Language.IntrinsicTyping.SECD

(source)

The content of this module is based on the MSc Thesis
Coinductive Formalization of SECD Machine in Agda
by Adam Krupička

Reexports

import public Data.Late
import public Data.List.Quantifiers

Definitions

data Ty : Type

Totality: total
Visibility: public export
Constructors:

TyInt : Ty
TyBool : Ty
TyPair : Ty -> Ty -> Ty
TyList : Ty -> Ty
TyFun : Ty -> Ty -> Ty

data Const : Ty -> Type

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Constructors:

AnInt : Int -> Const TyInt
True : Const TyBool
False : Const TyBool

fromInteger : Integer -> Const TyInt

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Stack : Type

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Env : Type

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FunDump : Type

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record State : Type

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Constructor:

MkState : Stack -> Env -> FunDump -> State

Projections:

.dump : State -> FunDump
.env : State -> Env
.stack : State -> Stack

.stack : State -> Stack

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stack : State -> Stack

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.env : State -> Env

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env : State -> Env

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.dump : State -> FunDump

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dump : State -> FunDump

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data Step : State -> State -> Type

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Visibility: public export
Constructors:

LDC : Const ty -> Step (MkState s e f) (MkState (ty :: s) e f)

  Load a constant of a base type

LDA : Elem ty e -> Step (MkState s e f) (MkState (ty :: s) e f)

  Load a value from an address in the environment

LDF : Steps (MkState [] (a :: e) ((a, b) :: f)) (MkState [b] (a :: e) ((a, b) :: f)) -> Step (MkState s e f) (MkState (TyFun a b :: s) e f)

  Load a recursive function

LDR : Elem (a, b) f -> Step (MkState s e f) (MkState (TyFun a b :: s) e f)

  Load a function for recursive application

APP : Step (MkState (a :: (TyFun a b :: s)) e f) (MkState (b :: s) e f)

  Apply a function to its argument

TAP : Step (MkState (a :: (TyFun a b :: s)) e f) (MkState (b :: s) e f)

  Apply a function to its argument, tail call

RTN : Step (MkState (b :: s) e ((a, b) :: f)) (MkState [b] e ((a, b) :: f))

  Return a value from inside a function

BCH : Steps (MkState s e f) (MkState s' e f) -> Steps (MkState s e f) (MkState s' e f) -> Step (MkState (TyBool :: s) e f) (MkState s' e f)

  Branch over a boolean

FLP : Step (MkState (a :: (b :: s)) e f) (MkState (b :: (a :: s)) e f)

  Flip the stack's top values

NIL : Step (MkState s e f) (MkState (TyList a :: s) e f)

  Nil constructor

CNS : Step (MkState (a :: (TyList a :: s)) e f) (MkState (TyList a :: s) e f)

  Cons constructor

HED : Step (MkState (TyList a :: s) e f) (MkState (a :: s) e f)

  Head destructor

TAL : Step (MkState (TyList a :: s) e f) (MkState (TyList a :: s) e f)

  Tail destructor

MKP : Step (MkState (a :: (b :: s)) e f) (MkState (TyPair a b :: s) e f)

  Pair constructor

FST : Step (MkState (TyPair a b :: s) e f) (MkState (a :: s) e f)

  First pair destructor

SND : Step (MkState (TyPair a b :: s) e f) (MkState (b :: s) e f)

  Second pair destructor

ADD : Step (MkState (TyInt :: (TyInt :: s)) e f) (MkState (TyInt :: s) e f)

  Addition of ints

SUB : Step (MkState (TyInt :: (TyInt :: s)) e f) (MkState (TyInt :: s) e f)

  Subtraction of ints

MUL : Step (MkState (TyInt :: (TyInt :: s)) e f) (MkState (TyInt :: s) e f)

  Multiplication of ints

EQB : Step (MkState (a :: (a :: s)) e f) (MkState (TyBool :: s) e f)

  Structural equality test

NOT : Step (MkState (TyBool :: s) e f) (MkState (TyBool :: s) e f)

  Boolean negation

data Steps : State -> State -> Type

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Visibility: public export
Constructors:

Nil : Steps s s
(::) : Step s t -> Steps t u -> Steps s u

data Stepz : State -> State -> Type

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Visibility: public export
Constructors:

Lin : Stepz s s
(:<) : Stepz s t -> Step t u -> Stepz s u

(<>>) : Stepz s t -> Steps t u -> Steps s u

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Fixity Declaration: infixr operator, level 6

(<><) : Stepz s t -> Steps t u -> Stepz s u

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Fixity Declaration: infixl operator, level 7

(++) : Steps s t -> Steps t u -> Steps s u

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Fixity Declaration: infixr operator, level 7

NUL : Steps (MkState (TyList a :: s) e f) (MkState (TyBool :: s) e f)

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LDL : List Int -> Steps (MkState s e f) (MkState (TyList TyInt :: s) e f)

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PLS : Step (MkState s e f) (MkState (TyFun TyInt (TyFun TyInt TyInt) :: s) e f)

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MAP : Step (MkState [] e f) (MkState [TyFun (TyFun a b) (TyFun (TyList a) (TyList b))] e f)

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Visibility: public export

FLD : Step (MkState [] e f) (MkState [TyFun (TyFun b (TyFun a b)) (TyFun b (TyFun (TyList a) b))] e f)

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SUM : Steps (MkState [] e f) (MkState [TyFun (TyList TyInt) TyInt] e f)

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Meaning : Ty -> Type

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fromConst : Const ty -> Meaning ty

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Meaning : List Ty -> Type

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0 Meaning : FunDump -> Type

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tail : Meaning (ab :: f) -> Meaning f

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lookup : Meaning f -> Elem (a, b) f -> Closure a b

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record Meaning : State -> Type

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Constructor:

MkMeaning : Meaning (st .stack) -> Meaning (st .env) -> Meaning (st .dump) -> Meaning st

Projections:

.dumpVal : Meaning st -> Meaning (st .dump)
.envVal : Meaning st -> Meaning (st .env)
.stackVal : Meaning st -> Meaning (st .stack)

.stackVal : Meaning st -> Meaning (st .stack)

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stackVal : Meaning st -> Meaning (st .stack)

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.envVal : Meaning st -> Meaning (st .env)

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envVal : Meaning st -> Meaning (st .env)

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.dumpVal : Meaning st -> Meaning (st .dump)

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dumpVal : Meaning st -> Meaning (st .dump)

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record Closure : Ty -> Ty -> Type

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Constructor:

MkClosure : Steps (MkState [] (a :: localEnv) ((a, b) :: localFunDump)) (MkState [b] (a :: localEnv) ((a, b) :: localFunDump)) -> Meaning localEnv -> Meaning localFunDump -> Closure a b

Projections:

.code : ({rec:0} : Closure a b) -> Steps (MkState [] (a :: localEnv {rec:0}) ((a, b) :: localFunDump {rec:0})) (MkState [b] (a :: localEnv {rec:0}) ((a, b) :: localFunDump {rec:0}))
.dumpVal : ({rec:0} : Closure a b) -> Meaning (localFunDump {rec:0})
.envVal : ({rec:0} : Closure a b) -> Meaning (localEnv {rec:0})
0 .localEnv : Closure a b -> Env
0 .localFunDump : Closure a b -> FunDump

0 .localEnv : Closure a b -> Env

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0 localEnv : Closure a b -> Env

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0 .localFunDump : Closure a b -> FunDump

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0 localFunDump : Closure a b -> FunDump

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.code : ({rec:0} : Closure a b) -> Steps (MkState [] (a :: localEnv {rec:0}) ((a, b) :: localFunDump {rec:0})) (MkState [b] (a :: localEnv {rec:0}) ((a, b) :: localFunDump {rec:0}))

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code : ({rec:0} : Closure a b) -> Steps (MkState [] (a :: localEnv {rec:0}) ((a, b) :: localFunDump {rec:0})) (MkState [b] (a :: localEnv {rec:0}) ((a, b) :: localFunDump {rec:0}))

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Visibility: public export

.envVal : ({rec:0} : Closure a b) -> Meaning (localEnv {rec:0})

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envVal : ({rec:0} : Closure a b) -> Meaning (localEnv {rec:0})

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.dumpVal : ({rec:0} : Closure a b) -> Meaning (localFunDump {rec:0})

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dumpVal : ({rec:0} : Closure a b) -> Meaning (localFunDump {rec:0})

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eqb : (ty : Ty) -> Meaning ty -> Meaning ty -> Bool

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eqbs : (ty : Ty) -> Meaning (TyList ty) -> Meaning (TyList ty) -> Bool

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steps : Meaning st -> Steps st st' -> Late (Meaning st')

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step : Meaning st -> Step st st' -> Late (Meaning st')

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run : Steps (MkState [] [] []) (MkState (ty :: {_:12217}) [] []) -> Nat -> Maybe (Meaning ty)

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