Talk:Simply typed lambda calculus

message: Hi. The current presentation talks about "type variables", while in my experience most authors talk about "type constants" or "base types" or "atomic types". I sympathize more with the second terminology — people like Pierce, Girard, Jacobs, Johnstone. The "type variables" terminology seems to be used by Barendregt in his article to clarify the connection with System F, but it is a bit strange because these "variables" don't vary over anything. Any objections if I change "type variables" to "base types"? Also, many of the authors allow some term constants, and product types, in STT. Any objections to mentioning these things? ComputScientist (talk) 13:55, 3 September 2009 (UTC)
replies: text: I even wrote a stub on type variable with that latter meaning, so yeah, terminology here should be changed. Be WP:BOLD. Pcap ping 14:04, 3 September 2009 (UTC)

text: You could mention (or detail if you have time) here the "simple extensions" as B.C. Pierce calls them in chapter 11 of his TaPL book.  Pcap ping 14:23, 3 September 2009 (UTC)
thread_title:  Type variables -> Base types or Atomic types 

message: The relationship with Type_theory#Simple_theory_of_types should be discussed somewhere in here too. Pcap ping 14:46, 3 September 2009 (UTC)
thread_title:  Another suggestion 

message: I tried to do a bit of cleaning up of the Semantics section, and also added some description of bidirectional type checking under "Alternative syntaxes".  One terminology question/quibble: in Typing rules, I am not sure what distinction you are drawing between "typing relation" and "typing judgment".  (I think you are using "relation" where I would use "judgment", and "judgment" where I would use "derivation"...)  Could you elaborate? Noamz (talk) 05:46, 26 September 2009 (UTC)
replies: text: Hi Noamz. My impression is that the "typing relation" is the set of all "typing judgements". That's to say, a judgement is a single triple  (\Gamma, e ,\sigma) whereas the typing relation is a set of judgements. A "judgement" is not a "derivation", but the rules let you derive which "judgements" are in the "relation". Do you agree? I think this is what the article says, but do clarify it if poss. ComputScientist (talk) 08:09, 26 September 2009 (UTC)
replies: text:  Okay, I can see how the article says that.  I think it would help to add something like, "Instances of the typing relation are called typing judgments.  The validity of a typing judgment is shown by providing a typing derivation, constructed using the following rules,..."  I'm going to go ahead and add that. Noamz (talk) 17:51, 26 September 2009 (UTC)
thread_title:  Typing relation/judgment/derivation 

message: The article claims that it is not currently known whether higher-order matching is decidable; however, http://homepages.inf.ed.ac.uk/cps/longmatch.pdf from C. Stirling claims that it is. The article claims for Stirling's work that "the complete version of the proof is still unpublished", but the linked-to paper (from 2009) seems fairly thorough to me. Barring any objection, I'll update the article. Neilc (talk) 07:20, 30 March 2010 (UTC)
thread_title:  Decidability of higher-order matching 

message: You claim that:
The equation (\lambda x:\sigma.t)\,u =_{\beta} t[x:=u] holds in context \Gamma whenever \Gamma,x:\sigma \vdash t:\sigma \to \tau and \Gamma\vdash u:\sigma. However, if we look at (\lambda x:\sigma.x)\,u, we have that the type of x a.k.a. t in this case is not \sigma \to \sigma but only \sigma. I think a fix should be requiring the type of t[x:=u] to be \tau instead.
:I think there was a mistake, and I think I've fixed it... ComputScientist (talk) 16:02, 2 December 2010 (UTC)
thread_title:  Typo 

message: In the presentation of the inference rules, there should be some words towards avoiding duplicate names with different types in the typing context. Specifically, either renaming of variables that would cause duplicates must be done or the typing context must be given a more detailed treatment to avoid such duplicates. Without doing so, it appears the judgment \Gamma,x:\tau_1,x:\tau_1\rightarrow\tau_2\vdash x x : \tau_2 would be typeable. --Chaosape (talk) 02:08, 2 January 2017 (UTC)
thread_title:  Duplicate variable names with different types in the typing context. 

message: I think that the syntax should make it clear that terms are defined up to alpha equivalence. Otherwise the typing rules don't work, for example \x\x.x would not type.  — Preceding unsigned comment added by Vasiliscul (talk • contribs) 14:05, 10 September 2018 (UTC)
thread_title:  Alpha equivalence?