data types Data structures generally have collection of operations or functions associated with them. An abstract data type is a data structure together with its collection of associated operations and functions. This is a familiar concept: 1. the integers support equality together with arithmetical operations including division with remainder and binary relational predicates; 2. reals, in thei...

AC-completion efficiently handles equality modulo associative and commutative function symbols. When the input is ground, the procedure terminates and provides a decision algorithm for the word problem. In this paper, we present a modular extension of ground ACcompletion for deciding formulas in the combination of the theory of equality with user-defined AC symbols, uninterpreted symbols and an...

We consider observational specifications of state-based systems which incorporate the declaration of a distinguished set of observer operations. These observers determine an indistinguishability relation for states which is called "observational equality". An important requirement for the non-observer operations is the compatibility with the observational equality. In the CafeOBJ language (and ...

In this paper we try to find a computational interpretation for strong form of extensionality, which call "converse extensionality". Converse extensionality principles, arise as the Dialectica axiom were first studied by Howard. order give these reconsider Brouwer's apartness relation, constructive inequality. Formally, provide categorical construction endow every typed combinatory algebra with...

ion Γ, x :j N ⊢ K :i L Γ ⊢ ((x :j N)K) :i ((x :j N)L) application Γ ⊢ N :i ((x :j L)M) Γ ⊢ K :j L Γ ⊢ N(K) :i M [x := K] These rules by themselves are almost useless since no expression can be assigned a type because to prove the conclusion of a rule one should have already proved the premise(s). So in order to start we need some axiom. The first thing one has to do is to settle the maximum lev...

Received ; accepted – 2 – ABSTRACT It is shown that, contrary to an existing claim, the near equality between the lifetime of the sun and the timescale of biological evolution on earth does not necessarily imply that extraterrestrial civilizations are exceedingly rare. Furthermore, on the basis of simple assumptions it is demonstrated that a near equality between these two timescales may be the...

Relation between codon usage and other biological phenomena in living organisms, has been proved in previous researches. In advance, recently, it is shown that the codon usage of co-expressed and co-function genes are similar. In this paper, we introduced a set of networks called codon usage equality networks, each network for an amino acid. These networks represent codon usage similarities bet...

AC-completion efficiently handles equality modulo associative and commutative function symbols. When the input is ground, the procedure terminates and provides a decision algorithm for the word problem. In this paper, we present a modular extension of ground AC-completion for deciding formulas in the combination of the theory of equality with user-defined AC symbols, uninterpreted symbols and a...

We consider observational specifications of state-based systems which incorporate the declaration of a distinguished set of observer operations. These observers determine an indistinguishability relation for states which is called "observational equality". An important requirement for the non-observer operations is the compatibility with the observational equality. In the CafeOBJ language (and ...

We propose inference systems for binary relations with composition laws of the form S T U in the context of resolution-type theorem proving. Particulary interesting examples include transitivity, partial orderings, equality and the combination of equality with other transitive relations. Our inference mechanisms are based on standard techniques from term rewriting and represent a re nement of c...