Talk:Intuitionistic type theory

message: I have extensively expanded and rewritten this page. I am happy for anybody who helps me by elimenating typos and bad expression and by inserting more references. In the past somebody rewrote parts of what I had written, changing the emphasis considerably, e.g. talking about "an" Intuitionistic Type Theory while people in the wider area usually refer to Intuitionistic Type Theory using capital letters in the same way they refer to Set Theory and not a set theory. Hence, I have changed this back. If anybody is unhappy about this, please let's discuss it here.
Thorsten 21:57, 21 May 2005 (UTC)
thread_title: Untitled

message: It's right to notice all the synonyms that have been used for this theory, but my impression is that few scholars will use Intuitionistic Type Theory to refer to the calculus, but instead talk of Martin Loef's type theory, because there are many proposed intuitionistic type theories.  I'd suggest moving the page, and say that the calculus has been called these other names. --- Charles Stewart 19:03, 23 May 2005 (UTC)
thread_title: Article name

message: Spelled with initial capitals, Type Theory refers to a functional programming language based on the same principles.
Who has added this nonsense???? I have removed it. If you want it back, please xplain.
--Thorsten 20:55, 7 June 2006 (UTC)
thread_title: Type Theory is the name of a Programming Language

message: At first glance it would seem that the "dependent sum" is a kind of product, and yet "dependent product" refers to something else. Can we have an explanation as to why these terms were chosen? Hairy Dude (talk) 20:03, 6 June 2008 (UTC)
replies: text: The terminology comes from indexed sums and products of sets. I tried to clarify. Sam (talk) 13:30, 7 June 2008 (UTC)
thread_title:  Explanation of term "dependent product/sum" 

message: Should the functor T not be named Ty?  The colon ":" is not a symbol of the Language of category theory so this should be explained; of which category is A:Ty(G) an object? Stephan Spahn (talk) 10:17, 15 May 2011 (UTC)
thread_title: Categorical models of Type Theory

message: The section Extensional versus intensional, as currently written, implies that, while calculating extensional types can be undecidable, a restriction of decidability can be imposed on the types used in the program or expression. But the halting problem (which is mentioned) prevents an implementation from being able to confirm the decidability of the type calculation (allowing an unbounded-time computation during compilation is a Bad Thing). This means that extensional types, which seem more flexible, rely on prudent use by the program or expression author to avoid disaster. In practice, this can only work in academic settings. I'm not sure whether these difficulties are due to the way this section is written or whether they imply that extensional types are not practical. In any case, some clarification seems to be needed. David Spector (talk) 10:50, 30 December 2011 (UTC)
thread_title:  Decidable extensional type checking? 

message: While the Wordpress blogger who so graciously hosts the link to the .pdf in the References section did apparently receive permission to host the scan, their blog has been essentially dead since 2010. I wonder what to do in such a situation. It would be unfortunate if the link rotted; while Google gladly brings up lecture notes under that title, I don't see any other permitted, available copies of the book. I've downloaded a copy of it, but I don't really want to go through the trouble of getting permission to host it. Even if I did, we'd be left with the same problem five-ish years down the road. What to do? ArXivFever (talk) 07:03, 1 March 2012 (UTC)
thread_title:  .pdf of Martin-Loef's Intuitionistic Type Theory 

message: I did a rewrite of the first 3 sections.  Mostly tried to make the language accessible to people who had not studied type theory before.  I did delete a few concepts, but mostly I tried to make the language easier without dumbing down the article.  Mdnahas (talk) 14:07, 1 June 2018 (UTC)
thread_title:  Significant Rewrite June 2018 

message: So, I believe I read somewhere that Nordstr ̈om Petersson Smith had the most referenced version of Martin-Loef Type Theory.  If I recall correctly, it said that those three had reformulated MLTT to match Barendregt's Lambda Cube.  That is, that variables were only bound by lambda and pi types.  I don't think the theory behaved any differently than previous theories --- it still proved the same things as one of the earlier theories --- but the rules of inference were slightly different.
I tried to find where I read that, but couldn't find it.
I did look NPS's paper and found they had two!  There is one on MLTT and one on programming with MLTT.  
The first paper says "The type theory presented in this chapter was put forward by Martin-L ̈of in 1986 with the specific intention that it should serve as a logical framework."   In fact, both papers say they use the theory from 1986.  But 1986 is later than any theory lists currently on the wikipedia page!  Is this formulation new?  — Preceding unsigned comment added by Mdnahas (talk • contribs) 01:09, 5 January 2022 (UTC)
replies: text: I read the NPS book ("Programming in ML Type Theory") quite closely for my doctorate and I recall no reference to Barendregt's cube. It is kind of separated into a logical framework, which is close to the lambda-Pi calculus and the calculus proper, although I don't recall it explicitly being called a logical framework. Take this all with a pinch of salt since it has been so long since I looked at the book: it's been 19 years since I defended my DPhil and that was quite a while after i finished the first draft of my dissertation. — Charles Stewart (talk) 16:26, 5 January 2022 (UTC)
thread_title: 1986 theory?