Scheming a mise-en-abîme in BQN (WIP)

We will build and interpreter for a subset of the Scheme programming language, following a Peter Norvig's essay. An alternative reference would have been of course SICP's metacircular evaluator¹, but I consider lispy to be a very elegant implementation targeting a non-Lisp host².

Our goal is to adhere to the Revised\(^5\) Report on the Algorithmic Language Scheme (R5RS). However, seasoned schemers will quickly notice that our implementation still has quite some distance to cover in reaching full compliance. Let's start by defining some utilities. It is sad that the 1-modifier is needed, after all, Booleans are not that special.

_bool ← {𝔽◶"#f"‿"#t"}

A global environment:

env ← ⟨
  "sin", "cos", "tan", "asin", "acos", "atan",
  "log", "+", "-", "*", "/", ">", "<", ">=", "<=", "="
  "abs", "append", "apply", "begin", "car", "cdr", "cons"
  "eq?", "expt", "equal?", "length", "list", "list?"
  "map", "max", "min", "not", "null?", "number?"
  "print", "round", "symbol?"
⟩ •HashMap ⟨
  ⋆⁼, +´, -´, ×´, ÷´, >´, <´, ≥´, ≤´, =´
  |, ∾´, {𝕎𝕩}´, {𝕩}, ⊑, 1⊸↓, ⋈´
  ≡´_bool, ⋆´, =´_bool, ≠, ⋈, 0⊸=_bool{•Type•BQN⎊1𝕩}
  {𝕎¨𝕩}´, ⌈´, ⌊´, 0⊸≠_bool¬, @⊸=_bool, •BQN⎊1
  •Show, ⌊0.5+⊢, 2⊸=_bool{•Type⊑𝕩}
⟩ ∾˜ •math •ns.Get¨ "sin"‿"cos"‿"tan"‿"asin"‿"acos"‿"atan"

The interpreter:

Scheme ← {
  T ← ' '=(-⟜1·+`·¬⊸∧⟜»⊸∨·+˝"( )"=⌜⊢)⊸⊔
  T𝕩
} ⋄ Scheme "(begin (+ 1 1) (* (+ 3 2) 1) (define a (+ 3 3)))"

Given the title of this post, it seems only fitting to test our interpreter with a quine:

Scheme "((lambda (x) (list x (list (quote quote) x)))
         (quote (lambda (x) (list x (list (quote quote) x)))))"

"((lambda (x) (list x (list (quote quote) x)))
         (quote (lambda (x) (list x (list (quote quote) x)))))"

Naturally, we can do more rigorous tests by comparing to my favorite Scheme implementation³. To achieve this, we'll leverage BQN's foreign function interface:

ch ← "../supp/chicken/libchicken.so" •FFI "*u8"‿"eval_scheme"‿">*u8:c8"
R5RS ← {@+𝕩.Read¨ ↕1⊸+•_while_(0≠𝕩.Read)0}Ch∾@

But fear not, there’s no room for monotony here. After all, people much prefer dealing with machinery to dealing with bureaucracies⁴:

("Not Compliant"⊸!Scheme≡R5RS)¨ "(+ 10 122)"‿"(* 4 2)"

⟨ ⟨ "(+ 10 122)" "132" ⟩ ⟨ "(* 4 2)" "8" ⟩ ⟩