adt-row-te.scrbl (1843B)
1 #lang scribble/manual 2 3 @require["util.rkt" 4 "adt-utils.rkt" 5 (for-label (only-meta-in 0 typed/racket))] 6 @(use-mathjax) 7 8 @title[#:style (with-html5 manual-doc-style) 9 #:version (version-text)]{Type validity rules (with ρ)} 10 11 @$inferrule[@${Δ ∪ \{ @repeated{@ρc} \} ⊢ τ} 12 @${Δ ⊢ @∀c[(@repeated{@ρc}) τ]} 13 @${@textsc{TE-CAll}}] 14 15 @$inferrule[@${Δ ∪ \{ @repeated{@ρf} \} ⊢ τ} 16 @${Δ ⊢ @∀f[(@repeated{@ρf}) τ]} 17 @${@textsc{TE-FAll}}] 18 19 20 @$p[ 21 @$inferrule[@${@ρc ∈ Δ \\ 22 @repeated{Δ ⊢ τᵢ} \\ 23 @alldifferent(@repeated{@|κ|ᵢ} @repeated{@|κ|ⱼ})} 24 @${Δ ⊢ @variantτ[@ρc @repeatset{-@ctorτ[@|κ|ᵢ]} 25 @repeatset{+@ctorτ[@κof[ⱼ τⱼ]]}]} 26 #:wide 'latex 27 @${@textsc{TE-CVariant}}] 28 29 @$inferrule[@${@ρf ∈ Δ \\ 30 @alldifferent(@repeated{@|ɐ|ᵢ} @repeated{@|ɐ|ⱼ}) \\ 31 @repeated{Δ ⊢ τⱼ}} 32 @${Δ ⊢ @recordτ[@ρf @repeatset{-@|ɐ|ᵢ} @repeatset{+@|ɐ|ⱼ:τⱼ}]} 33 @${@textsc{TE-FRecord}}]] 34 35 where 36 37 @$${ 38 \begin{aligned} 39 @alldifferent(@repeated{y}) &= @metatrue @textif ∀ i ≠ j . yᵢ ≠ yⱼ \\ 40 @alldifferent(@repeated{y}) &= @metafalse @otherwise 41 \end{aligned} 42 } 43 44 45 46 @$inferrule[@${@repeated{Δ ⊢ τᵢ} \\ 47 @alldifferent(@repeated{@|κ|ᵢ})} 48 @${Δ ⊢ @variantτ[@repeated{@ctorτ[@κof[ᵢ τᵢ]]}]} 49 @${@textsc{TE-Variant}}] 50 51 @$inferrule[@${@alldifferent(@repeated{@|ɐ|ᵢ}) \\ 52 @repeated{Δ ⊢ τᵢ}} 53 @${Δ ⊢ @recordτ[@repeated{@|ɐ|ᵢ : τᵢ}]} 54 @${@textsc{TE-Record}}] 55 56 @$inferrule[@${@repeated{Δ ⊢ τ}} 57 @${Δ ⊢ @ctorτ[@κof[τ]]} 58 @${@textsc{TE-Ctor}}]