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# Questions tagged [typed-lambda-calculus]

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### Can you always throw away the types when evaluating lambda expressions?

As I understand it, in the simply typed lambda calculus you can type-check your terms, then throw away all the types and do the evaluation exactly as if it was the untyped lambda calculus. Is that ...
• 133
168 views

### $\lambda$-definability and structure preserved by homomorphisms

I imagine there are some standard results that bear on this, but I'm having trouble finding a proof or refutation of it. Some prelimary definitions. A Henkin structure $A = (A^\cdot, ⟦\cdot⟧_A)$ for ...
• 433
173 views

### Constructive Strong Normalization of the Extended Calculus of Constructions

The extended calculus of constructions (ECC) is basically the calculus of constructions with cumulative universes. I use the definition which Zhaohui Luo used in his PhD theses which contained a proof ...
• 365
313 views

### Are there strongly normalizing lambda terms that cannot be given a System F type?

I know that all well-typed System F terms are strongly normalizing, but is the converse true as well? In other words, does System F typeability precisely characterize program termination? (And if so, ...
150 views

### Set-theoretic encoding of functions in type theory

Functions usually get encoded in set theory as follows. A function $A\to B$ is a subset $f\subset A\times B$ such that $\pi_1:f\to A$ is a bijection. In type theory to give a function $A\to B$ is to ...
123 views

### Dependent eliminator for empty type in intensional Martin-Löf type theory

In calculus of inductive constructions you can just say that the empty type is the type with no constructors and it automatically builds the dependent eliminator. But let's say I'm setting up ...
99 views

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