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28,547
Recursive Function Definition
"... Abstract. Using the notions of unique fixed point, converging equivalence relation, and contracting function, we generalize the technique of well-founded recursion. We are able to define functions in the Isabelle theorem prover that recursively call themselves an infinite number of times. In particu ..."
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by showing that the functions for filtering and flattening infinite lists have simple recursive definitions. 1 Well-founded recursion Rather than specify recursive functions by possibly inconsistent axioms, several higher order logic (HOL) theorem provers[3, 9, 12] provide well-founded recursive function
Non-primitive Recursive Function Definitions
- Proceedings of the 8th International Workshop on Higher Order Logic Theorem Proving and Its Applications (LNCS 971
, 1995
"... This paper presents an approach to the problem of introducing non-primitive recursive function definitions in higher order logic. A recursive specification is translated into a domain theory version, where the recursive calls are treated as potentially non-terminating. Once we have proved termin ..."
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Cited by 2 (0 self)
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This paper presents an approach to the problem of introducing non-primitive recursive function definitions in higher order logic. A recursive specification is translated into a domain theory version, where the recursive calls are treated as potentially non-terminating. Once we have proved
Recursive function definition for types with binders
- In Seventeenth International Conference on Theorem Proving in Higher Order Logics
, 2004
"... Abstract. This work describes the proof and uses of a theorem allowing definition of recursive functions over the type of λ-calculus terms, where terms with bound variables are identified up to α-equivalence. The theorem embodies what is effectively a principle of primitive recursion, and the analog ..."
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Cited by 15 (0 self)
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Abstract. This work describes the proof and uses of a theorem allowing definition of recursive functions over the type of λ-calculus terms, where terms with bound variables are identified up to α-equivalence. The theorem embodies what is effectively a principle of primitive recursion
Quantification in Tail-recursive Function Definitions
"... ABSTRACT We investigate the logical issues behind axiomatizing equations that contain both recursive calls and quantifiers in ACL2. We identify a class of such equations, named extended tail-recursive equations, that can be uniformly introduced in the logic. We point out some potential benefits of t ..."
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ABSTRACT We investigate the logical issues behind axiomatizing equations that contain both recursive calls and quantifiers in ACL2. We identify a class of such equations, named extended tail-recursive equations, that can be uniformly introduced in the logic. We point out some potential benefits
Syntactic Control of Type Polymorphism for Recursive Function Definitions
, 1994
"... High-level languages, such as ML, conciliate strong typing with a flexible programming style by relying to compile-time inference for determining the type of expressions instead of requiring extensive type declarations. In ML-like languages, one of the most advanced and pleasant typing concept is po ..."
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is polymorphism, which permits to represent the type of generic functions. But there is limitation to the policy of giving polymorphic types to generic functions in ML-like languages: recursive functions are treated as having a single type inside their definition. This feature, even if non intuitive, has strong
Unfolding Recursive Function Definitions Using the Paradoxical Combinator
, 1996
"... Function unfolding is a well-known program transformation technique: it is often used to reduce execution overheads incurred by an implementation’s function-calling mechanism and to localise information available in global definitions (localization simplifies further optimizations such as constant p ..."
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propagation and the static evaluation of expressions). Unfolding function definitions that exhibit either self- or mutual-recursion presents a problem for automated transformation systems: sophisticated control mechanisms may need to be incorporated into the unfolding process to ensure termination
Recursive Function Definition over Coinductive Types
, 1999
"... Using the notions of unique xed point, converging equivalence relation, and contracting function, we generalize the technique of well-founded recursion. We are able to de ne functions in the Isabelle theorem prover that recursively call themselves an in nite number of times. In particular, we can ea ..."
Abstract
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Cited by 15 (0 self)
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Using the notions of unique xed point, converging equivalence relation, and contracting function, we generalize the technique of well-founded recursion. We are able to de ne functions in the Isabelle theorem prover that recursively call themselves an in nite number of times. In particular, we can
Syntactic Type Polymorphism for Recursive Function Definitions
, 1994
"... . Higher-order programming languages, such as ML, permit a flexible programming style by using compile-time type inference together with the concept of type polymorphism, which allows to specify the types of generic functions. In ML, however, recursive functions must always be given a unique (monomo ..."
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Cited by 1 (1 self)
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(monomorphic) type inside their definition. Giving polymorphic types to recursive functions is known as the problem of polymorphic recursion which has been shown equivalent to the problem of semi-unification, known as undecidable. We show that the absence of a decidable specification to give polymorphic types
Syntactic Type Polymorphism for Recursive Function Definitions
, 1994
"... . Higher-order programming languages, such as ML, permit a flexible programming style by using compile-time type inference together with the concept of type polymorphism, which allows to specify the types of generic functions. In ML, however, recursive functions must always be given a unique (monomo ..."
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(monomorphic) type inside their definition. Giving polymorphic types to recursive functions is known as the problem of polymorphic recursion which has been shown equivalent to the problem of semi-unification, known as undecidable. We show that the absence of a decidable specification to give polymorphic types
Algebraic Correctness Proofs for Compiling Recursive Function Definitions with Strictness Information
, 2004
"... Adding appropriate strictness information to recursive function definitions we achieve a uniform treatment of lazy and eager evaluation strategies. By restriction to first--order functions over basic types we develop a pure stack implementation that avoids a heap even for lazy arguments. We present ..."
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Adding appropriate strictness information to recursive function definitions we achieve a uniform treatment of lazy and eager evaluation strategies. By restriction to first--order functions over basic types we develop a pure stack implementation that avoids a heap even for lazy arguments. We present
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