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ObjectOriented Type Inference
 OOPSLA'91
, 1991
"... We present a new approach to inferring types in untyped objectoriented programs with inheritance, assignments, and late binding. It guarantees that all messages are understood, annotates the program with type information, allows polymorphic methods, and can be used as the basis of an optimizing co ..."
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Cited by 222 (18 self)
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We present a new approach to inferring types in untyped objectoriented programs with inheritance, assignments, and late binding. It guarantees that all messages are understood, annotates the program with type information, allows polymorphic methods, and can be used as the basis of an optimizing compiler. Types are finite sets of classes and subtyping is set inclusion. Using a trace graph, our algorithm constructs a set of conditional type constraints and computes the least solution by least fixedpoint derivation.
The complexity of type inference for higherorder typed lambda calculi
 In. Proc. 18th ACM Symposium on the Principles of Programming Languages
, 1991
"... We analyse the computational complexity of type inference for untyped X,terms in the secondorder polymorphic typed Xcalculus (F2) invented by Girard and Reynolds, as well as higherorder extensions F3,F4,...,/ ^ proposed by Girard. We prove that recognising the i^typable terms requires exponential ..."
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Cited by 28 (11 self)
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We analyse the computational complexity of type inference for untyped X,terms in the secondorder polymorphic typed Xcalculus (F2) invented by Girard and Reynolds, as well as higherorder extensions F3,F4,...,/ ^ proposed by Girard. We prove that recognising the i^typable terms requires exponential time, and for Fa the problem is nonelementary. We show as well a sequence of lower bounds on recognising the i^typable terms, where the bound for Fk+1 is exponentially larger than that for Fk. The lower bounds are based on generic simulation of Turing Machines, where computation is simulated at the expression and type level simultaneously. Nonaccepting computations are mapped to nonnormalising reduction sequences, and hence nontypable terms. The accepting computations are mapped to typable terms, where higherorder types encode reduction sequences, and firstorder types encode the entire computation as a circuit, based on a unification simulation of Boolean logic. A primary technical tool in this reduction is the composition of polymorphic functions having different domains and ranges. These results are the first nontrivial lower bounds on type inference for the Girard/Reynolds
An Analysis of the CoreML Language: Expressive Power and Type Reconstruction
 In Proc. 21st Int'l Coll. Automata, Languages, and Programming
, 1994
"... CoreML is a basic subset of most functional programming languages. It consists of the simply typed (or monomorphic) calculus, simply typed equality over atomic constants, and let as the only polymorphic construct. We present a synthesis of recent results which characterize this "toy" language' ..."
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Cited by 5 (3 self)
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CoreML is a basic subset of most functional programming languages. It consists of the simply typed (or monomorphic) calculus, simply typed equality over atomic constants, and let as the only polymorphic construct. We present a synthesis of recent results which characterize this "toy" language's expressive power as well as its type reconstruction (or type inference) problem. More specifically: (1) CoreML can express exactly the ELEMENTARY queries, where a program input is a database encoded as a term and a query program is a term whose application to the input normalizes to the output database. In addition, it is possible to express all the PTIME queries so that this normalization process is polynomial in the input size. (2) The polymorphism of let can be explained using a simple algorithmic reduction to monomorphism, and provides flexibility, without affecting expressibility. Algorithms for type reconstruction offer the additional convenience of static typing without type declarations. Given polymorphism, the price of this convenience is an increase in complexity from lineartime in the size of the program typed (without let) to completeness in exponentialtime (with let).
Analysis of Objects with Dynamic and Multiple Inheritance
 In ECOOP '93 Conference Proceedings
, 1995
"... . We have designed and implemented a type inference algorithm for the Self language. The algorithm can guarantee the safety and disambiguity of message sends, and provide useful information for browsers and optimizing compilers. Self features objects with dynamic inheritance. This construct has unt ..."
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Cited by 2 (0 self)
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. We have designed and implemented a type inference algorithm for the Self language. The algorithm can guarantee the safety and disambiguity of message sends, and provide useful information for browsers and optimizing compilers. Self features objects with dynamic inheritance. This construct has until now been considered incompatible with type inference because it allows the inheritance graph to change dynamically. Our algorithm handles this by deriving and solving type constraints that simultaneously define supersets of both the possible values of expressions and of the possible inheritance graphs. The apparent circularity is resolved by computing a global fixedpoint, in polynomial time. The algorithm has been implemented and can successfully handle the Self benchmark programs, which exist in the "standard Self world" of more than 40,000 lines of code. Keywords: Languages and their implementation, tools and environments. 1 Introduction The choice between static and dynamic typing ...