In this paper we propose higher-order rewrite systems without bound variables. In order to prove their connuence under the assumption of orthogonality, we study a simple proof method which employs a characterization of the diamond property of a parallel reduction. By an application of the proof method, we obtain a new connuence result for orthogonal higher-order conditional rewrite systems.

Every theory we will consider will be in a language that has a name ṅ for each n ∈ ω. For example, the name for 2 ∈ ω in the language LΩ of arithmetic is the term “1 + 1”. The results stated will only apply to countable languages. This requirement is implicit in the hypothesis of the existence of an enumeration of all formulas with one free variable, for example. We also assume that formulas an...

In this paper, we introduce a new fragment of the rst-order temporal language, called the monodic fragment, in which all formulas beginning with a temporal operator (Since or Until) have at most one free variable. We show that the satissability problem for monodic formulas in various linear time structures can be reduced to the satissability problem for a certain fragment of classical rst-order...

We propose a unifying method for analysis of scheduling problems in real-time systems. The method is based on ACSR-VP, a real-time process algebra with value-passing capabilities. We use ACSR-VP to describe an instance of a scheduling problem as a process that has parameters of the problem as free variables. The specification is analyzed by means of a symbolic algorithm. The outcome of the anal...

In this proof pearl, we demonstrate the power of higherorder encodings in the logical framework Twelf[PS99] by investigating proofs about an algorithmic specification of bounded subtype polymorphism, a problem from the POPLmark challenge [ABF05]. Our encoding and representation of the problem plays to the strengths of the logical framework LF. Higher-order abstract syntax is used to deal with i...

The equations that define the Lax pairs for generalized principal chiral models can be solved for any nondegenerate bilinear form on su(2). The solution is dependent on one free variable that can serve as the spectral parameter. 1 Formulation of the generalized chiral models Principal chiral models are important example of relativistically invariant field theory integrable by the inverse scatte...

Enzyme costs play a major role in the choice of metabolic routes, both in evolution and bioengineering. Given desired fluxes, necessary enzyme levels can be estimated based on known rate laws and on a principle of minimal enzyme cost. With logarithmic metabolite levels as free variables, enzyme cost functions and constraints in optimality and sampling problems can be handled easily. The set of ...

We give a Natural Deduction formulation of an adaptation of Gödel’s functional (Dialectica) interpretation to the extraction of (more) efficient programs from (classical) proofs. We adapt Jørgensen’s formulation of pure Dialectica translation by eliminating his “Contraction Lemma” and allowing free variables in the extracted terms (which is more suitable in a Natural Deduction setting). We also...