Intro

• Research software engineer
• Write proofs for imperative (concurrent) algorithms
• Programs that assume a global storage and manipulate pointers to it

List reversal

List reversal

• Written in some "midlevel" language
• You can compile it to machine code
• You can specify it with some abstraction

Compilation

.LBB2_1:
        cmp     qword ptr [rbp - 32], 0
        je      .LBB2_3
        mov     rax, qword ptr [rbp - 32]
        mov     rax, qword ptr [rax + 8]
        mov     qword ptr [rbp - 16], rax
        mov     rcx, qword ptr [rbp - 24]
        mov     rax, qword ptr [rbp - 32]
        mov     qword ptr [rax + 8], rcx
        mov     rax, qword ptr [rbp - 32]
        mov     qword ptr [rbp - 24], rax
        mov     rax, qword ptr [rbp - 16]
        mov     qword ptr [rbp - 32], rax
        jmp     .LBB2_1

Specification

reverse :=

list A :=   nil  
          | :: of A & list A

rev nil   = nil
rev x::xs = rev xs ++ x::nil

{is_list i l}
reverse
{is_list done (rev l)}

Language stack

• Interaction between machine and human
• The gap is large, so we have a series of languages
• Programming is about navigating this stack
• Can computers also help with this navigation?

Me and languages

• A linguist father
• Got a computer in early 90s for text processing
• "Computer obtains a mind", 1985-1990
• "Goedel, Escher, Bach", 1979

Me and languages

• Perceptrons, expert systems, semantics, learning
• Quines, fixpoints, self-modifying code
• Went to get a CS degree in mid 2000s

input to a program = string in a new language

the program itself = its interpreter

Language-Oriented Programming

Early work experience

• C/C++/Java (also some Smalltalk)
• Always about manipulating state ("mid-stack")
• Leaking abstractions: segfaults, null pointers, bizarre errors
• Spent a few years playing detective

Early work experience

• Nice theory, rough practice
• The computer is not a very coherent dialogue partner
• "This is just bit shuffling"
• Need to look for languages somewhere else

Biology

• Can sometimes be seen as "language stacks" incarnate
• Biosemiotics, code, signalling

Systems biology

Lin et al., Journal of Biological Engineering (2018)

"Synthesis of control unit for future biocomputer"

Functional programming

• Played with Lisp before
• Started getting interested in typed functional languages like OCaml and Scala (early 2010s)
• Began with parsers and data pipelines
• Bioperl, Biocaml, ...

Bioinformatics

• Applied to a PhD in Plant Systems Biology
• Studied for 2.5 years before dropping out
• More interested in quantitative effects than in big picture
• "Computational glue" pipelines (Perl, Fortran, MATLAB, etc), ad-hoc write-and-forget scripts
• Even less trustworthy!

Script troubles

e.g., this paper from 2019 suggests 150+ papers could have wrong results:

"The error is the result of a simple file sorting problem. On operating systems without default file name sorting, the script fails to match the files containing a conformer’s free energy with its chemical shift – leading to an overall wrong value."

Data engineering

• Went back to the industry, wishing for more rigor
• R&D in ad-tech
• Recommender engines, distributed data pipelines
• Started fully embracing FP (mid 2010s)
• "Stats and monads" department

Specs and types

list A :=   nil  
          | :: of A & list A

rev nil   = nil
rev x::xs = rev xs ++ x::nil

def rev[A] : List[A] => List[A] = {
  case Nil => Nil
  case (x::xs) => rev(xs) ++ List(x)
}

FP is executable specs:

Monads & DSLs

• Embrace Language-Oriented Programming, use mini-languages
• Need for meta-language constructs
• Monads model sequential composition

• cause => effect[result]

• In CS computation is thought of as directed
• E.g. multiplying numbers vs factoring primes

Scalability

• Trustworthiness is really useful for a foundation
• Performance will suffer
• Scale horizontally => parallelism & concurrency
• Pandora's box: all about fine-grained communication
• No longer interacting with computer 1-1, you're outnumbered
• Sequentiality also starts leaking

Break up monads

Applicatives

def pure[A](a: A): F[A]
def apply[A, B](f: F[A => B]): F[A] => F[B]

Arrows

Arrow[F[_, _]]

def lift[A,B](f: A => B): F[A,B]
def dimap[A,B,C,D](fab: F[A,B])
         (f: C=>A)(g: B=>D): F[C,D]
def second[A,B,C]
          (fa: F[A,B]): F[(C,A),(C,B)]
def split[A,B,C,D]
         (f: F[A,B], g: F[C,D]): F[(A,C),(B,D)]

Visual programming

Categorical cybernetics

Capucci, Gavranovic, Hedges, Rischel [2021]

"Towards foundations of categorical cybernetics"

Build on monads

• We wanted expressive declarative DSLs
• FP - higher-order functions + higher-order types
• Abstracts and hides some of the complexity
• The computer can have coherent dialogue but can be very excrutiating

Logic programming

• A second side of declarative is logic programming
• Solving as the default mode of computation
• Norvig's Corollary to Greenspun's Tenth Law of Programming: "Any sufficiently complicated LISP program is going to contain a slow implementation of half of Prolog"
• Filling the gaps: implicits

Proof engineering

• Dependent types are a powerful metalanguage
• Solving becomes undecidable, manual proofs
• Programming -> constructive math & logic
• Equality, ordering, choice, finiteness
• Countability ~ serialization

AI vs IA

• Thinking is scarce
• Moshe Vardi: fast vs slow reasoning
• Expressive specs mean more powerful tools
• Typechecker feedback loop
• An interesting dialogue with machine

List reversal in Coq/HTT

Demo!