The Complexity of Type Inference for Higher-Order Typed Lambda Calculi

The Complexity of Type Inference for Higher-Order Typed Lambda Calculi (1991)

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by Fritz Henglein , Harry G. Mairson

Venue:	J. Funct. Programming
Citations:	26 - 10 self

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Datum	Value	Source
TITLE	The Complexity of Type Inference for Higher-Order Typed Lambda Calculi	INFERENCE
AUTHOR NAME	Fritz Henglein	SVM HeaderParse 0.1
AUTHOR AFFIL	y	SVM HeaderParse 0.2
AUTHOR NAME	Harry G. Mairson	SVM HeaderParse 0.1
AUTHOR AFFIL	z; Computer Science Department; Brandeis University	SVM HeaderParse 0.2
AUTHOR ADDR	Waltham, Massachusetts 02254	SVM HeaderParse 0.1
ABSTRACT	We analyze the computational complexity of type inference for untyped -terms in the second-order polymorphic typed -calculus (F 2 ) invented by Girard and Reynolds, as well as higher-order extensions F 3 ; F 4 ; : : : ; F ! proposed by Girard. We prove that recognizing the F 2 - typable terms requires exponential time, and for F ! the problem is nonelementary. We show as well a sequence of lower bounds on recognizing the F k -typable terms, where the bound for F k+1 is exponentially larger than that for F k . The lower bounds are based on generic simulation of Turing Machines, where computation is simulated at the expression and type level simultaneously. Non-accepting computations are mapped to non-normalizing reduction sequences, and hence non-typable terms. The accepting computations are mapped to typable terms, where higher-order types encode reduction sequences, and first-order types encode the entire computation as a circuit, based on a unification simulation of Boolean logic. ...	user correction - Legacy Corrections
YEAR	1991	INFERENCE
VENUE	J. Funct. Programming	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	119--130	INFERENCE
VOLUME	4	INFERENCE
CITATIONS	49 found	ParsCit 1.0