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Generalized Dynamical Systems Spec

This is an (informal) technical specification for Generalized Dynamical Systems, based on https://github.com/cadCAD-org/spec.

See Generalized Dynamical Systems and Semantic Disambiguation and Term Standardization for Generalized Dynamical Systems (GDS) for inspiration.

The goals of this codebase are to:

  • develop a foundation for building GDS reference implementations
  • standardize the terminology used to refer to the structure of a GDS model

This README.md file is the spec, and is testable and executable!

make run
make test

Imports

module Main where

import qualified Data.Map.Strict as Map
import Data.Map (Map(), toList, fromListWith)
import Data.List (groupBy)
import Data.Sort (sortOn)
import Data.Tuple (fst)
import Data.Maybe (fromMaybe)

Types

Model State

type StateVariableKey = String
type StateVariableValue = Float
type StateVariable = (StateVariableKey, StateVariableValue)
type State = Map StateVariableKey StateVariableValue
type StateHistory = [State]

Model Policies

type PolicySignalKey = String
type PolicySignalValue = Float
type PolicySignal = (PolicySignalKey, PolicySignalValue)

Model Functions

type PolicyFunction = State -> [PolicySignal]
type StateUpdateFunction = State -> [PolicySignal] -> StateVariable

Model Structure

data PartialStateUpdateBlock = PartialStateUpdateBlock { policies :: [PolicyFunction], variables :: [StateUpdateFunction] }
type Model = [PartialStateUpdateBlock]

Simulation Logic

partialStateUpdate :: State -> PartialStateUpdateBlock -> State
partialStateUpdate s psub = updateState s $ applyPartialStateUpdate s
    where
        applyPartialStateUpdate :: State -> StateVariable
        applyPartialStateUpdate s = stateUpdateFunction s $ policyFunction s
            where
                policyFunction = head $ policies psub
                stateUpdateFunction = head $ variables psub
        updateState :: State -> StateVariable -> State
        updateState s v = Map.insert (fst v) (snd v) s

policySignalAggregation :: Num b => [(PolicySignalKey, b)] -> [(PolicySignalKey, b)]
policySignalAggregation = map sumGroup . groupBy fstEq . sortOn fst
  where
    sumGroup (x:xs) = (fst x, sum $ map snd (x:xs))
    sumGroup _ = error "This can never happen - groupBy cannot return empty groups"
    fstEq (a, _) (b, _) = a == b

simulation :: Model -> State -> StateHistory
simulation m initialState = take 10 (iterate (\s -> partialStateUpdate s (head m)) initialState)

Model Configuration

stateUpdateFunction :: StateUpdateFunction
stateUpdateFunction s _ = (\v -> ("a", v)) $ (+) 1 $ fromMaybe 0 (Map.lookup "a" s)

policyFunction :: PolicyFunction
policyFunction _ = [("signal", 1)]

partialStateUpdateBlock :: PartialStateUpdateBlock
partialStateUpdateBlock = PartialStateUpdateBlock [policyFunction] [stateUpdateFunction]

model = [partialStateUpdateBlock, partialStateUpdateBlock]

initialState :: State
initialState = Map.fromList [("a", 0), ("b", 0)]

Simulation Execution

results = simulation model initialState

main :: IO ()
main = print $ results

Simulation Results

[fromList [("a",0.0),("b",0.0)],fromList [("a",1.0),("b",0.0)],fromList [("a",2.0),("b",0.0)],fromList [("a",3.0),("b",0.0)],fromList [("a",4.0),("b",0.0)],fromList [("a",5.0),("b",0.0)],fromList [("a",6.0),("b",0.0)],fromList [("a",7.0),("b",0.0)],fromList [("a",8.0),("b",0.0)],fromList [("a",9.0),("b",0.0)]]