The type-theory tag has no usage guidance.

**10**

votes

**2**answers

1k views

### What is the manner of inconsistency of Girard's paradox in Martin Lof type theory

I am aware that assigning the type of Type to be Type (rather than stratifying to a hierarchy of types) leads to an inconsistency. But does this inconsistency allow the construction of a well-typed ...

**7**

votes

**4**answers

888 views

### Can dependent sums be encoded as dependent products?

Please forgive any unorthodox notation or obvious errors here... I'm trying to get an intuition for dependently typed languages, so I'm starting out by seeing which analogies I can take from the ...

**3**

votes

**1**answer

461 views

### What notions of universe does predicative type theory admit?

Palmgren (1997), On universes in type theory, discusses work of several theorists that provide what we might call a family of Large Universe Axioms (LUAs) for predicative type theory, culminating in ...

**6**

votes

**2**answers

661 views

### Recursively dependent types?

Is there such a thing as "recursively dependent types"? Specifically, I would like a dependent type theory containing a type $A(x)$ which depends on a variable $x: A(z)$, where $z$ is a particular ...

**13**

votes

**7**answers

2k views

### What is lambda calculus related to?

So I'm not much of a math guy but I've really enjoyed programming in Lisp and have become interested in the ideas of lambda calculus which it is based.
I was wondering if anyone had a suggestion ...