Dominic Orchard dorchard

When applying for a PhD, in the UK, it's almost certain you will need to write a research proposal. This proposal should be something you discuss with a potential PhD supervisor and should be something clearly aligned with their existing interests.

The proposal should:

Situate itself within the current literature, citing several papers (at least 5) that are most relevant, as well as other papers in the general field. This should ideally include at least one paper from your proposed supervisor as it will then show why working with that supervisor makes sense for you and them;
Demonstrate that you have read and understood (some of) these papers you are citing, and discuss their implications for your proposed work;
Propose a number of research questions and potential directions for tackling them in your PhD. The more specific and concrete the better, but sometimes at this stage it might only be possible to point to a general direction of inquiry. Some high-level grand goals can be fine as long as there

These are a list of writing "strategies" that can be helpful when writing (e.g., to get going or to get unstuck). A meta-strategy is to jump between strategies: Feeling stuck? Then pick another strategy. Each strategy can be applied at different granularities, e.g. for an entire book or paper, or chapter or section, or just a subsection or paragraph. Different approaches may work better for you in different phases of a project.

In all cases, remember to avoid premature optimisation; re-writing and editing comes later.

Lastly, always be writing. Writing is like a muscle; being comfortable with writing takes practice (and good writing takes even more practice).

1. Stream [of consciousness]

	# Run with
	#
	# python graph.py makefilename
	#
	# which generates dependencies.dot which can be compiled with graphviz
	# to a png via:
	#
	# dot -Tpng dependencies.dot -o dependencies.png
	#
	#

	from typing import TYPE_CHECKING

	flag : bool = True

	def greet(name: str) -> None:
	"""Say hello to everyone"""
	print("Hi " + name)
	return None

	greet("Manchester")

	import Data.Bits
	import Data.Word
	import Foreign ( Ptr, new, castPtr, Storable(peek, poke) )
	import System.IO.Unsafe
	import Unsafe.Coerce

	qsqrt :: Float -> Float
	qsqrt x = 1 / qRsqrt x

	qsqrt' :: Float -> Float

	\documentclass[10pt]{article}
	\usepackage{amssymb} %maths
	\usepackage{amsmath} %maths
	\usepackage[utf8]{inputenc} %useful to type directly diacritic characters
	\usepackage[margin=4cm]{geometry}

	\title{Indexed natural numbers}
	\author{Dominic Orchard}

	\begin{document}

	program example
	use naryfunc
	implicit none
	! Outputs 2 6 24
	write(,) mult(2), mult(2, 3), mult(2, 3, 4)
	end program example

	import GHC.Clock -- imported from the `base` library
	rand :: IO Double
	rand = do { x <- getMonotonicTime; return $ x - fromInteger (floor x) }

	module Flexible where

	-- Exploring flexible graded monads, based on the work of Katsumata, McDermott, Uustalu and Wu
	-- https://dylanm.org/drafts/flexibly-graded-presentations.pdf

	open import Function

	_⇒_ : {E : Set} -> (E -> Set) -> (E -> Set) -> Set
	_⇒_ {E} X Y = forall (e : E) -> X e -> Y e

	-- # Examples from the paper 'Linearity and Uniqueness: An Entente Cordiale'

	-- ## Linearity (see Section 2, Key ideas)

	-- Linearity (with cake)

	data Cake = Cake
	data Happy = Happy

	eat : Cake -> Happy