Questions tagged [polymorphisms]
The polymorphisms tag has no usage guidance.
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Polymorphism in SMT solvers
What are the theoretical limitations that avoid the adoption of type polymorphism à la System F in current SMT solvers?
I work in the context of program verification and I am surprised by the great ...
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1answer
43 views
Can we somehow get functoriality from purely type-theoretic reasoning?
In this question, I asked about how to prove naturality from parametric polymorphism, using parametricity. The current answer to that question simply assumes that the functors in question satisfy the ...
7
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2answers
186 views
Rigorous proof that parametric polymorphism implies naturality using parametricity?
This question asks for an informal explanation of why all polymorphic functions between functors are natural transformations (This is a claim made by Bartosz Milewski). One answer to that question ...
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1answer
24 views
"Reshaping" vs Polymorphism In Data Wrangling
A lot of the work in data science -- machine learning in particular --involves "reshaping" arrays, tables, and other data structures. These data transformations are not really lossy ...
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1answer
246 views
What's the difference between Row Polymorphism and Structural Typing?
The definitions I've stumbled across seem to indicate they express the same idea. That's that the relationship between record types is determined by their fields (or properties) rather than their ...
4
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1answer
373 views
Why do we need a separate notation for П-types?
Main
I am confused about the motivation behind the need for a separate notation for П-types, that you can find in type systems from λ2 on. The answer usually goes like so - think about how one can ...
2
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3answers
106 views
Uncurrying and Polymorphism
How do we uncurry functions when they are polymorphic? For example, is it possible to uncurry the following types? If so what is the uncurried type?
$\forall X. X \rightarrow int \rightarrow X$ ?
$...
4
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1answer
151 views
Why are all polymorphic functions between functors natural transformations?
Bartosz Milewski's Category Theory for Programmers says the following:
A parametrically polymorphic function between two functors (including the edge case of the Const functor) is always a natural ...
2
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2answers
63 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
142 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
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1answer
97 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 ...
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0answers
78 views
Do Rank-1 (prenex) polymorphism and Predicative polymorphism mean the same?
https://en.wikipedia.org/wiki/Parametric_polymorphism says:
Rank-1 (prenex) polymorphism
In a prenex polymorphic system, type variables may not be instantiated with polymorphic types.[4] ...
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60 views
What are the relation and differences between reification and type passing semantics?
https://en.wikipedia.org/wiki/Type_erasure says
type erasure refers to the load-time process by which explicit type annotations are removed from a program, before it is executed at run-time. ...
1
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2answers
221 views
How can an existential type be defined in terms of universal type?
In Types and Programming Languages by Pierce, how does the following achieve the definition of an existential type in terms of universal type, by polymorphic version of Church encoding of pairs?
...
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1answer
67 views
Why are ADT packages opened immediately after they are built, while existential objects opened as late as possible?
Section 24.2 in Types and Programming Languages by Pierce defines ADTs in existential types:
A conventional abstract data type (or ADT) consists of (1) a type name A, (2) a concrete representation ...
0
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1answer
120 views
How can mainstream OO languages support strong binary operations by classes?
Section 24.2 in Types and Programming Languages by Pierce compares ADT and existential objects,in terms of how well they support strong binary operations:
Other binary operations cannot be ...
0
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1answer
50 views
Are type abstraction values and universal types not for non functions, but only for functions?
In Types and Programming Languages by Pierce, Chapter 23 Universal Types has a summary of System F in the following figure, in particular, "type abstraction values" and their types "universal types".
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1answer
43 views
How does this allow list operations to be applied to lists with elements of any type?
In Types and Programming Languages by Pierce, Chapter 11 is simple extensions of the simply typed lambda calculus with any simple base types. Section 11.12 introduces Lists.
How does the section ...
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1answer
38 views
What does it mean that a let-binding can be treated polymorphically, only if its right-hand side is a syntactic value?
Types and Programming Languages by Pierce says:
22.7 Let polymorphism
A final point worth mentioning is that, in designing full-blown
programming languages with let-polymorphism, we need to ...
0
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1answer
32 views
What is the purpose of erasing a type application to a term-application in parametric polymorphism?
From Types and Programming Languages by Pierce
23 Polymorphism
23.7 Erasure and Evaluation Order
in a full-blown programming language, which may include side-
effecting features such as ...
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0answers
106 views
Is it possible to write a fully-decidable type system for the J language?
I'm experimenting with the J array language, a dynamically-typed array language with mutable assignment, subtyping, and function overloading (just like traditional APL).
It is unclear to me whether ...
5
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3answers
241 views
How exactly do we define parametric polymorphism?
My naive distinction between parametric polymorphism and ad-hoc polymorphism, is that:
In parametric polymorphism, the type is given as a variable: (pseudocode)
Function f: <.Type T> T $\to$ T {...
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0answers
92 views
Which languages, if any, implemented parametric polymorphism before ML?
In particular, was there any kind of implementation at the time Christopher Strachey wrote Fundamental Concepts in Programming Languages?
In that work, Strachey lists Ad Hoc and Parametric ...
6
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1answer
191 views
Relationship between Higher Kinded Polymorphism, type inference, and Currying
On Hacker News there is an interesting exchange about the async\await RFC for Rust.
The author of the proposal withoutboats is responding to a comment about the ...
2
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1answer
131 views
How to implement polymorphism in a turing complete environment?
I'm currently programming in an unnamed turing complete language which has support for pointers, primitive data types, structures, closures, and garbage collection, among other things.
I'm trying to ...
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3answers
2k views
Is subtype polymorphism a kind of ad hoc polymorphism?
"Ad-hoc polymorphism is obtained when a function works, or appears to work, on several different types (which may not exhibit a common structure) and may behave in unrelated ways for each type." – ...
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1answer
157 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:
...
7
votes
2answers
727 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 ...
0
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2answers
267 views
Can String be a subtype of Character in a programming language?
Could a programming language be designed so that there is an inheritance relationship between string and character (both of ...
3
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1answer
187 views
how type checking fails?
I was doing a type checking example in system f sub on paper to understand how it works.
according to Pierce's book Types and Programming Languages, numbers and their types are following in system f ...
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1answer
56 views
Can a $k$-ary relation have polymorphisms of arity greater than $k$?
To quote Hubie Chen's A Rendezvous of Logic, Complexity, and Algebra (2009) on constraint satisfaction and complexity,
An operation $f : D^m \to D$ is a polymorphism of a relation $R \subseteq D^k$
...
