Turing-Completeness Totally Free
نویسنده
چکیده
In this paper, I show that general recursive definitions can be represented in the free monad which supports the ‘effect’ of making a recursive call, without saying how these calls should be executed. Diverse semantics can be given within a total framework by suitable monad morphisms. The Bove-Capretta construction of the domain of a general recursive function can be presented datatype-generically as an instance of this technique. The paper is literate Agda, but its key ideas are more broadly transferable.
منابع مشابه
A Core Model for Choreographic Programming
We investigate the foundations of Choreographic Programming, a paradigm for writing concurrent programs that are deadlock free by construction, guided by the notion of computation. We start by introducing Minimal Choreographies (MC), a language that includes only the essential primitives of the paradigm. MC is minimal wrt Turing completeness: it implements all computable functions, and restrict...
متن کاملParallel Communicating Grammar Systems with Context-Free Components Are Turing Complete for Any Communication Model
Parallel Communicating Grammar Systems (PCGS) were introduced as a language-theoretic treatment of concurrent systems. A PCGS extends the concept of a grammar to a structure that consists of several grammars working in parallel, communicating with each other, and so contributing to the generation of strings. PCGS are generally more powerful than a single grammar of the same type; PCGS with cont...
متن کاملRandom Strings and Truth-table Degrees of Turing Complete C.e. Sets
We investigate the truth-table degrees of (co-)c.e. sets, in particular, sets of random strings. It is known that the set of random strings with respect to any universal prefix-free machine is Turing complete, but that truthtable completeness depends on the choice of universal machine. We show that for such sets of random strings, any finite set of their truth-table degrees do not meet to the d...
متن کاملMinimal Ingredients for Turing Completeness in Membrane Computing
In this paper we provide several computability results looking for minimal ingredients needed to obtain Turing completeness of various bio-inspired computation models (membrane systems). We emphasize the relevance of number two in reaching Turing completeness for several membrane systems.
متن کاملA Constructive Proof of the Turing Completeness of Circal
This paper gives a proof of the Turing completeness of the Circal process algebra by exhibiting a universal program capable of mapping any Turing machine description into Circal specifications that effectively simulate the behaviour of the given machine.
متن کامل