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salt

A language and code generation tool for equation-based modeling and simulations.

Introduction

SALT is an implementation of a domain-specific language for equation-based models. This implementation follows the work of Tom Short and the Julia Sims.jl library https://github.com/tshort/Sims.jl, which is in turn based on David Broman's MKL simulator and the work of George Giorgidze and Henrik Nilsson in functional hybrid modeling. Following Sims.jl, a nodal formulation is used based on David Broman's thesis http://www.bromans.com/david/publ/thesis-2010-david-broman.pdf:

David Broman. Meta-Languages and Semantics for
Equation-Based Modeling and Simulation. PhD thesis, Thesis No
1333. Department of Computer and Information Science, Linköping
University, Sweden,; 2010.

Library procedures

parseprocedure

Parses equation declarations in the syntax described in the next section, and returns an abstract syntax tree structure.

elaborateprocedure

Performs flattening of the given declarations and returns an equation set. The main steps in flattening are:

  • Creation of a name resolution environment (parameters,fields,externals,constants,variables,functions).
  • Replacing of fixed initial values.
  • Flattening models and populating equation, definition, function lists.
  • Populating list of initials.
  • Populating event list from event and structural event definitions.
  • Handles structural events.
simcreateprocedure

Given an equation set, creates a simulation runtime representation.

codegen-ODEprocedure

Given a simulation runtime representation, creates an abstract code representation aimed at ODE solvers.

codegen-ODE/MLprocedure

Given a simulation runtime representation, creates a code representation aimed at ODE solvers in the Standard ML language.

Model description language

Definitions

Definitions serve to define unknowns (state variables), parameters (constants during integration), and units of measurement.

(define millivolt = unit Potential (1e-3 * volt)) 

(define Vinit = parameter (dim Potential) -65.0 * millivolt) 

(define v = unknown (dim Potential) -65.0 * mV)

Equations

Equations serve to define differential and algebraic equations.

 ((der(u)) = (s - u) / tau)
  ((s) = b * ((v - a) ^ 3))
  

Events

(event (v - Vthreshold)
       ((v := Vreset))
)

Examples

;; Van der Pol oscillator
(define vdp 
  (parse 
   `(
     (define x = unknown -0.25)
     (define y = unknown 1.0)
     ((der(x)) = (1 - y ^ 2) * x - y )
     ((der(y)) = x)
     )
   ))


;; Izhikevich Fast Spiking neuron
(define izhfs 
  (parse 
   `(
     (define millivolt = unit Potential (1e-3 * volt))

     (define Isyn = parameter (dim Current) 0.0 * nA)
     (define Iext = parameter (dim Current) 400.0 * nA)

     (define k     = parameter 1.0)
     (define Vinit = parameter (dim Potential)  -65.0 * millivolt)
     (define Vpeak = parameter (dim Potential)   25.0 * mV)
     (define Vt    = parameter (dim Potential)  -55.0 * mV)
     (define Vr    = parameter (dim Potential)  -40.0 * mV)
     (define Vb    = parameter (dim Potential)  -55.0 * mV)
     (define Cm    = parameter (dim Capacitance) 20.0 * uF)

     (define FS_a = parameter  0.2)
     (define FS_b = parameter  (dim Current)   0.025 * nA)
     (define FS_c = parameter  (dim Potential) -45.0 * mV)
     (define FS_U = parameter  (dim Current) FS_b * (Vinit / mV))

     (define v  = unknown (dim Potential) -65.0 * mV)
     (define u  = unknown (dim Current) FS_U)
     (define s  = unknown (dim Current) 0.0 * nA)

     ((der(v)) = (((k * (v - Vr) * (v - Vt) / millivolt) + (((- u) + Iext) * megaohm)) / Cm) / megaohm)
     ((der(u)) = (FS_a * (s - u)) / ms)
     ((s) = FS_b * ((v - Vb) / mV) ^ 3)


     (event (v - Vpeak)
            ((v := FS_c)
             (u := u)
             (s := s)
             )
            )
     ))
  )


;; A routine to generate and compile Standard ML code 
(define (compile-model name model #!key (solver 'rk4b) (compile #f) (dir "tests"))
  (pp model)

  (define elab (elaborate model))
  (print "elaborate is done")
  (pp elab)

  (define sim (simcreate elab))
  (pp sim)
  (pp (codegen-ODE sim solver))
  (let* ((sml-path (make-pathname dir (string-append (->string name) ".sml")))
         (mlb-path (make-pathname dir (string-append (->string name) "_run.mlb")))
         (port (open-output-file sml-path)))
    (codegen-ODE/ML sim out: port solver: solver libs: '(interp))
    (close-output-port port)
    (if compile
        (run (mlton -mlb-path-var ,(sprintf "'SALT_HOME ~A'" SALT-DIR)
                    -mlb-path-var ,(sprintf "'RK_LIB $(SALT_HOME)/sml-lib/rk'")
                    -mlb-path-var ,(sprintf "'DYNAMICS_LIB $(SALT_HOME)/sml-lib/dynamics'")
                    ,mlb-path))))

)

(compile-model 'vdp vdp)
(compile-model 'izhfs izhfs)

Version history

License

Copyright 2015-2017 Ivan Raikov

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or (at
your option) any later version.

This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.

A full copy of the GPL license can be found at http://www.gnu.org/licenses/.

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