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$% Typography and symbols \newcommand{\msf}[1]{\mathsf{#1}} \newcommand{\ctx}{\Gamma} \newcommand{\qamp}{&\quad} \newcommand{\qqamp}{&&\quad} \newcommand{\Coloneqq}{::=} \newcommand{\proves}{\vdash} \newcommand{\star}[1]{#1^{*}} \newcommand{\eps}{\varepsilon} \newcommand{\nul}{\varnothing} \newcommand{\brc}[1]{\{{#1}\}} \newcommand{\binopm}[2]{#1~\bar{\oplus}~#2} \newcommand{\mag}[1]{|{#1}|} \newcommand{\aequiv}{\equiv_\alpha} \newcommand{\semi}[2]{{#1};~{#2}} % Untyped lambda calculus \newcommand{\fun}[2]{\lambda ~ {#1} ~ . ~ {#2}} \newcommand{\app}[2]{#1 ~ #2} \newcommand{\fix}[1]{\msf{fix}~#1} % Typed lambda calculus - expressions \newcommand{\funt}[3]{\lambda ~ \left(#1 : #2\right) ~ . ~ #3} \newcommand{\lett}[4]{\msf{let} ~ \hasType{#1}{#2} = #3 ~ \msf{in} ~ #4} \newcommand{\rec}[3]{\msf{rec}(#1; ~ x.y.#2)(#3)} \newcommand{\case}[5]{\msf{case} ~ {#1} ~ \{ L(#2) \to #3 \mid R(#4) \to #5 \}} \newcommand{\pair}[2]{\left({#1},~{#2}\right)} \newcommand{\proj}[2]{#1 . #2} \newcommand{\inj}[3]{\msf{inj} ~ #1 = #2 ~ \msf{as} ~ #3} \newcommand{\letv}[3]{\msf{let} ~ {#1} = {#2} ~ \msf{in} ~ {#3}} \newcommand{\fold}[2]{\msf{fold}~{#1}~\msf{as}~{#2}} \newcommand{\unfold}[1]{\msf{unfold}~{#1}} \newcommand{\poly}[2]{\Lambda~{#1}~.~{#2}} \newcommand{\polyapp}[2]{{#1}~\left[{#2}\right]} % Typed lambda calculus - types \newcommand{\tint}{\msf{int}} \newcommand{\tbool}{\msf{bool}} \newcommand{\tfun}[2]{#1 \rightarrow #2} \newcommand{\tprod}[2]{#1 \times #2} \newcommand{\tsum}[2]{#1 + #2} \newcommand{\trec}[2]{\mu~{#1}~.~{#2}} \newcommand{\tvoid}{\msf{void}} \newcommand{\tunit}{\msf{unit}} \newcommand{\tpoly}[2]{\forall~{#1}~.~{#2}} % WebAssembly \newcommand{\wconst}[1]{\msf{i32.const}~{#1}} \newcommand{\wbinop}[1]{\msf{i32}.{#1}} \newcommand{\wgetlocal}[1]{\msf{get\_local}~{#1}} \newcommand{\wsetlocal}[1]{\msf{set\_local}~{#1}} \newcommand{\wload}{\msf{i32.load}} \newcommand{\wstore}{\msf{i32.store}} \newcommand{\wsize}{\msf{memory.size}} \newcommand{\wgrow}{\msf{memory.grow}} \newcommand{\wunreachable}{\msf{unreachable}} \newcommand{\wblock}[1]{\msf{block}~{#1}} \newcommand{\wblockr}[2]{\msf{block}~{#1}~{#2}} \newcommand{\wloop}[1]{\msf{loop}~{#1}} \newcommand{\wbr}[1]{\msf{br}~{#1}} \newcommand{\wbrif}[1]{\msf{br\_if}~{#1}} \newcommand{\wreturn}{\msf{return}} \newcommand{\wcall}[1]{\msf{call}~{#1}} \newcommand{\wlabel}[2]{\msf{label}~\{#1\}~{#2}} \newcommand{\wframe}[1]{\msf{frame}~{#1}} \newcommand{\wtrapping}{\msf{trapping}} \newcommand{\wbreaking}[1]{\msf{breaking}~{#1}} \newcommand{\wreturning}[1]{\msf{returning}~{#1}} \newcommand{\wconfig}[5]{\{\msf{module}~{#1};~\msf{mem}~{#2};~\msf{locals}~{#3};~\msf{stack}~{#4};~\msf{instrs}~{#5}\}} \newcommand{\wfunc}[3]{\{\msf{params}~{#1};~\msf{locals}~{#2};~\msf{body}~{#3}\}} \newcommand{\wmodule}[1]{\{\msf{funcs}~{#1}\}} \newcommand{\wci}{\msf{instrs}} \newcommand{\wcs}{\msf{stack}} \newcommand{\wcl}{\msf{locals}} \newcommand{\wcm}{\msf{mem}} \newcommand{\wcmod}{\msf{module}} \newcommand{\wsteps}[2]{\steps{\brc{#1}}{\brc{#2}}} % assign4.3 custom \newcommand{\wtry}[2]{\msf{try}~{#1}~\msf{catch}~{#2}} \newcommand{\wraise}{\msf{raise}} \newcommand{\wraising}[1]{\msf{raising}~{#1}} % session types \newcommand{\ssend}[2]{\msf{send}~{#1};~{#2}} \newcommand{\srecv}[2]{\msf{recv}~{#1};~{#2}} \newcommand{\soffer}[4]{\msf{offer}~\{{#1}\colon({#2})\mid{#3}\colon({#4})\}} \newcommand{\schoose}[4]{\msf{choose}~\{{#1}\colon({#2})\mid{#3}\colon({#4})\}} \newcommand{\srec}[2]{\mu~{#1}~.~{#2}} \newcommand{\dual}[1]{\overline{#1}} % Inference rules \newcommand{\inferrule}[3][]{\cfrac{#2}{#3}\;{#1}} \newcommand{\ir}[3]{\inferrule[\text{(#1)}]{#2}{#3}} \newcommand{\s}{\hspace{1em}} \newcommand{\nl}{\\[2em]} \newcommand{\evalto}{\boldsymbol{\overset{*}{\mapsto}}} \newcommand{\steps}[2]{#1 \boldsymbol{\mapsto} #2} \newcommand{\evals}[2]{#1 \evalto #2} \newcommand{\subst}[3]{[#1 \rightarrow #2] ~ #3} \newcommand{\dynJ}[2]{#1 \proves #2} \newcommand{\dynJC}[1]{\dynJ{\ctx}{#1}} \newcommand{\typeJ}[3]{#1 \proves \hasType{#2}{#3}} \newcommand{\typeJC}[2]{\typeJ{\ctx}{#1}{#2}} \newcommand{\hasType}[2]{#1 : #2} \newcommand{\val}[1]{#1~\msf{val}} \newcommand{\num}[1]{\msf{Int}(#1)} \newcommand{\err}[1]{#1~\msf{err}} \newcommand{\trans}[2]{#1 \leadsto #2} \newcommand{\size}[1]{\left|#1\right|}$