Re: [Haskell-cafe] Reddy on Referential Transparency
Uday Reddy has followed up with another substantial and interesting post on referential transparency here: http://stackoverflow.com/questions/210835/what-is-referential-transparency/11740176#11740176 The thrust of his argument appears to be that functional programmers have created a lot of confusion around the ideas of referential transparency. I sympathize but I think he is going too far. As I see it, while the very close association of functional programming and related concepts with referential transparency may have led to some confusion around the concept that doesn't mean that the specific means that functional programmers have been using to increase (classically understood) RT in functional programs is somehow invalid. Reddy has responded to my comment here http://stackoverflow.com/a/11680011/306550 and I have followed up in turn. Chris ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Reddy on Referential Transparency
On 7/27/12 1:49 PM, Ross Paterson wrote: So a language is referentially transparent if replacing a sub-term with another with the same denotation doesn't change the overall meaning? But then isn't any language RT with a sufficiently cunning denotational semantics? Or even a dumb one that gives each term a distinct denotation. Yes, but such denotations aren't useful for very much. The whole point of denotational semantics is to assert that some (primitive) expressions denote the same thing, and then to derive that other expressions (e.g., whole programs) denote the same thing. If we say that every expression is different from every other expression, then ---for example--- the only semantics-preserving transformation is the identity transformation. Our semantics is, thus, worthless for vetting whether a compiler's transformation is okay or not. In fact, this model explains exactly nothing about the *meaning* of those expressions. -- Live well, ~wren ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Reddy on Referential Transparency
Except in the complexity gymnastics and the fragility of the conclusions. Humans can't do large scale complex brain gymnastics - that's why abstraction exists - if your proof process doesn't abstract (and in the C case you need to know *everything* about *everything* and have to prove it all in one go and that proof will not survive a single change) then it isn't feasible. Haskell gives you the means to manage the complexity - and grasping complexity is humanities current challenge... Neil On 28 Jul 2012, at 05:43, damodar kulkarni wrote: So a language is referentially transparent if replacing a sub-term with another with the same denotation doesn't change the overall meaning? But then isn't any language RT with a sufficiently cunning denotational semantics? Or even a dumb one that gives each term a distinct denotation. That's neat ... I mean, by performing sufficiently complicated brain gymnastics, one can do equational reasoning on C subroutines (functions!) too. So, there is no big difference between C and Haskell when it comes to equational reasoning... Regards, Damodar On Sat, Jul 28, 2012 at 1:47 AM, Alexander Solla alex.so...@gmail.com wrote: On Fri, Jul 27, 2012 at 12:06 PM, Ross Paterson r...@soi.city.ac.uk wrote: On Fri, Jul 27, 2012 at 07:19:40PM +0100, Chris Dornan wrote: So a language is referentially transparent if replacing a sub-term with another with the same denotation doesn't change the overall meaning? Isn't this just summarizing the distinguishing characteristic of a denotational semantics? Right, so where's the substance here? My understanding is that RT is about how easy it is to carry out _syntactical_ transformations of a program that preserve its meaning. For example, if you can freely and naively inline a function definition without having to worry too much about context then your PL is deemed to possess lots of RT-goodness (according to FP propaganda anyway; note you typically can't freely inline function definitions in a procedural programming language because the actual arguments to the function may involve dastardly side effects; even with a strict function-calling semantics divergence will complicate matters). Ah, but we only think that because of our blinkered world-view. Another way of looking at it is that the denotational semanticists have created a beautiful language to express the meanings of all those ugly languages, and we're programming in it. A third way to look at it is that mathematicians, philosophers, and logicians invented the semantics denotational semanticists have borrowed, specifically because of the properties derived from the philosophical commitments they made. Computer science has habit of taking ideas from other fields and merely renaming them. Denotational semantics is known as model theory to everyone else. Let's consider a referentially /opaque/ context: quotation marks. We might say It is necessary that four and four are eight. And we might also say that The number of planets is eight. But we cannot unify the two by substitution and still preserve truth functional semantics. We would get It is necessary that four and four are the number of planets (via strict substitution joining on 'eight') or a more idiomatic phrasing like It is necessary that the number of planets is four and four. This is a big deal in logic, because there are a lot of languages which quantify over real things, like time, possibility and necessity, etc., and some of these are not referentially transparent. In particular, a model for such a language will have to use frames to represent context, and there typically is not a unique way to create the framing relation for a logic. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Reddy on Referential Transparency
On Sat, 28 Jul 2012, damodar kulkarni kdamodar2...@gmail.com wrote: So a language is referentially transparent if replacing a sub-term with another with the same denotation doesn't change the overall meaning? But then isn't any language RT with a sufficiently cunning denotational semantics? Or even a dumb one that gives each term a distinct denotation. That's neat ... I mean, by performing sufficiently complicated brain gymnastics, one can do equational reasoning on C subroutines (functions!) too. So, there is no big difference between C and Haskell when it comes to equational reasoning... Regards, Damodar The general theory of equational reasoning is often applicable because often we have a collection of sentences S of the form x = y where x and y are terms, and often we have a set of models M, where given a system of backround assumptions, we can ask of the above sentence, call it s, whether in some particular model m, is it the case that eval(x) = eval(y) where now the sentence above is not a sentence of S, but rather a fact, under assumptions, about the model m, namely that what the term x means in m is equal to what the term y means in m. Here we have written what the term x refers to in m as eval(x). For example x might be (vector-ref part-of-backround 17) in some Lisp source code, given as text, and y might (vector-ref part-of-backround 116), and part-of-backround is some vector which comes from, in general both the model m and, this is a scare phrase, the backround assumptions. Oi, please forgive tangle here! Note that the = in the sentence s is not the same = as in the model m, and we should in a first text write them with different symbols. As terms x and y are not equal-as-terms. It is only their values in m that are equal-in-m. (Obtuse Precisian Crank Further Remark: And the general theory of equality often applies to whatever sort of object lies in the vector part-of-backround at position 17, and also to whatever lies at position 116. THE ARGUMENT IS COMPLETE! But see http://iml.univ-mrs.fr/~girard/TS2.pdf for more and different.) Personal remark: I remember the wonderful feeling of having a weight lifted from me when I read this in Roger C. Lyndon's Notes on Logic: Oi, ah, I cannot find the quote tonight. The quote was something like In this book we shall work at the level of precision which today is standard in works on the theory of groups, say. by which Lyndon meant that certain extraordinarily finicky considerations were, by the date of composition, standard, and the reader might be trusted to handle these without error. Of course, as a beginner coming to Haskell, and as an old Lisper (my first Lisp was LISP 1.5, for which see http://www.softwarepreservation.org/projects/LISP/book/LISP%201.5%20Programmers%20Manual.pdf) I wish that Haskell made more patent to my un-practiced eye more of such finicky details^Wbasics. Naturally what I'd like is Haskell source code presented in the usual parenthesized prefix notation of Lisp, with of course, every term having an immediately available complete explicit typing, which could perhaps be presented when one clicks on the term (perhaps plists might be part of the mechanism). BRING OUT THE CORE! oo--JS. On Sat, Jul 28, 2012 at 1:47 AM, Alexander Solla alex.so...@gmail.comwrote: On Fri, Jul 27, 2012 at 12:06 PM, Ross Paterson r...@soi.city.ac.ukwrote: On Fri, Jul 27, 2012 at 07:19:40PM +0100, Chris Dornan wrote: So a language is referentially transparent if replacing a sub-term with another with the same denotation doesn't change the overall meaning? Isn't this just summarizing the distinguishing characteristic of a denotational semantics? Right, so where's the substance here? My understanding is that RT is about how easy it is to carry out _syntactical_ transformations of a program that preserve its meaning. For example, if you can freely and naively inline a function definition without having to worry too much about context then your PL is deemed to possess lots of RT-goodness (according to FP propaganda anyway; note you typically can't freely inline function definitions in a procedural programming language because the actual arguments to the function may involve dastardly side effects; even with a strict function-calling semantics divergence will complicate matters). Ah, but we only think that because of our blinkered world-view. Another way of looking at it is that the denotational semanticists have created a beautiful language to express the meanings of all those ugly languages, and we're programming in it. A third way to look at it is that mathematicians, philosophers, and logicians invented the semantics denotational semanticists have borrowed, specifically because of the properties derived from the philosophical commitments they made. Computer science has habit of taking ideas from other fields and merely renaming them. Denotational semantics is known as model
[Haskell-cafe] Reddy on Referential Transparency
Café, For those who havent seen it Uday Reddy has a comprehensive answer to a request to explain referential transparency on Stack Overflow. http://stackoverflow.com/questions/210835/what-is-referential-transparency/9 859966#9859966 For good measure he finishes with a rather scathing assessment of functional programmers claim to ownership of RT: Functional programmers don't know much of this research. Their ideas on referential transparency are to be taken with a large grain of salt. Marvellous! 'Tis rare to find such a robust assessment combined with understanding (and it certainly makes me think a bit). Have we become a bit complacent about RT? Chris ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Reddy on Referential Transparency
Have we become a bit complacent about RT? We're not complacent, we just know things without having to check references. Just kidding, of course, functional programmers tend to enjoy improving their understanding!-) The Strachey reference is worth reading - great that it is online these days, but it can be useful to complement it with others. Before Quine, there was Carroll, who explored meaning [1] and referential opacity [2], among other things. Also useful is Sondergaard and Sestoft [3], which explores both the history and the differences between not-quite-equivalent definitions. I happen to disagree with Reddy's assertion that having to explain a complicated language with the help of a less complicated one is perfectly adequate. Reddy himself has done good work on semantics of programming languages, but I'm a programmer first - if the language I work with does not give me the qualities that its semantics give me, then my means of expression and understanding are limited by the translation. All to be taken with grain of salt, active mind and sense of humor. Claus [1, Chapter 6] http://en.wikiquote.org/wiki/Through_the_Looking-Glass [2, the name of the song] http://homepages.tcp.co.uk/~nicholson/alice.html [3] Søndergaard, Sestoft (1990). Referential transparency, definiteness and unfoldability. Acta Informatica 27 (6): 505-517. http://www.itu.dk/people/sestoft/papers/SondergaardSestoft1990.pdf ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Reddy on Referential Transparency
Claus Reinke [mailto:claus.rei...@talk21.com]: I happen to disagree with Reddy's assertion that having to explain a complicated language with the help of a less complicated one is perfectly adequate. Reddy himself has done good work on semantics of programming languages, but I'm a programmer first - if the language I work with does not give me the qualities that its semantics give me, then my means of expression and understanding are limited by the translation. I also disagree. Haskell makes extensive use of translation into a core but those translations work so well because of the strong referential transparency guarantees that you get with Haskell. Equational reasoning locally and leaning on types for refactoring are intimately integrated into my functional programming process (as I bet they are for most Haskell programmers) -- I think the academic promise of RT has become quite 'real'. Something that may not be obvious to someone who doesn't program Haskell at scale is the major benefits of 'ghc -Wall'. Working with the -Wall subset of Haskell (as many do on production code) problems with accidental variable capture is much more difficult to do -- a terrific safeguard when (equationally) working code. Chris ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Reddy on Referential Transparency
On Fri, Jul 27, 2012 at 01:08:31PM +0100, Chris Dornan wrote: For those who haven’t seen it Uday Reddy has a comprehensive answer to a request to explain referential transparency on Stack Overflow. http://stackoverflow.com/questions/210835/what-is-referential-transparency/9 859966#9859966 For good measure he finishes with a rather scathing assessment of functional programmers’ claim to ownership of RT: Functional programmers don't know much of this research. Their ideas on referential transparency are to be taken with a large grain of salt. Marvellous! 'Tis rare to find such a robust assessment combined with understanding (and it certainly makes me think a bit). So a language is referentially transparent if replacing a sub-term with another with the same denotation doesn't change the overall meaning? But then isn't any language RT with a sufficiently cunning denotational semantics? Or even a dumb one that gives each term a distinct denotation. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Reddy on Referential Transparency
So a language is referentially transparent if replacing a sub-term with another with the same denotation doesn't change the overall meaning? Isn't this just summarizing the distinguishing characteristic of a denotational semantics? My understanding is that RT is about how easy it is to carry out _syntactical_ transformations of a program that preserve its meaning. For example, if you can freely and naively inline a function definition without having to worry too much about context then your PL is deemed to possess lots of RT-goodness (according to FP propaganda anyway; note you typically can't freely inline function definitions in a procedural programming language because the actual arguments to the function may involve dastardly side effects; even with a strict function-calling semantics divergence will complicate matters). Chris ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Reddy on Referential Transparency
On Fri, Jul 27, 2012 at 07:19:40PM +0100, Chris Dornan wrote: So a language is referentially transparent if replacing a sub-term with another with the same denotation doesn't change the overall meaning? Isn't this just summarizing the distinguishing characteristic of a denotational semantics? Right, so where's the substance here? My understanding is that RT is about how easy it is to carry out _syntactical_ transformations of a program that preserve its meaning. For example, if you can freely and naively inline a function definition without having to worry too much about context then your PL is deemed to possess lots of RT-goodness (according to FP propaganda anyway; note you typically can't freely inline function definitions in a procedural programming language because the actual arguments to the function may involve dastardly side effects; even with a strict function-calling semantics divergence will complicate matters). Ah, but we only think that because of our blinkered world-view. Another way of looking at it is that the denotational semanticists have created a beautiful language to express the meanings of all those ugly languages, and we're programming in it. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Reddy on Referential Transparency
On Jul 27, 2012 8:07 PM, Ross Paterson r...@soi.city.ac.uk wrote: Another way of looking at it is that the denotational semanticists have created a beautiful language to express the meanings of all those ugly languages, and we're programming in it. I think that's the idea. Also works out for compiler writers, parallel implementations, etc. Problem is from a 'classical' programming perspective it's an acquired taste. Chris ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Reddy on Referential Transparency
On Fri, Jul 27, 2012 at 12:06 PM, Ross Paterson r...@soi.city.ac.uk wrote: On Fri, Jul 27, 2012 at 07:19:40PM +0100, Chris Dornan wrote: So a language is referentially transparent if replacing a sub-term with another with the same denotation doesn't change the overall meaning? Isn't this just summarizing the distinguishing characteristic of a denotational semantics? Right, so where's the substance here? My understanding is that RT is about how easy it is to carry out _syntactical_ transformations of a program that preserve its meaning. For example, if you can freely and naively inline a function definition without having to worry too much about context then your PL is deemed to possess lots of RT-goodness (according to FP propaganda anyway; note you typically can't freely inline function definitions in a procedural programming language because the actual arguments to the function may involve dastardly side effects; even with a strict function-calling semantics divergence will complicate matters). Ah, but we only think that because of our blinkered world-view. Another way of looking at it is that the denotational semanticists have created a beautiful language to express the meanings of all those ugly languages, and we're programming in it. A third way to look at it is that mathematicians, philosophers, and logicians invented the semantics denotational semanticists have borrowed, specifically because of the properties derived from the philosophical commitments they made. Computer science has habit of taking ideas from other fields and merely renaming them. Denotational semantics is known as model theory to everyone else. Let's consider a referentially /opaque/ context: quotation marks. We might say It is necessary that four and four are eight. And we might also say that The number of planets is eight. But we cannot unify the two by substitution and still preserve truth functional semantics. We would get It is necessary that four and four are the number of planets (via strict substitution joining on 'eight') or a more idiomatic phrasing like It is necessary that the number of planets is four and four. This is a big deal in logic, because there are a lot of languages which quantify over real things, like time, possibility and necessity, etc., and some of these are not referentially transparent. In particular, a model for such a language will have to use frames to represent context, and there typically is not a unique way to create the framing relation for a logic. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Reddy on Referential Transparency
So a language is referentially transparent if replacing a sub-term with another with the same denotation doesn't change the overall meaning? But then isn't any language RT with a sufficiently cunning denotational semantics? Or even a dumb one that gives each term a distinct denotation. That's neat ... I mean, by performing sufficiently complicated brain gymnastics, one can do equational reasoning on C subroutines (functions!) too. So, there is no big difference between C and Haskell when it comes to equational reasoning... Regards, Damodar On Sat, Jul 28, 2012 at 1:47 AM, Alexander Solla alex.so...@gmail.comwrote: On Fri, Jul 27, 2012 at 12:06 PM, Ross Paterson r...@soi.city.ac.ukwrote: On Fri, Jul 27, 2012 at 07:19:40PM +0100, Chris Dornan wrote: So a language is referentially transparent if replacing a sub-term with another with the same denotation doesn't change the overall meaning? Isn't this just summarizing the distinguishing characteristic of a denotational semantics? Right, so where's the substance here? My understanding is that RT is about how easy it is to carry out _syntactical_ transformations of a program that preserve its meaning. For example, if you can freely and naively inline a function definition without having to worry too much about context then your PL is deemed to possess lots of RT-goodness (according to FP propaganda anyway; note you typically can't freely inline function definitions in a procedural programming language because the actual arguments to the function may involve dastardly side effects; even with a strict function-calling semantics divergence will complicate matters). Ah, but we only think that because of our blinkered world-view. Another way of looking at it is that the denotational semanticists have created a beautiful language to express the meanings of all those ugly languages, and we're programming in it. A third way to look at it is that mathematicians, philosophers, and logicians invented the semantics denotational semanticists have borrowed, specifically because of the properties derived from the philosophical commitments they made. Computer science has habit of taking ideas from other fields and merely renaming them. Denotational semantics is known as model theory to everyone else. Let's consider a referentially /opaque/ context: quotation marks. We might say It is necessary that four and four are eight. And we might also say that The number of planets is eight. But we cannot unify the two by substitution and still preserve truth functional semantics. We would get It is necessary that four and four are the number of planets (via strict substitution joining on 'eight') or a more idiomatic phrasing like It is necessary that the number of planets is four and four. This is a big deal in logic, because there are a lot of languages which quantify over real things, like time, possibility and necessity, etc., and some of these are not referentially transparent. In particular, a model for such a language will have to use frames to represent context, and there typically is not a unique way to create the framing relation for a logic. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
