Talk:System F

message: I tried to add a reference to the use of system F in GP. The process to cite is opaque and I don't get it. I don't have time to go through the 5 pages of documentation that are on the site (not one of which even contains a simple example that I can just reuse).  —Preceding unsigned comment added by 205.193.82.252 (talk) 16:25, 3 April 2009 (UTC)
replies: text: Barendregt's system maybe, haven't seen it used outside of untyped, but I see no reason it can't be used in System-F. Rajakhr (talk) 03:37, 6 April 2010 (UTC)

text: System-F is strongly normalizing and thus not turing complete. Rajakhr (talk) 03:37, 6 April 2010 (UTC)

text: Added citations to Reynolds & Girard. Noamz (talk) 20:20, 6 April 2010 (UTC)
thread_title: Older comments

message: According to a comment posted by Dr. Charles Stewart on a thread at Lambda-the-Ultimate on 2008-10-20: "Look at the introduction (pp2-12) of Girard's thesis, Interpretation fonctionnelle et elimination des coupures de l'arithmetique d'ordre superieur (PDF: fragment only), where the term [System F] is introduced by explicit contrast to Gödel's System T, which —being Girard— he doesn't refer to System T there directly as such but as "le système de Gödel OF_1", ie. the order-functional-one system of Gödel. I have heard that Girard delights in the carefully obscure, but I think this is where System F is named. For completeness sake, Gödel described his System T in his 1958 Dialectica paper, which was later translated into english under the title On a Hitherto Unexploited Extension of the Finitary Standpoint. I have the idea that the T stands for "type", as in "primitive recursive functionals of finite type", cf. Avigad & Feferman's Gödel’s Functional (“Dialectica”) Interpretation, although, as for F, I am not quite sure." --Omnipaedista (talk) 23:28, 14 June 2011 (UTC)
thread_title: Etymology

message: As far as I can tell, the non-superscript occurrences of "Boolean" in the definitions of e.g. AND, i.e.,
: \mathrm{AND} = \lambda x^{\mathsf{Boolean}} \lambda y^{\mathsf{Boolean}}{.} x\, \mathsf{Boolean}\, y\, \mathbf{F}
are (i) undefined notation (type where a term would be expected) and (ii) not necessary, in the sense that
: \mathrm{AND} = \lambda x^{\mathsf{Boolean}} \lambda y^{\mathsf{Boolean}}{.} x\, y\, \mathbf{F}
should be a sufficient and correct definition. I may however be missing something subtle. 130.239.128.243 (talk) 15:17, 7 October 2011 (UTC)
replies: text: Those occurrences of \mathsf{Boolean}  occurring within the lambda expressions would actually be necessary. Any universal quantification of a type variable in the type of an expression means that the expression needs to be "fed in" an extra argument which specifies a type; a "type expression", if you will. That type argument is bound by that "big lambda" at the beginning of the expressions for T and F; i.e., the fed in "type expression" is bound to a type variable. \mathsf{Boolean} would be a meta-symbol (outside of the System F itself) which is shorthand for the "type expression" \forall \alpha : \alpha \rightarrow \alpha \rightarrow \alpha .  18:18, 14 July 2012 (UTC)

text: In the definition of \mathrm{AND}, x is of type \mathsf{Boolean} which means that x would require three — not two — parameters; the first parameter being a "type expression", and the next two parameters being lambda expressions. (That should become clear by looking at the definitions of both T and F; both are lambda expressions which have three lambdas, not two; the first lambda being big. Also, T and F should be the only possible expressions of type \mathsf{Boolean}; after a type is fed to such "Boolean", two values of that type are fed to it, and then a value of that type is expected as output. An arbitrary constant output could not be returned because it might easily not correspond to the required type (fed in at the beginning), which leaves basically just two choices for output: either the second or the third parameter, both of which have the required type.)  18:32, 14 July 2012 (UTC)
thread_title:  Boolean in some formulae 

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thread_title:  External links modified