COP4020 Programming Languages. Logical programming with Prolog Prof. Xin Yuan

Transcription

1 COP4020 Programming Languages Logical programming with Prolog Prof. Xin Yuan

2 Topics Logic programming with Prolog COP4020 Spring

3 Definitions: Prolog Terms Terms are symbolic expressions that are Prolog s building blocks A Prolog program consists of Horn clauses (axioms) that consist of terms Data structures processed by a Prolog program are terms A term is either a variable: a name beginning with an upper case letter a constant: a number or string an atom: a symbol or a name beginning with a lower case letter a structure of the form: functor(arg 1, arg 2,..., arg n ) where functor is an atom and arg i are sub-terms a list (also a structure with a functor) of the form [term 1, term 2,, term n ] Examples: X, Y, ABC, and Alice are variables 7, 3.14, and hello are constants foo, barfly, and + are atoms bin_tree(foo, bin_tree(bar, glarch)) and +(3,4) are structures COP4020 Spring

4 Term Manipulation Terms can be analyzed and constructed Built-in predicates functor and arg, for example:?- functor(foo(a,b,c), foo, 3). yes?- functor(bar(a,b,c), F, N). F = bar N = 3?- functor(t, bee, 2). T = bee(_g1,_g2)?- functor(t, bee, 2), arg(1, T, a), arg(2, T, b). T = bee(a,b) The univ operator =.. Break up a term into a list or form a term from a list.?- foo(a,b,c) =.. L L = [foo,a,b,c]?- T =.. [bee,a,b] T = bee(a,b) COP4020 Spring

5 Unification and Variable Instantiation Variables are used in clauses: A variable is instantiated to a term as a result of unification, which takes place when goals are matched to head predicates Goal in query: rainy(c) Fact: rainy(seattle) Unification is the result of the goal-fact match: C=seattle Unification is recursive: An uninstantiated variable unifies with anything, even with other variables which makes them identical (aliases) An atom unifies with an identical atom A constant unifies with an identical constant A structure unifies with another structure if the functor and number of arguments are the same and the arguments unify recursively Once a variable is instantiated to a non-variable term, it cannot be changed: proofs cannot be tampered with COP4020 Spring

6 Examples of Unification The built-in predicate =(A,B) succeeds if and only if A and B can be unified, where the goal =(A,B) may be written as A = B?- a = a. yes?- a = 5. No?- 5 = 5.0. No?- a = X. X = a?- foo(a,b) = foo(a,b). Yes?- foo(a,b) = foo(x,b). X = a?- foo(x,b) = Y. Y = foo(x,b)?- foo(z,z) = foo(a,b). no COP4020 Spring

7 Prolog Lists A list is of the form: [elt 1,elt 2,..., elt n ] where elt i are terms The special list form [elt 1,elt 2,..., elt n tail] denotes a list whose tail list is tail Examples?- [a,b,c] = [a T]. T = [b,c]?- [a,b,c] = [a,b T]. T = [c]?- [a,b,c] = [a,b,c T]. T = [] COP4020 Spring

8 List Operations: List Membership List membership definitions: member(x, [X T]). member(x, [H T]) :- member(x, T).?- member(b, [a,b,c]). Execution: member(b,[a,b,c]) does not match member(x,[x T]) member(b,[a,b,c]) matches predicate member(x 1,[H 1 T 1 ]) with X 1 =b, H 1 =a, and T 1 =[b,c] Sub-goal to prove: member(b, [b,c]) member(b,[b,c]) matches predicate member(x 2,[X 2 T 2 ]) with X 2 =b and T 2 =[c] The sub-goal is proven, so member(b,[a,b,c]) is proven (deduced) Note: variables can be "local" to a clause (like the formal arguments of a function) Local variables such as X 1 and X 2 are used to indicate a match of a (sub)-goal and a head predicate of a clause COP4020 Spring

9 Predicates and Relations Predicates are not functions with distinct inputs and outputs Predicates are more general and define relationships between objects (terms) member(b,[a,b,c]) relates term b to the list that contains b?- member(x, [a,b,c]). X = a ; % type ';' to try to find more solutions X = b ; %... try to find more solutions X = c ; %... try to find more solutions no?- member(b, [a,y,c]). Y = b?- member(b, L). L = [b _G255] where L is a list with b as head and _G255 as tail, where _G255 is a new variable COP4020 Spring

10 Predicates and Relations?- member(b, L). L = [b _G545] ; L = [_G544, b _G548] ; L = [_G544, _G547, b _G551] ; L = [_G544, _G547, _G550, b _G554] ; L = [_G544, _G547, _G550, _G553, b _G557] ; L = [_G544, _G547, _G550, _G553, _G556, b _G560] ; L = [_G544, _G547, _G550, _G553, _G556, _G559, b _G563]. COP4020 Spring

11 Example: List Append L3 = L1 L2. How to write this in Prolog? Predicates do not have return value Implication? L1, L2, L3 must be arguments to a predicate, the programming will then specify the relation. Append(L1, L2, L3). Define this recursively Case 1: when L1 is empty Case 2: when L1 is not empty Prolog has not if constructs, how to do two cases? COP4020 Spring

12 Example: List Append Append(L1, L2, L3). %L3 = L1 L2 Define this recursively Case 1: when L1 is empty append([], L2, L2). Case 2: when L1 is not empty append([h T], L2, [H append(t, L2) ]) of course this is incorrect, append does not have a return value. Solution: append ([H T], L2, [H L]) :- append(t, L2, L). Final solution: append([], A, A). append([h T], A, [H L]) :- append(t, A, L). COP4020 Spring

13 Example: List Append List append predicate definitions: append([], A, A). append([h T], A, [H L]) :- append(t, A, L). Prolog append is more power then the append function in other languages?- append([a,b,c], [d,e], X). X = [a,b,c,d,e]?- append(y, [d,e], [a,b,c,d,e]). Y = [a,b,c]?- append([a,b,c], Z, [a,b,c,d,e]). Z = [d,e]?- append([a,b],[],[a,b,c]). No?- append([a,b],[x Y],[a,b,c]). X = c Y = [] COP4020 Spring

14 Example: take out one element from a list predicate prototype: takeout(item, SrcL, DstL) Three cases: SrcL is empty SrcL is not empty: the first element is Item (take out this item) SrcL is not empty: the first element is not Item (Keep this item) COP4020 Spring

15 Example: take out one element from a list Example6.pl Item may or may not be in SrcL Three cases: SrcL is empty: takeout(item, [], []). SrcL is not empty: the first element is Item (take out this item) takeout(item, [Item L], L). SrcL is not empty: the first element is not Item (Keep this item) Takeout(Item, [X L], [X L1]) :- takeout(item, L, L1). Item must be in SrcL? COP4020 Spring

16 Permutation of a list perm(l1, L2). %L2 is a permutation of L1 perm([], []). perm([x Y], Z) :- perm(y, W), takeout(x, Z, W). Example7.pl COP4020 Spring

17 Example: sorting Interface: sort(list, Sortedlist). All variables must start with a capital letter. Naïve_sort (very inefficient sorting) naive_sort(list,sorted):-perm(list,sorted),is_sorted(sorted). How to write is_sorted? COP4020 Spring

18 Example: sorting How to write is_sorted? is_sorted([]). is_sorted([_]). is_sorted([x, Y L]) :- X < Y, is_sorted([y L]). COP4020 Spring