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Update SIMPLICITY.md
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5HT authored Feb 22, 2025
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Showing 1 changed file with 12 additions and 8 deletions.
20 changes: 12 additions & 8 deletions intro/SIMPLICITY.md
Original file line number Diff line number Diff line change
Expand Up @@ -50,18 +50,22 @@ def cat : Category := П (context), conditions ⊢ n (objects | morphisms | cohe
<superscript> ::= "¹" | "²" | "³" | "⁴" | "⁵" | "⁶" | "⁷" | "⁸" | "⁹"
<n> ::= <digit> | <digit> <n>
<context> ::= <hypothesis> | <hypothesis> "," <context>
<hypothesis> ::= <id> ":" <type-term> | "(" <decl-list> ")" | <id> "=" <t> "<" <t> | <id> "=" <t> "∘" <t>
<decl-list> ::= <id> ":" <type-term> | <identifier> ":" <type-term> "," <decl-list>
<hypothesis> ::= <id> ":" <type-term> % Single declaration, e.g., a : Simplex
| "(" <id-list> ":" <type-term> ")" % Grouped declaration, e.g., (a b c : Simplex)
| <id> "=" <t> "<" <t> % Map, e.g., ∂₁ = C₂ < C₃
| <id> "=" <t> "∘" <t> % Equality, e.g., ac = ab ∘ bc
<id-list> ::= <id> | <id> <id-list> % e.g., a b c
<elements> ::= <element-list> | ε
<element-list> ::= <id> | <id> "," <element-list>
<constraints> ::= <constraint-list> | ε
<constraint-list> ::= <constraint> | <constraint> "," <constraint-list>
<constraint> ::= <t> "=" <t> | <id> "<" <id> % Equality (e.g., a ∘ a = e) | Map (e.g., ∂₁ < C₂)
<t> ::= <id> % e.g., a
| <t> "∘" <t> % e.g., a ∘ b
| <t> "^-1" % e.g., a^-1
| <t> "^" <superscript> % e.g., a³
| "e" % identity
<constraint> ::= <t> "=" <t> % Equality (e.g., a ∘ a = e)
| <id> "<" <id> % Map (e.g., ∂₁ < C₂)
<t> ::= <id> % e.g., a
| <t> "∘" <t> % e.g., a ∘ b
| <t> "^-1" % e.g., a^-1
| <t> "^" <superscript> % e.g., a³
| "e" % identity
```

Meaning of <n> Across Types:
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