preserves/cheatsheet.md

---
no_site_title: true
title: "Preserves Cheatsheets"
---

Tony Garnock-Jones <tonyg@leastfixedpoint.com>  
June 2022. Version 0.7.0.

## Machine-Oriented Binary Syntax

For a value `v`, we write `«v»` for the binary encoding of `v`.

                          «#f» = [0xA0]
                          «#t» = [0xA1]
                           «F» = [0xA2] ++ binary32(F)     if F ∈ Float
                           «D» = [0xA2] ++ binary64(D)     if D ∈ Double
                           «x» = [0xA3] ++ intbytes(x)     if x ∈ SignedInteger
                           «S» = [0xA4] ++ utf8(S) ++ [0]  if S ∈ String
                                 [0xA5] ++ S               if S ∈ ByteString
                                 [0xA6] ++ utf8(S)         if S ∈ Symbol

               «<L F_1...F_m>» = [0xA7] ++ seq(«L», «F_1», ..., «F_m»)
                 «[X_1...X_m]» = [0xA8] ++ seq(«X_1», ..., «X_m»)
                «#{E_1...E_m}» = [0xA9] ++ seq(«E_1», ..., «E_m»)
         «{K_1:V_1...K_m:V_m}» = [0xAA] ++ seq(«K_1», «V_1», ..., «K_m», «V_m»)

            seq(R_1, ..., R_m) = len(|R_1|) ++ R_1 ++...++ len(|R_m|) ++ R_m

                        len(m) = e(m, 128)

                       e(v, d) = [v + d]                           if v < 128
                                 e(v / 128, 0) ++ [(v % 128) + d]  if v ≥ 128

                         «#!V» = [0xAB] ++ «V»

The functions `binary32(F)` and `binary64(D)` yield big-endian 4- and
8-byte IEEE 754 binary representations of `F` and `D`, respectively.

The function `intbytes(x)` gives the big-endian two's-complement signed
binary representation of `x`, taking exactly as many whole bytes as
needed to unambiguously identify the value and its sign. `intbytes(0)`
is the empty byte sequence.

When reading, the length of the input is supplied externally. This means
that, when reading a length/value pair in a `seq()`, each length should
be passed down to the decoder for the corresponding value, so that the
decoder knows when to stop.

**Annotations.** To annotate a `Repr` `r` (that *MUST NOT* itself
already be annotated) with some sequence of `Value`s `[v_1, ..., v_m]`,
surround `r` as follows:

    [0xBF] ++ len(|r|) ++ r ++ len(|«v_1»|) ++ «v_1» ++...++ len(|«v_m»|) ++ «v_m»