Timeline for Relationship of lambda calculus to the rest of math
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Dec 11, 2016 at 0:05 | comment | added | Justin Hilburn | If you are just trying to connect programming languages and mathematics I would learn the typed lambda calculus and look at mathoverflow.net/questions/903/… | |
| Dec 10, 2016 at 22:57 | comment | added | Justin Hilburn | The different kind of semantics are explained here en.wikipedia.org/wiki/Semantics_(computer_science) | |
| Dec 10, 2016 at 22:51 | comment | added | Justin Hilburn | I would hold off on learning domain theory for a while. Church doesn't make any effort to give a denotation to lambda terms in his book. He gives an operational semantics instead (the algorithm for reducing a lambda term to a normal form). | |
| Dec 10, 2016 at 22:29 | comment | added | Polymer | You've convinced me this is the correct answer, even though I'm not sure I understand it. Generally when I'm trying to understand properties of a function definition, the "language" isn't directly important (homomorphisms are conceptual, not syntactical). I evidently tried and failed to separate the syntax of lambda calculus from the concept of a certain function I thought was introduced. Thank you for your time. Any recommendations for learning Domain theory would be appreciated. | |
| Dec 10, 2016 at 22:07 | vote | accept | Polymer | ||
| Dec 10, 2016 at 21:58 | comment | added | Justin Hilburn | It is just like how there are many different models of the theory of groups, i.e., particular groups. It doesn't make sense to say that an element of a group is "really" a matrix even though that might be true in a particular model. | |
| Dec 10, 2016 at 21:47 | comment | added | Justin Hilburn | As you said, one way of doing this makes lambda terms into elements of a domain. | |
| Dec 10, 2016 at 21:46 | comment | added | Justin Hilburn | I think you need to be more careful about the distinction between a language and a semantics for that language. Lambda terms aren't anything but strings of symbols obeying a certain grammar and rewriting rules. One may attempt to associate mathematical objects to lambda terms (give a denotational semantics) but there are many ways to this. | |
| Dec 10, 2016 at 19:46 | comment | added | Polymer | So if I understand this answer correctly. Untyped lambda calculus is deceptively complicated. The lambda terms are "really" continuous functions of some odd space. Is that correct? | |
| Dec 10, 2016 at 18:55 | history | edited | Justin Hilburn | CC BY-SA 3.0 |
added 56 characters in body
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| Dec 10, 2016 at 18:47 | history | answered | Justin Hilburn | CC BY-SA 3.0 |