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5
votes
0answers
148 views

Feasible Type Theories

I am looking for references about efficient type theories, efficiency in the sense of computational complexity, and type theory in the sense of Martin-Lof's type theories. Has there been any studies ...
3
votes
0answers
192 views

An elegant formulation for typed sets

Fix a poset $T$, which we'll think of as a set of "types," interpreting $a \leq b$ as "$a$ is more general than $b$." Construct a category of TSet as follows. Objects: Pairs ($X$, $\tau : X ...
1
vote
0answers
69 views

Natural relations between substitutions

Consider two contexts $\Gamma,\Delta$ (from some background type theory), and substitutions $s_1,s_2:\Gamma\rightarrow \Delta$. In the case of $1$-element contexts, we get that a substitution is ...