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# Andrej Bauerandrejbauer

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Created Apr 19, 2018
Use of effects and handlers to compute the tree representation of a functional.
View functional2tree.eff
 (** This code is compatible with Eff 5.0, see http://www.eff-lang.org *) (** We show that with algebraic effects and handlers a total functional [(int -> bool) -> bool] has a tree representation. *) (* A tree representation of a functional. *) type tree = | Answer of bool | Question of int * tree * tree
Last active Feb 4, 2017
Elimination of constants and function symbols from set theory

Official Zermelo-Fraenkel set theory only has the elementhood relation symbol ∈, and nothing else. Other constants, such as ∅, ⊆, ∩, ∪, f[x], etc. can be mechanically eliminated. The result of the elimination is a formula which is logically equivalent to the original, but is more complicated.

This program eliminates constants and function symbols, and generates LaTeX showing the formula before and after the elimination.

Last active Aug 6, 2016
Example of Andromeda ML-programming
View example.m31
 (* In Andromeda everything the user writes is "meta-level programming. *) (* ML-level natural numbers *) mltype rec mlnat = | zero | succ of mlnat end (* We can use the meta-level numbers to define a program which computes n-fold iterations of f. Here we give an explicit type of iterate because the ML-type inference cannot tell
Created Dec 28, 2013
A simple program to compute the Mandelbrot set.
View mandelbrot.ml
 (* The Mandelbrot set. Compile with: ocamlbuild mandelbrot.native Example usage: ./mandelbrot.native --xmin 0.27085 --xmax 0.27100 --ymin 0.004640 --ymax 0.004810 --xres 1000 --maxiter 1024 --file pic.ppm
Created Jun 18, 2013
Twelf seems very finicky about certain details. Here I explore how associative lists depend in unreasonable ways on the complexity of the value type.
View assoc.elf
 % Testing how lookup in an associative list works. % We consider associative lists with keys of type key and values % of type value. % % Ideally, we want key to be any type with decidable % equality and value to be any type. However, we use natural numbers % as keys so that we can convince Twelf that key has decidable equality. % Is there a way to tell Twelf "assume key has decidable equality"? %
Created Dec 12, 2012
A lemma which explains how transport and function extensionalty interact.
View gist:4272538
 Variable A : Type. Variable P : A -> Type. Variable Q : forall x, P x -> Type. Lemma transport_funext (f g : forall x, P x) (n : forall x, Q x (f x)) (E : forall x, f x = g x) (x : A) : (transport (fun h => forall x, Q x (h x)) (funext E) n) x = transport (Q x) (E x) (n x).
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