rev/mpl

developtheweb@protonmail.com 3cf435b41e Initial commit: Mathematical Programming Language (MPL)

A proof-of-concept parser demonstrating that programming languages can be built
entirely from mathematical notation, enabling cognitive universality in computing.

MPL replaces English keywords with mathematical symbols, making programming
accessible to the 80% of humanity who don't speak English. Every design decision
follows the Fatima Test: "Will this make sense to a 10-year-old who doesn't
speak English?"

Current implementation:
- Complete ANTLR 4 grammar with 70+ mathematical operators
- Parser supporting all major programming paradigms
- Zero grammar ambiguities
- ASCII escape sequences for every Unicode symbol

This release contains:
- Core parser implementation
- Grammar specification
- Example programs
- Comprehensive documentation
- Whitepaper outlining the vision

Note: This is a parser-only proof of concept. Programs can be parsed but not
executed. The interpreter and runtime are future work.

2025-07-26 18:39:08 -04:00

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MPL Glyph Escape Sequences

This document provides the authoritative mapping between ASCII escape sequences and UTF-8 glyphs for the Mathematical Programming Language (MPL).

Core Mathematical Symbols

Greek Letters (Variables)

ASCII Escape	Unicode	Glyph	Usage
`\alpha`	U+03B1	α	Variable
`\beta`	U+03B2	β	Variable
`\gamma`	U+03B3	γ	Variable
`\delta`	U+03B4	δ	Variable
`\epsilon`	U+03B5	ε	Variable
`\zeta`	U+03B6	ζ	Variable
`\eta`	U+03B7	η	Variable
`\theta`	U+03B8	θ	Variable
`\iota`	U+03B9	ι	Variable
`\kappa`	U+03BA	κ	Variable
`\lambda` or `\lam`	U+03BB	λ	Lambda/Function
`\mu`	U+03BC	μ	Variable
`\nu`	U+03BD	ν	Variable
`\xi`	U+03BE	ξ	Variable
`\omicron`	U+03BF	ο	Variable
`\pi`	U+03C0	π	Variable/Constant
`\rho`	U+03C1	ρ	Variable
`\sigma`	U+03C3	σ	Variable
`\tau`	U+03C4	τ	Variable
`\upsilon`	U+03C5	υ	Variable
`\phi`	U+03C6	φ	Variable
`\chi`	U+03C7	χ	Variable
`\psi`	U+03C8	ψ	Variable
`\omega`	U+03C9	ω	Variable

Set Theory

ASCII Escape	Unicode	Glyph	Usage
`\emptyset`	U+2205	∅	Empty set
`\union` or `\cup`	U+222A	∪	Set union
`\intersect` or `\cap`	U+2229	∩	Set intersection
`\subset`	U+2282	⊂	Proper subset
`\supset`	U+2283	⊃	Proper superset
`\in`	U+2208	∈	Element of
`\notin`	U+2209	∉	Not element of
`\subseteq`	U+2286	⊆	Subset or equal
`\supseteq`	U+2287	⊇	Superset or equal

Logic

ASCII Escape	Unicode	Glyph	Usage
`\and` or `\wedge`	U+2227	∧	Logical and
`\or` or `\vee`	U+2228	∨	Logical or
`\not` or `\neg`	U+00AC	¬	Logical not
`\implies` or `\Rightarrow`	U+27F9	⟹	Implication
`\iff` or `\Leftrightarrow`	U+27FA	⟺	If and only if
`\forall`	U+2200	∀	Universal quantifier
`\exists`	U+2203	∃	Existential quantifier

Operations

ASCII Escape	Unicode	Glyph	Usage
`\times`	U+00D7	×	Multiplication
`\div`	U+00F7	÷	Division
`\ast`	U+2217	∗	Generic operator
`\circ`	U+2218	∘	Function composition

Relations

ASCII Escape	Unicode	Glyph	Usage
`\neq` or `\ne`	U+2260	≠	Not equal
`\leq` or `\le`	U+2264	≤	Less than or equal
`\geq` or `\ge`	U+2265	≥	Greater than or equal
`\approx`	U+2248	≈	Approximately equal
`\sim`	U+223C	∼	Similar to

Special Symbols

ASCII Escape	Unicode	Glyph	Usage
`\leftarrow` or `\gets`	U+2190	←	Assignment
`\coloneq`	U+225C	≜	Definition
`\rightarrow` or `\to`	U+2192	→	Function type

Effect Extensions

ASCII Escape	Unicode	Glyph	Usage
`\raise`	U+21AF	↯	Raise exception
`\handle`	U+21B4	↴	Handle exception
`\parallel`	U+2016	‖	Parallel composition
`\lceil`	U+2308	⌈	Atomic section start
`\rceil`	U+2309	⌉	Atomic section end
`\oplus`	U+2295	⊕	Allocate resource
`\ominus`	U+2296	⊖	Release resource
`\module`	U+1D49C	𝓜	Module declaration
`\Leftarrow`	U+21D0	⇐	Import
`\Rightarrow`	U+21D2	⇒	Export
`\send`	U+21C0	⇀	Send (network)
`\receive`	U+21BD	↽	Receive (network)

Additional Operators

ASCII Escape	Unicode	Glyph	Usage
`\langle`	U+27E8	⟨	Choice type/angle bracket left
`\rangle`	U+27E9	⟩	Choice type/angle bracket right
`\path`	U+1F5AB	🖫	File path prefix
`\up`	U+21E1	⇡	Stream position up
`\down`	U+21E3	⇣	Stream position down
`\swap`	U+21C6	⇆	Atomic swap
`\llangle`	U+27EA	⟪	Deep update path start
`\rrangle`	U+27EB	⟫	Deep update path end
`\ulcorner`	U+231C	⌜	Code quotation start
`\urcorner`	U+231D	⌝	Code quotation end
`\llcorner`	U+231E	⌞	Code evaluation start
`\lrcorner`	U+231F	⌟	Code evaluation end
`\query`	U+003F	?	Introspection
`\break`	U+2A08	⧈	Breakpoint
`\trace`	U+270E	✎	Trace/log
`\delay`	U+23F2	⏲	Delay
`\periodic`	U+27F3	⟳	Periodic task
`\lbracket`	U+3014	〔	RAII scope start
`\rbracket`	U+3015	〕	RAII scope end

Type System Symbols

ASCII Escape	Unicode	Glyph	Usage
`\nat` or `\N`	U+2115	ℕ	Natural numbers
`\int` or `\Z`	U+2124	ℤ	Integers
`\rat` or `\Q`	U+211A	ℚ	Rational numbers
`\real` or `\R`	U+211D	ℝ	Real numbers
`\complex` or `\C`	U+2102	ℂ	Complex numbers
`\bool` or `\B`	U+1D539	𝔹	Booleans
`\bot`	U+22A5	⊥	Bottom type

String Escape Sequences

String literals in MPL support the following escape sequences within double-quoted strings:

Escape Sequence	Character	Description
`\\`	`\`	Backslash
`\"`	`"`	Double quote
`\n`	LF	Line feed (newline)
`\r`	CR	Carriage return
`\t`	TAB	Horizontal tab
`\0`	NUL	Null character
`\u{XXXXXX}`	Unicode	Unicode code point (1-6 hex digits)

Examples:

"Hello\nWorld" - String with newline
"Path: \"C:\\Users\"" - Escaped quotes and backslashes
"Unicode: \u{1F600}" - Unicode emoji 😀
"""Raw string - no \n escapes""" - Raw multi-line string

Usage Notes

Input methods:
- Direct Unicode input (recommended for supported editors)
- ASCII escape sequences (for compatibility)
- Editor-specific shortcuts (e.g., Ctrl+Alt+g → γ)
Lexer behavior:
- Escapes are processed during tokenization
- Unknown escapes result in compilation error
- Mixed Unicode/ASCII in same file is allowed
Pretty-printing:
- Always outputs Unicode glyphs (never escapes)
- Configurable fallback to ASCII for terminals without Unicode support

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