src/Keys.bend
mylsm-lsm-store@0.5.0.0 · 156 lines · 0 definitions
1import Base
2import bend-mathlib@0.7.0.0/string.bend as MString
3import bend-mathlib@0.7.0.0/bool.bend as MBool
4
5# Total-order comparison for keys. Base's String.cmp hands the strings back
6# beside the verdict ((s1, s2), c); we take reusable copies and unpack via a
7# helper (a match cannot scrutinize the computed call directly).
8def unpack(pair: (String & String) & Cmp) -> Cmp:
9 match pair:
10 case ((_, _), c):
11 c
12
13# Handle cmp in the key ordering and comparison.
14def cmp(+s1: String, +s2: String) -> Cmp:
15 unpack(String.cmp(s1, s2))
16
17# Handle eq in the key ordering and comparison.
18def eq(+s1: String, +s2: String) -> Bool:
19 String.eq(s1, s2)
20
21# Small, coherent views of Cmp used by key-order laws and sorted-run code.
22def cmp_is_lt(ord: Cmp) -> Bool:
23 Cmp.is_lt(ord)
24
25# Compare whether is eq holds for the key ordering and comparison.
26def cmp_is_eq(ord: Cmp) -> Bool:
27 Cmp.is_eq(ord)
28
29# Compare whether is gt holds for the key ordering and comparison.
30def cmp_is_gt(ord: Cmp) -> Bool:
31 Cmp.is_gt(ord)
32
33# Compare whether is le holds for the key ordering and comparison.
34def cmp_is_le(ord: Cmp) -> Bool:
35 Cmp.is_le(ord)
36
37# Handle lt in the key ordering and comparison.
38def lt(+s1: String, +s2: String) -> Bool:
39 cmp_is_lt(cmp(s1, s2))
40
41# Handle le in the key ordering and comparison.
42def le(+s1: String, +s2: String) -> Bool:
43 cmp_is_le(cmp(s1, s2))
44
45# Compare whether reverse holds for the key ordering and comparison.
46def cmp_reverse(ord: Cmp) -> Cmp:
47 match ord:
48 case LT{}:
49 GT{}
50 case EQ{}:
51 EQ{}
52 case GT{}:
53 LT{}
54
55# Handle implies in the key ordering and comparison.
56def implies(s1: Bool, s2: Bool) -> Bool:
57 match s1:
58 case False{}:
59 True{}
60 case True{}:
61 s2
62
63# Select f for the key ordering and comparison.
64def iff(+s1: Bool, +s2: Bool) -> Bool:
65 Bool.and(implies(s1, s2), implies(s2, s1))
66
67# True exactly when one of three arbitrary predicates is true.
68def one_hot3(first: Bool, second: Bool, third: Bool) -> Bool:
69 match first second third:
70 case True{} False{} False{}:
71 True{}
72 case False{} True{} False{}:
73 True{}
74 case False{} False{} True{}:
75 True{}
76 case _ _ _:
77 False{}
78
79# Cmp is intrinsically one-hot; this predicate gives K6 a reusable statement.
80def cmp_one_hot(+ord: Cmp) -> Bool:
81 one_hot3(cmp_is_lt(ord), cmp_is_eq(ord), cmp_is_gt(ord))
82
83# Compare whether one hot proof holds for the key ordering and comparison.
84def cmp_one_hot_proof(+ord: Cmp) -> {cmp_one_hot(ord) == True{} : Bool}:
85 match ord:
86 case LT{}:
87 {==}
88 case EQ{}:
89 {==}
90 case GT{}:
91 {==}
92
93# `String.eq` is defined by the EQ projection of `String.cmp` (Cmp.is_eq of
94# Pair.snd since bend 2.0.33); matching the handed-back comparison pair
95# exposes that definitional correspondence.
96def cmp_eq_pair(
97 pair: (String & String) & Cmp
98) -> {cmp_is_eq(unpack(pair)) == Cmp.is_eq(Pair.snd(String & String, Cmp, pair)) : Bool}:
99 match pair:
100 case ((a, b), c):
101 match c:
102 case LT{}:
103 {==}
104 case EQ{}:
105 {==}
106 case GT{}:
107 {==}
108
109# Compare whether eq bridge holds for the key ordering and comparison.
110def cmp_eq_bridge(+s1: String, +s2: String) -> {cmp_is_eq(cmp(s1, s2)) == eq(s1, s2) : Bool}:
111 cmp_eq_pair(String.cmp(s1, s2))
112
113# Reflexivity chain for open keys. Every product law about keyed lookup
114# rewrites with str_eq_refl; it rests on the layers below, down to bits,
115# proved in bend-mathlib's bool and string modules (hash-pinned by version).
116# (Proving Base's own primitives is the one exception to the trust-root
117# rule: without open-key comparison facts, NO keyed law is provable.)
118
119# Evaluate refl for the key ordering and comparison.
120def bool_refl(+flag: Bool) -> {Bool.cmp(flag, flag) == EQ{} : Cmp}:
121 MBool.cmp_refl(flag)
122
123# Handle word refl in the key ordering and comparison.
124def word_refl(width: Nat, +word: Word(width)) -> {Word.cmp(width, word, word) == EQ{} : Cmp}:
125 match width word:
126 case 0n WNil{}:
127 {==}
128 case 1n+p WCon{ab, at}:
129 match ab:
130 case False{}:
131 %Equal.sym(Cmp, Word.cmp(p, at, at), EQ{}, word_refl(p, at)) : {Word.cmp.fin(False{}, False{}, _) == EQ{} : Cmp}
132 {==}
133 case True{}:
134 %Equal.sym(Cmp, Word.cmp(p, at, at), EQ{}, word_refl(p, at)) : {Word.cmp.fin(True{}, True{}, _) == EQ{} : Cmp}
135 {==}
136
137# Encode or decode a 32-bit word for refl for the key ordering and comparison.
138def u32_refl(+val: U32) -> {U32.cmp(val, val) == EQ{} : Cmp}:
139 MString.u32_cmp_refl(val)
140
141# Handle char refl in the key ordering and comparison.
142def char_refl(+ch: Char) -> {Char.cmp(ch, ch) == ((ch, ch), EQ{}) : (Char & Char) & Cmp}:
143 MString.char_cmp_refl(ch)
144
145# Handle s cmp pair refl in the key ordering and comparison.
146def s_cmp_pair_refl(+str: String) -> {String.cmp(str, str) == ((str, str), EQ{}) : (String & String) & Cmp}:
147 MString.cmp_refl(str)
148
149# Handle str refl in the key ordering and comparison.
150def str_refl(+str: String) -> {cmp(str, str) == EQ{} : Cmp}:
151 %Equal.sym((String & String) & Cmp, String.cmp(str, str), ((str, str), EQ{}), s_cmp_pair_refl(str)) : {unpack(_) == EQ{} : Cmp}
152 {==}
153
154# Handle str eq refl in the key ordering and comparison.
155def str_eq_refl(+str: String) -> {eq(str, str) == True{} : Bool}:
156 MString.eq_refl(str)