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andrejbauer / functional2tree.eff
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
@andrejbauer
andrejbauer / README.markdown
Last active Feb 4, 2017
Elimination of constants and function symbols from set theory
View README.markdown

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.

@andrejbauer
andrejbauer / example.m31
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
@andrejbauer
andrejbauer / mandelbrot.ml
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
@andrejbauer
andrejbauer / assoc.elf
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"?
%
@andrejbauer
andrejbauer / gist:4272538
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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