[Haskell-cafe] semantics

Conal Elliott conal at conal.net
Wed Feb 9 01:55:30 CET 2011

On Tue, Feb 8, 2011 at 7:04 AM, Patrick Browne <patrick.browne at dit.ie>wrote:

> Consider the following definitions:
> 1. Denotational semantics can be considered as relation between syntax
> and mathematical objects (the meaning of the syntax).
> 2. Operational semantics can be considered as set of rules for
> performing computation.
> Question 1
> Applying these definitions in a Haskell context can I say that the
> lambda calculus provides both the operational and denotational
> semantics for Haskell programs at value level for definition and
> evaluations.
> Question 2
> Does it make sense to use these definitions at type level? If so, what
> exactly do they represent?
> Thanks,
> Pat

Here's my personal denotational answer to question 2: I think of a type as
denoting a collection of (mathematical) values. If an expression e has type
T, then the meaning (value) of e is a member of the collection denoted by T.
This simple principle, which is fundamental to how I think of functional
programming, has consequences in library design, which I've discussed at
http://conal.net/blog/posts/notions-of-purity-in-haskell/ .

Regards, - Conal
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