#+TITLE: Guise Syntax Specification (BNF)
#+AUTHOR: Guise Language Project
#+DATE: 2025-01-04

* Introduction

This document provides a formal BNF (Backus-Naur Form) grammar specification for the Guise programming language. Guise is a purely functional, statically-typed, stack-based language with S-expression syntax.

* Notation Conventions

- =<name>= : Non-terminal symbol
- ="literal"= : Terminal symbol (literal text)
- =|= : Alternative (or)
- =*= : Zero or more repetitions
- =+= : One or more repetitions
- =?= : Optional (zero or one)
- =()= : Grouping

* Lexical Elements

** Whitespace

#+BEGIN_SRC bnf
<whitespace> ::= <space> | <tab> | <newline> | <carriage-return>
<ws>         ::= <whitespace>*
#+END_SRC

** Comments

#+BEGIN_SRC bnf
<comment>    ::= ";;" <any-char-except-newline>* <newline>
#+END_SRC

** Identifiers

#+BEGIN_SRC bnf
<identifier> ::= <initial> <subsequent>*
<initial>    ::= <letter> | <special-initial>
<subsequent> ::= <initial> | <digit> | <special-subsequent>

<letter>     ::= "a" | "b" | ... | "z" | "A" | "B" | ... | "Z"
<digit>      ::= "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"

<special-initial>     ::= "!" | "$" | "%" | "&" | "*" | "/" | ":" | "<" | "="
                        | ">" | "?" | "^" | "_" | "~" | "+" | "-"
<special-subsequent>  ::= <special-initial> | "." | "@" | "#"
#+END_SRC

Examples: =square=, =make-point=, =++=, =foo->bar=, =h:helper=

** Literals

*** Numbers

#+BEGIN_SRC bnf
<number>     ::= <prefix>? <complex>
<complex>    ::= <real>
               | <real> "+" <imag> "i"
               | <real> "-" <imag> "i"
               | <imag> "i"
               | "+" "i"
               | "-" "i"

<real>       ::= <sign>? <ureal>
<imag>       ::= <sign>? <ureal>
<ureal>      ::= <uinteger>
               | <uinteger> "/" <uinteger>
               | <decimal>

<decimal>    ::= <uinteger> <suffix>
               | "." <digit>+ <suffix>
               | <digit>+ "." <digit>* <suffix>

<uinteger>   ::= <digit>+
<suffix>     ::= <exponent>?
<exponent>   ::= ("e" | "E") <sign>? <digit>+

<prefix>     ::= <radix> <exactness>?
               | <exactness> <radix>?

<radix>      ::= "#b" | "#B"    ; binary
               | "#o" | "#O"    ; octal
               | "#d" | "#D"    ; decimal
               | "#x" | "#X"    ; hexadecimal

<exactness>  ::= "#e" | "#E"    ; exact
               | "#i" | "#I"    ; inexact

<sign>       ::= "+" | "-"
<digit>      ::= "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
#+END_SRC

Examples:
- Decimal: =42=, =-17=, =3.14=, =2.5e10=, =-1.23e-4=
- Binary: =#b11010= (26), =#b-1010= (-10)
- Octal: =#o77= (63), =#o-755= (-493)
- Hexadecimal: =#xab= (171), =#xFF= (255), =#x-1a= (-26)
- Explicit decimal: =#d100= (100)
- Rational: =1/2=, =22/7=, =-3/4=
- Complex: =3+4i=, =-2-5i=, =1.5+2.5i=
- Exactness: =#e3.14= (exact), =#i5= (inexact)
- Combined: =#b#e1010= (exact binary)

*** Strings

#+BEGIN_SRC bnf
<string>     ::= '"' <string-char>* '"'
<string-char>::= <any-char-except-quote-or-backslash>
               | <escape-sequence>

<escape-sequence> ::= "\\" | "\"" | "\n" | "\t" | "\r"
#+END_SRC

Examples: ="hello"=, ="Hello, World!"=, ="line1\nline2"=

*** Booleans

#+BEGIN_SRC bnf
<boolean>    ::= "#t" | "#f" | "#true" | "#false"
#+END_SRC

*** Characters

#+BEGIN_SRC bnf
<character>  ::= "#\\" <any-char>
               | "#\\newline" | "#\\space" | "#\\tab"
#+END_SRC

Examples: =#\a=, =#\Z=, =#\newline=, =#\space=

*** Symbols

#+BEGIN_SRC bnf
<symbol>     ::= <identifier>
#+END_SRC

Note: In Guise, all identifiers are symbols when they appear as literals.

** Keywords

#+BEGIN_SRC bnf
<keyword>    ::= "define" | "module" | "import" | "public" | "private"
               | "quotation" | "match" | "let"
               | "sum" | "product" | "⊕" | "⊗"
               | "only" | "prefix" | "rename" | "except"
#+END_SRC

** Type Markers

#+BEGIN_SRC bnf
<arrow>      ::= "->"
<sum-marker> ::= "⊕" | "sum"
<prod-marker>::= "⊗" | "product"
#+END_SRC

* Expressions

** Program

#+BEGIN_SRC bnf
<program>    ::= <top-level>*

<top-level>  ::= <definition>
               | <module-def>
               | <import-stmt>
               | <expression>
#+END_SRC

** Atomic Expressions

#+BEGIN_SRC bnf
<atom>       ::= <number>
               | <string>
               | <boolean>
               | <character>
               | <symbol>
#+END_SRC

** Quotations

#+BEGIN_SRC bnf
<quotation>  ::= "'" "(" <expression>* ")"
               | "(" "quotation" <expression>* ")"
#+END_SRC

Examples:
- ='(dup *)=
- ='(1 +)=
- ='()=
- =(quotation dup dup * *)=

** List Literals

#+BEGIN_SRC bnf
<list-literal> ::= "#(" <expression>* ")"
#+END_SRC

Examples:
- =#(1 2 3)=
- =#("a" "b" "c")=
- =#(#(1 2) #(3 4))= (nested)

** Sequences

#+BEGIN_SRC bnf
<sequence>   ::= "(" <expression>* ")"
<expression> ::= <atom>
               | <quotation>
               | <list-literal>
               | <sequence>
#+END_SRC

* Type Annotations

** Type Variables

#+BEGIN_SRC bnf
<type-var>   ::= "'" <letter> <letter-or-digit>*
#+END_SRC

Examples: ='a=, ='b=, ='result=, ='T=

** Primitive Types

#+BEGIN_SRC bnf
<prim-type>  ::= "int" | "float" | "number"
               | "bool" | "string" | "char" | "symbol"
#+END_SRC

** Compound Types

#+BEGIN_SRC bnf
<compound-type> ::= <quotation-type>
                  | <list-type>
                  | <tuple-type>
                  | <custom-type>

<quotation-type> ::= "(" "quot" "(" <stack-effect> ")" ")"
<list-type>      ::= "(" "list" <type> ")"
<tuple-type>     ::= "(" "tuple" <type>+ ")"
<custom-type>    ::= <identifier>
#+END_SRC

Examples:
- =(quot (int -> int))=
- =(quot ('a -> 'a 'a))=
- =(list int)=
- =(tuple float float)=
- =Point=, =Maybe=

** Type Expressions

#+BEGIN_SRC bnf
<type>       ::= <type-var>
               | <prim-type>
               | <compound-type>
#+END_SRC

** Stack Effects

#+BEGIN_SRC bnf
<stack-effect> ::= <type>* <arrow> <type>*
#+END_SRC

Examples:
- =number -> number=
- =int int -> int=
- ='a -> 'a 'a=
- ='a 'b -> 'b 'a=
- =-> int= (nullary, produces int)
- =int ->= (consumes int, produces nothing)

* Definitions

** Word Definitions

#+BEGIN_SRC bnf
<word-def>   ::= "(" "define" <visibility>? <identifier>
                 "(" <stack-effect> ")" <expression>* ")"

<visibility> ::= "public" | "private"
#+END_SRC

Examples:
#+BEGIN_SRC scheme
(define square (number -> number)
  (dup *))

(define public distance (Point Point -> float)
  (x. swap x. - dup *
   y. swap y. - dup *
   + sqrt))

(define private helper (int -> int)
  (2 *))
#+END_SRC

** Primitive Definitions

#+BEGIN_SRC bnf
<prim-def>   ::= "(" "define" "primitive" <identifier>
                 "(" <stack-effect> ")" ")"
#+END_SRC

Example:
#+BEGIN_SRC scheme
(define primitive dup ('a -> 'a 'a))
(define primitive + (number number -> number))
#+END_SRC

** Product Type Definitions (Tuples)

#+BEGIN_SRC bnf
<product-def> ::= "(" "define" <visibility>? <identifier> <prod-marker>?
                  <field-spec>+ <default-spec>* ")"

<field-spec>  ::= "(" <identifier> <type> ")"
<default-spec>::= "(" <identifier> <type> "=" <expression> ")"
#+END_SRC

Examples:
#+BEGIN_SRC scheme
;; Implicit product type
(define Point (x float) (y float))

;; Explicit with ⊗
(define Vec3 ⊗ (x float) (y float) (z float))

;; With explicit defaults
(define Config
  (port int = 8080)
  (host string = "localhost")
  (debug bool = #f))

;; Public tuple in module
(define public Person (name string) (age int))
#+END_SRC

** Sum Type Definitions

#+BEGIN_SRC bnf
<sum-def>    ::= "(" "define" <visibility>? <identifier> <sum-marker>
                 <variant>+ ")"

<variant>    ::= "(" <identifier> <type>* ")"
#+END_SRC

Examples:
#+BEGIN_SRC scheme
;; Basic sum type with ⊕
(define Maybe ⊕
  (Just 'a)
  (Nothing))

;; Using 'sum' keyword
(define Either sum
  (Left 'a)
  (Right 'b))

;; Result type
(define Result ⊕
  (Ok 'ok)
  (Err 'err))

;; Enum-style
(define Color sum
  (Red)
  (Green)
  (Blue)
  (RGB int int int))

;; Recursive type
(define List ⊕
  (Nil)
  (Cons 'a (List 'a)))
#+END_SRC

** Module Definitions

#+BEGIN_SRC bnf
<module-def> ::= "(" "define" "module" <identifier>
                 <import-stmt>?
                 <module-body>* ")"

<module-body>::= <word-def>
               | <prim-def>
               | <product-def>
               | <sum-def>
#+END_SRC

Example:
#+BEGIN_SRC scheme
(define module math
  (import
    (helpers (prefix h:))
    (numeric-types (only int float)))

  (define public square (number -> number)
    (dup *))

  (define public cube (number -> number)
    (dup dup * *))

  (define private internal-helper (int -> int)
    (2 *)))
#+END_SRC

* Module System

** Import Statements

#+BEGIN_SRC bnf
<import-stmt> ::= "(" "import" <import-spec>+ ")"

<import-spec> ::= <identifier>
                | "(" <identifier> <import-modifier>+ ")"

<import-modifier> ::= <only-modifier>
                    | <prefix-modifier>
                    | <rename-modifier>
                    | <except-modifier>
#+END_SRC

** Import Modifiers

#+BEGIN_SRC bnf
<only-modifier>   ::= "(" "only" <identifier>+ ")"
<prefix-modifier> ::= "(" "prefix" <identifier> ")"
<rename-modifier> ::= "(" "rename" <rename-pair>+ ")"
<except-modifier> ::= "(" "except" <identifier>+ ")"

<rename-pair>     ::= "(" <identifier> <identifier> ")"
#+END_SRC

Examples:
#+BEGIN_SRC scheme
;; Simple import
(import stack-ops numeric-types)

;; Only specific bindings
(import (math (only square cube)))

;; With prefix
(import (helpers (prefix h:)))

;; With rename
(import (geometry (rename (distance point-distance))))

;; Multiple modifiers
(import
  (numeric-types (only int float) (prefix num:)))

;; Except modifier
(import (collections (except filter map)))

;; Complex example
(import
  stack-ops
  (math (only square) (prefix m:))
  (geometry (rename (distance dist)))
  (collections (except fold)))
#+END_SRC

* Pattern Matching (Future)

** Match Expressions

#+BEGIN_SRC bnf
<match-expr> ::= "(" "match" <match-case>+ ")"

<match-case> ::= "(" <pattern> "→" <expression>* ")"

<pattern>    ::= <literal-pattern>
               | <variable-pattern>
               | <variant-pattern>
               | <tuple-pattern>
               | <wildcard-pattern>

<literal-pattern>  ::= <number> | <string> | <boolean>
<variable-pattern> ::= <identifier>
<variant-pattern>  ::= "(" <identifier> <pattern>* ")"
<tuple-pattern>    ::= "(" <identifier> <pattern>* ")"
<wildcard-pattern> ::= "_"
#+END_SRC

Examples:
#+BEGIN_SRC scheme
;; Match on Maybe
(42 make-just match
  (Nothing → 0)
  ((Just x) → x))

;; Match on list
(my-list match
  (Nil → 0)
  ((Cons x xs) → (xs length 1 +)))

;; Match on custom tuple
(point match
  ((Point x y) → (x y + 2 /)))
#+END_SRC

* Lexical Scoping (Future)

** Let Bindings

#+BEGIN_SRC bnf
<let-expr>   ::= "(" "let" "(" <binding>+ ")" <expression>* ")"

<binding>    ::= "(" <identifier> ")"
               | "(" <identifier>+ ")"
#+END_SRC

Example:
#+BEGIN_SRC scheme
;; Bind single value
(5 let ((x))
  (x x *))

;; Bind multiple values
(1 2 3 let ((z y x))
  (x y + z *))
#+END_SRC

* Complete Grammar Summary

#+BEGIN_SRC bnf
;; ========================================
;; LEXICAL ELEMENTS
;; ========================================

<identifier>  ::= <initial> <subsequent>*
<number>      ::= <integer> | <float>
<string>      ::= '"' <string-char>* '"'
<boolean>     ::= "#t" | "#f"
<character>   ::= "#\\" <any-char>
<comment>     ::= ";;" <text> <newline>

;; ========================================
;; EXPRESSIONS
;; ========================================

<program>     ::= <top-level>*
<top-level>   ::= <definition> | <module-def> | <import-stmt> | <expression>

<expression>  ::= <atom>
                | <quotation>
                | <list-literal>
                | <sequence>

<atom>        ::= <number> | <string> | <boolean> | <character> | <symbol>
<quotation>   ::= "'" "(" <expression>* ")" | "(" "quotation" <expression>* ")"
<list-literal>::= "#(" <expression>* ")"
<sequence>    ::= "(" <expression>* ")"

;; ========================================
;; TYPES
;; ========================================

<type>        ::= <type-var> | <prim-type> | <compound-type>
<type-var>    ::= "'" <identifier>
<prim-type>   ::= "int" | "float" | "number" | "bool" | "string" | "char"
<compound-type> ::= <quotation-type> | <list-type> | <tuple-type> | <custom-type>

<stack-effect> ::= <type>* "->" <type>*

;; ========================================
;; DEFINITIONS
;; ========================================

<definition>  ::= <word-def> | <prim-def> | <product-def> | <sum-def>

<word-def>    ::= "(" "define" <visibility>? <identifier>
                  "(" <stack-effect> ")" <expression>* ")"

<prim-def>    ::= "(" "define" "primitive" <identifier>
                  "(" <stack-effect> ")" ")"

<product-def> ::= "(" "define" <visibility>? <identifier> <prod-marker>?
                  <field-spec>+ ")"

<sum-def>     ::= "(" "define" <visibility>? <identifier> <sum-marker>
                  <variant>+ ")"

<module-def>  ::= "(" "define" "module" <identifier>
                  <import-stmt>? <module-body>* ")"

;; ========================================
;; MODULE SYSTEM
;; ========================================

<import-stmt> ::= "(" "import" <import-spec>+ ")"
<import-spec> ::= <identifier> | "(" <identifier> <import-modifier>+ ")"

<import-modifier> ::= "(" "only" <identifier>+ ")"
                    | "(" "prefix" <identifier> ")"
                    | "(" "rename" <rename-pair>+ ")"
                    | "(" "except" <identifier>+ ")"
#+END_SRC

* Examples

** Simple Expressions

#+BEGIN_SRC scheme
;; Stack operations
(5 3 +)           ; → 8
(dup *)           ; → square top of stack
(swap drop)       ; → keep second element

;; With quotations
'(dup *)          ; → push quotation
(5 '(dup *) call) ; → 25
#+END_SRC

** Word Definitions

#+BEGIN_SRC scheme
;; Basic word
(define square (number -> number)
  (dup *))

;; Multiple inputs/outputs
(define pythagorean (number number -> number)
  (dup * swap dup * + sqrt))

;; Higher-order
(define twice ('a (quot ('a -> 'a)) -> 'a)
  (dup call call))
#+END_SRC

** Type Definitions

#+BEGIN_SRC scheme
;; Product type (tuple)
(define Point (x float) (y float))

;; Sum type (tagged union)
(define Maybe ⊕
  (Just 'a)
  (Nothing))

;; Using the types
(3.0 4.0 make-point)      ; Creates Point
(42 make-just)            ; Creates Maybe
#+END_SRC

** Modules

#+BEGIN_SRC scheme
;; Define a module
(define module math
  (import (helpers (prefix h:)))

  (define public square (number -> number)
    (dup *))

  (define private helper (number -> number)
    (2 *)))

;; Use a module
(import math)
(5 square)  ; → 25
#+END_SRC