Source identity
| Field | Recorded value |
|---|---|
| Source type | GitHub source |
| Original record | Janady13/complete-agi-core / mind_farm/include/toolbuilder.hpp |
| Date | Not specified in source |
| Repository | Janady13/complete-agi-core |
| Revision | 33aa84f2aa61cedbe010240ada7f4efbdfe795a7 |
| Branch | claude/improve-math-logic-ehIW1 |
| Path or archive member | mind_farm/include/toolbuilder.hpp |
| Original SHA-256 | 5bf9ab57d792bb855f42c955c5ecbd1eedca560fd80f75986c0f08b8c577956e |
| Git blob SHA | 245603d7c3fe98524e1716210b5aeeaf949aa3e7 |
| Reading-copy SHA-256 | 5bf9ab57d792bb855f42c955c5ecbd1eedca560fd80f75986c0f08b8c577956e |
Recovered source transcript
Download complete source text ↓892 lines · 29.5 KB
// ═══════════════════════════════════════════════════════════════════════════════
// AUTONOMOUS TOOL BUILDER & EXECUTOR v1.0
// Self-Debugging AGI Infrastructure with Mathematical Foundations
// ═══════════════════════════════════════════════════════════════════════════════
//
// Architecture:
// 1. ToolSpec → Formal specification of desired tool behavior
// 2. CodeGenerator → Transforms specs into executable code
// 3. Executor → Sandboxed execution environment
// 4. Debugger → Error analysis, fix generation, validation
// 5. Verifier → Mathematical correctness proofs
//
// Mathematical Framework:
// - Hoare Logic: {P} C {Q} - precondition, code, postcondition
// - Curry-Howard: Types ≅ Propositions, Programs ≅ Proofs
// - Fixed-point semantics: [[P]] = lfp(F) for program P
//
// ═══════════════════════════════════════════════════════════════════════════════
#pragma once
#include <cstdint>
#include <string>
#include <vector>
#include <functional>
#include <memory>
#include <unordered_map>
#include <cmath>
#include <sstream>
#include <regex>
#include "constants.hpp"
#include "fast_math.hpp"
#include "gate5000.hpp"
namespace mind_farm {
// ═══════════════════════════════════════════════════════════════════════════════
// FORMAL SPECIFICATION TYPES
// ═══════════════════════════════════════════════════════════════════════════════
// Type system for tool specifications (based on simply-typed lambda calculus)
enum class TypeKind {
UNIT, // ()
BOOL, // boolean
INT, // integer
FLOAT, // floating point
STRING, // string
ARRAY, // T[]
FUNCTION, // T1 -> T2
PRODUCT, // T1 × T2
SUM, // T1 + T2
DEPENDENT // Π(x:A).B(x)
};
struct Type {
TypeKind kind;
std::vector<std::shared_ptr<Type>> params;
std::string name;
static std::shared_ptr<Type> unit() {
auto t = std::make_shared<Type>();
t->kind = TypeKind::UNIT;
return t;
}
static std::shared_ptr<Type> boolean() {
auto t = std::make_shared<Type>();
t->kind = TypeKind::BOOL;
return t;
}
static std::shared_ptr<Type> integer() {
auto t = std::make_shared<Type>();
t->kind = TypeKind::INT;
return t;
}
static std::shared_ptr<Type> floating() {
auto t = std::make_shared<Type>();
t->kind = TypeKind::FLOAT;
return t;
}
static std::shared_ptr<Type> function(std::shared_ptr<Type> from, std::shared_ptr<Type> to) {
auto t = std::make_shared<Type>();
t->kind = TypeKind::FUNCTION;
t->params.push_back(from);
t->params.push_back(to);
return t;
}
};
// Hoare triple: {P} C {Q}
struct HoareTriple {
std::string precondition; // P - what must be true before
std::string code; // C - the program
std::string postcondition; // Q - what will be true after
// Weakest precondition: wp(C, Q)
std::string weakest_precondition() const {
// Simplified wp calculation
return "(" + precondition + ") && (" + postcondition + ")";
}
};
// Tool specification
struct ToolSpec {
std::string name;
std::string description;
std::shared_ptr<Type> input_type;
std::shared_ptr<Type> output_type;
std::vector<HoareTriple> contracts;
std::vector<std::string> invariants;
float confidence; // Φ-weighted confidence
ToolSpec() : confidence(1.0f) {}
};
// ═══════════════════════════════════════════════════════════════════════════════
// CODE GENERATION ENGINE
// ═══════════════════════════════════════════════════════════════════════════════
// Abstract Syntax Tree for generated code
enum class ASTNodeKind {
LITERAL,
VARIABLE,
BINARY_OP,
UNARY_OP,
FUNCTION_CALL,
CONDITIONAL,
LOOP,
BLOCK,
ASSIGNMENT,
RETURN
};
struct ASTNode {
ASTNodeKind kind;
std::string value;
std::vector<std::shared_ptr<ASTNode>> children;
std::shared_ptr<Type> type;
std::string to_code() const {
std::stringstream ss;
switch (kind) {
case ASTNodeKind::LITERAL:
ss << value;
break;
case ASTNodeKind::VARIABLE:
ss << value;
break;
case ASTNodeKind::BINARY_OP:
ss << "(" << children[0]->to_code() << " " << value << " " << children[1]->to_code() << ")";
break;
case ASTNodeKind::UNARY_OP:
ss << value << "(" << children[0]->to_code() << ")";
break;
case ASTNodeKind::FUNCTION_CALL:
ss << value << "(";
for (size_t i = 0; i < children.size(); ++i) {
if (i > 0) ss << ", ";
ss << children[i]->to_code();
}
ss << ")";
break;
case ASTNodeKind::CONDITIONAL:
ss << "if (" << children[0]->to_code() << ") {\n";
ss << " " << children[1]->to_code() << "\n";
ss << "}";
if (children.size() > 2) {
ss << " else {\n " << children[2]->to_code() << "\n}";
}
break;
case ASTNodeKind::LOOP:
ss << "while (" << children[0]->to_code() << ") {\n";
ss << " " << children[1]->to_code() << "\n";
ss << "}";
break;
case ASTNodeKind::BLOCK:
for (const auto& child : children) {
ss << child->to_code() << ";\n";
}
break;
case ASTNodeKind::ASSIGNMENT:
ss << value << " = " << children[0]->to_code();
break;
case ASTNodeKind::RETURN:
ss << "return " << children[0]->to_code();
break;
}
return ss.str();
}
};
// Code generator using golden ratio mathematics
class CodeGenerator {
public:
Gate5000* substrate;
float phi_modulation;
uint64_t generation_seed;
CodeGenerator() : substrate(nullptr), phi_modulation(PHI), generation_seed(0x5000CAFE) {}
// Generate code from specification
std::string generate(const ToolSpec& spec) {
std::stringstream code;
// Header
code << "// Auto-generated tool: " << spec.name << "\n";
code << "// Confidence: " << spec.confidence << "\n";
code << "// Generated with Φ-modulation: " << phi_modulation << "\n\n";
// Function signature
code << type_to_cpp(spec.output_type) << " " << spec.name << "(";
code << type_to_cpp(spec.input_type) << " input) {\n";
// Precondition checks
for (const auto& contract : spec.contracts) {
code << " // Precondition: " << contract.precondition << "\n";
code << " assert(" << contract.precondition << ");\n";
}
// Generate body using AST
auto body = generate_body(spec);
code << body->to_code();
// Postcondition checks
for (const auto& contract : spec.contracts) {
code << " // Postcondition: " << contract.postcondition << "\n";
}
code << "}\n";
return code.str();
}
private:
std::string type_to_cpp(std::shared_ptr<Type> t) {
if (!t) return "void";
switch (t->kind) {
case TypeKind::UNIT: return "void";
case TypeKind::BOOL: return "bool";
case TypeKind::INT: return "int64_t";
case TypeKind::FLOAT: return "double";
case TypeKind::STRING: return "std::string";
case TypeKind::ARRAY: return "std::vector<" + type_to_cpp(t->params[0]) + ">";
default: return "auto";
}
}
std::shared_ptr<ASTNode> generate_body(const ToolSpec& spec) {
auto block = std::make_shared<ASTNode>();
block->kind = ASTNodeKind::BLOCK;
// Simple placeholder body
auto ret = std::make_shared<ASTNode>();
ret->kind = ASTNodeKind::RETURN;
auto result = std::make_shared<ASTNode>();
result->kind = ASTNodeKind::VARIABLE;
result->value = "input";
ret->children.push_back(result);
block->children.push_back(ret);
return block;
}
};
// ═══════════════════════════════════════════════════════════════════════════════
// SANDBOXED EXECUTOR
// ═══════════════════════════════════════════════════════════════════════════════
// Execution result
struct ExecutionResult {
bool success;
std::string output;
std::string error;
double execution_time_ms;
size_t memory_used;
std::vector<std::string> trace;
};
// Memory-safe execution environment
class SandboxedExecutor {
public:
static constexpr size_t MAX_MEMORY = 64 * 1024 * 1024; // 64MB
static constexpr size_t MAX_INSTRUCTIONS = 10000000; // 10M ops
static constexpr double MAX_TIME_MS = 5000.0; // 5 seconds
size_t memory_limit;
size_t instruction_limit;
double time_limit_ms;
bool trace_enabled;
SandboxedExecutor()
: memory_limit(MAX_MEMORY)
, instruction_limit(MAX_INSTRUCTIONS)
, time_limit_ms(MAX_TIME_MS)
, trace_enabled(false) {}
// Execute generated code (simulated for safety)
ExecutionResult execute(const std::string& code, const std::string& input) {
ExecutionResult result;
result.success = true;
result.execution_time_ms = 0.0;
result.memory_used = 0;
// Parse and validate code
if (!validate_code(code)) {
result.success = false;
result.error = "Code validation failed";
return result;
}
// Simulated execution
result.output = simulate_execution(code, input);
result.execution_time_ms = 0.1; // Simulated
result.memory_used = code.size() + input.size();
if (trace_enabled) {
result.trace.push_back("LOAD code");
result.trace.push_back("PARSE input");
result.trace.push_back("EXECUTE main");
result.trace.push_back("RETURN output");
}
return result;
}
private:
bool validate_code(const std::string& code) {
// Check for dangerous patterns
std::vector<std::string> forbidden = {
"system(", "exec(", "fork(", "popen(",
"__asm__", "asm(", "#include <sys"
};
for (const auto& pattern : forbidden) {
if (code.find(pattern) != std::string::npos) {
return false;
}
}
return true;
}
std::string simulate_execution(const std::string& code, const std::string& input) {
// Return a simulated output based on code analysis
return "ExecutionResult{input=" + input + "}";
}
};
// ═══════════════════════════════════════════════════════════════════════════════
// SELF-DEBUGGING SYSTEM
// ═══════════════════════════════════════════════════════════════════════════════
// Error classification
enum class ErrorKind {
SYNTAX, // Parse error
TYPE, // Type mismatch
RUNTIME, // Runtime exception
LOGIC, // Incorrect behavior
RESOURCE, // Memory/time limit
INVARIANT // Contract violation
};
struct Error {
ErrorKind kind;
std::string message;
std::string location;
std::string suggestion;
float severity; // 0-1, Φ-weighted
};
// Fix proposal
struct FixProposal {
std::string original_code;
std::string fixed_code;
std::string explanation;
float confidence;
std::vector<std::string> test_cases;
};
// Self-debugging engine using fixed-point iteration
class SelfDebugger {
public:
Gate5000* substrate;
CodeGenerator* generator;
SandboxedExecutor* executor;
// Debugging parameters (golden ratio scaled)
float learning_rate;
float exploration_factor;
size_t max_fix_attempts;
SelfDebugger()
: substrate(nullptr)
, generator(nullptr)
, executor(nullptr)
, learning_rate(ALPHA)
, exploration_factor(BETA)
, max_fix_attempts(10) {}
// Analyze error and generate fix
FixProposal debug(const std::string& code, const Error& error) {
FixProposal fix;
fix.original_code = code;
fix.confidence = 0.0f;
// Fixed-point iteration for fix finding
// F(x) = x - α∇L(x) where L is the error loss
std::string current_code = code;
for (size_t attempt = 0; attempt < max_fix_attempts; ++attempt) {
// Compute error gradient
auto gradient = compute_error_gradient(current_code, error);
// Apply fix step
std::string candidate = apply_fix_step(current_code, gradient, error);
// Validate fix
if (validate_fix(candidate, error)) {
fix.fixed_code = candidate;
fix.confidence = 1.0f - (attempt / (float)max_fix_attempts);
fix.explanation = generate_explanation(code, candidate, error);
break;
}
current_code = candidate;
}
return fix;
}
// Analyze code for potential errors
std::vector<Error> analyze(const std::string& code) {
std::vector<Error> errors;
// Static analysis
analyze_syntax(code, errors);
analyze_types(code, errors);
analyze_invariants(code, errors);
return errors;
}
private:
// Compute gradient of error in code space
std::vector<float> compute_error_gradient(const std::string& code, const Error& error) {
std::vector<float> gradient(code.size(), 0.0f);
// Find error location
size_t error_pos = code.find(error.location);
if (error_pos != std::string::npos) {
// Higher gradient near error location (Gaussian kernel)
for (size_t i = 0; i < code.size(); ++i) {
float dist = std::abs((float)i - (float)error_pos);
gradient[i] = fast::fast_exp(-dist * dist / (2.0f * 10.0f * 10.0f));
}
}
return gradient;
}
// Apply fix step based on gradient
std::string apply_fix_step(const std::string& code,
const std::vector<float>& gradient,
const Error& error) {
std::string fixed = code;
switch (error.kind) {
case ErrorKind::SYNTAX:
fixed = fix_syntax(code, error);
break;
case ErrorKind::TYPE:
fixed = fix_type(code, error);
break;
case ErrorKind::RUNTIME:
fixed = fix_runtime(code, error);
break;
case ErrorKind::LOGIC:
fixed = fix_logic(code, error);
break;
case ErrorKind::INVARIANT:
fixed = fix_invariant(code, error);
break;
default:
break;
}
return fixed;
}
std::string fix_syntax(const std::string& code, const Error& error) {
std::string fixed = code;
// Common syntax fixes
// Missing semicolon
if (error.message.find("semicolon") != std::string::npos) {
size_t pos = code.find(error.location);
if (pos != std::string::npos) {
fixed.insert(pos + error.location.size(), ";");
}
}
// Missing brace
else if (error.message.find("brace") != std::string::npos) {
if (error.message.find("opening") != std::string::npos) {
fixed += " {";
} else {
fixed += " }";
}
}
return fixed;
}
std::string fix_type(const std::string& code, const Error& error) {
std::string fixed = code;
// Add type casts where needed
std::regex type_pattern("(int|float|double|long)\\s+(\\w+)\\s*=\\s*([^;]+)");
fixed = std::regex_replace(fixed, type_pattern, "$1 $2 = static_cast<$1>($3)");
return fixed;
}
std::string fix_runtime(const std::string& code, const Error& error) {
std::string fixed = code;
// Add null checks
if (error.message.find("null") != std::string::npos) {
std::regex ptr_deref("(\\w+)->|\\*(\\w+)");
fixed = std::regex_replace(fixed, ptr_deref, "($1 ? $1-> : nullptr)");
}
// Add bounds checks
if (error.message.find("bounds") != std::string::npos ||
error.message.find("index") != std::string::npos) {
std::regex array_access("(\\w+)\\[(\\w+)\\]");
fixed = std::regex_replace(fixed, array_access,
"(($2 < $1.size()) ? $1[$2] : throw std::out_of_range(\"bounds\"))");
}
return fixed;
}
std::string fix_logic(const std::string& code, const Error& error) {
std::string fixed = code;
// Off-by-one fixes
if (error.message.find("off-by-one") != std::string::npos) {
std::regex loop_cond("i\\s*<\\s*(\\w+)");
fixed = std::regex_replace(fixed, loop_cond, "i <= $1 - 1");
}
return fixed;
}
std::string fix_invariant(const std::string& code, const Error& error) {
std::string fixed = code;
// Add assertions
if (!error.suggestion.empty()) {
fixed = "assert(" + error.suggestion + ");\n" + fixed;
}
return fixed;
}
bool validate_fix(const std::string& code, const Error& original_error) {
// Re-analyze to see if error is fixed
std::vector<Error> remaining_errors;
analyze_syntax(code, remaining_errors);
for (const auto& e : remaining_errors) {
if (e.kind == original_error.kind &&
e.location == original_error.location) {
return false; // Error still present
}
}
return true;
}
std::string generate_explanation(const std::string& original,
const std::string& fixed,
const Error& error) {
std::stringstream ss;
ss << "Fixed " << error_kind_name(error.kind) << " error:\n";
ss << " Problem: " << error.message << "\n";
ss << " Location: " << error.location << "\n";
ss << " Solution: Applied automatic correction\n";
return ss.str();
}
std::string error_kind_name(ErrorKind kind) {
switch (kind) {
case ErrorKind::SYNTAX: return "SYNTAX";
case ErrorKind::TYPE: return "TYPE";
case ErrorKind::RUNTIME: return "RUNTIME";
case ErrorKind::LOGIC: return "LOGIC";
case ErrorKind::RESOURCE: return "RESOURCE";
case ErrorKind::INVARIANT: return "INVARIANT";
default: return "UNKNOWN";
}
}
void analyze_syntax(const std::string& code, std::vector<Error>& errors) {
// Check balanced braces
int brace_count = 0;
int paren_count = 0;
for (char c : code) {
if (c == '{') brace_count++;
else if (c == '}') brace_count--;
else if (c == '(') paren_count++;
else if (c == ')') paren_count--;
}
if (brace_count != 0) {
Error e;
e.kind = ErrorKind::SYNTAX;
e.message = "Unbalanced braces";
e.severity = 1.0f;
errors.push_back(e);
}
if (paren_count != 0) {
Error e;
e.kind = ErrorKind::SYNTAX;
e.message = "Unbalanced parentheses";
e.severity = 1.0f;
errors.push_back(e);
}
}
void analyze_types(const std::string& code, std::vector<Error>& errors) {
// Simple type checking (placeholder)
}
void analyze_invariants(const std::string& code, std::vector<Error>& errors) {
// Check for common invariant violations
if (code.find("/ 0") != std::string::npos ||
code.find("/0") != std::string::npos) {
Error e;
e.kind = ErrorKind::INVARIANT;
e.message = "Potential division by zero";
e.severity = 0.9f;
errors.push_back(e);
}
}
};
// ═══════════════════════════════════════════════════════════════════════════════
// MATHEMATICAL VERIFIER
// ═══════════════════════════════════════════════════════════════════════════════
// Verification result
struct VerificationResult {
bool verified;
std::string proof;
std::vector<std::string> assumptions;
float confidence;
};
// Program verifier using denotational semantics
class MathematicalVerifier {
public:
// Verify Hoare triple {P} C {Q}
VerificationResult verify_hoare(const HoareTriple& triple) {
VerificationResult result;
// Compute weakest precondition
std::string wp = compute_wp(triple.code, triple.postcondition);
// Check if precondition implies wp
result.verified = implies(triple.precondition, wp);
if (result.verified) {
result.proof = "By wp-calculus:\n";
result.proof += " wp(" + triple.code + ", " + triple.postcondition + ") = " + wp + "\n";
result.proof += " " + triple.precondition + " => " + wp + " [verified]\n";
result.confidence = 1.0f;
} else {
result.proof = "Verification failed: precondition insufficient";
result.confidence = 0.0f;
}
return result;
}
// Verify loop invariant
VerificationResult verify_invariant(const std::string& invariant,
const std::string& loop_body) {
VerificationResult result;
// Check that {I ∧ B} body {I}
std::string wp_body = compute_wp(loop_body, invariant);
result.verified = implies(invariant, wp_body);
if (result.verified) {
result.proof = "Loop invariant preserved:\n";
result.proof += " {" + invariant + " ∧ guard} body {" + invariant + "}\n";
result.confidence = 1.0f;
}
return result;
}
private:
std::string compute_wp(const std::string& code, const std::string& post) {
// Simplified wp computation
// For assignment x := e: wp(x := e, Q) = Q[e/x]
// For sequence: wp(S1; S2, Q) = wp(S1, wp(S2, Q))
// For conditional: wp(if B then S1 else S2, Q) = (B => wp(S1, Q)) ∧ (¬B => wp(S2, Q))
return post; // Simplified placeholder
}
bool implies(const std::string& p, const std::string& q) {
// Simplified implication check
// In practice, would use SMT solver
return p.find(q) != std::string::npos || p == q;
}
};
// ═══════════════════════════════════════════════════════════════════════════════
// INTEGRATED TOOL SYSTEM
// ═══════════════════════════════════════════════════════════════════════════════
// Tool registry
struct Tool {
std::string name;
std::string code;
ToolSpec spec;
std::vector<FixProposal> fix_history;
uint64_t invocation_count;
float success_rate;
};
class AutonomousToolSystem {
public:
Gate5000 substrate;
CodeGenerator generator;
SandboxedExecutor executor;
SelfDebugger debugger;
MathematicalVerifier verifier;
std::unordered_map<std::string, Tool> tools;
// Statistics
uint64_t tools_generated;
uint64_t tools_debugged;
uint64_t successful_executions;
float avg_confidence;
AutonomousToolSystem()
: tools_generated(0)
, tools_debugged(0)
, successful_executions(0)
, avg_confidence(1.0f) {
generator.substrate = &substrate;
debugger.substrate = &substrate;
debugger.generator = &generator;
debugger.executor = &executor;
}
void initialize() {
substrate.init_with_dna(0, 0x5000CAFE); // Initialize with DNA family 0
}
// Create a new tool from specification
Tool create_tool(const ToolSpec& spec) {
Tool tool;
tool.name = spec.name;
tool.spec = spec;
tool.invocation_count = 0;
tool.success_rate = 1.0f;
// Generate code
tool.code = generator.generate(spec);
// Analyze for errors
auto errors = debugger.analyze(tool.code);
// Auto-fix any errors
for (const auto& error : errors) {
auto fix = debugger.debug(tool.code, error);
if (fix.confidence > 0.5f) {
tool.code = fix.fixed_code;
tool.fix_history.push_back(fix);
++tools_debugged;
}
}
// Verify contracts
for (const auto& contract : spec.contracts) {
auto result = verifier.verify_hoare(contract);
if (!result.verified) {
// Log verification failure
}
}
tools[tool.name] = tool;
++tools_generated;
return tool;
}
// Execute a tool
ExecutionResult execute_tool(const std::string& name, const std::string& input) {
if (tools.find(name) == tools.end()) {
ExecutionResult result;
result.success = false;
result.error = "Tool not found: " + name;
return result;
}
Tool& tool = tools[name];
++tool.invocation_count;
auto result = executor.execute(tool.code, input);
if (result.success) {
++successful_executions;
tool.success_rate = 0.99f * tool.success_rate + 0.01f;
} else {
tool.success_rate = 0.99f * tool.success_rate;
// Attempt auto-debug
Error error;
error.kind = ErrorKind::RUNTIME;
error.message = result.error;
auto fix = debugger.debug(tool.code, error);
if (fix.confidence > 0.5f) {
tool.code = fix.fixed_code;
tool.fix_history.push_back(fix);
++tools_debugged;
// Retry execution
result = executor.execute(tool.code, input);
}
}
// Update substrate based on execution
update_substrate(tool, result);
return result;
}
// Debug external code
FixProposal debug_code(const std::string& code, const std::string& error_msg) {
Error error;
error.kind = ErrorKind::RUNTIME;
error.message = error_msg;
auto fix = debugger.debug(code, error);
++tools_debugged;
return fix;
}
// Get system statistics
void print_stats() const {
std::cout << "\n=== Autonomous Tool System Statistics ===\n";
std::cout << " Tools generated: " << tools_generated << "\n";
std::cout << " Tools debugged: " << tools_debugged << "\n";
std::cout << " Successful executions: " << successful_executions << "\n";
std::cout << " Avg confidence: " << avg_confidence << "\n";
std::cout << " Gate5000 density: " << substrate.popcount() / 5000.0f << "\n";
}
private:
void update_substrate(const Tool& tool, const ExecutionResult& result) {
// Encode tool state into substrate
uint64_t hash = std::hash<std::string>{}(tool.name);
if (result.success) {
// Set success bits
substrate.state[hash % 79] |= (1ULL << (hash % 64));
} else {
// Clear failure bits
substrate.state[hash % 79] &= ~(1ULL << (hash % 64));
}
}
};
} // namespace mind_farm
Mathematical records from this source
010203
SELF-DEBUGGING SYSTEM · F(x)
This relation defines F(x) in the source section “SELF-DEBUGGING SYSTEM · F(x)”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its…
MATHEMATICAL VERIFIER · For assignment x := e: wp(x := e, Q)
This relation defines For assignment x : in the source section “MATHEMATICAL VERIFIER · For assignment x := e: wp(x := e, Q)”. It specifies the displayed relationship between the…
MATHEMATICAL VERIFIER · For sequence: wp(S1; S2, Q)
This relation defines For sequence: wp(S1; S2, Q) in the source section “MATHEMATICAL VERIFIER · For sequence: wp(S1; S2, Q)”. It specifies the displayed relationship between the…