# From Operational to Denotational Semantics

@inproceedings{Smith1991FromOT, title={From Operational to Denotational Semantics}, author={Scott F. Smith}, booktitle={MFPS}, year={1991} }

In this paper operational equivalence of simple functional programs is defined, and certain basic theorems proved thereupon. These basic theorems include congruence, least fixed-point, an analogue to continuity, and fixed-point induction. We then show how any ordering on programs for which these theorems hold can be easily extended to give a fully abstract cpo for the language, giving evidence that any operational semantics with these basic theorems proven is complete with respect to a…

## 36 Citations

### From Operational Semantics to Domain TheoryIan

- Mathematics
- 1995

This paper builds domain theoretic concepts upon an operational foundation. The basic operational theory consists of a single step reduction system from which an operational ordering and equivalence…

### From Operational Semantics to Domain Theory

- MathematicsInf. Comput.
- 1996

domain theoretic concepts are extended to include concepts from domain theory, including the notions of directed set, least upper bound, complete partial order, monotonicity, continuity, finite element,?-algebraicity, full abstraction, and least fixed point properties, and are used to construct a (strongly) fully abstract continuous model for the authors' language.

### CPO Models for Compact GSOS Languages

- Computer ScienceInf. Comput.
- 1996

In this paper, we present a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the GSOS format of Bloom, Istrail, and Meyer. The…

### Full Abstraction and the Context Lemma

- Computer ScienceTACS
- 1991

A general notion of rewriting system of the kind used for evaluating simply typed l-terms in Scott''s PCF is defined, showing that any denotational semantics that is adequate for PCF cannot be fully abstract for any extension of PCF satisfying the Context Lemma.

### Full Abstraction and the Context Lemma 1

- Computer Science
- 1991

A general notion of rewriting system of the kind used for evaluating simply typed -terms in Scott's PCF is presented, showing that any denotational semantics that is adequate for PCF cannot be fully abstract for any extension of PCF satisfying the Context Lemma.

### From SOS rules to proof principles: an operational metatheory for functional languages

- Computer SciencePOPL '97
- 1997

This paper defines a rule format, Globally Deterministic SOS (GDSOS), and establishes some proof principles for reasoning about equivalence which are sound for all languages which can be expressed in this format.

### CPO Models for GSOS Languages - Part I: Compact GSOS Languages

- Computer Science
- 1994

This paper presents a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the GSOS format of Bloom, Istrail and Meyer, and gets several general results on the bisimulation preorder.

### A Lambda-Calculus with letrec, case, constructors and non-determinism

- Computer ScienceArXiv
- 2000

This shows that the combination of a context lemma and a meta-rewriting on reductions using complete sets of commuting (forking, resp.) diagrams is a useful and successful method for providing a semantics of a functional programming language and proving correctness of program transformations.

### Reasoning about local variables with operationally-based logical relations

- Computer ScienceProceedings 11th Annual IEEE Symposium on Logic in Computer Science
- 1996

A parametric logical relation between the phrases of an Algol-like language is presented and provides an applicative characterisation of contextual equivalence for the language and provides a useful (and complete) method for proving equivalences.

### Structural Operational Semantics

- Computer ScienceHandbook of Process Algebra
- 2001

The importance of giving precise semantics to programming and specification languages was recognized since the sixties with the development of the first high-level programming languages and was already advocated by McCarthy in [147], and elaborated upon in references like [142, 143].

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