Sequences as relations

src/test/resources/laws/SequencesAsRelationsTest.mch

 MACHINE SequencesAsRelationsTest
-VARIABLES x
-INVARIANT x : 1..3
-INITIALISATION x := 1
-OPERATIONS
-foo = PRE 1 = 1 THEN x := 2 END 
-ASSERTIONS
- {} = [];
- {(1,1)} = [1]
- /*[] /: seq1({1,2});
- iseq({1,2}) ={[], [1], [2], [1, 2], [2, 1]};
- [1] : iseq({1,2});
- iseq1({1,2}) ={[1], [2], [1, 2], [2, 1]};
- [1] : iseq1({1,2});
- perm({1,2}) = {[1,2], [2,1]};
- rev([1,2,3]) = [3,2,1];
- conc([[1,2],[3],[4,5]]) = [1,2,3,4,5];
- [1,2,3,4] /|\ 3 = [1,2,3];
- [1,2,3,4] \|/ 3 = [4];
- 1 -> [2,3] = [1,2,3];
- last([1,2]) = 2;
- front([1,2,3]) = [1,2]*/
+PROPERTIES
+ {} = []
+& {(1,1)} = [1]
+
+/* Set of injective Sequence */
+& iseq({}) = {{}}
+& iseq({1}) = {{},{(1,1)}}
+
+/* Set of non empty injective Sequence */
+& iseq1({}) = {}
+& iseq1({1}) = {{(1,1)}}
+
+/* Size */
+& size({}) = 0
+& size({(1,1),(2,2)}) = 2
+
+/* Concatenation */
+& {(1,1),(2,2)}^{(1,3)} = {(1,1),(2,2),(3,3)}
+& {(1,1),(2,2)}^{} = {(1,1),(2,2)}
+& {}^{(1,1),(2,2)} = {(1,1),(2,2)}
+& {}^{} = {}
+
+/* Prepand */
+& 1 -> {(1,2),(2,3)} = {(1,1),(2,2),(3,3)}
+& 1 -> {} = {(1,1)}
+
+/* Append */
+& {(1,1),(2,2)} <- 3 = {(1,1),(2,2),(3,3)}
+& {} <- 1 = {(1,1)}
+
+/* Front */
+& front({(1,1)}) = {}
+& front({(1,1),(2,2),(3,3)}) = {(1,1),(2,2)}
+
+/* First */
+& first({(1,1)}) = 1
+& first({(1,1),(2,2)}) = 1
+
+/* Tail */
+& tail({(1,1)}) = {}
+& tail({(1,1),(2,2),(3,3)}) = {(1,2),(2,3)}
+
+/* Last */
+& last({(1,1)}) = 1
+& last({(1,1),(2,2)}) = 2
+
+/* Reverse */
+& rev({}) = {}
+& rev({(1,1)}) = {(1,1)}
+& rev({(1,1),(2,2),(3,3)}) = {(1,3),(2,2),(3,1)}
+
+/* Generalized Concatenation */
+& conc({(1,{(1,1),(2,2)}),(2,{(1,3)})}) = {(1,1),(2,2),(3,3)}
+& conc({(1,{(1,1),(2,2)}),(2,{})}) = {(1,1),(2,2)}
+& conc({(1,{}), (2,{(1,1),(2,2)})}) = {(1,1),(2,2)}
+& conc({(1,{}),(2,{})}) = {}
+
+/* Perm */
+& perm({3,4}) = {{(1,3),(2,4)},{(1,4),(2,3)}}
+& perm({}) = {{}}
+
+/* Take first elements */
+& {(1,1),(2,2)} /|\ 1 = {(1,1)}
+& {(1,1),(2,2)} /|\ 2 = {(1,1),(2,2)}
+& {(1,1)} /|\ 0 = {}
+& {} /|\ 0 = {}
+
+& {(1,1),(2,2)} \|/ 1 = {(1,2)}
+& {(1,1),(2,2)} \|/ 0 = {(1,1),(2,2)}
+& {(1,1)} \|/ 1 = {}
+& {} \|/ 0 = {}
 END
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