Evolving algebras 1993: Lipari guide
Specification and validation methods
Sequential abstract-state machines capture sequential algorithms
ACM Transactions on Computational Logic (TOCL)
Current trends in theoretical computer science
The Art of Computer Programming Volumes 1-3 Boxed Set
The Art of Computer Programming Volumes 1-3 Boxed Set
Abstract State Machines: A Method for High-Level System Design and Analysis
Abstract State Machines: A Method for High-Level System Design and Analysis
Palindrome recognition using a multidimensional tape
Theoretical Computer Science
A call-by-name lambda-calculus machine
Higher-Order and Symbolic Computation
Church's lambda delta calculus
LPAR'00 Proceedings of the 7th international conference on Logic for programming and automated reasoning
Böhm's theorem, church's delta, numeral systems, and ershov morphisms
Processes, Terms and Cycles
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We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family of computable functions (taken as primitive tools, i.e., kind of oracle functions for the algorithm), for every constant K big enough, each computation step of the algorithm can be simulated by exactly K successive reductions in a natural extension of lambda calculus with constants for functions in the above considered family. The proof is based on a fixed point technique in lambda calculus and on Gurevich sequential Thesis which allows to identify sequential deterministic algorithms with Abstract State Machines. This extends to algorithms for partial computable functions in such a way that finite computations ending with exceptions are associated to finite reductions leading to terms with a particular very simple feature.