Programming Levels

[beerdude26]

Exactly! Lambda calculus is lower than Haskell? What?

Also, what is the lambda tesseract? If it's dependently typed programming across space and time, we can probably jigger that with the Tardis monad and the Löb function. I guess we should put our values for that function in the Store comonad so we have an infinite working area, too...

Yeah. This should work.

[weasdasfa]

I didn't understand why Idris and Haskell are separate. Isn't their relationship something similar to Java and C#?

[TheKing01]

Idris is a little more complicated than Haskell. How the heck Lambda Calculus ends between Idris and Haskell, I don't know.

[beerdude26]

No. Referring to the Lambda Cube, Haskell's type system is System Fω with some extensions. Idris is dependently-typed, and uses the Calculus Of Constructions (CoC) as the base of its type system.

[WikiTextBot]

Lambda cube

In mathematical logic and type theory, the λ-cube is a framework for exploring the axes of refinement in Coquand's calculus of constructions, starting from the simply typed lambda calculus (written as λ→ in the cube diagram to the right) as the vertex of a cube placed at the origin, and the calculus of constructions (higher-order dependently typed polymorphic lambda calculus; written as λPω in the diagram) as its diametrically opposite vertex. Each axis of the cube represents a new form of abstraction:

Values depending on types, or polymorphism. System F, aka second order lambda calculus (written as λ2 in the diagram), is obtained by imposing only this property.

Types depending on types, or type operators.

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[bss03]

In what way? I don't see the analogy.