topics_compiler/slides/main.md

theme, paginate, _paginate, footer, _footer, style

theme	paginate	_paginate	footer	_footer	style
dracula	true	false	Topics in Compilers and Concurrency · Julius Fischer · 10.06.2026		h1 { position: absolute; top: 60px; left: 75px; right: 75px; }

Destination Calculus:

A Linear 𝜆-Calculus for Purely Functional Memory Writes

Topics in Compiler and Concurrency

Julius Fischer

10. Juni 2026

\def\leftcirc{{\triangleleft\kern-0.1em\circ}}
\def\myor{{\;|\;}}

---

What are Destinations?

• Destination Passing Style
  • Imperative
  • Function takes destination instead of returning structure

---

Example in C

int* vec_add(int v1[], int v2[], int size) {
    int* res =  malloc(size * sizeof(int));
    for (int i = 0; i < size; i++) {
        res[i] = v1[i] + v2[i];
    }
    return res;
}

• Add an 'out parameter'

void dps_vec_add(int res[], int v1[], int v2[], int size) {
    for (int i = 0; i < size; i++) {
        res[i] = v1[i] + v2[i];
    }
}

---

Motivation for DPS

• Typical functional map implementation

map f (x:xs) = (f x : map f xs1)
> (f x : map f xs) 
> (map f x1 : (f x2 : map f xs2)) 
> ...

• Not tail recursive
  • Performance issue
  • Inefficient stack growth

map f (x:xs) dest = map f xs (push dest (f x))
> map f xs1 (push dest (f x1))
> map f xs2 (push dest (f x2))

---

DPS in functional languages

• Just add pointers to mutable data?
  • Int \mapsto Int \mapsto \textcolor{red}{T}
  • \textcolor{red}{T *}\mapsto Int \mapsto Int \mapsto \dots
• Multiple issues with this
  • Memory safety
  • Multilpe writes on shared memory
  • Purity

---

Destination Calculus

• Basic FP terms

t, u := x \myor t' t \;|\; t ; t' \;|\; \dots

• Case for all datatypes

\begin{align}
    \dots \myor 
    &case_m\;t\;of\;(v_1, v_2) \mapsto u \myor\\
    &case_m\;t\;of\;(Inl\;v_1) \mapsto u \myor \dots
\end{align}

• Additions for destination passing

\begin{align}
    \dots \myor
    &
    new_\ltimes \myor
    from_\ltimes t \myor
    to_\ltimes t \myor
    upd_\ltimes \; t \; with \; x \mapsto t' \myor\\
    &
    t \blacktriangleleft t' \myor
    t  \leftcirc t' \myor
    t \triangleleft () \myor
    t \triangleleft Inl \myor
    t \triangleleft (,) \myor \dots
\end{align}

---

Referenes