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Source for wiki BottomScheme version 1

author

cowan

comment

ipnr

127.11.51.1

name

BottomScheme

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0

text

Bottom Scheme is a tiny subset of R7RS-small.  It is not really a Scheme at all, because it omits assignment, macros, modules, proper tail calls except in named `let`, multiple values, `call/cc`, `dynamic-wind`, mutable pairs and strings, I/O (except for `read-char` and `write-char`), and essentially all non-primitive procedures.

== Specification ==

This list is organized according to the R7RS-small report.

2.1 Identifiers

No case-folding directives.

2.2 Whitespace

Only `;` comments.

2.3 Other notations

Parens, apostrophe, quoted strings, `#t` and `#f`, and number, vector, and bytevector constants.  No backquoting, character constants, number bases, or labels.

4.1 Primitive expression types

Variables, constants, procedure calls, `lambda` without improper formals, `if`.

4.2 Derived expression types

Only `cond` without `=>`, `and`, `or`, `let`, `letrec`, `begin`, and named `let` (with the restriction that the bound procedure can only be invoked in tail positions within the lexical scope of the `let`).

5.5 Record-type definitions

Full support for `define-record-type`.

6.1 Equivalence predicates

Only `eqv?` (for which `eq?` is a synonym).  Programmers are encouraged to provide their own definition of `equal?`.

6.2.1 Numerical types

All types are supported.

6.2.2 Exactness

The only exact numbers are integers within a fixed range.

6.2.4 Implementation extensions

Inexact real numbers are IEEE doubles; inexact complex numbers are pairs of IEEE doubles in the rectangular representation.

6.2.5 Syntax of numerical constants

`/` is not supported, because all exact numbers are integers.  Base and exactness prefixes are not supported.  The notations `-0.0`, `+inf.0`, `-inf.0`, and `+nan.0` are supported.

6.2.6 Numerical operations

Predicates:  `number?`, `real?`, `exact?`, `inexact?`.  Arithmetic:  `+`, `-`, `*`, `/` with two arguments only; `/` always returns an inexact value.  Transcendental functions:  `exp`, `log` (one argument), `sin`, `cos`, `tan`, `asin`, `acos`, `atan` (one argument), `sqrt`, `expt` always return complex numbers.  Complex: `make-rectangular`, `real-part`, `imag-part`.  Conversion: `exact`, `inexact`.

As an enhancement to R7RS-small, the non-generic arithmetic functions `fx+`, `fx-`, `fx*`, `fl+`, `fl-`, `fl*`, `fl/`, `cx+`, `cx-`, `cx*`, `cx/` are provided.

6.3 Booleans

Only `#t` and `#f` notations, `not`, `boolean?`.

6.4 Pairs and lists

Pairs are immutable.  Only `pair?`, `cons`, `car`, `cdr`, `null?`

6.5 Symbols

Only `symbol?`, `symbol->string`, `string->symbol`.

6.6 Characters

Not supported; use single-character strings instead.

6.7 Strings

Full support for string literals.  Strings are immutable.  All Unicode characters are supported except U+0000 (NUL).  Only `string?`, `string-length`, `string=?`, `string<?`, `string>?`, `substring`, `list->string`.

6.8 Vectors

Full support for vector literals.  Only `vector?`, `make-vector` (one argument), `vector-length`, `vector-ref`, `vector-set!`.

6.9 Bytevectors

Full support for bytevector literals.  Only `bytevector?`, `make-bytevector` (one argument), `bytevector-length`, `bytevector-u8-ref`, `bytevector-u8-set!`.

6.10 Control features

Only `procedure?`, `apply`.

6.11 Exceptions

Only `error`.

6.13 Input and output

Only `read-char` (no arguments), `eof-object`, `eof-object?`, `write-char` (no arguments), `display` (mostly for debugging).

== Implementation ==

These notes assume a 64-bit system.

With the basic object 64 bits in size, NaN-boxing is a plausible technique.  In this scheme, IEEE doubles are represented as immediates, and all other objects are stuffed into the signaling NaN space (high-order bit is 0, next 11 bits are 1, next bit is 1).  This limits them to 52 bits in size, which is enough to hold 64-bit pointers in current architectures, since they are only 47 bits in size (excluding the kernel area).  Because a pointer to a 64-bit value always has the low-order three bits zero, they can be used for the following tagging scheme:

 * 000 - 48-bit fixnum
 * 001 - pointer to compnum
 * 010 - immediate `#t`, `#f`, end of file object, and undefined-value pseudo-object
 * 011 - pointer to vector (the -1 element is a 48-bit fixnum length)
 * 100 - pointer to Scheme pair (direct dereference gets the cdr)
 * 101 - pointer to bytevector (padded to multiple of 64 bits, preceded by a 48-bit fixnum length)
 * 110 - pointer to string (padded to multiple of 64 bits, preceded by a 48-bit fixnum length)
 * 111 - pointer to procedure, symbol, or record (first word points to a type object)

time

2015-04-17 00:16:04

version

1