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2answers
81 views
What is the single type in a dynamic typing language?
Regarding static typing and dynamic typing, Practical Foundation of Programming Languages by Harper says:
There have been many attempts by advocates of dynamic typing to
distinguish dynamic from ...
2
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1answer
56 views
Do dynamic/static languages associate types or classes to values or variables?
In Practical Foundation of Programming Languages by Harper
There have been many attempts by advocates of dynamic typing to
distinguish dynamic from static languages. It is useful to consider
...
0
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1answer
40 views
Doubts on the behavior of Unit Type in a type system
I have a doubt about the Unit Type in the context of Type Theory and its use in different case scenarios.
To start with, a Unit Type can be seen as a nullary Product Type, namely Unit, with one only ...
5
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2answers
587 views
Does the underlying computational calculus in type theories affect decidability?
I'm looking for a high-level explanation although if that isn't possible or difficult, I'd prefer references to books/papers.
I understand that modern type theory is inspired by Curry-Howard ...
2
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2answers
62 views
What is the differences and similarities between refinement type and liquid types?
Looking at the examples here and here both refinement type and liquid types look very similar. What are the differences and similarities?
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3answers
353 views
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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1answer
49 views
Dynamic testing of down casts as explained in TAPL
On page 195 of Pierce's TAPL book, he states that one can replace a down-cast operator by some sort of dynamic type test. Then he gives the following rules:
T-Typetest:
$\dfrac{\Gamma \vdash t_1:S \;...
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votes
5answers
361 views
Are assembly languages untyped?
I'm writing my Bsc thesis about type systems of various languages and I want to have a short section about assembly languages. Initially I thought I'll bring up assembly as a counter example to ...
3
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0answers
26 views
What the type of an overloaded function should be?
Anecdotally, Virgill III language forbids overloading since overloading resolution is at odds with the language support of functions as first-class citizen, when resolution can't happen at compile ...
2
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0answers
88 views
How could 'Complete and Easy Bidirectional Type Checking' handle invariant parameters on type constructors
The paper Complete and Easy Bidirectional Typechecking for Higher-Rank Polymorphism provides examples for checking if one function type is a subtype of another, which I think demonstrates checking ...
2
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2answers
54 views
Are type variables really only used in mathematical conversation about types?
Are type variables really only used in mathematical conversation about types? i.e. are type variables (meta-variables that only contain the type classification label) only exist in proofs for types ...
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1answer
119 views
What is the difference between $ \alpha \to \alpha $ vs $ \forall \alpha. \alpha \to \alpha$?
I was studying polymorphic types and I was finding the distinction with monomorphic types difficult to pin down (context CS 421). From the course I linked the have the following (vague attempt) at a ...
5
votes
1answer
90 views
What does $ \forall \alpha_1, \dots , \alpha_n . \tau $ mean formally as a type?
I was learning about polymorphic types but I couldn't understand the notation, can someone explain it means (context cs421 UIUC):
$$ \forall \alpha_1, \dots , \alpha_n . \tau $$
its supposed to be a ...
10
votes
1answer
1k views
Why does Coq include let-expressions in its core language
Coq includes let-expressions in its core language.
We can translate let-expressions to applications like this:
let x : t = v in b ~> (\(x:t). b) v
I understand ...
8
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1answer
520 views
Representation of the concatenation at the type level
I would like to learn more about concatenative programming through the creation of a small simple language, based on the stack and following the concatenative paradigm.
Unfortunately, I haven't found ...
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0answers
41 views
Real world example of contraction and weakening
Can you provide me a real world example of contraction and weakening in the type system of a popular language like Java, Kotlin, etc.? I heard that Rust has got explicit contraction but I donĀ“t ...
3
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0answers
155 views
Type inference for System F-omega
There have been some nice papers about simple type inference for System F: "HMF: Simple Type Inference for First-Class Polymorphism", "Practical type inference for arbitrary-rank types", and "Complete ...
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5answers
1k views
Is there any use case for the bottom type as a function parameter type?
If a function has return type of ā„ (bottom type), that means it never returns. It can for example exit or throw, both fairly ordinary situations.
Presumably if a function had a parameter of type ā„ it ...
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1answer
51 views
Add type checking/inference to my programming language
I am currently creating my own compiled programming language, and I have come to a point where I would like to start working on the type system and introduce some type checking. Ideally I would like ...
1
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1answer
61 views
How does C++'s type checking work when passing overloaded or templated functions as parameter
As I understand, C++ in general features 'one-way' type checking. That is checking the sub-expressions and get their types, and see if the types so far satisfy the constraints imposed by the current ...
4
votes
2answers
211 views
Check if a lambda constructor is well-typed
In basic type inference for š-calculus with parametric polymorphism à la Hindley–Milner,
when can we say that we cannot give a type to a lambda constructor?
For example
$$(Ī»x.Ī»y.y(x\ ...
5
votes
1answer
124 views
Static type analysis with dynamic scoping?
Both in school and out, I have only ever encountered dynamic scoping paired with dynamic typing. Is there any published work (even if just academic, not yet implemented in a "real" programming ...
6
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1answer
79 views
Type system with subtyping on abstract data types?
Consider this example on binary trees in some ML-like language:
...
2
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0answers
35 views
Question about let syntax in type systems
I'm on the Wikipedia page for Hindley-Milner type systems, on the section about "let polymorphism": https://en.wikipedia.org/wiki/Hindley%E2%80%93Milner_type_system#Let-polymorphism
I'm a bit ...
2
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0answers
26 views
How does the free program identifiers (fpi) extend over constraints and type schemes in $HM(X)$?
Chapter 10 of Advanced Topics in Types and Programming Languages; gives a very comprehensive description of type inference by constraints solving.
They introduce the free program indentifiers of an ...
5
votes
1answer
311 views
Drawbacks of adding type equality to 1ML
In the 1ML ā Core and Modules United (F-ing First-Class Modules) paper, the author gives the following example for why module types do not form a lattice under subtyping:
...
7
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2answers
396 views
LET REC recursive expression static typing rule
I'm taking a programming languages course and had a question regarding the typing rules for a recursive let rec expression in a static typing system.
To be more ...
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0answers
56 views
Propositional extentionality in the lean theorem prover?
Propositional extentionality in the lean theorem prover is stated as the following axiom:
axiom proptext {a b : Prop} : (a $\iff$ b) \to a = b
My confusion about this is as follows: Previously Iā...
2
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0answers
108 views
Relation between āformal verificationā, āformal proofā, and ātype systemsā for software verification?
I have a vague understanding what formal verification is about, a vague understanding of what the cutting edge is of type theory for programming languages, and a better understanding of formal proofs.
...
2
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0answers
40 views
What is the difference between ADTs and ASDLs?
ASDL stands for Abstract Syntax Description Language (ASDL), whereby ADT stands for Algebraic data type.
By looking at Python.asdl it appears to me to be the same thingy, just with different names, ...
5
votes
1answer
106 views
Type system for Query DSL with only simple GADTs: what typing judgments are needed?
Background
I have several F# codebases with reasonably high level of complexity of code. In order to convince myself that the code is solid I do whatever I can to write as much of it as possible type-...
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2answers
122 views
Symbolic Evaluation for Type Inference in a Dynamic Language
Say I have the following contrived example code:
...
3
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1answer
165 views
Assertion of Type Inference Rules/Type Checking
I have a problem in a book I am trying to accomplish.
I understand the overall type of the expression is boolean and how it derives. (y * x) will be rule 4 (counting from top right). (y * x) + x when ...
2
votes
1answer
84 views
What is the type system (or class of type systems) that that ensures all your tree Branches end in Leaves?
I've come across this situation numerous times in the past few years where I have some classes like (pseudo-Java):
...
11
votes
2answers
230 views
Reducing products in HoTT to church/scott encodings
So I am currently going though the HoTT book with some people. I made the claim that most inductive types we will see can be reduced to types containing only dependent function types and universes by ...
10
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1answer
3k views
Is there a difference between type safety and type soundness?
I've been trying to tease apart the definitions of type safety and type soundness and I'm having a heck of a time of it. I asked a professor recently and after a bit of thought he said that there ...
4
votes
1answer
186 views
Linear/affine lifetimes without subtyping
Are there any type systems similar to rust that don't depend on subtyping ? Can we express that one value must be consumed or dropped before another? For instance if I had an array of huge values on ...
4
votes
1answer
143 views
What's the advantage of “value restriction” over its alternatives?
What is the motivation to pick "value restriction" over other candidates?
Examples of alternatives:
Enclosing pureness into the function type, for example:
...
8
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0answers
280 views
Type-classes for type inference
I'm creating a semantic analyzer with type inference. For the basics I've got a type variable and a type construct with name and a list of types.
I want to support overloading and I know that Haskell ...
7
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2answers
710 views
Higher-ranked polymorphism without explicit application or subtyping?
So, I'm familiar with two main strategies of having higher-ranked polymorphism in a language:
System-F style polymorphism, where functions are explicitly typed, and instantiation happens explicitly ...
8
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2answers
1k views
Relation between type-checking decidability, typability decidability and strong normalization
Yo! This is probably a stupid question, however I've never seen it written down explicitly if, for instance, decidability of type-checking is equivalent to the strong normalization property. Therefore ...
