***
*** Specification of predator/prey model as a chemical reaction network
***

mod PRED-PREY is
	protecting NAT .
	protecting FLOAT .

	sort System .

	*** Multiplicities of the species and time
	op <_,_,_> : Nat Nat Float -> System [ctor] .

	vars Prey Pred : Nat .
	var  T DT : Float .

	rl [prey]      : <   s Prey,     Pred, T      >
	              => < s s Prey,     Pred, T + DT > [nonexec metadata "10.0"] .
	rl [prey_pred] : <   s Prey,   s Pred, T      >
	              => <     Prey, s s Pred, T + DT > [nonexec metadata "0.01"] .
	rl [pred]      : <     Prey,   s Pred, T      >
	              => <     Prey,     Pred, T + DT > [nonexec metadata "10.0"] .

	op initial : -> System .
	eq initial = < 1000, 1000, 0.0 > .
endm

smod PRED-PREY-STRAT is
	protecting PRED-PREY .
	protecting CONVERSION .

	*** A single reaction
	strat step @ System .

	var  S           : System .
	vars Prey Pred N : Nat .
	vars T DT        : Float .

	sd step := matchrew S s.t. < Prey, Pred, T > := S
	             /\ DT := 1.0 / (float(10 * Prey) + 0.01 * float(Prey * Pred)
	                             + float(10 * Pred))
	           by S using choice(
	                10 * Prey                 : prey[DT <- DT],
	                0.01 * float(Prey * Pred) : prey_pred[DT <- DT],
	                10 * Pred                 : pred[DT <- DT]
	           ) .

	*** Execute the given number of steps
	strat repeat : Nat @ System .

	sd repeat(0) := idle .
	sd repeat(s N) := step ? repeat(N) : idle .
endsm

eof

*** More interesting results can be obtained by executing many steps
*** and plotting the trajectory
srew initial using step .
srew initial using repeat(100) .