Questions tagged [type-inference]

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Conservative Approximation of Kleene-Mycroft Iteration for Polymorphic Recursion?

To perform type inference in the presence of polymorphic recursion, one can use a Kleene-Mycroft iteration to compute the principal type of an expression. To type $\mathsf{fix}\ f\ldotp e$, we define $...
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1answer
108 views

Verified type checkers

Most of the work on programming language metatheory mechanization focus on the declarative properties of the languages (e.g., type soundness), but fail to address the algorithmic side, i.e. the type ...
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1answer
159 views

Can Isorecursive types capture mutually recursive data types?

I've been reading TAPL, and reached the section on recursive types. I understand the type operator $\mu$. For example, the two type expressions are equivalent ...
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2answers
225 views

Extending Hindley-Milner to type mutable references

I have been trying to implement a programming language from scratch, and have gotten reasonably far. It reads just like Python, other than the fact that let is used ...
3
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1answer
135 views

Universe polymorphism: the inference of universes and their constraints

When making a universe polymorphic definition in Coq, universes and their constraints are automatically inferred. Are they somewhat the most general ones (in a sense similar to the principal type ...
6
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1answer
160 views

General Induction Principle

Let us suppose that we want to provide for each inductive type an axiom describing the associated elimination/induction principle. For example, given a definition for the naturals: ...
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2answers
175 views

Decidability of type inference and type checking in MLTT

In Martin-Löf's An Intuitionistic Theory of Types: Predicative Part it is proved that type checking $a \colon A$ is decidable subject to $a$ being typeable in the first place, by proving a ...
7
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1answer
245 views

Avoiding Cycles with Unification and Subtyping

Context I realize that subtyping often doesn't admit principle types, and that inference in the presence of subtypes is undecidable. I'm working in a context where typechecking should simply fail ...
6
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1answer
949 views

What is the difference between System F and Hindley-Milner type system?

Hindley-Milner type system is some restriction of System F, which allows type inference. But from simple descriptions I cannot see, what is the difference between them?
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3answers
872 views

What should a proof of correctness for a typechecker actually be proving?

I've been programming for several years, but am very unfamiliar with theoretical CS. I've recently been trying to study programming languages, and as part of that, type checking and inference. My ...
5
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1answer
225 views

Recursive types and the empty type

In John Mitchell's book "The Foundations of Programming Languages", he considers a typed lambda calculus with unit, exponential, product, (binary) coproduct types, and arbitrary recursive types (p126)....
7
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2answers
297 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 ...
10
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2answers
285 views

Higher-rank polymorphism over unboxed types

I have a language in which types are unboxed by default, with type inference based on Hindley–Milner. I’d like to add higher-rank polymorphism, mainly for working with existential types. I think I ...
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2answers
685 views

Subtypes as subsets of SML datatypes

One of the few things that I dislike about Okasaki's book on purely functional data structures is that his code is littered with inexhaustive pattern matching. As an example, I'll give his ...
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0answers
40 views

Abduction in a Herbrand Constraint System

I have a simple constraint system with a finite set $C$ of constant symbols, an infinite set $V$ of variables, and two relation symbols - $R_1$, a preorder, and $R_2$, an equivalence relation. ...
7
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1answer
310 views

Decidability of parametric higher-order type unification

I'm making a language that has higher-kinded types (like Haskell) and allows type synonyms to appear partially applied in type expressions (unlike Haskell). As an example, consider the following ...
5
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1answer
335 views

Can all linear lambda calculi be linearity checked syntactically?

Given a lambda calculus with explicit linearity and usual application and abstraction, can the linearity check be done on an untyped syntax tree if we keep track of the structural types? Are the ...
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1answer
65 views

Why is the polymorphic weight 1

I am reading through through a paper called HMF: Simple Type Inference for First-Class Polymorphism by Daan Leijen of Microsoft Research. In the paper it describes how to calculate the polymorphic ...
5
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1answer
204 views

Can type inference be classified in two groups: unification-based and control-flow-based?

I recently came across the 1995 paper Safety analysis versus type inference (pdf link) by Palsberg and Schartzbach that contrasts unification-based type inference and static analysis methods based on ...
5
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1answer
521 views

Is this behavior in a programming language inconsistent?

I'm developing a tiny programming language to try to wrap my head around type inference, and I'm trying to figure out if its behavior makes sense or not. Here's the problem: The identity function <...
7
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1answer
781 views

Practical implementation of Hindley–Milner with typeclasses — matching vs most general unifier

I'm trying to get a deep understanding of a (great) paper "Typing Haskell in Haskell". I'm having difficulties understanding the implementation of two methods there — the ...
3
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1answer
463 views

Generalization and instantiation of types in Hindley-Milner type inference

I’m currently reading Heeren, B., Hage, J., & Swiestra, D. (2002). Generalizing Hindley-Milner Type Inference Algorithms in an attempt to understand Hindley-Milner-style type inference. I'm ...
3
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1answer
502 views

Occurs check in type inference

I'm reading about type inference in chapter 30 of Programming Languages: Application and Interpretation and I'm trying to understand exactly how the occurs check works in an example I came up with. ...
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1answer
897 views

What are the practical issues with intersection and union types?

I'm designing a simple statically typed functional programming language as a learning experience. It appears that the type system I have implemented so far could (with a little extra work) ...
9
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1answer
422 views

A simple proof that decidability of typability in System F ($\lambda 2$) implies decidability of type checking?

Suppose we don't know Joe B. Wells's result from 1994 that both typability and type checking are undecidable in System F (AKA $\lambda 2$). In Barendregt's Lambda calculi with types (1992) I found a ...
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1answer
131 views

How to generalize a map of type for many operators?

I am formalizing the type system for a small language, and thus writing inference rules. Taking unary - operator for example, its entry may be a number as well as ...
9
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2answers
322 views

Research on call-site based type inference?

I'm trying to learn more about whole-program type checking and type inferencing systems that use information from function call sites to compute type information (in addition to the standard approach ...
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3answers
2k views

Type inference for imperative statements other than assignment

In my search for research papers about type systems for imperative languages, I only find solutions for a language with mutable references but without genuine imperative control structures such as ...
9
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1answer
455 views

What is the role of the Bicolored Calculus of Constructions?

So, I'm reading a bit about elaboration, particularly, algorithms based on the Bicolored Calculus of Construction, and I'm a bit confused. I don't understand what exactly the purpose of the $CC^{bi}$ ...
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2answers
391 views

the type system does not tell the whole story due to “exception”

I am wondering whether it is a bad style to use "exception". For example, in Ocaml, the exception does not appear as the .mli file. So it appears to me that "exception" is something that cannot be ...
7
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1answer
325 views

Implications of the rule of cumulativity in the Calculus of Constructions

Please help me understand some type theory research. As suggested in "Type Checking with Universes" by Robert Harper and Robert Pollack, we can add the following rule to our otherwise standard COC or ...
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2answers
424 views

With equirecursive types are there downsides to making all types potentially recursive?

By this I mean to ask, is it a bad idea to have all type constructor term expressions abstracted with $\mu$ just in case they need to be recursive? For example, $Bool : Type;$ $Bool = (\mu Bool' ...
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2answers
1k views

Context Sensitive Grammars and Types

1) What, if any, is the relationship between static typing and formal grammars? 2) In particular, would it be possible for a linear bounded automaton to check whether, say, a C++ or SML program was ...
5
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1answer
166 views

Nested automatization of type inference of forall elimination

Following a previous question about how to automatize the type inference in a forall elimination of an application, now suppose we want to do the same but for a nested forall, say $(\Lambda X_1.\...
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1answer
430 views

In System F à la Church, can we automatize type inference for the for-all elimination?

The question is the following. Generally when one have a term like $\Lambda X.t$, we can eliminate the forall by applying this term to a type, as instance $(\Lambda X.t)[T]\to t[X:=T]$. Now, suppose ...
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395 views

Type inference with subtype constraints and polymorphism using Trifonov and Smith's constraint maps

Trifonov and Smith's Subtyping Constrained Types (1996) introduces constraint maps to represent consistent closed constraint sets (such maps providing sets of lower and upper bounds to each variable ...