@ngnghm.bsky.social
On algebraic data types and fixed-point of polynomials: since the derivative of µ(P) is List(P'), then µ=∫List. Now, List(X)=1+X+X²+X³+…+Xⁿ+…=1/(1-X). Hence µ(X)=X+X²/2+X³/3+…+Xⁿ/n+…=-Log(1-X). I'm not sure what that means, but I am amazed.
March 2, 2025 at 3:48 AM
On algebraic data types and fixed-point of polynomials: since the derivative of µ(P) is List(P'), then µ=∫List. Now, List(X)=1+X+X²+X³+…+Xⁿ+…=1/(1-X). Hence µ(X)=X+X²/2+X³/3+…+Xⁿ/n+…=-Log(1-X). I'm not sure what that means, but I am amazed.
Funny how Lispers had no problem combining OO and FP long before any idiot invented an opposition between the two.
Maybe "my two-bit typesystem can only handle a tiny subset of OO|FP" isn't good justification to claim that anything outside it is worthless?
Maybe "my two-bit typesystem can only handle a tiny subset of OO|FP" isn't good justification to claim that anything outside it is worthless?
February 5, 2025 at 7:16 AM
Funny how Lispers had no problem combining OO and FP long before any idiot invented an opposition between the two.
Maybe "my two-bit typesystem can only handle a tiny subset of OO|FP" isn't good justification to claim that anything outside it is worthless?
Maybe "my two-bit typesystem can only handle a tiny subset of OO|FP" isn't good justification to claim that anything outside it is worthless?
BLEG: Data types and formal series
A list of a is a type t such that t = 1+a*t.
Solving: t = 1/(1-a)
Its formal series: 1 + a + a*a + a*a*a + ...
t is indeed the sum of lists of size n for all n!
What series are reachable as fixpoint of polynomials? Who studied that, especially wrt data types?
A list of a is a type t such that t = 1+a*t.
Solving: t = 1/(1-a)
Its formal series: 1 + a + a*a + a*a*a + ...
t is indeed the sum of lists of size n for all n!
What series are reachable as fixpoint of polynomials? Who studied that, especially wrt data types?
January 12, 2025 at 5:33 PM
BLEG: Data types and formal series
A list of a is a type t such that t = 1+a*t.
Solving: t = 1/(1-a)
Its formal series: 1 + a + a*a + a*a*a + ...
t is indeed the sum of lists of size n for all n!
What series are reachable as fixpoint of polynomials? Who studied that, especially wrt data types?
A list of a is a type t such that t = 1+a*t.
Solving: t = 1/(1-a)
Its formal series: 1 + a + a*a + a*a*a + ...
t is indeed the sum of lists of size n for all n!
What series are reachable as fixpoint of polynomials? Who studied that, especially wrt data types?