almost

slides/main.md

@@ -1,5 +1,4 @@
 ---
-theme: dracula
 paginate: true
 _paginate: false
 footer: Topics in Compilers and Concurrency · Julius Fischer · 10.06.2026
@@ -12,19 +11,24 @@ style: |
     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{{\;|\;}}
+\def\dest{{\rightarrow}}
+\def\lad{\lambda_d\;}
+\newcommand{\htype}[1]{{\lfloor #1 \rfloor}}
+\newcommand{\ampar}[3]{{\;_#1\langle #2 \;_{\tiny \land} \; #3 \rangle}}
+\newcommand{\mapstom}[1]{{\sideset{_#1}{}\mapsto}}
 
 $$
 
+# Destination Calculus:
+## A Linear 𝜆-Calculus for Purely Functional Memory Writes
+## Thomas Bagrel, Arnaud Spiwack
+#### Topics in Compiler and Concurrency
+#### Julius Fischer 
+
+###### 10. Juni 2026
 ---
 # What are Destinations?
 - Destination Passing Style
@@ -77,7 +81,17 @@ map f (x:xs) dest = map f xs (push dest (f x))
     - Purity
 
 ---
-# Destination Calculus
+# Destination Calculus: Terminology 
+- Holes
+Values $h_1, h_2, \dots$ 
+- Destination
+$\dest h_1 \dest h_2, \dots$
+- Ampars
+$\ampar{H}{v_1}{v_2}$, i.e. $\ampar{{\{h\}}}{(h, 15)}{\dest h}$
+- $v_1$ "value with holes"
+- $v_2$ "value of destinations"
+---
+# Destination Calculus: Terms in $\lad$
 - Basic FP terms
 $$
 t, u := x \myor t' t \;|\; t ; t' \;|\; \dots
@@ -86,8 +100,8 @@ $$
 $$
 \begin{align}
     \dots \myor 
-    &case_m\;t\;of\;(v_1, v_2) \mapsto u \myor\\
+    &case\;t\;of\;(v_1, v_2) \mapsto u \myor\\
-    &case_m\;t\;of\;(Inl\;v_1) \mapsto u \myor \dots
+    &case\;t\;of\;(Inl\;v_1) \mapsto u \myor \dots
 \end{align}
 $$
 - Additions for destination passing
@@ -107,6 +121,68 @@ $$
     t \triangleleft (,) \myor \dots
 \end{align}
 $$
+---
+# Destination Calculus: Constructors
+- Usually constructors are required
+$Inl, Inr, (a, b), \lambda x \mapsto t$
+- In $\lad$ we simply 'refine' holes
+$Inl \; t \triangleq from_\ltimes' (upd_\ltimes\; new_\ltimes\; with \; d \mapsto d \triangleleft Inl \blacktriangleleft t)$
+$\lambda x \mapsto t \; \triangleq from_\ltimes' (upd_\ltimes\; new_\ltimes\; with \; d \mapsto d \triangleleft (\lambda x \mapsto t))$
 
 --- 
-# Referenes
+# Destination Calculus: Map example
+![h:450](img/map_dps.jpg)
+[1] Thomas Bagel
+
+---
+# Destination Calculus: Linearity and Modality
+- Double writes are an issue
+    - If a hole is used more than once $(dest \blacktriangleleft v_1; dest \blacktriangleleft v_2; \dots)$
+    - In types like $\htype{\htype{T}}$
+- Solved using modality of *Multiplicity* and *Age*
+$m = p \cdot a$
+$p = 1 \myor \omega$ 
+$a =\; \uparrow^k \myor \infty$ for $k \in \mathbb{N}_0$
+- With $1 \underset{\raise{0.4em}{\leftarrow}}{<}^p \omega, \uparrow^k \underset{\raise{0.4em}{\leftarrow}}{<}^a \infty$
+
+--- 
+# Destination Calculus: Linearity and Modality
+- Add modalities to variable bindings
+$$
+\begin{align}
+    \dots \myor 
+    &case_m\;t\;of\;(v_1, v_2) \mapsto u \myor\\
+    &case_m\;t\;of\;(Inl\;v_1) \mapsto u \myor\\
+    &\lambda x\; \mapstom{m} \; t \myor \dots
+\end{align}
+$$
+- And add add exponential modality to weaken constraints
+$$
+\begin{align}
+    \dots \myor 
+    &Mod_m\; t \myor \dots
+\end{align}
+$$
+
+---
+# Destination Calculus: Typing
+- Mostly standard
+
+---
+# Referenes and Further Reading
+
+---
+# Extra Slides If needed
+
+---
+
+# Example for linear types
+
+![](img/linear_works.jpg)
+[1] Page 7
+
+---
+
+# Example for linear types
+![](img/linear_fails.jpg)
+[1] Page 8

slides/makefile

@@ -5,4 +5,7 @@ all: clean bib compile
 clean:
 	rm -rf ./out
 compile: 
-	marp main.md --theme ./themes/academic.css -o out/presentation.html
+	mkdir out
+	cp -r img ./out/img
+	marp main.md --base . -o out/presentation.html
+	#marp main.md --base . --allow-local-files -o out/presentation.pdf