What’s a tree? First define a sequence or length n> 0 as a total map s: {1,.. n}→ X. Let Nil be the empty sequence. If s is a sequence of length n, and x is an element, then u
Linked lists
What’s a linked list? Let V be a set of values and A be a set of “addresses”. Say a map f is a “linked list element” compatible with values V and addresses A if and only if f(value)∈ V
New and or notable.
My new favorite line: “My good sir, I worry that your groundbreaking treatise will go overlooked here on Twitter” This is a great essay on programming: Operant Conditioning by Software Bugs. This is a good point on mathematics versus the
Xor patterns
The xor i mod 128 “multiplication table” as presented by Mathematica. Here is the mod 64 matrix.
More UB madness from LLVM/Clang
Via @johnregehr this further tale of compiler “optimizations” that break correct C code without even a warning by deleting a necessary null pointer check. In this example, Bar contains a stack of Foos. Sometimes the Foo stack is empty, so
informal methods applied to networks and timeouts
Distributed computation involves many interesting issues concerning shared data. Here I want to sketch out what networks look like using applied (informal) mathematics so we can look at some algorithms for consensus and data consistency. No formal methods or category
Current reading: meltdown and spectre edition
Google project zero and then The two attacks. and remediation for Spectre in LLVM. Test code. (via Lobste.rs) Limits of ASLR. Spanner,True Time and CAP See also Synchronous Processors. and processor architecture. Some papers by Stephen Kell (also via lobste.rs
Types considered harmful. From a remark by Wolfram.
Originally Nov 30, 2017. (revised 2021,2023) Russell introduced what is often viewed as his most original contribution to mathematical logic: his theory of types—which in essence tries to distinguish between sets, sets of sets, etc. by considering them to be
the terrible effect of Krohn-Rhodes
One of the most interesting theorems in computer science is the Krohn-Rhodes theorem that shows a strong link between basic computer science and group theory. Crudely, the KR theorem extends Jordan-Holder \( (H_1 \triangleleft H_2 … \triangleleft H_n=G)\) to state