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Reference-request is used when the author needs to know about work related to the question.

26 votes
1 answer
727 views

Unification and Gaussian Elimination

Does anyone knows of references that precisely spell out the connection between the unification algorithm and Gaussian elimination? I'm particularly interested in the relationship between triangular s …
Neel Krishnaswami's user avatar
9 votes
3 answers
338 views

Resumption-based IO systems?

I've been playing around with resumptions lately, mostly from Abramsky's classic paper Retracing Some Paths in Process Algebra. They are quite slick (basically solutions to the domain equation $R = I …
Neel Krishnaswami's user avatar
22 votes
3 answers
3k views

Generalizations of Brzozowski's method of derivatives of regular expressions to grammars?

Brzozowski's method of derivatives is a very pretty technique for building deterministic automata from regular expressions in a nicely algebraic way. I've worked out some cute generalizations of this …
Neel Krishnaswami's user avatar
18 votes
1 answer
481 views

Parametricity and projective eliminations for dependent records

It's well-known that in System F, you can encode binary products with the type $$ A \times B \triangleq \forall\alpha.\; (A \to B \to \alpha) \to \alpha $$ You can then define projection functions $\p …
Neel Krishnaswami's user avatar
14 votes
0 answers
309 views

Categorical semantics for S5 modal logic?

Does anyone know where I can look to find out what the generally categorical semantics of S5 is? For S4, the answer is well-known: we want a Cartesian closed category with a product-preserving comon …
Neel Krishnaswami's user avatar
16 votes
2 answers
501 views

Uses of quasi-PERs/difunctional relations/zig-zag relations?

Given sets $A$ and $B$, a difunctional relation $(\sim) \subseteq A \times B$ between them is defined to be a relation satisfying the following property: If $a \sim b$ and $a' \sim b'$ and $a \sim …
Neel Krishnaswami's user avatar
10 votes
1 answer
329 views

Unification-based elimination rule for equality

A few years back, I ran across the following left-rule for equality in sequent calculus: $$ \frac{s \doteq t \leadsto \theta \qquad \theta(\Gamma) \vdash \theta(C)} {\Gamma, s \doteq t …
Neel Krishnaswami's user avatar
15 votes
1 answer
646 views

Fixed point theorems for constructive metric spaces?

Banach's fixed point theorem says that if we have a nonempty complete metric space $A$, then any uniformly contractive function $f : A \to A$ it has a unique fixed point $\mu(f)$. However, the proof o …
Neel Krishnaswami's user avatar
11 votes
2 answers
350 views

References to programming languages based on conditional logics

Conditional logics are logics which augment traditional logical implication with modal operators corresponding to other notions of condition (for example, the causal conditional $A\; \square\!\!\!\!\t …
Neel Krishnaswami's user avatar
15 votes
2 answers
484 views

Proof theory of biproducts?

A category has biproducts when the same objects are both the products and coproducts. Has anyone investigated the proof theory of categories with biproducts? Perhaps the best-known example is the cat …
Neel Krishnaswami's user avatar
12 votes
1 answer
323 views

Reference for the fact that (0=1) implies false requires a universe in MLTT

It's a fairly well-known fact that deriving a contradiction from a disequality (for example, $(0=1) \to \bot$) in Martin-Loef type theory requires a universe. The proof is also fairly straightforwar …
Neel Krishnaswami's user avatar