The Expressive Power of Higher-order Types or, Life without CONS

The Expressive Power of Higher-order Types or, Life without CONS (2001)

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by Neil D. Jones

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Datum	Value	Source
TITLE	The Expressive Power of Higher-order Types or, Life without CONS	user correction - Legacy Corrections
AUTHOR NAME	Neil D. Jones	user correction
AUTHOR AFFIL	DIKU, Department of Computer Science, University of Copenhagen	user correction
AUTHOR ADDR	Copenhagen, Denmark	user correction
ABSTRACT	Compare first-order functional programs with higher-order programs allowing functions as function parameters. Can the the first program class solve fewer problems than the second? The answer is no: both classes are Turing complete, meaning that they can compute all partial recursive functions. In particular, higher-order values may be first-order simulated by use of the list constructor ‘cons’ to build function closures. This paper uses complexity theory to prove some expressivity results about small programming languages that are less than Turing complete. Complexity classes of decision problems are used to characterize the expressive power of functional programming language features. An example: second-order programs are more powerful than first-order, since a function f of type [Bool]-〉Bool is computable by a cons-free first-order functional program if and only if f is in PTIME, whereas f is computable by a cons-free second-order program if and only if f is in EXPTIME. Exact characterizations are given for those problems of type [Bool]-〉Bool solvable by programs with several combinations of operations on data: presence or absence of constructors; the order of data values: 0, 1, or higher; and program control structures: general recursion, tail recursion, primitive recursion.	user correction
YEAR	2001	user correction
CITATIONS	36 found	ParsCit 1.0