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Topic: Type inference

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	Type inference for Python \| Lambda the Ultimate
		A question was raised in that thread having to do with why static type inference in these languages is difficult.
		In another discussion, I suggested type feedback as a way to collect otherwise undeclared type info to augment a DT (dynamically typed) language when an IDE execution environment can be assumed as context for collecting and storing info, and presenting some UI to a developer for using that info.
		The whole point of "soft" type inference approaches is to be able to get some of the benefits of static type analysis without the requirement that the entire program be explicitly well-typed.
	www.lambda-the-ultimate.org /node/1519 (1783 words)

	Type inference and union types \| Lambda the Ultimate
		At the time of type checking we may freely propogate information about the type of a union without worrying about what its compiled representation will be, so it doesn't make sense to me to say that the inference algorithm can not cope with untagged union types.
		Type inference with untagged unions is not neccessarily completely useless.
		These would present somewhat of a problem for a type inference algorithm, since the invariants may be of arbitrary complexity and thus cannot necessarily be evaluated at compile time.
	lambda-the-ultimate.org /node/1814 (1918 words)

	Type inference - Wikipedia, the free encyclopedia
		Type inference is a feature present in some strongly statically typed programming languages.
		Type inference refers to the ability to automatically either partially or fully deduce the type of the value derived from the eventual evaluation of an expression.
		The origin of this algorithm is the type inference algorithm for the simply typed lambda calculus, which was devised by Haskell B. Curry and Robert Feys in 1958.
	en.wikipedia.org /wiki/Type_inference (705 words)

	Datatype - Wikipedia, the free encyclopedia
		In computer science, a datatype or data type (often simply a type) is a name or label for a set of values and some operations which one can perform on that set of values.
		Types usually have associations either with values in memory or with objects such as variables.
		Type systems that allow polymorphism generally do so in order to improve the potential for code re-use: in a language with polymorphism, programmers need only implement data structures (such as lists or dictionaries) once, rather than once for each element-type which they may use.
	en.wikipedia.org /wiki/Data_type (2658 words)

	Eric White's Blog : Local Variable Type Inference
		Local variable type inference is a feature in C# 3.0 where you can use the var keyword instead of explicitly specifying the type of a variable.
		To declare a variable to hold the results of such a query expression it is necessary to use type inference.
		Type inference can be used only for declaring variables with local scope.
	blogs.msdn.com /ericwhite/pages/Local-Variable-Type-Inference.aspx (477 words)

	Type inference for Python \| Lambda the Ultimate
		The paper Type Feedback vs. Concrete Type Inference has a table in section 4 which summarizes the main differences between the approaches.
		In another discussion, I suggested type feedback as a way to collect otherwise undeclared type info to augment a DT (dynamically typed) language when an IDE execution environment can be assumed as context for collecting and storing info, and presenting some UI to a developer for using that info.
		The whole point of "soft" type inference approaches is to be able to get some of the benefits of static type analysis without the requirement that the entire program be explicitly well-typed.
	lambda-the-ultimate.org /node/1519 (1783 words)

	Bibliography
		Type Reconstruction with Recursive Types and Atomic Subtyping.
		Abstract: The type inference problem for partial types, introduced by Thatte \cite{Thatte}, is the problem of deducing types under a subtype relation with a largest element \O\ and closed under the usual antimonotonic rule for function types.
		We propose a type system which allows us to classify these kinds of values and to classify programs by the type of their result, as is usual in strongly-typed programming languages.
	www.cs.neu.edu /home/wand/pubs.html (6892 words)

	The Fishbowl: Type Inference and Java
		The debate between static and dynamic typing is a long one, and not one I have a definite opinion on.
		And with 1.5 and the introduction of generics, the type system is getting even stupider, giving you more and more places where you have to tell the compiler what types to expect because it's too stupid to work it out for itself.
		The second, and arguably more pressing problem, is that types are good documentation and if they're not written down explictly in the source code then you'll quickly wish that your IDE could annotate the presentation of the source code with the inferred types in some useful manner.
	fishbowl.pastiche.org /2004/05/18/type_inference_and_java (1613 words)

	BOO - Type Inference
		Type inference means you don't have to worry about declaring types everywhere just to make the compiler happy.
		Type inference means you can be productive without giving up the safety net of the type system nor sacrificing performance.
		The type of an array is inferred as the [least generic type] that could safely hold all of its enclosing elements.
	boo.codehaus.org /Type+Inference (753 words)

	Practical Type Inference Based on Success Typings \| Lambda the Ultimate
		We show that it is possible to reconstruct a significant portion of the type information which is implicit in a program, automatically annotate function interfaces, and detect definite type clashes without fundamental changes to the philosophy of the language or imposing a type system which unnecessarily rejects perfectly reasonable programs.
		Unlike most static type systems, success typings incorporate subtyping and never disallow a use of a function that will not result in a type clash during runtime.
		Type inference, whether starting from the bottom or the top of the type treilli is still "using the same coordinates".
	www.lambda-the-ultimate.org /node/1910 (620 words)

	Type Inference
		The most common type of type inference is called HindleyMilnerTypeInference and is found in various forms in MlLanguage and HaskellLanguage.
		...firstly because the type of x and y aren't defined at their first use (first sign that type inference isn't supported), but even beyond that, because when add() is instantiated, it doesn't know what types x and y are, and cannot cope with that.
		A similar language with actual type inference might see that x and y are double, since they are used that way after the template instantiation, and given that knowledge, work backwards to see that add() should be specialized on (double, double).
	c2.com /cgi/wiki?TypeInference (2013 words)

	Type Inference
		An instance of a type scheme is obtained by replacing each of the type variables occurring in it with a type scheme, with the same type scheme replacing each occurrence of a given type variable.
		The free type variables in the solution to the system of equations may be thought of as determining the "degrees of freedom" or "range of polymorphism" of the type of an expression --- the constraints are solvable for any choice of types to substitute for these free type variables.
		In practice we often allow the type checker to infer the principal type of a variable, but it is often good form to explicitly indicate the intended type as a consistency check and for documentation purposes.
	www.cs.cmu.edu /People/rwh/introsml/core/typeinf.htm (1989 words)

	Type Inference
		An instance of a type scheme is obtained by replacing each of the type variables occurring in it with a type scheme, with the same type scheme replacing each occurrence of a given type variable.
		The free type variables in the solution to the system of equations may be thought of as determining the "degrees of freedom" or "range of polymorphism" of the type of an expression --- the constraints are solvable for any choice of types to substitute for these free type variables.
		In practice we often allow the type checker to infer the principal type of a variable, but it is often good form to explicitly indicate the intended type as a consistency check and for documentation purposes.
	www-2.cs.cmu.edu /People/rwh/introsml/core/typeinf.htm (1989 words)

	type inference -
		The output of p52p6 may be run through the inferencer, but not even native Perl6 code will be required to make it through the type inferencer without errors.
		Eval"" by default forces the type inferencer to assume the worst for all subroutine, all global variables, and all lexical variables captured by a closure.
		The efficiency of powerful type inferencing algorithms isn't all that good, and my intuition says that Perl6 is going to need all the power it can get.
	dev.perl.org /perl6/rfc/4.html (668 words)

	Type inference (Site not responding. Last check: 2007-10-31)
		The second pass traverses the tree to propagate type constraints which are inherent in the structure of the program, and uses these constraint types to select a unique interpretation for each leaf node.
		As a result, the bottom-up pass of the type inference phase, upon entry into a given lexical level, recursively invokes the type inference algorithm on the set of types which are used in that level.
		These must be determined by a process of simultaneous type inference which interleaves the usual bottom-up and top-down phases on each set of mutually-recursive types to determine unique interpretations.
	www.aldor.org /docs/reports/i94acomp/node8.html (469 words)

	Constraint-Based Type Inference for Guarded Algebraic Data Types - Simonet, Pottier (ResearchIndex)
		Abstract: Guarded algebraic data types, which subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, and phantom types, and are closely related to inductive types, have the distinguishing feature that, when typechecking a function defined by cases, every branch must be checked under di#erent typing assumptions.
		Constraint-based type inference for guarded algebraic data types.
		126 Type inference with polymorphic recursion - Henglein - 1993 ACM DBLP
	citeseer.ist.psu.edu /669510.html (569 words)

	Static Type Inference (Site not responding. Last check: 2007-10-31)
		Type inference can also take place in a declaration, if it is combined with an assignment.
		Since the declared type of the right hand side of the assignment is known, its type is used as the type of the variable.
		The type of the arguments to a function call are also known and can be used to infer the type of a creation expression in a call to the function.
	www.gnu.org /software/sather/docs-1.2/tutorial/type-inference.html (360 words)

	Lecture 18: Pattern Matching, Polymorphic Type Inference, and Unification (Site not responding. Last check: 2007-10-31)
		Type inference refers to the process of determining the appropriate types for expressions based on how they are used.
		Both polymorphic type inference and pattern matching in ML are instances of a very general mechanism called unification.
		Note that in the former clause, the type variable is associated with the variable, and in the latter, it is associated with the occurrence of the subexpression in
	www.cs.cornell.edu /Courses/cs312/2001FA/lecture/lec18.htm (1651 words)

	Type inference - Computing Reference - eLook.org (Site not responding. Last check: 2007-10-31)
		where "-" is the turnstile symbol (LaTeX \vdash) and G is a type assignment for the free variables of expression x.
		We then use unification on type variables to match the partial application of plus to its first argument against the App rule, yielding a type (Int -> Int) and a substitution X = Int.
		This process is used both to infer types for expressions and to check that any types given by the user are consistent.
	www.elook.org /computing/type-inference.htm (274 words)

	Type Inference (Site not responding. Last check: 2007-10-31)
		(underscore) where a type should be and the compiler tries to figure out the type for you.
		Inference is even more useful because of Cyclone's advanced typing constructs.
		's type to be a nullable pointer to an unconstrained type.
	research.att.com /projects/cyclone/online-manual/main-screen006.html (495 words)

	CCured Type Inference (Site not responding. Last check: 2007-10-31)
		The inferencer then checks the remaining nodes to see if the types they represent are involved in pointer arithmetic.
		The end result of the inferencer is the graph, which serves as a mapping from types in the program to pointer kinds.
		There is an alternative lower-level way to inspect the result of the inference, which is described in Appendix A.
	manju.cs.berkeley.edu /ccured/ccured005.html (457 words)

	Citebase - Type Inference for Guarded Recursive Data Types (Site not responding. Last check: 2007-10-31)
		We reduce type inference for GRDTs to unification under a mixed prefix.
		Inference is incomplete because the set of type constraints allowed to appear in the type system is only a subset of those type constraints generated by type inference.
		We present refined procedures to infer types incrementally and to assist the user in identifying which pieces of type information are missing.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:cs/0507037 (397 words)

	InfoQ: Is Type Inference a Good Idea for Java 7?
		Type inference actually makes some sense in languages like JavaScript and PHP that are built around this, and had this feature from day 1.
		Type inference is just a case of complete laziness and is brought to us by the same sort of people who think that typing is the most time consuming part of the exercise.
		Scala has local type inference, and it doesn't seem to bring some sort of problem: the type sys tem is not less strong.
	www.infoq.com /news/2007/04/type-inference (1544 words)

	Strong Typing and Perl
		Since type checking in C and Pascal is a failure (and I have a big fit about this and foam at the mouth so that nobody dares disagree) there are two directions to go.
		The big benefits here are: The type system is very fine-grained and flexible, so that there are many many types and you can be very specific about what type a certain value has.
		Finally, I talk about the possibility of adding good static type checking to Perl, and conclude that it's a lost cause because one of the essential features of Perl is that it automatically converts values from one type to another, which defeats the possibility of checking.
	perl.plover.com /yak/typing/typing.html (380 words)

	Programming languages (Site not responding. Last check: 2007-10-31)
		Haskell is a non-strict, polymorphic functional language with type inference and controlled side effects and supports overloading via type classes.
		Charity (Calgary) is a terminating, polymorphic language supporting type inference and algebraic, and higher-order coalgebraic, datatypes.
		Cayenne is a programming language with dependent types; type checking in Cayenne is undecidable (i.e., the checker may not terminate), but the system is extremely expressive.
	www.cs.uu.nl /people/franka/lang (1580 words)

	[Haskell] Type inference and principal typings for record concatenation and mixin modules
		The technical report is: Type Inference and Principal Typings for Symmetric Record Concatenation and Mixin Modules by Henning Makholm and J. Wells http://www.macs.hw.ac.uk/~makholm/papers/bowtini-long.pdf In this report we present a new type system, Bowtie, for a lambda calculus with records and a symmetric record concatenation operation.
		The system has been designed to allow feasible _type inference_ with a complexity of O(nmalpha(n)) where n is the input size and m the number of different field labels in the program, as well as _compositional type* inference_ and a notion of _principal typings_.
		We have also made available a web-accessible type inference demo for Bowtie/Martini; it can be found at http://www.macs.hw.ac.uk/DART/software/Bowtini/ We hope you enjoy our paper and web demo and we welcome any feedback.
	www.haskell.org /pipermail/haskell/2005-March/015593.html (381 words)

	Aggressive Type Inference
		Type inference in functional languages is, in turn, based on work in the early 1960s on automatic theorem provers.
		These type inference systems are conservative in the sense that, given a variable X, they will always compute a superset of X's type [1].
		Type inference is a difficult task for dynamically-typed languages such as Python.
	www.python.org /workshops/2000-01/proceedings/papers/aycock/aycock.html (3402 words)

	Type inference - Nemerle Homepage
		The situation becomes more involved when there are type parameters that are used in return type but not in type of function parameters.
		Nemerle type inference engine very often produces such type variables just to kill them a moment later by replacing them with a real type.
		Nemerle supports type inference for parameters of local functions (that is functions defined and visible only inside some other function).
	nemerle.org /Type_inference (923 words)

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