Results 1 
5 of
5
Eekelen. Polynomial size analysis of firstorder functions
, 2007
"... Abstract. We present a sizeaware type system for firstorder shapely function definitions. Here, a function definition is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of shapely function definitions may be matrix multiplica ..."
Abstract

Cited by 24 (13 self)
 Add to MetaCart
(Show Context)
Abstract. We present a sizeaware type system for firstorder shapely function definitions. Here, a function definition is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of shapely function definitions may be matrix multiplication and the Cartesian product of two lists. The type checking problem for the type system is shown to be undecidable in general. We define a natural syntactic restriction such that the type checking becomes decidable, even though size polynomials are not necessarily linear or monotonic. Furthermore, a method that infers polynomial size dependencies for a nontrivial class of function definitions is suggested. 1
Size Analysis of Algebraic Data Types
"... We present a sizeaware type system for a firstorder functional language with algebraic data types, where types are annotated with polynomials over size variables. We define how to generate typing rules for each data type, provided its user defined size function meets certain requirements. As an ex ..."
Abstract

Cited by 10 (4 self)
 Add to MetaCart
We present a sizeaware type system for a firstorder functional language with algebraic data types, where types are annotated with polynomials over size variables. We define how to generate typing rules for each data type, provided its user defined size function meets certain requirements. As an example, a program for balancing binary trees is type checked. The type system is shown to be sound with respect to the operational semantics in the class of shapely functions. Type checking is shown to be undecidable, however, decidability for a large subset of programs is guaranteed.
Type Checking and Weak Type Inference for Polynomial Size Analysis of FirstOrder Functions
"... Abstract. We present a sizeaware type system for firstorder shapely functions. Here, a function is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of shapely functions are matrix multiplication and the Cartesian product of tw ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We present a sizeaware type system for firstorder shapely functions. Here, a function is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of shapely functions are matrix multiplication and the Cartesian product of two lists. The type checking problem for the type system is shown to be undecidable in general. We define a natural syntactic restriction such that the type checking becomes decidable, even though size polynomials are not necessarily linear. Furthermore, an algorithm for weak type inference for this system is given. 1