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1d3f990 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 | //! Proof IR — internal representation of proof terms
use serde::{Deserialize, Serialize};
use std::collections::HashMap;
/// Proof terms (Curry-Howard isomorphism)
#[derive(Debug, Clone, Serialize, Deserialize)]
pub enum ProofTerm {
/// Variable reference (assumption)
Var(String),
/// Abstraction: λx. proof
Abs {
var: String,
proof: Box<ProofTerm>,
},
/// Application: proof1 proof2
App {
func: Box<ProofTerm>,
arg: Box<ProofTerm>,
},
/// Constant proof (axiom)
Const(String),
/// Pair: (proof1, proof2)
Pair(Box<ProofTerm>, Box<ProofTerm>),
/// Projection: fst(proof), snd(proof)
Fst(Box<ProofTerm>),
Snd(Box<ProofTerm>),
}
impl ProofTerm {
pub fn var(name: &str) -> Self {
ProofTerm::Var(name.into())
}
pub fn app(func: Self, arg: Self) -> Self {
ProofTerm::App {
func: Box::new(func),
arg: Box::new(arg),
}
}
pub fn pair(left: Self, right: Self) -> Self {
ProofTerm::Pair(Box::new(left), Box::new(right))
}
}
/// Proof obligations — propositions that need to be discharged
#[derive(Debug, Clone, Serialize, Deserialize)]
pub enum ProofObligation {
/// Memory mutation preserves invariants
InvariantPreservation {
address: usize,
old_value: i64,
new_value: i64,
invariants: Vec<String>,
},
/// Semantic equivalence before/after transformation
SemanticPreservation {
before: String,
after: String,
},
/// Loop invariant maintenance
LoopInvariantMaintenance {
header: usize,
invariant: String,
},
}
impl ProofObligation {
pub fn to_string(&self) -> String {
match self {
ProofObligation::InvariantPreservation {
address,
old_value,
new_value,
invariants,
} => {
format!(
"preserve_invariants({}, {} -> {}, {})",
address,
old_value,
new_value,
invariants.join(", ")
)
}
ProofObligation::SemanticPreservation { before, after } => {
format!("semantic_equiv({} ≡ {})", before, after)
}
ProofObligation::LoopInvariantMaintenance { header, invariant } => {
format!("loop_invariant({}, {})", header, invariant)
}
}
}
}
/// Proof context — tracks hypotheses and proven facts
#[derive(Debug, Clone)]
pub struct ProofContext {
hypotheses: HashMap<String, String>,
proven_facts: HashMap<String, ProofTerm>,
}
impl ProofContext {
pub fn new() -> Self {
Self {
hypotheses: HashMap::new(),
proven_facts: HashMap::new(),
}
}
pub fn add_hypothesis(&mut self, name: String, ty: String) {
self.hypotheses.insert(name, ty);
}
pub fn add_proof(&mut self, obligation: ProofObligation, proof: ProofTerm) {
let key = obligation.to_string();
self.proven_facts.insert(key, proof);
}
pub fn construct_proof(&self, obligation: &ProofObligation) -> anyhow::Result<ProofTerm> {
// Simple proof construction: for invariant preservation, assume the invariant holds
match obligation {
ProofObligation::InvariantPreservation { invariants, .. } => {
if invariants.is_empty() {
Ok(ProofTerm::var("invariant_holds"))
} else {
// For multiple invariants, construct a tuple
let proof = invariants
.iter()
.fold(ProofTerm::var("_"), |acc, inv| {
ProofTerm::pair(acc, ProofTerm::var(inv))
});
Ok(proof)
}
}
_ => Ok(ProofTerm::var("axiom")),
}
}
pub fn has_proof_for(&self, obligation: &ProofObligation) -> bool {
let key = obligation.to_string();
self.proven_facts.contains_key(&key)
}
}
impl Default for ProofContext {
fn default() -> Self {
Self::new()
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_proof_term_creation() {
let proof = ProofTerm::var("x");
assert!(matches!(proof, ProofTerm::Var(_)));
}
#[test]
fn test_proof_obligation() {
let ob = ProofObligation::InvariantPreservation {
address: 0,
old_value: 5,
new_value: 10,
invariants: vec!["x > 0".into()],
};
let s = ob.to_string();
assert!(s.contains("preserve_invariants"));
}
#[test]
fn test_proof_context() {
let mut ctx = ProofContext::new();
ctx.add_hypothesis("x".into(), "Int".into());
assert!(ctx.hypotheses.contains_key("x"));
}
}
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