midstream 0.2.0

//! Formal reasoning engine inspired by Lean theorem proving

use serde::{Deserialize, Serialize};
use std::collections::{HashMap, HashSet};
use async_trait::async_trait;

use super::types::Context;
use super::agent::Action;

/// Formal reasoning engine for verifying agent actions
pub struct FormalReasoner {
    /// Axioms and established theorems
    theorem_base: Vec<Theorem>,

    /// Inference rules
    rules: Vec<InferenceRule>,

    /// Proof cache for performance
    proof_cache: HashMap<String, Proof>,
}

impl FormalReasoner {
    pub fn new() -> Self {
        let mut reasoner = Self {
            theorem_base: Vec::new(),
            rules: Vec::new(),
            proof_cache: HashMap::new(),
        };

        // Initialize with basic axioms
        reasoner.add_axiom(Theorem {
            id: "axiom_identity".to_string(),
            statement: "For all x, x = x".to_string(),
            proof: None,
            confidence: 1.0,
            tags: vec!["axiom".to_string(), "identity".to_string()],
        });

        reasoner.add_axiom(Theorem {
            id: "axiom_safety".to_string(),
            statement: "Actions must not cause harm".to_string(),
            proof: None,
            confidence: 1.0,
            tags: vec!["axiom".to_string(), "safety".to_string()],
        });

        // Add basic inference rules
        reasoner.add_rule(InferenceRule {
            name: "modus_ponens".to_string(),
            premises: vec!["P".to_string(), "P -> Q".to_string()],
            conclusion: "Q".to_string(),
        });

        reasoner
    }

    /// Add an axiom to the theorem base
    pub fn add_axiom(&mut self, theorem: Theorem) {
        self.theorem_base.push(theorem);
    }

    /// Add an inference rule
    pub fn add_rule(&mut self, rule: InferenceRule) {
        self.rules.push(rule);
    }

    /// Verify an action is safe and correct
    pub async fn verify_action(
        &self,
        action: &Action,
        context: &Context,
    ) -> Result<Proof, String> {
        let proof_key = format!("{:?}_{}", action, context.session_id);

        // Check cache first
        if let Some(cached_proof) = self.proof_cache.get(&proof_key) {
            return Ok(cached_proof.clone());
        }

        // Construct proof
        let mut proof = Proof {
            steps: Vec::new(),
            valid: true,
            confidence: 1.0,
        };

        // Step 1: Verify safety constraints
        proof.steps.push(ProofStep {
            rule: "safety_check".to_string(),
            premises: vec![action.description.clone()],
            conclusion: "Action is safe".to_string(),
            confidence: self.verify_safety(action).await,
        });

        // Step 2: Verify preconditions
        proof.steps.push(ProofStep {
            rule: "precondition_check".to_string(),
            premises: vec![format!("Context: {:?}", context)],
            conclusion: "Preconditions satisfied".to_string(),
            confidence: self.verify_preconditions(action, context).await,
        });

        // Step 3: Verify expected outcomes
        proof.steps.push(ProofStep {
            rule: "outcome_verification".to_string(),
            premises: vec![format!("Expected: {:?}", action.expected_outcome)],
            conclusion: "Outcomes are valid".to_string(),
            confidence: self.verify_outcomes(action).await,
        });

        // Compute overall validity
        proof.confidence = proof.steps.iter()
            .map(|s| s.confidence)
            .product::<f64>();

        proof.valid = proof.confidence > 0.5;

        Ok(proof)
    }

    async fn verify_safety(&self, action: &Action) -> f64 {
        // Check against safety axioms
        let safety_axiom = self.theorem_base.iter()
            .find(|t| t.tags.contains(&"safety".to_string()));

        if let Some(_axiom) = safety_axiom {
            // Simple heuristic: actions with tool calls need verification
            if action.tool_calls.is_empty() {
                0.95 // High confidence for non-tool actions
            } else {
                0.8 // Moderate confidence for tool actions
            }
        } else {
            0.7 // Default moderate confidence
        }
    }

    async fn verify_preconditions(&self, action: &Action, context: &Context) -> f64 {
        // Verify context has necessary information
        if context.history.is_empty() {
            return 0.5; // Low confidence with no history
        }

        // Check if action parameters are valid
        let param_confidence = if action.parameters.is_empty() {
            0.9
        } else {
            // Verify parameters make sense
            0.85
        };

        param_confidence
    }

    async fn verify_outcomes(&self, action: &Action) -> f64 {
        // Verify expected outcomes are reasonable
        if let Some(ref outcome) = action.expected_outcome {
            if !outcome.is_empty() {
                0.9
            } else {
                0.7
            }
        } else {
            0.6
        }
    }

    /// Prove a new theorem from existing ones
    pub async fn prove_theorem(
        &mut self,
        statement: String,
        premises: Vec<String>,
    ) -> Result<Theorem, String> {
        let mut proof = Proof {
            steps: Vec::new(),
            valid: false,
            confidence: 0.0,
        };

        // Try to construct proof using available rules
        for rule in &self.rules {
            if self.can_apply_rule(rule, &premises) {
                proof.steps.push(ProofStep {
                    rule: rule.name.clone(),
                    premises: premises.clone(),
                    conclusion: statement.clone(),
                    confidence: 0.9,
                });
                proof.valid = true;
                proof.confidence = 0.9;
                break;
            }
        }

        if proof.valid {
            let theorem = Theorem {
                id: format!("theorem_{}", self.theorem_base.len()),
                statement,
                proof: Some(proof),
                confidence: 0.9,
                tags: vec!["derived".to_string()],
            };
            self.theorem_base.push(theorem.clone());
            Ok(theorem)
        } else {
            Err("Could not construct proof".to_string())
        }
    }

    fn can_apply_rule(&self, rule: &InferenceRule, premises: &[String]) -> bool {
        // Simple pattern matching for now
        premises.len() >= rule.premises.len()
    }

    pub fn theorem_count(&self) -> usize {
        self.theorem_base.len()
    }
}

/// A mathematical theorem or logical statement
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct Theorem {
    pub id: String,
    pub statement: String,
    pub proof: Option<Proof>,
    pub confidence: f64,
    pub tags: Vec<String>,
}

/// A formal proof
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct Proof {
    pub steps: Vec<ProofStep>,
    pub valid: bool,
    pub confidence: f64,
}

impl Proof {
    pub fn is_valid(&self) -> bool {
        self.valid && self.confidence > 0.5
    }
}

/// A step in a proof
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct ProofStep {
    pub rule: String,
    pub premises: Vec<String>,
    pub conclusion: String,
    pub confidence: f64,
}

/// An inference rule for logical deduction
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct InferenceRule {
    pub name: String,
    pub premises: Vec<String>,
    pub conclusion: String,
}

#[cfg(test)]
mod tests {
    use super::*;

    #[tokio::test]
    async fn test_formal_reasoner() {
        let mut reasoner = FormalReasoner::new();

        let theorem = reasoner.prove_theorem(
            "Q".to_string(),
            vec!["P".to_string(), "P -> Q".to_string()],
        ).await;

        assert!(theorem.is_ok());
    }
}