PLanCompS. Peter D Mosses Swansea University. SSLF12: Summer School on Language Frameworks Sinaia, Romania, July 2012

Transcription

1 PLanCompS Peter D Mosses Swansea University SSLF12: Summer School on Language Frameworks Sinaia, Romania, July

2 PLANCOMPS Programming Languages (incl. DSLs) C# Java translation Components and their Specifications reusable fundamental constructs funcons 2

3 Acknowledgements SSLF12 organisers and participants EPSRC grant Martin Churchill (Swansea) 3

4 Outline Topics: I. Fundamental constructs (funcons) II. Language specification III. Funcon specification IV. Funcon equivalence 4

5 Fundamental constructs (funcons) 5

6 Funcons This lecture : concepts notation (basic) tool support Subsequent lectures : translating languages to funcons formal specification of funcons proving algebraic properties of funcons 6

7 Meta-notation lowercase (abbreviated) words : names constants, operations underscores allowed ( _, not - ) Capitalised (often single letters) : meta-variables over individuals over types 7

8 Computations vs Data computes : the type of entity corresponding to executable code data : the type of entity corresponding to given or computed info 8

9 Computations vs Data computes(x) : X is a subtype of data an element of computes(x) can only compute elements of X an element of X trivially computes itself hence X < computes(x) 9

10 Primitive data types bool the Boolean truth values true, false not (bool) : bool and, or (bool, bool) : bool equal (X, X) : bool 10

11 Primitive data types int the (unbounded) integers int_plus, int_minus, (int, int) : int int_less, int_less-equal, (int, int) : bool float 11

12 Primitive data types char string constructor atomic symbols q(term) 12

13 Composite data types list(x) (finite) lists with items all of type X nil : list(x) cons (X, list(x)) : list(x) constructed tagged lists of values construct (constructor, list(val)) : val 13

14 Composite data types map(x,y) (finite, partial) maps from X to Y empty : map(x,y) lookup (map(x,y), X) : Y update (map(x,y), X, Y) : map(x,y) over (map(x,y), map(x,y)) : map(x,y) env = map(id, bindable) store = map(variable, storable) 14

15 Computation types Expressions expr = computes(val) Propositions prop = computes(bool) Commands (statements) comm = computes(done) done is the singleton type {skip} Declarations decl = computes(env) 15

16 Computation operations Conditionals cond (bool, expr, expr) : expr cond (bool, comm, comm) : comm cond (bool, X, X) : X cond (true, V1, V2) = V1 cond (false, V1, V2) = V2 16

17 Lifting data operations to computations Implicit lifting of data argument(s) : cond (bool, comm, comm) : comm to computations : cond (prop, comm, comm) : comm cond (expr, comm, comm) : comm cond(e, C1, C2) evaluates E first well-formed only if bool < val 17

18 Lifting data operations to computations int_plus (int, int) : int implicit lifting of both data argument types and result type : int_plus (expr, expr) : expr int_plus (E1, E2) evaluates E1, E2 interleaved well-formed only if int < val explicit lifting for (left-to-right) sequential evaluation : seq F (E1,, En) not used in these lectures 18

19 Funcons for control flow skip : done seq (comm, computes(x)) : computes(x) seq (comm, comm) : comm seq (comm, expr) : expr seq (comm, decl) : decl cond (expr, comm, comm) : comm cond_loop (expr, comm) : comm 19

20 More funcons Still to come : bindings effects patterns abstractions 20

21 Tool support SWI-Prolog : Prolog code for funcon execution : Installation: unzip plcs-1.zip edit plcs-1/load.pl : :- cd( /absolute/path/to/plcs-1 ). 21

22 Executing funcons :-? [load]. :-? run(skip). 22

23 More funcons Still to come : bindings effects patterns abstractions 23

24 Funcons for bindings Binding of identifiers id to bindable values decl = computes(env) bound (id) : expr let_bind (id, bindable) : env let (env, computes(x)) : computes(x) over (env, env) : env accum (env, decl) : decl recursive (decl) : decl 24

25 Funcons for effects Allocation of variables for storing storable values alloc (storable) : computes(variable) deref (variable) : computes(storable) assign (variable, storable) : comm effect (val) : done 25

26 Tool support 26

27 Funcons for patterns Matching a pattern against a given val when a pattern matches, it computes an env otherwise it fails (abrupt termination, stuck) id_patt (id) : pattern id_patt(i) matches any value and binds I to it const_patt (val) : pattern const_patt(v) matches only the value V cstr_patt (constructor, list(pattern)) : pattern cstr_patt(c, LP) matches only constructed values 27

28 Funcons for patterns seq_patt (pattern, pattern) : pattern seq_patt(p1,p2) tries P1 first, then P2 if P1 fails match (val, pattern) : decl match(v, P) tries to match P against V 28

29 Funcons for abstraction Abstractions abs(x,y) to be given an X and computing a Y abs (patt(x), computes(y)) : abs(x,y) closure (abs,env) : abs abs_over (abs,abs) : abs curry (abs) : abs give (X, abs(x,y)) : computes(y) given : abs(x,x) catch (Y, abs(x,y)) : computes(y) throw (X) : computes(y) 29

30 Function abstraction A function is data formed from an abstraction fun (abs) : function possibly open dynamic scopes lambda (abs) : computes(function) always closed - static scopes apply_cbv (function, val) : computes(val) call by value : argument always evaluated 30

31 Funcons This lecture : concepts notation (basic) tool support Subsequent lectures : translating languages to funcons formal specification of funcons proving algebraic properties of funcons 31