I think the issue here might be the overloading of terms - lambda calculus is both the system of notation and the common name for the conceptual underpinnings of computational theory. While there is little to no similarity between the abstracted study of change over a domain and a notational system, the idea of function composition or continuous function theory (or even just computation as a concept) are all closely related with basic concepts from “calculus calculus” like limit theory and integral progression.
I’m pretty sure the term was coined in the interwar era, so it’s kind of interesting if people are just calling the concept of functions “lambda calculus” now. Obviously they’re much older than that.
and the common name for the conceptual underpinnings of computational theory.
the idea of function composition or continuous function theory (or even just computation as a concept) are all closely related with basic concepts from “calculus calculus” like limit theory and integral progression.
Okay, meta question here: What would a ‘connection’ that you’re willing to accept actually look like? Those I’ve already presented are what I would call pretty explicit connections between the two fields (and fragmenting this into an explanation of how lambda calculus relies and expands on functional mechanics is going to be a loooong diversion). It’s starting to feel like you’re pretty entrenched in your initial position, and are just looking for an internet debate.
I wouldn’t say entrenched, because I think this is honestly the first time I’ve seen the two come up together outside of their shared name. I was surprised, but then again sometimes reality is surprising.
Both have function composition, and expressions which contain free variables in multiple places. At the time, that was just a shorthand for what they were trying to express about slight changes. A bit later, formal analysis was axiomised, and is full of infinite things like Cauchy sequences and general topology. In the 20th century, substitution of a composed function into free variables becomes an object of study of it’s own, and found to be able to produce full complexity without anything else being added, being Turing equivalent.
All the infinite and continuous stuff that makes calculus work, at least as it’s considered abstractly, doesn’t really translate into a discrete system. You can numerically approximate it, and I guess you could even use lambda calculus-like functional language to do that, but I’m not mad that never came up in my math courses, like in your original comment.
If there’s nothing more to add to that, I am sorry for wasting your time.
I think the issue here might be the overloading of terms - lambda calculus is both the system of notation and the common name for the conceptual underpinnings of computational theory. While there is little to no similarity between the abstracted study of change over a domain and a notational system, the idea of function composition or continuous function theory (or even just computation as a concept) are all closely related with basic concepts from “calculus calculus” like limit theory and integral progression.
edit: clarity
I’m pretty sure the term was coined in the interwar era, so it’s kind of interesting if people are just calling the concept of functions “lambda calculus” now. Obviously they’re much older than that.
What? Nobody’s doing that, it’s just a distinct area of mathematics - I’m pretty confused where you got that idea from at all.
So, I took it from these parts together:
I’m still not seeing the connection otherwise.
Okay, meta question here: What would a ‘connection’ that you’re willing to accept actually look like? Those I’ve already presented are what I would call pretty explicit connections between the two fields (and fragmenting this into an explanation of how lambda calculus relies and expands on functional mechanics is going to be a loooong diversion). It’s starting to feel like you’re pretty entrenched in your initial position, and are just looking for an internet debate.
I wouldn’t say entrenched, because I think this is honestly the first time I’ve seen the two come up together outside of their shared name. I was surprised, but then again sometimes reality is surprising.
Both have function composition, and expressions which contain free variables in multiple places. At the time, that was just a shorthand for what they were trying to express about slight changes. A bit later, formal analysis was axiomised, and is full of infinite things like Cauchy sequences and general topology. In the 20th century, substitution of a composed function into free variables becomes an object of study of it’s own, and found to be able to produce full complexity without anything else being added, being Turing equivalent.
All the infinite and continuous stuff that makes calculus work, at least as it’s considered abstractly, doesn’t really translate into a discrete system. You can numerically approximate it, and I guess you could even use lambda calculus-like functional language to do that, but I’m not mad that never came up in my math courses, like in your original comment.
If there’s nothing more to add to that, I am sorry for wasting your time.